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Coursework

2010-10-15T15:38:49Z

Nm607: /* Coursework not to be attempted at any time: Antimodelling Molecules */

[[Second_Year_Modelling_Workshop|Back to introduction]]
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== Molecular modelling Coursework to be attempted during Scheduled Sessions ==

These projects are arranged in increasing order of difficulty, and time taken to complete. You should do as many as you can in the 2 hour session allocated to you, and return to finish the rest if you wish at your convenience. At the end of the session, we will conduct a ''number auction''. For each project, the bidding will start with the first volunteer offering an energy for the system (or one of the isomers). If anyone has a lower energy for that molecule, they will then bid that energy. The winner will be the one with the lowest energy.

=== Conformational analysis I: Chair and Boat-like conformations of Cyclohexane ===
{|
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<jmol><jmolApplet><title>Chiralane</title><color>white</color>
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#Construct '''[[chair]]''' and '''[[boat]]'''-like '''[[conformation]]s''' of [[cyclohexane]]. Compare the energies of both forms.
#Check carefully if your boat really is a boat, or whether it has any apparent distorsion.
#Try changing one or more of the CH2 groups into an oxygen and see if that affects things.
#For the record, the point group symmetries of the various species which may be involved are D3d for the chair conformation, C2v for a boat geometry, and D2 for any twisted boat form. Is any of these forms '''chiral'''?
#The molecule on the left is called '''chiralane'''. Are its rings boats or chairs?
|}
====References ====
# The first suggestion of two forms for cyclohexane goes as far back as H. Sachse, ''Chem. Ber'', 1890, '''23''', 1363 and ''Z. Physik. Chem.'', 1892, 10, 203. This is nicely explained [http://www.chem.yale.edu/~chem125/125/history/Baeyer/Sachse.html here]. E. Mohr, ''J. Prakt. Chem.'', 1918, '''98''', 315 and ''Chem. Ber.'', 1922, '''55''', 230, translated Sachse's argument into a pictorial one.
# The article that put [[conformational analysis]] on the map: D. H. R. Barton and R. C. Cookson, ''The principles of conformational analysis'', ''Q. Rev. Chem. Soc.'', '''1956''', ''10'', 44. {{DOI|10.1039/QR9561000044}}
#[http://en.wikipedia.org/wiki/Chair_conformation Wikipedia article]
#D. A. Dixon and A. Komornicki, ''Ab initio conformational analysis of cyclohexane'', ''J. Phys. Chem.'', '''1990''', ''94'', 5630 - 5636; {{DOI|10.1021/j100377a041}}.
#A nice exploration of the potential energy surfaces for cyclohexane can be viewed [http://www.springer.com/carey-sundberg/cyclohex/cyclohex.php here].
# For a more modern application of this technique, see I. Columbus, R. E. Hoffman, and S. E. Biali, ''Stereochemistry and Conformational Anomalies of 1,2,3- and 1,2,3,4-Polycyclohexylcyclohexanes''. ''J. Am. Chem. Soc.'', '''1996''', ''118'', 6890 - 6896; {{DOI|10.1021/ja960380h}}.
# The second molecule shown in this section is called [6.6]chiralane. It is peculiar for having many six-membered saturated rings, all of them as twist-boats rather than chairs! (a chair has a plane of symmetry, a twist boat only axes, which of course allows it to be chiral). See [http://petitjeanmichel.free.fr/itoweb.petitjean.graphs.html#CHIR here] for more details.
# More detail on the conformation of rings (and acyclic systems) will be found in the [http://www.ch.ic.ac.uk/local/organic/conf/ lecture course] on the topic to be given in the spring term.

=== Enantiomers vs Diastereomers Part 1: Butanes and Helicenes. ===

This problem illustrates, using models, the difference between an enantiomer and a diastereomer.

#[[Image:diastereo.gif|thumb|right|2-bromo-3-chlorobutane]][[Image:pentahelicene.gif|thumb|right|Pentahelicene]]The compound 2-bromo-3-chlorobutane has two [[chiral]] centres, and four isomers (22) are therefore possible. Calculate all four isomers, and for each be careful to label each of the two stereo centres '''R''' or '''S''' as you go. For each of the four isomers '''R,R''', '''S,S''', '''R,S''', '''S,R''' you will have to think about whether you have obtained the lowest energy [[conformer]].
#Can your four energies be grouped in any way? You should think about the expected difference between '''enantiomers''', '''diastereomers''' and '''conformers'''.
{|
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#Construct some helicenes (pentahelicene or [5]helicene is shown on the right), using '''conjugated''' bonds for all the ring bonds. Benzene, naphthalene, phenanthrene and benzophenanthrene are in fact the first four members of this series. At what point in this series can you detect helicity cropping up? This is manifested by a non-planar helical wind of the molecule. If you do detect it, note how the wind is either left or right handed, ie the two forms are '''enantiomers''' of each other. Try displaying the molecule in '''spacefill mode''' (see above) to see if you can identify the source of the helicity. (Note: the smallest helicene which can be resolved experimentally into enantiomers is in fact [5]helicene]).
#The higher helicenes are well known (up to about [14]helicene) and amongst the ''most chiral'' molecules known (in terms of how much they rotate the plane of polarised light).
#[7]circulene is a known molecule, with a unique saddle-shaped structure, shown on the left (there is no real need for you to build this model, but do please do so if you are curious). [http://en.wikipedia.org/wiki/Graphene Graphene] is a related polymeric molecule, of much topical interest in the semi-conducting and other industries (Nobel Prize 2010).
|}
==== References ====

#[http://en.wikipedia.org/wiki/Diastereomer Wikipedia article on Diastereomers]
#[http://en.wikipedia.org/wiki/Helicene Wikipedia article on Helicenes and related molecules]
#R. H. Janke, G. Haufe, E.-U. Würthwein, and J. H. Borkent, ''Racemization Barriers of Helicenes: A Computational Study'', ''J. Am. Chem. Soc.'', '''1996''', ''118'' 6031 - 6035 {{DOI|10.1021/ja950774t}}

=== Conformational analysis II: ''cis'' and ''trans''-decalins, Steroids and Podcasts! ===
{|
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<jmol><jmolApplet><title>Elimination</title><color>white</color>
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<uploadedFileContents>elim1.xyz</uploadedFileContents>
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<jmol><jmolApplet><title>Woodward</title><color>white</color>
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# [[Image:cis-decalin.gif|thumb|right|cis Decalin]]This is the famous molecule that started the whole molecular mechanics modelling ball rolling. [http://www.ch.ic.ac.uk/video/barton/barton1.pdf Barton] in 1948 sought to find out which [[conformation]] of ''cis''-decalin was the most stable (see [http://www.ch.ic.ac.uk/video/barton/index_qt.html here] for video). You should be able to find at least three conformations of this molecule. Try locating these, and conclude which is the most stable. Identify any [[chair]] rings and any [[boat]].
#Measure some dihedral angles to see if the [[staggered]] relationships hold (i.e. for such a relationship, the dihedral angle should be close to 60 degrees).
#A key step in Woodward's famous synthesis of [http://en.wikipedia.org/wiki/Cortisone cortisone] is a quinone+butadiene [[Diels-Alder]] reaction to give a cis-decalin (left), with an assumption that [[epimerisation]] to a trans-decalin is thermodynamically favourable. [[Image:Cortisone.gif|thumb|left|cis Cortisone]]Can you verify whether the trans-isomer is indeed more stable? Its not so obvious, since this compound has two extra double bonds in the rings and six sp2 centres which might perturb things.
#[[Image:App.gif|thumb|right|trans Decalin]]The two diastereomeric ''trans''-decalin tosylates react quite differently with NaBH4. Construct models for both isomers (use methoxy as a model for the Tosyl group) and from the [[antiperiplanar]] alignments of bonds that you can find in each isomer, can you make a connection to the reactivity of each form? Consider very carefully where you would put a lone pair located on the nitrogen (i.e. include the N-Lp "bond" in your antiperiplanar alignments) asuming the this atom is tetrahedral rather than planar. Does this lone pair play any part in either reaction in this position?. Note that the relative energy of the axial/equatorial N-Methyl group will not be an accurate reflection of any [[antiperiplanar]] alignments, since these are predominantly electronic in origin, and this mechanics method does not take these into account.
##'''Optional:''' The second (elimination) reaction is very slow compared to the first. Discuss with tutors why this might be so (for Hints, see [[organic:entropy|here]] or [[organic:ngp|here]]).
##'''Optional''': These reactions do not appear to occur for the corresponding ''cis''-decalins6. Why not?

|}

==== References and Footnotes ====
# D. H. R. Barton, ''Interactions between non-bonded atoms, and the structure of cis-decalin'', ''J. Chem. Soc.'', '''1948''', 340-342. {{DOI|10.1039/JR9480000340}}
#[http://en.wikipedia.org/wiki/Decalin Wikipedia article]
# For a modern application of mechanics to this molecule, see J. M. A. Baas, B. Van de Graaf, D. Tavernier, and P. Vanhee, ''Empirical force field calculations. 10. Conformational analysis of cis-decalin'', ''J. Am. Chem. Soc.'', '''1981''', ''103'', 5014 - 5021; {{DOI|10.1021/ja00407a007}}.
# For a video-Podcast of Barton and Woodward (and other Nobel prize winners), subscribe [http://www.ch.ic.ac.uk/video/index.rss here]
# R. B. Woodward, F. Sondheimer, and D. Taub, ''The total Synthesis of Cortisone'', ''J. Am. Chem. Soc.'', '''1951''', ''73'', 4057 - 4057. {{DOI|10.1021/ja01152a551}}.
# P.-W. Phuan and M. C. Kozlowski, ''Control of the Conformational Equilibria in Aza-cis-Decalins: Structural Modification, Solvation, and Metal Chelation'', ''J. Org. Chem.'', '''2002''', ''67'', 6339 - 6346; {{DOI|10.1021/jo025544t}}

=== Menthone/''iso''menthone and Bridgehead enols: Thermodynamic vs Kinetic Control Part 1.===

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#[[Image:Menthone.gif|thumb|right|Menthone]] Beckmann (of rearrangement fame) in 1889 dissolved optically active levorotatory (-) (S,R)-menthone ([α]D -28°) in conc. sulfuric acid, followed by quenching on ice to give what Beckmann assumed was pure (and what we would nowadays call [[diastereomeric]]) (+) (R,R)-isomenthone, [α]D +28°. He suggested for the first time that such an isomerisation, involving epimerisation at the asymmetric centre next to the keto group, proceeded via an intermediate enol in which the tetrahedral asymmetric carbon becomes planar. But this famous (perhaps even notorious2) early example of a [[reaction mechanism]] makes an interesting assumption, which can be tested by molecular modelling.
# Two possible enols can be formed, only one of which allows the [S] asymmetric carbon to become planar and then protonate to the [R] epimer. This is the so called [[thermodynamic enol]]. The other, which leaves the [S]-centre untouched is the [[kinetic enol]]. Find out if simple molecular modelling correctly predicts that the thermodynamic enol is indeed the more stable of the two. '''Hint:''' Model the enol and '''not''' the ketone. Consider carefully any conformational isomers possible.
# Given that the optical rotation3 of pure (+)-isomenthone is now known to be [α]D +101° rather than +28°, we can infer that Beckmann's product contains only 43% isomenthone and hence still contains 57% of original menthone, corresponding to an equilibrium constant of K= 0.75. This can be related to a (free energy) difference using the equation ΔG = -RT ln K, or ΔG = 0.7 kJ/mol (menthone being lower in energy by this amount compared to isomenthone). Can this energy difference be verified using molecular mechanics modelling? Can you explain why menthone is the more stable? (For another hint, or possibly a fright, visit [http://chemistry.gsu.edu/glactone/modeling/Luise/organic/cychexon.html this page]).
|}

==== References and footnotes ====
# E. Beckmann, ''Annalen'', '''1889''', ''250'', 322. {{DOI|10.1002/jlac.18892500306}}.
# Many of Beckmann's misconceptions were corrected by O. Wallach, ''Annalen'', '''1893''', ''276'', 296. {{DOI|10.1002/jlac.18932760306}}. The notoriety is because the coincidence of equal but opposite optical rotations obtained in this experiment led Beckmann to believe that he had obtained the [[enantiomer]] of menthone, and not as we now know, the impure (R,R) [[diastereomer]]. It should be borne in mind that the concept of tetrahedral and asymmetric carbon was only 15 years old at this time (see [http://en.wikipedia.org/wiki/Jacobus_van_%27t_Hoff Jacobus Henricus van't Hoff] and [http://en.wikipedia.org/wiki/Achille_Le_Bel Joseph Achille Le Bel]). Nevertheless confusion over this aspect persisted for some time after, and was often evident in the writings of even very famous chemists of the time (and Beckmann was very famous)!.
#[http://en.wikipedia.org/wiki/Menthone Wikipedia article]
# From about 1890-1935, mechanistic organic chemistry was born. In the absence of UV, IR, NMR, MS and X-Ray techniques, the [http://en.wikipedia.org/wiki/Polarimeter polarimeter] occupied a pivotal role. Many of the great discoveries in reaction mechanisms (keto-enol tautomerism as seen here, [[Organic:tutorial:meerwein| carbocations]], the Walden inversion, etc) relied on polarimetric measurements.
# A notorious modern example of (unwanted) epimerisation of a ketone is [http://en.wikipedia.org/wiki/Thalidomide Thalidomide], where one epimer inhibits morning sickness in pregnant women, and the other epimer is teratogenic, causing fetal abnormalities. The equilibrium in this case does not require conc. sulfuric acid, but can occur at physiological pH.

== Additional Molecular modelling Coursework ==

Please feel free to try these problems in your own time, and to discuss these with your organic tutors and lecturers. Note also that the relevant lectures may occur in the spring as well as autumn terms.
=== Axial/Equatorial preferences in cyclohexane and cyclohexanone and Hydrogen Bonding ===
{|
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#Construct a chair cyclohexane and replace firstly one of the [[axial]] hydrogens with the following groups: '''methyl''', '''t-butyl''', '''OH'''. Calculate the energy of the axial isomer.
# Then repeat (either by deleting/redrawing or by moving) for the equatorial forms. Compare the energies of the two isomers. Does any energy difference increase with the size of the group? Does OH fit into this in terms of size?
# [[Image:Thiomethylcyclohexanone.gif|right|thumb|thiomethyl cyclohexanone]]The dissolving metal reduction of cyclohexanones in a protic solvent (i.e. one capable of hydrogen bonding) is thermodynamically controlled and gives the more stable, equatorial alcohol. In fact, its probably the alkoxide that is the product, not the free alcohol. It is thought the alkoxide is actually a lot larger than the alcohol, accounting for the substantial equatorial preference. Can you think why its larger? [Ghemical cannot in fact model this, since the force field does not include parameters for the alkoxide anion].
# Determine the axial/equatorial preference of 2-methylthio-cyclohexanone (Hint: there are many conformations possible, and you should try a few to see if you can get the lowest).
|}
==== References and Footnotes ====

# A. H. Lewin and S. Winstein, ''NMR. Spectra and Conformational Analysis of 4-Alkylcyclohexanols'' ''J. Am. Chem. Soc.''; '''1962''', ''84'', 2464 - 2465; {{DOI|10.1021/ja00871a049}}
#F. R. Jensen and L. H. Gale, ''The Conformational Preference of the Bromo and Methyl Groups in Cyclohexane by IR Spectral Analysis'', ''J. Org. Chem.'', '''1960''', ''25'', 2075 - 2078. {{DOI|10.1021/jo01082a001}}
# K. B. Wiberg, J. D. Hammer, H. Castejon, W. F. Bailey, E. L. DeLeon, and R. M. Jarret, ''Conformational Studies in the Cyclohexane Series. 1. Experimental and Computational Investigation of Methyl, Ethyl, Isopropyl, and tert-Butylcyclohexanes'', ''J. Org. Chem.'', '''1999''', ''64'', 2085 - 2095; {{DOI|10.1021/jo990056f}}. The salient point here is that the [[enthalpy]] and [[entropy]] of this series differ in their trends.
# Just when you are starting to think that things are quite simple, along comes the observation: S. E. Biali, ''Axial monoalkyl cyclohexanes'', ''J. Org. Chem.'', '''1992''', ''57'', 2979 - 2980; {{DOI|10.1021/jo00037a001}}
# And this one with knobs on: ''In all-trans-1,2,3,4,5,6-hexaisopropylcyclohexane, all the alkyl groups are located at axial rather than equatorial positions: O. Golan, Z. Goren, and S. E. Biali, ''Axial-equatorial stability reversal in all-trans-polyalkylcyclohexanes'', ''J. Am. Chem. Soc.'', '''1990''', ''112'', 9300 - 9307. {{DOI|10.1021/ja00181a036}}.
#J. A. Anderson, K. Crager, Kelly, L.Fedoroff, G. S. Tschumper, Gregory S. ''Anchoring the potential energy surface of the cyclic water trimer.'' ''J. Chem. Physics'', '''2004''', ''121'', 11023-11029. {{DOI|10.1063/1.1799931}}.
#R. R. Fraser, N. C. Faibish, ''On the purported axial preference in 2-methylthio- and 2-methoxycyclohexanones: steric effects versus orbital interactions'', ''Can. J. Chem.'', '''1995''', ''73'', 88-94.
=== How to induce room temperature hydrolysis of a peptide ===
{|
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<title>Pentahelicene</title><color>white</color><size>150</size>
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<uploadedFileContents>peptide-13.3.mol</uploadedFileContents>
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[[Image:amide-cleavage.png|thumb|right|Peptide hydrolysis]] This introduces a further example of how simple conformational analysis can quickly rationalize kinetic behaviour. At neutral pH and 25° the half life for hydrolysis of a peptide bond is around 500 years (and thank goodness, or we would ourselves all rapidly hydrolise to a mush!). Some enzymes however can achieve this in less than 1 second, an acceleration of 1013! Organic chemists are not quite so clever, but they can achieve room temperature hydrolysis of a peptide in 21 minutes by careful conformational design. The two isomers shown on the right differ only in their stereochemistry, one hydrolysing quickly, the other slowly. Build a model of each compound, and calculate two isomers for each, varying in whether the ring N-substituent is oriented axial or equatorial with respect to the decalin ring. On the basis of your two pairs of energies, can you rationalise the observed kinetic behaviour? Do you know why both of these compounds take very much less than 500 years to hydrolise the peptide bond?

'''Hint1:''' Use the chair-chair conformation for cis-decalin as your template for constructing this system.

'''Hint2:''' When constructing your models, think if there are any hydrogen bonds that might stabilize the structure!

'''Hint3:''' Hydrolysis can only occur when the OH group can approach the carbonyl of the peptide bond close enough to react, and at the right angle of approach.
|}

==== Reference ====

# M. Fernandes, F. Fache, M. Rosen, P.-L. Nguyen, and D. E. Hansen, 'Rapid Cleavage of Unactivated, Unstrained Amide Bonds at Neutral pH', ''J. Org. Chem.,'' '''2008''', ASAP: {{DOI|10.1021/jo800706y}}

=== Caryophyllene: The phenomenon of Atropisomerism ===

# [[Image:caryophyllene-ketone.gif|thumb|right|Caryophyllene ketone]] [http://en.wikipedia.org/wiki/Caryophyllene Caryophyllene], a constituent of many essential oils, include clove oil, has a [[trans]] alkene contained in a 9-membered ring. One interesting property is that it has 4 [[diastereoisomers]] possible, originating from a total of three asymmetric centres present in the molecule. Two of these are conventional chiral centres, one is present in the form of a disymmetric trans double bond. To understand why such a bond can result in two configurations, one must appreciate that (concurrent) rotation about the two C-C single bonds adjacent to the alkene is in fact restricted, because to the hydrogen labelled Ha cannot easily pass by the edge of the 4-membered ring. Construct this molecule (in fact the ketone rather than the alkene) and optimize its geometry. Note in particular that the ring junction is ''trans'' and not ''cis''.
# You will find you may well have obtained one of two forms. In the first, the Ha hydrogen will be opposite the C=O group, in the other it will be adjacent to it. Record the energy of whatever form you got. At the end of the course, we will try to find the ''winner'' with the lowest energy (this is not as trivial as it sounds!).
# Next, take your structure, and try to ''flip'' the [[trans]] alkene bond around so that eg if the methyl were previously pointing up, now it will point down. You may find a combination of erasing/redrawing or of moving, will accomplish this. You may also find another trick useful, of deleting all hydrogens, and then re-sprouting them back on again. Re-optimise your structure and compare the energy with your first isomer.
# Another feature of this model is that you can judge which group is in the so-called shielded region of the carbonyl group magnetic anisotropy. Using this information, you can see if there are any anomalous 1H chemical shifts that might need explaining!

==== References ====
# M. Clericuzio, G. Alagona, C. Ghio, and L. Toma, ''Ab Initio and Density Functional Evaluations of the Molecular Conformations of -Caryophyllene and 6-Hydroxycaryophyllene'', ''J. Org. Chem.'' '''2000''', ''65'', 6910 - 6916. {{DOI|10.1021/jo000404+}}.
#[http://en.wikipedia.org/wiki/Caryophyllene Wikipedia article]
# For a recent application of this phenomenon, see P. C. Bulman Page, B. R. Buckley, S. D.R. Christie, M. Edgar, A. M. Poulton, M. R.J. Elsegood and V. McKee, ''A new paradigm in N-heterocyclic carbenoid ligands'', ''J. Organometallic Chem.'', '''2005''', ''690'', 6210-6216. D {{DOI|10.1016/j.jorganchem.2005.09.015}}.

=== Germacrene: Conformational analysis of medium sized rings ===

{|
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# [[Image:Germacrene.gif|thumb|right|Germacrene and the thermal reaction product]]Germacrene is a natural product with a ten-membered ring; it has the triene structure shown. Assuming that it adopts a crown conformation, build a three-dimensional model.
# On heating, germacrene is converted into one of the stereoisomers of the divinylcyclohexane, via a [3,3] sigmatropic pericyclic reaction. Predict from your model for Germacrene whether the product will have the two vinyl groups [[cis]] or [[trans]] to one another.
|}

==== References ====

# K. Shimazaki, M. Mori, K. Okada, T. Chuman, H. Goto, K. Sakakibara and M. Hirota, ''Conformational analyses of periplanone analogs by molecular mechanics calculations'', '' J. Chem. Ecology'', '''1991''', ''17'', 779-88. {{DOI|10.1007/BF00994200}}.
# H. Shirahama, E. Sawa and T. Matsumoto, ''Conformational aspects of germacrene B. Are the germacrenes resolvable ?'', ''Tetrahedron Lett.'', '''1979''', ''20'', 2245-2246. {{DOI|10.1016/S0040-4039(01)93687-1}}. See also {{DOI|10.1039/P19750002332}} for an explanation of the selective epoxidation of germacrene.

=== Xestoquinone: Regio and Stereoselectivity in the Diels Alder reaction===

# [[Image:xestoquinone.gif|thumb|right|Xestoquinone precursor]] This compound is a precursor to a natural product called Xestoquinone. It has four alkene groups, which can individually be considered as the alkene component in a π2s + π4s [[Diels Alder]] [[cycloaddition]]. The pair of alkenes ''a+b'' or ''c+d'' can also act as the diene component in the π2s + π4s [[Diels Alder]] [[cycloaddition]]. Construct a model of the product of e.g. forming a bond between alkene ''a'' or alkene ''b'' and diene ''c+d'', and then reverse the addition by using either ''c'' or ''d'' adding to the diene ''a+b''. The stereochemistry of addition should always be [[suprafacial]], i.e. preserving the stereochemical relationships of the alkenes. You should very carefully check that this is so in your final model.
# Whilst you should stop at '''two''' models, it is possible to construct many more. For example, one might be able to add to either the ''top'' face of alkene ''b'' or to its ''bottom'' face. Identify the model with the lower energy, and save it for the end of the workshop. We will identify the isomer of lowest energy from everyone's results, this being a communal [[Monte Carlo]] experiment to find the [[global minimum]].

==== References ====

#[http://en.wikipedia.org/wiki/Diels-Alder_reaction Wikipedia article]
#For the original literature on this synthesis, see R. Carlini, K. Higgs, C. Older, S. Randhawa, and R. Rodrigo, ''Intramolecular Diels-Alder and Cope Reactions of o-Quinonoid Monoketals and Their Adducts: Efficient Syntheses of (±)-Xestoquinone and Heterocycles Related to Viridin'', ''J. Org. Chem.'', '''1997''', ''62'', 2330 - 2331. {{DOI|10.1021/jo970394l}} where you can check to see which isomers actually do form!

=== Aldol Reaction and anti-Bredt Rings ===

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# [[Image:Aldol.gif|thumb|right|Aldol Reaction]]When the diketone shown is treated with base, it undergoes an aldol condensation. Two obvious possibililties are elimination of the combination Ha and Oa, or of the alternative combination Hb and Ob. In fact, only a single product is formed. On the basis of energies for both products, can you predict which one is actually formed?
# Measure a few dihedral angles, ie to find out how planar the alkene present is. Does this suggest a reason why one isomer is less stable than the other?
# There is a third very remote structural possibility. If you have time, verify that this third product truly is unlikely.
|}

==== References ====
#[http://en.wikipedia.org/wiki/Bredt's_Rule Bredt's Rule]
# I. Novak, ''Molecular Modeling of Anti-Bredt Compounds'', ''J. Chem. Inf. Model.'', '''2005''', ''45'', 334 - 338. {{DOI|10.1021/ci0497354}}
# See also this article A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, ''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins'', ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}} in conjunction with Project 9.

=== Conformational Preference for asymmetric hydride reduction of a ketone ===

# [[Image:Felkin.gif|thumb|right|Asymmetric hydride reduction]]The hydride ([http://en.wikipedia.org/wiki/Lithium_aluminium_hydride BH4, AlH4, etc]) reduction of the ketone shown here is stereospecific, resulting in an alcohol with the stereochemistry shown (known as the [http://en.wikipedia.org/wiki/Chiral_induction Cram or the Felkin-Anh] rule). Construct a model of the ketone and establish which of at least two conformations is the lowest in energy.
# If the hydride anion is delivered from the least hindered position, is the conformation you have consistent with the stereochemistry shown for the product?
# You can see from Ref 4 that the situation can be far more complex, depending on many other factors.

====References ====
# [http://en.wikipedia.org/wiki/Chiral_induction Wikipedia article]
# D. J. Cram and D. R. Wilson, ''Studies in Stereochemistry. XXXII. Models for 1,2-Asymmetric Induction'', ''J. Am. Chem. Soc.'', '''1963''', ''85'', 1245 - 1249. {{DOI|10.1021/ja00892a008}}.
# Y. Yamamoto, K. Matsuoka, and H. Nemoto, ''Anti-Cram selective reduction of acyclic ketones via electron transfer initiated processes'', ''J. Am. Chem. Soc.'', '''1988''', ''110'', 4475 - 4476; {{DOI|10.1021/ja00221a093}}.
# A. Mengel and O. Reiser, ''Around and beyond Cram's Rule'', ''Chem. Rev.'', '''1999''', ''99'', 1191 - 1224. {{DOI|10.1021/cr980379w}}.

=== Enantiomers vs Diastereomers Part 2: NMR Coupling constants ===

#[[Image:karplus.gif|thumb|Axial-equatorial interconversion|right]]In Project 2.2 above, we saw how the energies of diastereomeric compounds could be compared with the corresponding enantiomers. In this extension, we show how molecular modelling can cast light on the conformation adopted by 2-ethyl-4-methyl-1-oxa-cyclopentane-3-carboxylic acid estimated using measured 1H NMR coupling constants. The (2S,3S,4S) diastereomer has couplings of 3JH2,H3 8.3 Hz and 3JH3,H4 9.8 Hz. Two possible conformations of this diastereomer are shown on the right. They differ in that one has Et axial, and Me/COOH equatorial, and the other Et equatorial and Me/COOH axial.
#[[Image:karplus.jpg|Karplus plot|thumb|left]]By calculating the geometries of both conformations, and measuring the dihedral angle H2-C-C-H3 and H3-C-C-H4, one can assess by using the Karplus equation (left, taken from Ref 2 and relevant for a cyclopentane, but the values for which might be modified by the presence of electronegative substituents), which conformation leads to the best agreement between the calculated angle and the measured coupling constants (Hint: on the basis of the predicted couplings, you should be able to eliminate one of the two conformations shown for this molecule).
#[[Image:5-circulene.gif|thumb|5-circulene|right]]In Project 2.2 we also introduced molecules such as helicenes and circulenes. The 1H NMR of the [5]-circulene shown to the right revealed a complex spectrum at δ 2.98 ppm and again at 3.75 ppm. On the face of it, the four protons labeled Ha and Hb should all be equivalent, and the spectrum should be a single peak, not two complex multiplets. Indeed, if the NMR is recorded at high temperatures, this is exactly what is observed. By constructing a model of the [5]-circulene shown, can you explain why at normal temperatures, the NMR spectrum is so complex? 
#[[Image:Lab_expt.jpg|thumb|Synthesis lab experiment|right]]A practical application of this technique is to determine the stereochemistry of the product of the reaction between E,E-2,4-hexadien-1-ol and maleic anhydride. You will have the 1H NMR spectrum of your sample recorded, and evident from that will be peak multiplicities of the various proton resonances. You should endeavour from your analysis to come up with a suggestion for the structure of compound '''Y''', and from this, estimates of the numerical values (but not the signs) of the 2J and 3J couplings visible. Now using the techniques described above, construct a model of your proposed structure for '''Y'''. Measure the dihedral angles for all the 3J couplings, and very approximately estimate what the corresponding 3J might be from the diagram above. Does this help you assign the stereochemistry of the product?
#'''Advanced topic''': Part of the spectroscopic analysis of the compound '''Y''' involves interpreting the IR spectrum. Theory can be used in fact to simulate the full IR spectrum. In section 5.3 below, you will find instructions on how to use the model you have calculated here to initiate a so called '''density functional''' calculation. This will provide you with the required IR simulation. Follow these instructions, and open the resulting .log file in Gaussview. Go to the '''Results''' menu and select '''vibrations'''. The IR spectrum will be displayed. Does it match the one you have recorded for yourself?

==== References ====

#M. Karplus, ''Vicinal Proton Coupling in Nuclear Magnetic Resonance'', '' J. Am. Chem. Soc.'', '''1963''', ''85'', 2870 - 2871; {{DOI|10.1021/ja00901a059}}
#A. Wu, D. Cremer, A. A. Auer, and J. Gauss, ''Extension of the Karplus Relationship for NMR Spin-Spin Coupling Constants to Nonplanar Ring Systems: Pseudorotation of Cyclopentane'', ''J. Phys. Chem. A,'', '''2002''', ''106'', 657 -667; {{DOI|10.1021/jp013160l}}
#C. A. Stortz and M. S. Maier, ''Configurational assignments of diastereomeric γ-lactones using vicinal H–H NMR coupling constants and molecular modelling'', ''J. Chem. Soc., Perkin Trans. 2'', '''2000''', 1832 - 1836. {{DOI|10.1039/b003862h}}
# A. H. Abdourazak, A. Sygula, and P. W. Rabideau ''Locking the bowl-shaped geometry of corannulene: cyclopentacorannulene'', ''J. Am. Chem. Soc.'', '''1993''', ''115'', 3010 - 3011. {{DOI|10.1021/ja00060a073}}

=== Bridgehead enols: Thermodynamic vs Kinetic Control Part 2.===
{|
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#[[Image:Bredt.gif|thumb|right|Brendanone]] The ketone Brendan-2-one shown right exhibits unusual behaviour.6 When treated with NaOD/MeOD, deuterium substitution occurs easily and rapidly only in position Hb. Enolisation must of necessity form a bridgehead double bond (''anti-Bredt''), but clearly one isomer is more stable than the other possible form. Does molecular modelling predict this correctly?
#The unusually facile enolisation of this ketone (given that it forms an anti-Bredt enol) can also be investigated by molecular modelling. '''Measure''' the dihedral angle between the C-Ha or C-Hb vector and the carbonyl group. Assuming that the ''ideal'' angle for proton removal is around 90°, which proton is better set up for abstraction? Might this be kinetic rather than thermodynamic control?
#[[Image:Cortisone.gif|thumb|right|Cortisone]]One could also revisit Problem 2.3.3 above. Here, proton abstraction forms an enol which eventually epimerises the bridgehead position to form a ''trans'' ring junction. Why should this proton be particularly easy to remove? From what you have learnt above, would this be for kinetic or for thermodynamic reasons (or both?). Are all the relevant effects modelled using the mechanics approach or is consideration of the electrons also necessary?
|}
==== References and Footnotes====

# A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, {{doi-inline|10.1021/ja00837a043|''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins''}}, ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}}.

===Sulfonylation of Naphthalene: Thermodynamic vs Kinetic Control Part 3.===

[[Image:Sulfonylation.gif|right|thumb|Sulfonylation of naphthalene]]The sulfonylation of naphthalene using sulfuric acid is a good example of a mechanism combining both steric and electronic influences. The Molecular mechanics method intrinsic to the Ghemical program can only model the former, and not the latter. It is a worthwhile exercise to establish whether this anticipated deficiency does indeed lead to a model which only partially explains experiment.

It has been known for some time that treating naphthalene with sulfuric acids at low temperatures produces mostly substitution at the 1-position of the naphthalene. Heating the reaction mixture, or conducting the reaction at elevated temperatures produces mostly the 2-isomer. This is indeed a classic example of [[kinetic]] vs [[thermodynamic]] control, the 1-isomer being the kinetic one and the 2-isomer the thermodynamic one. To model the kinetic reaction, we have to inspect the [[transition state]] for the reaction, and here we can approximate this by the [[Wheland Intermediate]]. To model the thermodynamic reaction, we have to inspect the product (rather than the transition state) for the reaction.

#Build models for all four species shown in the diagram on the right. For the two products, define ''conjugated'' bond types for all the ring bonds, and define the sulfonyl group with two S=O double bonds and one S-O single bond. Take care to optimise the conformation of the sulfonyl group with respect to the aromatic ring. For the two Wheland intermediates, the limitations of Ghemical will force us to ''cheat''. Ghemical does not have parameters for a carbocation. So define the C2-C3 bond as conjugated (for the 1-Wheland intermediate). When you '''add hydrogens''' it will in fact add a second hydrogen to C2. Delete this one hydrogen. Ghemical will calculated the energy regardless of not knowing C2 is actually a carbonium ion! For the 2-Wheland intermediate, ensure that you use '''exactly''' the same number of ''conjugated'' bond types as you did for the 1-isomer (the two models in a mechanics sense are only comparable if you have the same total number of bond types in each model). You will have to decide whether these (undoubted) approximations have produced reasonable models or not (is the naphthalene framework planar for example, as it should be?).
#Record the pairs of energies (two for the 1- and 2-products, and two for each preceeding transition (Wheland) state.
#By turning the spacefilling representation on, which of the two products has the least unfavourable steric interactions between the sulfonic acid group and any adjacent hydrogens? Does this match with their relative energies?
#Do any unfavourable steric interactions observed in the product(s) also exist in the Wheland intermediates (as models for the transition states)?
#The relative stability of the Wheland intermediates is always assumed to be an '''electronic''' phenomenon. The conventional explanation is that the 1-Wheland isomer is stablized by both one aromatic ring '''and''' an allyl cation conjugated to it. The 2-Wheland isomer is stabilised by one aromatic ring conjugated to a secondary carbocation and an alkene. This type of ''cross conjugation'' is conventionally assumed to be less favourable. Does a purely mechanical approach to this problem reproduce this expectation? Or is this ''mechanical'' approximation to an ''electronic'' model too severe? It seems a good point to stop this course, since the next time you will build models, it will indeed be using methods which properly approximate the electronic components.
====References====

#R. Lantz, ''Mechanism of the monosulfonation of naphthalene'', ''Compt. Rend''. '''1935''', ''201'', 149-52.
#G. W. Wheland, ''A Quantum Mechanical Investigation of the Orientation of Substituents in Aromatic Molecules'', ''J. Am. Chem. Soc.'' '''1942''', ''64'', 900 - 908; {{DOI|10.1021/ja01256a047}}
#C. A. Reed, N. L. P. Fackler, K-C. Kim, D. Stasko, D. R. Evans, P. D. W. Boyd, and C. E. F. Rickard, ''Isolation of Protonated Arenes (Wheland Intermediates) with BArF and Carborane Anions. A Novel Crystalline Superacid'', ''J. Am. Chem. Soc.'' '''1999''', ''121'', 6314 - 6315 {{DOI|10.1021/ja981861z}}

== Coursework not to be attempted at any time: Antimodelling Molecules ==

The following represent molecules that should '''not''' be modelled under any circumstances! You should instead attempt to '''NAME''' them.

[[Image:Contraceptive.gif|Contraceptive (NO in every conceivable position)]] [[Image:Paradise.gif|Paradise lost]] [[Image:Synoptic.gif|Synoptic]] [[Image:Cisters.gif|Cisters]] [[Image:Transisters.gif|Transisters]] [[Image:Metaphor.gif|Metaphor]] [[Image:Metastasis.gif|Metastasis]] [[Image:Cyclone.gif|Cyclone]] [[Image:Anticyclone.gif|Anticyclone]] [[Image:Arsole.gif|Arsole]] [[Image:Orthodox.gif|Orthodox]] [[Image:Synthesis.gif|Synthesis and Antithesis]] [[Image:Aphrodisiac.gif|Name this yourself. Does Meg Ryan spring to mind?]] [[Image:Cyclops.gif|Cyclops]] [[Image:Paradox.gif|Paradox]] [[Image:Transparent.gif|Transparent]] [[Image:Encyclopedia.gif|Encyclopedia]] [[Image:Maths.jpg|Find X]] [[Image:VanderMaxforce.jpg|150px|Max Whitby stuck to a strangely attractive Lamp Post]] [[Image:nanoballet.jpg|200px|Nanoballet dancer]] [[Image:NanoCossacks.jpg|200px|NanoCossacks]]
[[Image:Paralysis.png|500px|Paralysis]] [[Image:Mcdonalds.png|350px|Old McDonald's Molecule: ene-yne-ene-yne-one]]
[[Image:Silenedione.png|200px|Celine Dion]] [[Image:Sundial.png|200px|Sun Dial]]
[[Image:Iownu.png|200px|I Own You!]]

If you know of any other antimodelling molecules, please add them here!

====Acknowledgements ====

Some of these cartoons are from [http://www.nearingzero.net/sci_chemistry.html here], and six are original. A superb collection of '''''silly names''''' is maintained
by [http://www.chm.bris.ac.uk/sillymolecules/sillymols.htm Paul May] [[Organic:Model_answers|.]] See {{DOI|10.1021/jo0349227}} for the nanoputians.

----
[[Second_Year_Modelling_Workshop|Back to introduction]]
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File:Iownu.png

2010-10-15T15:38:17Z

Nm607:

Coursework

2010-10-15T15:33:42Z

Nm607: /* Coursework not to be attempted at any time: Antimodelling Molecules */

[[Second_Year_Modelling_Workshop|Back to introduction]]
----
== Molecular modelling Coursework to be attempted during Scheduled Sessions ==

These projects are arranged in increasing order of difficulty, and time taken to complete. You should do as many as you can in the 2 hour session allocated to you, and return to finish the rest if you wish at your convenience. At the end of the session, we will conduct a ''number auction''. For each project, the bidding will start with the first volunteer offering an energy for the system (or one of the isomers). If anyone has a lower energy for that molecule, they will then bid that energy. The winner will be the one with the lowest energy.

=== Conformational analysis I: Chair and Boat-like conformations of Cyclohexane ===
{|
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#Construct '''[[chair]]''' and '''[[boat]]'''-like '''[[conformation]]s''' of [[cyclohexane]]. Compare the energies of both forms.
#Check carefully if your boat really is a boat, or whether it has any apparent distorsion.
#Try changing one or more of the CH2 groups into an oxygen and see if that affects things.
#For the record, the point group symmetries of the various species which may be involved are D3d for the chair conformation, C2v for a boat geometry, and D2 for any twisted boat form. Is any of these forms '''chiral'''?
#The molecule on the left is called '''chiralane'''. Are its rings boats or chairs?
|}
====References ====
# The first suggestion of two forms for cyclohexane goes as far back as H. Sachse, ''Chem. Ber'', 1890, '''23''', 1363 and ''Z. Physik. Chem.'', 1892, 10, 203. This is nicely explained [http://www.chem.yale.edu/~chem125/125/history/Baeyer/Sachse.html here]. E. Mohr, ''J. Prakt. Chem.'', 1918, '''98''', 315 and ''Chem. Ber.'', 1922, '''55''', 230, translated Sachse's argument into a pictorial one.
# The article that put [[conformational analysis]] on the map: D. H. R. Barton and R. C. Cookson, ''The principles of conformational analysis'', ''Q. Rev. Chem. Soc.'', '''1956''', ''10'', 44. {{DOI|10.1039/QR9561000044}}
#[http://en.wikipedia.org/wiki/Chair_conformation Wikipedia article]
#D. A. Dixon and A. Komornicki, ''Ab initio conformational analysis of cyclohexane'', ''J. Phys. Chem.'', '''1990''', ''94'', 5630 - 5636; {{DOI|10.1021/j100377a041}}.
#A nice exploration of the potential energy surfaces for cyclohexane can be viewed [http://www.springer.com/carey-sundberg/cyclohex/cyclohex.php here].
# For a more modern application of this technique, see I. Columbus, R. E. Hoffman, and S. E. Biali, ''Stereochemistry and Conformational Anomalies of 1,2,3- and 1,2,3,4-Polycyclohexylcyclohexanes''. ''J. Am. Chem. Soc.'', '''1996''', ''118'', 6890 - 6896; {{DOI|10.1021/ja960380h}}.
# The second molecule shown in this section is called [6.6]chiralane. It is peculiar for having many six-membered saturated rings, all of them as twist-boats rather than chairs! (a chair has a plane of symmetry, a twist boat only axes, which of course allows it to be chiral). See [http://petitjeanmichel.free.fr/itoweb.petitjean.graphs.html#CHIR here] for more details.
# More detail on the conformation of rings (and acyclic systems) will be found in the [http://www.ch.ic.ac.uk/local/organic/conf/ lecture course] on the topic to be given in the spring term.

=== Enantiomers vs Diastereomers Part 1: Butanes and Helicenes. ===

This problem illustrates, using models, the difference between an enantiomer and a diastereomer.

#[[Image:diastereo.gif|thumb|right|2-bromo-3-chlorobutane]][[Image:pentahelicene.gif|thumb|right|Pentahelicene]]The compound 2-bromo-3-chlorobutane has two [[chiral]] centres, and four isomers (22) are therefore possible. Calculate all four isomers, and for each be careful to label each of the two stereo centres '''R''' or '''S''' as you go. For each of the four isomers '''R,R''', '''S,S''', '''R,S''', '''S,R''' you will have to think about whether you have obtained the lowest energy [[conformer]].
#Can your four energies be grouped in any way? You should think about the expected difference between '''enantiomers''', '''diastereomers''' and '''conformers'''.
{|
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#Construct some helicenes (pentahelicene or [5]helicene is shown on the right), using '''conjugated''' bonds for all the ring bonds. Benzene, naphthalene, phenanthrene and benzophenanthrene are in fact the first four members of this series. At what point in this series can you detect helicity cropping up? This is manifested by a non-planar helical wind of the molecule. If you do detect it, note how the wind is either left or right handed, ie the two forms are '''enantiomers''' of each other. Try displaying the molecule in '''spacefill mode''' (see above) to see if you can identify the source of the helicity. (Note: the smallest helicene which can be resolved experimentally into enantiomers is in fact [5]helicene]).
#The higher helicenes are well known (up to about [14]helicene) and amongst the ''most chiral'' molecules known (in terms of how much they rotate the plane of polarised light).
#[7]circulene is a known molecule, with a unique saddle-shaped structure, shown on the left (there is no real need for you to build this model, but do please do so if you are curious). [http://en.wikipedia.org/wiki/Graphene Graphene] is a related polymeric molecule, of much topical interest in the semi-conducting and other industries (Nobel Prize 2010).
|}
==== References ====

#[http://en.wikipedia.org/wiki/Diastereomer Wikipedia article on Diastereomers]
#[http://en.wikipedia.org/wiki/Helicene Wikipedia article on Helicenes and related molecules]
#R. H. Janke, G. Haufe, E.-U. Würthwein, and J. H. Borkent, ''Racemization Barriers of Helicenes: A Computational Study'', ''J. Am. Chem. Soc.'', '''1996''', ''118'' 6031 - 6035 {{DOI|10.1021/ja950774t}}

=== Conformational analysis II: ''cis'' and ''trans''-decalins, Steroids and Podcasts! ===
{|
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# [[Image:cis-decalin.gif|thumb|right|cis Decalin]]This is the famous molecule that started the whole molecular mechanics modelling ball rolling. [http://www.ch.ic.ac.uk/video/barton/barton1.pdf Barton] in 1948 sought to find out which [[conformation]] of ''cis''-decalin was the most stable (see [http://www.ch.ic.ac.uk/video/barton/index_qt.html here] for video). You should be able to find at least three conformations of this molecule. Try locating these, and conclude which is the most stable. Identify any [[chair]] rings and any [[boat]].
#Measure some dihedral angles to see if the [[staggered]] relationships hold (i.e. for such a relationship, the dihedral angle should be close to 60 degrees).
#A key step in Woodward's famous synthesis of [http://en.wikipedia.org/wiki/Cortisone cortisone] is a quinone+butadiene [[Diels-Alder]] reaction to give a cis-decalin (left), with an assumption that [[epimerisation]] to a trans-decalin is thermodynamically favourable. [[Image:Cortisone.gif|thumb|left|cis Cortisone]]Can you verify whether the trans-isomer is indeed more stable? Its not so obvious, since this compound has two extra double bonds in the rings and six sp2 centres which might perturb things.
#[[Image:App.gif|thumb|right|trans Decalin]]The two diastereomeric ''trans''-decalin tosylates react quite differently with NaBH4. Construct models for both isomers (use methoxy as a model for the Tosyl group) and from the [[antiperiplanar]] alignments of bonds that you can find in each isomer, can you make a connection to the reactivity of each form? Consider very carefully where you would put a lone pair located on the nitrogen (i.e. include the N-Lp "bond" in your antiperiplanar alignments) asuming the this atom is tetrahedral rather than planar. Does this lone pair play any part in either reaction in this position?. Note that the relative energy of the axial/equatorial N-Methyl group will not be an accurate reflection of any [[antiperiplanar]] alignments, since these are predominantly electronic in origin, and this mechanics method does not take these into account.
##'''Optional:''' The second (elimination) reaction is very slow compared to the first. Discuss with tutors why this might be so (for Hints, see [[organic:entropy|here]] or [[organic:ngp|here]]).
##'''Optional''': These reactions do not appear to occur for the corresponding ''cis''-decalins6. Why not?

|}

==== References and Footnotes ====
# D. H. R. Barton, ''Interactions between non-bonded atoms, and the structure of cis-decalin'', ''J. Chem. Soc.'', '''1948''', 340-342. {{DOI|10.1039/JR9480000340}}
#[http://en.wikipedia.org/wiki/Decalin Wikipedia article]
# For a modern application of mechanics to this molecule, see J. M. A. Baas, B. Van de Graaf, D. Tavernier, and P. Vanhee, ''Empirical force field calculations. 10. Conformational analysis of cis-decalin'', ''J. Am. Chem. Soc.'', '''1981''', ''103'', 5014 - 5021; {{DOI|10.1021/ja00407a007}}.
# For a video-Podcast of Barton and Woodward (and other Nobel prize winners), subscribe [http://www.ch.ic.ac.uk/video/index.rss here]
# R. B. Woodward, F. Sondheimer, and D. Taub, ''The total Synthesis of Cortisone'', ''J. Am. Chem. Soc.'', '''1951''', ''73'', 4057 - 4057. {{DOI|10.1021/ja01152a551}}.
# P.-W. Phuan and M. C. Kozlowski, ''Control of the Conformational Equilibria in Aza-cis-Decalins: Structural Modification, Solvation, and Metal Chelation'', ''J. Org. Chem.'', '''2002''', ''67'', 6339 - 6346; {{DOI|10.1021/jo025544t}}

=== Menthone/''iso''menthone and Bridgehead enols: Thermodynamic vs Kinetic Control Part 1.===

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#[[Image:Menthone.gif|thumb|right|Menthone]] Beckmann (of rearrangement fame) in 1889 dissolved optically active levorotatory (-) (S,R)-menthone ([α]D -28°) in conc. sulfuric acid, followed by quenching on ice to give what Beckmann assumed was pure (and what we would nowadays call [[diastereomeric]]) (+) (R,R)-isomenthone, [α]D +28°. He suggested for the first time that such an isomerisation, involving epimerisation at the asymmetric centre next to the keto group, proceeded via an intermediate enol in which the tetrahedral asymmetric carbon becomes planar. But this famous (perhaps even notorious2) early example of a [[reaction mechanism]] makes an interesting assumption, which can be tested by molecular modelling.
# Two possible enols can be formed, only one of which allows the [S] asymmetric carbon to become planar and then protonate to the [R] epimer. This is the so called [[thermodynamic enol]]. The other, which leaves the [S]-centre untouched is the [[kinetic enol]]. Find out if simple molecular modelling correctly predicts that the thermodynamic enol is indeed the more stable of the two. '''Hint:''' Model the enol and '''not''' the ketone. Consider carefully any conformational isomers possible.
# Given that the optical rotation3 of pure (+)-isomenthone is now known to be [α]D +101° rather than +28°, we can infer that Beckmann's product contains only 43% isomenthone and hence still contains 57% of original menthone, corresponding to an equilibrium constant of K= 0.75. This can be related to a (free energy) difference using the equation ΔG = -RT ln K, or ΔG = 0.7 kJ/mol (menthone being lower in energy by this amount compared to isomenthone). Can this energy difference be verified using molecular mechanics modelling? Can you explain why menthone is the more stable? (For another hint, or possibly a fright, visit [http://chemistry.gsu.edu/glactone/modeling/Luise/organic/cychexon.html this page]).
|}

==== References and footnotes ====
# E. Beckmann, ''Annalen'', '''1889''', ''250'', 322. {{DOI|10.1002/jlac.18892500306}}.
# Many of Beckmann's misconceptions were corrected by O. Wallach, ''Annalen'', '''1893''', ''276'', 296. {{DOI|10.1002/jlac.18932760306}}. The notoriety is because the coincidence of equal but opposite optical rotations obtained in this experiment led Beckmann to believe that he had obtained the [[enantiomer]] of menthone, and not as we now know, the impure (R,R) [[diastereomer]]. It should be borne in mind that the concept of tetrahedral and asymmetric carbon was only 15 years old at this time (see [http://en.wikipedia.org/wiki/Jacobus_van_%27t_Hoff Jacobus Henricus van't Hoff] and [http://en.wikipedia.org/wiki/Achille_Le_Bel Joseph Achille Le Bel]). Nevertheless confusion over this aspect persisted for some time after, and was often evident in the writings of even very famous chemists of the time (and Beckmann was very famous)!.
#[http://en.wikipedia.org/wiki/Menthone Wikipedia article]
# From about 1890-1935, mechanistic organic chemistry was born. In the absence of UV, IR, NMR, MS and X-Ray techniques, the [http://en.wikipedia.org/wiki/Polarimeter polarimeter] occupied a pivotal role. Many of the great discoveries in reaction mechanisms (keto-enol tautomerism as seen here, [[Organic:tutorial:meerwein| carbocations]], the Walden inversion, etc) relied on polarimetric measurements.
# A notorious modern example of (unwanted) epimerisation of a ketone is [http://en.wikipedia.org/wiki/Thalidomide Thalidomide], where one epimer inhibits morning sickness in pregnant women, and the other epimer is teratogenic, causing fetal abnormalities. The equilibrium in this case does not require conc. sulfuric acid, but can occur at physiological pH.

== Additional Molecular modelling Coursework ==

Please feel free to try these problems in your own time, and to discuss these with your organic tutors and lecturers. Note also that the relevant lectures may occur in the spring as well as autumn terms.
=== Axial/Equatorial preferences in cyclohexane and cyclohexanone and Hydrogen Bonding ===
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#Construct a chair cyclohexane and replace firstly one of the [[axial]] hydrogens with the following groups: '''methyl''', '''t-butyl''', '''OH'''. Calculate the energy of the axial isomer.
# Then repeat (either by deleting/redrawing or by moving) for the equatorial forms. Compare the energies of the two isomers. Does any energy difference increase with the size of the group? Does OH fit into this in terms of size?
# [[Image:Thiomethylcyclohexanone.gif|right|thumb|thiomethyl cyclohexanone]]The dissolving metal reduction of cyclohexanones in a protic solvent (i.e. one capable of hydrogen bonding) is thermodynamically controlled and gives the more stable, equatorial alcohol. In fact, its probably the alkoxide that is the product, not the free alcohol. It is thought the alkoxide is actually a lot larger than the alcohol, accounting for the substantial equatorial preference. Can you think why its larger? [Ghemical cannot in fact model this, since the force field does not include parameters for the alkoxide anion].
# Determine the axial/equatorial preference of 2-methylthio-cyclohexanone (Hint: there are many conformations possible, and you should try a few to see if you can get the lowest).
|}
==== References and Footnotes ====

# A. H. Lewin and S. Winstein, ''NMR. Spectra and Conformational Analysis of 4-Alkylcyclohexanols'' ''J. Am. Chem. Soc.''; '''1962''', ''84'', 2464 - 2465; {{DOI|10.1021/ja00871a049}}
#F. R. Jensen and L. H. Gale, ''The Conformational Preference of the Bromo and Methyl Groups in Cyclohexane by IR Spectral Analysis'', ''J. Org. Chem.'', '''1960''', ''25'', 2075 - 2078. {{DOI|10.1021/jo01082a001}}
# K. B. Wiberg, J. D. Hammer, H. Castejon, W. F. Bailey, E. L. DeLeon, and R. M. Jarret, ''Conformational Studies in the Cyclohexane Series. 1. Experimental and Computational Investigation of Methyl, Ethyl, Isopropyl, and tert-Butylcyclohexanes'', ''J. Org. Chem.'', '''1999''', ''64'', 2085 - 2095; {{DOI|10.1021/jo990056f}}. The salient point here is that the [[enthalpy]] and [[entropy]] of this series differ in their trends.
# Just when you are starting to think that things are quite simple, along comes the observation: S. E. Biali, ''Axial monoalkyl cyclohexanes'', ''J. Org. Chem.'', '''1992''', ''57'', 2979 - 2980; {{DOI|10.1021/jo00037a001}}
# And this one with knobs on: ''In all-trans-1,2,3,4,5,6-hexaisopropylcyclohexane, all the alkyl groups are located at axial rather than equatorial positions: O. Golan, Z. Goren, and S. E. Biali, ''Axial-equatorial stability reversal in all-trans-polyalkylcyclohexanes'', ''J. Am. Chem. Soc.'', '''1990''', ''112'', 9300 - 9307. {{DOI|10.1021/ja00181a036}}.
#J. A. Anderson, K. Crager, Kelly, L.Fedoroff, G. S. Tschumper, Gregory S. ''Anchoring the potential energy surface of the cyclic water trimer.'' ''J. Chem. Physics'', '''2004''', ''121'', 11023-11029. {{DOI|10.1063/1.1799931}}.
#R. R. Fraser, N. C. Faibish, ''On the purported axial preference in 2-methylthio- and 2-methoxycyclohexanones: steric effects versus orbital interactions'', ''Can. J. Chem.'', '''1995''', ''73'', 88-94.
=== How to induce room temperature hydrolysis of a peptide ===
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[[Image:amide-cleavage.png|thumb|right|Peptide hydrolysis]] This introduces a further example of how simple conformational analysis can quickly rationalize kinetic behaviour. At neutral pH and 25° the half life for hydrolysis of a peptide bond is around 500 years (and thank goodness, or we would ourselves all rapidly hydrolise to a mush!). Some enzymes however can achieve this in less than 1 second, an acceleration of 1013! Organic chemists are not quite so clever, but they can achieve room temperature hydrolysis of a peptide in 21 minutes by careful conformational design. The two isomers shown on the right differ only in their stereochemistry, one hydrolysing quickly, the other slowly. Build a model of each compound, and calculate two isomers for each, varying in whether the ring N-substituent is oriented axial or equatorial with respect to the decalin ring. On the basis of your two pairs of energies, can you rationalise the observed kinetic behaviour? Do you know why both of these compounds take very much less than 500 years to hydrolise the peptide bond?

'''Hint1:''' Use the chair-chair conformation for cis-decalin as your template for constructing this system.

'''Hint2:''' When constructing your models, think if there are any hydrogen bonds that might stabilize the structure!

'''Hint3:''' Hydrolysis can only occur when the OH group can approach the carbonyl of the peptide bond close enough to react, and at the right angle of approach.
|}

==== Reference ====

# M. Fernandes, F. Fache, M. Rosen, P.-L. Nguyen, and D. E. Hansen, 'Rapid Cleavage of Unactivated, Unstrained Amide Bonds at Neutral pH', ''J. Org. Chem.,'' '''2008''', ASAP: {{DOI|10.1021/jo800706y}}

=== Caryophyllene: The phenomenon of Atropisomerism ===

# [[Image:caryophyllene-ketone.gif|thumb|right|Caryophyllene ketone]] [http://en.wikipedia.org/wiki/Caryophyllene Caryophyllene], a constituent of many essential oils, include clove oil, has a [[trans]] alkene contained in a 9-membered ring. One interesting property is that it has 4 [[diastereoisomers]] possible, originating from a total of three asymmetric centres present in the molecule. Two of these are conventional chiral centres, one is present in the form of a disymmetric trans double bond. To understand why such a bond can result in two configurations, one must appreciate that (concurrent) rotation about the two C-C single bonds adjacent to the alkene is in fact restricted, because to the hydrogen labelled Ha cannot easily pass by the edge of the 4-membered ring. Construct this molecule (in fact the ketone rather than the alkene) and optimize its geometry. Note in particular that the ring junction is ''trans'' and not ''cis''.
# You will find you may well have obtained one of two forms. In the first, the Ha hydrogen will be opposite the C=O group, in the other it will be adjacent to it. Record the energy of whatever form you got. At the end of the course, we will try to find the ''winner'' with the lowest energy (this is not as trivial as it sounds!).
# Next, take your structure, and try to ''flip'' the [[trans]] alkene bond around so that eg if the methyl were previously pointing up, now it will point down. You may find a combination of erasing/redrawing or of moving, will accomplish this. You may also find another trick useful, of deleting all hydrogens, and then re-sprouting them back on again. Re-optimise your structure and compare the energy with your first isomer.
# Another feature of this model is that you can judge which group is in the so-called shielded region of the carbonyl group magnetic anisotropy. Using this information, you can see if there are any anomalous 1H chemical shifts that might need explaining!

==== References ====
# M. Clericuzio, G. Alagona, C. Ghio, and L. Toma, ''Ab Initio and Density Functional Evaluations of the Molecular Conformations of -Caryophyllene and 6-Hydroxycaryophyllene'', ''J. Org. Chem.'' '''2000''', ''65'', 6910 - 6916. {{DOI|10.1021/jo000404+}}.
#[http://en.wikipedia.org/wiki/Caryophyllene Wikipedia article]
# For a recent application of this phenomenon, see P. C. Bulman Page, B. R. Buckley, S. D.R. Christie, M. Edgar, A. M. Poulton, M. R.J. Elsegood and V. McKee, ''A new paradigm in N-heterocyclic carbenoid ligands'', ''J. Organometallic Chem.'', '''2005''', ''690'', 6210-6216. D {{DOI|10.1016/j.jorganchem.2005.09.015}}.

=== Germacrene: Conformational analysis of medium sized rings ===

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# [[Image:Germacrene.gif|thumb|right|Germacrene and the thermal reaction product]]Germacrene is a natural product with a ten-membered ring; it has the triene structure shown. Assuming that it adopts a crown conformation, build a three-dimensional model.
# On heating, germacrene is converted into one of the stereoisomers of the divinylcyclohexane, via a [3,3] sigmatropic pericyclic reaction. Predict from your model for Germacrene whether the product will have the two vinyl groups [[cis]] or [[trans]] to one another.
|}

==== References ====

# K. Shimazaki, M. Mori, K. Okada, T. Chuman, H. Goto, K. Sakakibara and M. Hirota, ''Conformational analyses of periplanone analogs by molecular mechanics calculations'', '' J. Chem. Ecology'', '''1991''', ''17'', 779-88. {{DOI|10.1007/BF00994200}}.
# H. Shirahama, E. Sawa and T. Matsumoto, ''Conformational aspects of germacrene B. Are the germacrenes resolvable ?'', ''Tetrahedron Lett.'', '''1979''', ''20'', 2245-2246. {{DOI|10.1016/S0040-4039(01)93687-1}}. See also {{DOI|10.1039/P19750002332}} for an explanation of the selective epoxidation of germacrene.

=== Xestoquinone: Regio and Stereoselectivity in the Diels Alder reaction===

# [[Image:xestoquinone.gif|thumb|right|Xestoquinone precursor]] This compound is a precursor to a natural product called Xestoquinone. It has four alkene groups, which can individually be considered as the alkene component in a π2s + π4s [[Diels Alder]] [[cycloaddition]]. The pair of alkenes ''a+b'' or ''c+d'' can also act as the diene component in the π2s + π4s [[Diels Alder]] [[cycloaddition]]. Construct a model of the product of e.g. forming a bond between alkene ''a'' or alkene ''b'' and diene ''c+d'', and then reverse the addition by using either ''c'' or ''d'' adding to the diene ''a+b''. The stereochemistry of addition should always be [[suprafacial]], i.e. preserving the stereochemical relationships of the alkenes. You should very carefully check that this is so in your final model.
# Whilst you should stop at '''two''' models, it is possible to construct many more. For example, one might be able to add to either the ''top'' face of alkene ''b'' or to its ''bottom'' face. Identify the model with the lower energy, and save it for the end of the workshop. We will identify the isomer of lowest energy from everyone's results, this being a communal [[Monte Carlo]] experiment to find the [[global minimum]].

==== References ====

#[http://en.wikipedia.org/wiki/Diels-Alder_reaction Wikipedia article]
#For the original literature on this synthesis, see R. Carlini, K. Higgs, C. Older, S. Randhawa, and R. Rodrigo, ''Intramolecular Diels-Alder and Cope Reactions of o-Quinonoid Monoketals and Their Adducts: Efficient Syntheses of (±)-Xestoquinone and Heterocycles Related to Viridin'', ''J. Org. Chem.'', '''1997''', ''62'', 2330 - 2331. {{DOI|10.1021/jo970394l}} where you can check to see which isomers actually do form!

=== Aldol Reaction and anti-Bredt Rings ===

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# [[Image:Aldol.gif|thumb|right|Aldol Reaction]]When the diketone shown is treated with base, it undergoes an aldol condensation. Two obvious possibililties are elimination of the combination Ha and Oa, or of the alternative combination Hb and Ob. In fact, only a single product is formed. On the basis of energies for both products, can you predict which one is actually formed?
# Measure a few dihedral angles, ie to find out how planar the alkene present is. Does this suggest a reason why one isomer is less stable than the other?
# There is a third very remote structural possibility. If you have time, verify that this third product truly is unlikely.
|}

==== References ====
#[http://en.wikipedia.org/wiki/Bredt's_Rule Bredt's Rule]
# I. Novak, ''Molecular Modeling of Anti-Bredt Compounds'', ''J. Chem. Inf. Model.'', '''2005''', ''45'', 334 - 338. {{DOI|10.1021/ci0497354}}
# See also this article A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, ''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins'', ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}} in conjunction with Project 9.

=== Conformational Preference for asymmetric hydride reduction of a ketone ===

# [[Image:Felkin.gif|thumb|right|Asymmetric hydride reduction]]The hydride ([http://en.wikipedia.org/wiki/Lithium_aluminium_hydride BH4, AlH4, etc]) reduction of the ketone shown here is stereospecific, resulting in an alcohol with the stereochemistry shown (known as the [http://en.wikipedia.org/wiki/Chiral_induction Cram or the Felkin-Anh] rule). Construct a model of the ketone and establish which of at least two conformations is the lowest in energy.
# If the hydride anion is delivered from the least hindered position, is the conformation you have consistent with the stereochemistry shown for the product?
# You can see from Ref 4 that the situation can be far more complex, depending on many other factors.

====References ====
# [http://en.wikipedia.org/wiki/Chiral_induction Wikipedia article]
# D. J. Cram and D. R. Wilson, ''Studies in Stereochemistry. XXXII. Models for 1,2-Asymmetric Induction'', ''J. Am. Chem. Soc.'', '''1963''', ''85'', 1245 - 1249. {{DOI|10.1021/ja00892a008}}.
# Y. Yamamoto, K. Matsuoka, and H. Nemoto, ''Anti-Cram selective reduction of acyclic ketones via electron transfer initiated processes'', ''J. Am. Chem. Soc.'', '''1988''', ''110'', 4475 - 4476; {{DOI|10.1021/ja00221a093}}.
# A. Mengel and O. Reiser, ''Around and beyond Cram's Rule'', ''Chem. Rev.'', '''1999''', ''99'', 1191 - 1224. {{DOI|10.1021/cr980379w}}.

=== Enantiomers vs Diastereomers Part 2: NMR Coupling constants ===

#[[Image:karplus.gif|thumb|Axial-equatorial interconversion|right]]In Project 2.2 above, we saw how the energies of diastereomeric compounds could be compared with the corresponding enantiomers. In this extension, we show how molecular modelling can cast light on the conformation adopted by 2-ethyl-4-methyl-1-oxa-cyclopentane-3-carboxylic acid estimated using measured 1H NMR coupling constants. The (2S,3S,4S) diastereomer has couplings of 3JH2,H3 8.3 Hz and 3JH3,H4 9.8 Hz. Two possible conformations of this diastereomer are shown on the right. They differ in that one has Et axial, and Me/COOH equatorial, and the other Et equatorial and Me/COOH axial.
#[[Image:karplus.jpg|Karplus plot|thumb|left]]By calculating the geometries of both conformations, and measuring the dihedral angle H2-C-C-H3 and H3-C-C-H4, one can assess by using the Karplus equation (left, taken from Ref 2 and relevant for a cyclopentane, but the values for which might be modified by the presence of electronegative substituents), which conformation leads to the best agreement between the calculated angle and the measured coupling constants (Hint: on the basis of the predicted couplings, you should be able to eliminate one of the two conformations shown for this molecule).
#[[Image:5-circulene.gif|thumb|5-circulene|right]]In Project 2.2 we also introduced molecules such as helicenes and circulenes. The 1H NMR of the [5]-circulene shown to the right revealed a complex spectrum at δ 2.98 ppm and again at 3.75 ppm. On the face of it, the four protons labeled Ha and Hb should all be equivalent, and the spectrum should be a single peak, not two complex multiplets. Indeed, if the NMR is recorded at high temperatures, this is exactly what is observed. By constructing a model of the [5]-circulene shown, can you explain why at normal temperatures, the NMR spectrum is so complex? 
#[[Image:Lab_expt.jpg|thumb|Synthesis lab experiment|right]]A practical application of this technique is to determine the stereochemistry of the product of the reaction between E,E-2,4-hexadien-1-ol and maleic anhydride. You will have the 1H NMR spectrum of your sample recorded, and evident from that will be peak multiplicities of the various proton resonances. You should endeavour from your analysis to come up with a suggestion for the structure of compound '''Y''', and from this, estimates of the numerical values (but not the signs) of the 2J and 3J couplings visible. Now using the techniques described above, construct a model of your proposed structure for '''Y'''. Measure the dihedral angles for all the 3J couplings, and very approximately estimate what the corresponding 3J might be from the diagram above. Does this help you assign the stereochemistry of the product?
#'''Advanced topic''': Part of the spectroscopic analysis of the compound '''Y''' involves interpreting the IR spectrum. Theory can be used in fact to simulate the full IR spectrum. In section 5.3 below, you will find instructions on how to use the model you have calculated here to initiate a so called '''density functional''' calculation. This will provide you with the required IR simulation. Follow these instructions, and open the resulting .log file in Gaussview. Go to the '''Results''' menu and select '''vibrations'''. The IR spectrum will be displayed. Does it match the one you have recorded for yourself?

==== References ====

#M. Karplus, ''Vicinal Proton Coupling in Nuclear Magnetic Resonance'', '' J. Am. Chem. Soc.'', '''1963''', ''85'', 2870 - 2871; {{DOI|10.1021/ja00901a059}}
#A. Wu, D. Cremer, A. A. Auer, and J. Gauss, ''Extension of the Karplus Relationship for NMR Spin-Spin Coupling Constants to Nonplanar Ring Systems: Pseudorotation of Cyclopentane'', ''J. Phys. Chem. A,'', '''2002''', ''106'', 657 -667; {{DOI|10.1021/jp013160l}}
#C. A. Stortz and M. S. Maier, ''Configurational assignments of diastereomeric γ-lactones using vicinal H–H NMR coupling constants and molecular modelling'', ''J. Chem. Soc., Perkin Trans. 2'', '''2000''', 1832 - 1836. {{DOI|10.1039/b003862h}}
# A. H. Abdourazak, A. Sygula, and P. W. Rabideau ''Locking the bowl-shaped geometry of corannulene: cyclopentacorannulene'', ''J. Am. Chem. Soc.'', '''1993''', ''115'', 3010 - 3011. {{DOI|10.1021/ja00060a073}}

=== Bridgehead enols: Thermodynamic vs Kinetic Control Part 2.===
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#[[Image:Bredt.gif|thumb|right|Brendanone]] The ketone Brendan-2-one shown right exhibits unusual behaviour.6 When treated with NaOD/MeOD, deuterium substitution occurs easily and rapidly only in position Hb. Enolisation must of necessity form a bridgehead double bond (''anti-Bredt''), but clearly one isomer is more stable than the other possible form. Does molecular modelling predict this correctly?
#The unusually facile enolisation of this ketone (given that it forms an anti-Bredt enol) can also be investigated by molecular modelling. '''Measure''' the dihedral angle between the C-Ha or C-Hb vector and the carbonyl group. Assuming that the ''ideal'' angle for proton removal is around 90°, which proton is better set up for abstraction? Might this be kinetic rather than thermodynamic control?
#[[Image:Cortisone.gif|thumb|right|Cortisone]]One could also revisit Problem 2.3.3 above. Here, proton abstraction forms an enol which eventually epimerises the bridgehead position to form a ''trans'' ring junction. Why should this proton be particularly easy to remove? From what you have learnt above, would this be for kinetic or for thermodynamic reasons (or both?). Are all the relevant effects modelled using the mechanics approach or is consideration of the electrons also necessary?
|}
==== References and Footnotes====

# A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, {{doi-inline|10.1021/ja00837a043|''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins''}}, ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}}.

===Sulfonylation of Naphthalene: Thermodynamic vs Kinetic Control Part 3.===

[[Image:Sulfonylation.gif|right|thumb|Sulfonylation of naphthalene]]The sulfonylation of naphthalene using sulfuric acid is a good example of a mechanism combining both steric and electronic influences. The Molecular mechanics method intrinsic to the Ghemical program can only model the former, and not the latter. It is a worthwhile exercise to establish whether this anticipated deficiency does indeed lead to a model which only partially explains experiment.

It has been known for some time that treating naphthalene with sulfuric acids at low temperatures produces mostly substitution at the 1-position of the naphthalene. Heating the reaction mixture, or conducting the reaction at elevated temperatures produces mostly the 2-isomer. This is indeed a classic example of [[kinetic]] vs [[thermodynamic]] control, the 1-isomer being the kinetic one and the 2-isomer the thermodynamic one. To model the kinetic reaction, we have to inspect the [[transition state]] for the reaction, and here we can approximate this by the [[Wheland Intermediate]]. To model the thermodynamic reaction, we have to inspect the product (rather than the transition state) for the reaction.

#Build models for all four species shown in the diagram on the right. For the two products, define ''conjugated'' bond types for all the ring bonds, and define the sulfonyl group with two S=O double bonds and one S-O single bond. Take care to optimise the conformation of the sulfonyl group with respect to the aromatic ring. For the two Wheland intermediates, the limitations of Ghemical will force us to ''cheat''. Ghemical does not have parameters for a carbocation. So define the C2-C3 bond as conjugated (for the 1-Wheland intermediate). When you '''add hydrogens''' it will in fact add a second hydrogen to C2. Delete this one hydrogen. Ghemical will calculated the energy regardless of not knowing C2 is actually a carbonium ion! For the 2-Wheland intermediate, ensure that you use '''exactly''' the same number of ''conjugated'' bond types as you did for the 1-isomer (the two models in a mechanics sense are only comparable if you have the same total number of bond types in each model). You will have to decide whether these (undoubted) approximations have produced reasonable models or not (is the naphthalene framework planar for example, as it should be?).
#Record the pairs of energies (two for the 1- and 2-products, and two for each preceeding transition (Wheland) state.
#By turning the spacefilling representation on, which of the two products has the least unfavourable steric interactions between the sulfonic acid group and any adjacent hydrogens? Does this match with their relative energies?
#Do any unfavourable steric interactions observed in the product(s) also exist in the Wheland intermediates (as models for the transition states)?
#The relative stability of the Wheland intermediates is always assumed to be an '''electronic''' phenomenon. The conventional explanation is that the 1-Wheland isomer is stablized by both one aromatic ring '''and''' an allyl cation conjugated to it. The 2-Wheland isomer is stabilised by one aromatic ring conjugated to a secondary carbocation and an alkene. This type of ''cross conjugation'' is conventionally assumed to be less favourable. Does a purely mechanical approach to this problem reproduce this expectation? Or is this ''mechanical'' approximation to an ''electronic'' model too severe? It seems a good point to stop this course, since the next time you will build models, it will indeed be using methods which properly approximate the electronic components.
====References====

#R. Lantz, ''Mechanism of the monosulfonation of naphthalene'', ''Compt. Rend''. '''1935''', ''201'', 149-52.
#G. W. Wheland, ''A Quantum Mechanical Investigation of the Orientation of Substituents in Aromatic Molecules'', ''J. Am. Chem. Soc.'' '''1942''', ''64'', 900 - 908; {{DOI|10.1021/ja01256a047}}
#C. A. Reed, N. L. P. Fackler, K-C. Kim, D. Stasko, D. R. Evans, P. D. W. Boyd, and C. E. F. Rickard, ''Isolation of Protonated Arenes (Wheland Intermediates) with BArF and Carborane Anions. A Novel Crystalline Superacid'', ''J. Am. Chem. Soc.'' '''1999''', ''121'', 6314 - 6315 {{DOI|10.1021/ja981861z}}

== Coursework not to be attempted at any time: Antimodelling Molecules ==

The following represent molecules that should '''not''' be modelled under any circumstances! You should instead attempt to '''NAME''' them.

[[Image:Contraceptive.gif|Contraceptive (NO in every conceivable position)]] [[Image:Paradise.gif|Paradise lost]] [[Image:Synoptic.gif|Synoptic]] [[Image:Cisters.gif|Cisters]] [[Image:Transisters.gif|Transisters]] [[Image:Metaphor.gif|Metaphor]] [[Image:Metastasis.gif|Metastasis]] [[Image:Cyclone.gif|Cyclone]] [[Image:Anticyclone.gif|Anticyclone]] [[Image:Arsole.gif|Arsole]] [[Image:Orthodox.gif|Orthodox]] [[Image:Synthesis.gif|Synthesis and Antithesis]] [[Image:Aphrodisiac.gif|Name this yourself. Does Meg Ryan spring to mind?]] [[Image:Cyclops.gif|Cyclops]] [[Image:Paradox.gif|Paradox]] [[Image:Transparent.gif|Transparent]] [[Image:Encyclopedia.gif|Encyclopedia]] [[Image:Maths.jpg|Find X]] [[Image:VanderMaxforce.jpg|150px|Max Whitby stuck to a strangely attractive Lamp Post]] [[Image:nanoballet.jpg|200px|Nanoballet dancer]] [[Image:NanoCossacks.jpg|200px|NanoCossacks]]
[[Image:Paralysis.png|500px|Paralysis]] [[Image:Mcdonalds.png|350px|Old McDonald's Molecule: ene-yne-ene-yne-one]]
[[Image:Silenedione.png|250px|Celine Dion]] [[Image:Sundial.png|250px|Sun Dial]]

If you know of any other antimodelling molecules, please add them here!

====Acknowledgements ====

Some of these cartoons are from [http://www.nearingzero.net/sci_chemistry.html here], and six are original. A superb collection of '''''silly names''''' is maintained
by [http://www.chm.bris.ac.uk/sillymolecules/sillymols.htm Paul May] [[Organic:Model_answers|.]] See {{DOI|10.1021/jo0349227}} for the nanoputians.

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[[Second_Year_Modelling_Workshop|Back to introduction]]
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Coursework

2010-10-15T15:33:20Z

Nm607: /* Coursework not to be attempted at any time: Antimodelling Molecules */

[[Second_Year_Modelling_Workshop|Back to introduction]]
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== Molecular modelling Coursework to be attempted during Scheduled Sessions ==

These projects are arranged in increasing order of difficulty, and time taken to complete. You should do as many as you can in the 2 hour session allocated to you, and return to finish the rest if you wish at your convenience. At the end of the session, we will conduct a ''number auction''. For each project, the bidding will start with the first volunteer offering an energy for the system (or one of the isomers). If anyone has a lower energy for that molecule, they will then bid that energy. The winner will be the one with the lowest energy.

=== Conformational analysis I: Chair and Boat-like conformations of Cyclohexane ===
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#Construct '''[[chair]]''' and '''[[boat]]'''-like '''[[conformation]]s''' of [[cyclohexane]]. Compare the energies of both forms.
#Check carefully if your boat really is a boat, or whether it has any apparent distorsion.
#Try changing one or more of the CH2 groups into an oxygen and see if that affects things.
#For the record, the point group symmetries of the various species which may be involved are D3d for the chair conformation, C2v for a boat geometry, and D2 for any twisted boat form. Is any of these forms '''chiral'''?
#The molecule on the left is called '''chiralane'''. Are its rings boats or chairs?
|}
====References ====
# The first suggestion of two forms for cyclohexane goes as far back as H. Sachse, ''Chem. Ber'', 1890, '''23''', 1363 and ''Z. Physik. Chem.'', 1892, 10, 203. This is nicely explained [http://www.chem.yale.edu/~chem125/125/history/Baeyer/Sachse.html here]. E. Mohr, ''J. Prakt. Chem.'', 1918, '''98''', 315 and ''Chem. Ber.'', 1922, '''55''', 230, translated Sachse's argument into a pictorial one.
# The article that put [[conformational analysis]] on the map: D. H. R. Barton and R. C. Cookson, ''The principles of conformational analysis'', ''Q. Rev. Chem. Soc.'', '''1956''', ''10'', 44. {{DOI|10.1039/QR9561000044}}
#[http://en.wikipedia.org/wiki/Chair_conformation Wikipedia article]
#D. A. Dixon and A. Komornicki, ''Ab initio conformational analysis of cyclohexane'', ''J. Phys. Chem.'', '''1990''', ''94'', 5630 - 5636; {{DOI|10.1021/j100377a041}}.
#A nice exploration of the potential energy surfaces for cyclohexane can be viewed [http://www.springer.com/carey-sundberg/cyclohex/cyclohex.php here].
# For a more modern application of this technique, see I. Columbus, R. E. Hoffman, and S. E. Biali, ''Stereochemistry and Conformational Anomalies of 1,2,3- and 1,2,3,4-Polycyclohexylcyclohexanes''. ''J. Am. Chem. Soc.'', '''1996''', ''118'', 6890 - 6896; {{DOI|10.1021/ja960380h}}.
# The second molecule shown in this section is called [6.6]chiralane. It is peculiar for having many six-membered saturated rings, all of them as twist-boats rather than chairs! (a chair has a plane of symmetry, a twist boat only axes, which of course allows it to be chiral). See [http://petitjeanmichel.free.fr/itoweb.petitjean.graphs.html#CHIR here] for more details.
# More detail on the conformation of rings (and acyclic systems) will be found in the [http://www.ch.ic.ac.uk/local/organic/conf/ lecture course] on the topic to be given in the spring term.

=== Enantiomers vs Diastereomers Part 1: Butanes and Helicenes. ===

This problem illustrates, using models, the difference between an enantiomer and a diastereomer.

#[[Image:diastereo.gif|thumb|right|2-bromo-3-chlorobutane]][[Image:pentahelicene.gif|thumb|right|Pentahelicene]]The compound 2-bromo-3-chlorobutane has two [[chiral]] centres, and four isomers (22) are therefore possible. Calculate all four isomers, and for each be careful to label each of the two stereo centres '''R''' or '''S''' as you go. For each of the four isomers '''R,R''', '''S,S''', '''R,S''', '''S,R''' you will have to think about whether you have obtained the lowest energy [[conformer]].
#Can your four energies be grouped in any way? You should think about the expected difference between '''enantiomers''', '''diastereomers''' and '''conformers'''.
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#Construct some helicenes (pentahelicene or [5]helicene is shown on the right), using '''conjugated''' bonds for all the ring bonds. Benzene, naphthalene, phenanthrene and benzophenanthrene are in fact the first four members of this series. At what point in this series can you detect helicity cropping up? This is manifested by a non-planar helical wind of the molecule. If you do detect it, note how the wind is either left or right handed, ie the two forms are '''enantiomers''' of each other. Try displaying the molecule in '''spacefill mode''' (see above) to see if you can identify the source of the helicity. (Note: the smallest helicene which can be resolved experimentally into enantiomers is in fact [5]helicene]).
#The higher helicenes are well known (up to about [14]helicene) and amongst the ''most chiral'' molecules known (in terms of how much they rotate the plane of polarised light).
#[7]circulene is a known molecule, with a unique saddle-shaped structure, shown on the left (there is no real need for you to build this model, but do please do so if you are curious). [http://en.wikipedia.org/wiki/Graphene Graphene] is a related polymeric molecule, of much topical interest in the semi-conducting and other industries (Nobel Prize 2010).
|}
==== References ====

#[http://en.wikipedia.org/wiki/Diastereomer Wikipedia article on Diastereomers]
#[http://en.wikipedia.org/wiki/Helicene Wikipedia article on Helicenes and related molecules]
#R. H. Janke, G. Haufe, E.-U. Würthwein, and J. H. Borkent, ''Racemization Barriers of Helicenes: A Computational Study'', ''J. Am. Chem. Soc.'', '''1996''', ''118'' 6031 - 6035 {{DOI|10.1021/ja950774t}}

=== Conformational analysis II: ''cis'' and ''trans''-decalins, Steroids and Podcasts! ===
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# [[Image:cis-decalin.gif|thumb|right|cis Decalin]]This is the famous molecule that started the whole molecular mechanics modelling ball rolling. [http://www.ch.ic.ac.uk/video/barton/barton1.pdf Barton] in 1948 sought to find out which [[conformation]] of ''cis''-decalin was the most stable (see [http://www.ch.ic.ac.uk/video/barton/index_qt.html here] for video). You should be able to find at least three conformations of this molecule. Try locating these, and conclude which is the most stable. Identify any [[chair]] rings and any [[boat]].
#Measure some dihedral angles to see if the [[staggered]] relationships hold (i.e. for such a relationship, the dihedral angle should be close to 60 degrees).
#A key step in Woodward's famous synthesis of [http://en.wikipedia.org/wiki/Cortisone cortisone] is a quinone+butadiene [[Diels-Alder]] reaction to give a cis-decalin (left), with an assumption that [[epimerisation]] to a trans-decalin is thermodynamically favourable. [[Image:Cortisone.gif|thumb|left|cis Cortisone]]Can you verify whether the trans-isomer is indeed more stable? Its not so obvious, since this compound has two extra double bonds in the rings and six sp2 centres which might perturb things.
#[[Image:App.gif|thumb|right|trans Decalin]]The two diastereomeric ''trans''-decalin tosylates react quite differently with NaBH4. Construct models for both isomers (use methoxy as a model for the Tosyl group) and from the [[antiperiplanar]] alignments of bonds that you can find in each isomer, can you make a connection to the reactivity of each form? Consider very carefully where you would put a lone pair located on the nitrogen (i.e. include the N-Lp "bond" in your antiperiplanar alignments) asuming the this atom is tetrahedral rather than planar. Does this lone pair play any part in either reaction in this position?. Note that the relative energy of the axial/equatorial N-Methyl group will not be an accurate reflection of any [[antiperiplanar]] alignments, since these are predominantly electronic in origin, and this mechanics method does not take these into account.
##'''Optional:''' The second (elimination) reaction is very slow compared to the first. Discuss with tutors why this might be so (for Hints, see [[organic:entropy|here]] or [[organic:ngp|here]]).
##'''Optional''': These reactions do not appear to occur for the corresponding ''cis''-decalins6. Why not?

|}

==== References and Footnotes ====
# D. H. R. Barton, ''Interactions between non-bonded atoms, and the structure of cis-decalin'', ''J. Chem. Soc.'', '''1948''', 340-342. {{DOI|10.1039/JR9480000340}}
#[http://en.wikipedia.org/wiki/Decalin Wikipedia article]
# For a modern application of mechanics to this molecule, see J. M. A. Baas, B. Van de Graaf, D. Tavernier, and P. Vanhee, ''Empirical force field calculations. 10. Conformational analysis of cis-decalin'', ''J. Am. Chem. Soc.'', '''1981''', ''103'', 5014 - 5021; {{DOI|10.1021/ja00407a007}}.
# For a video-Podcast of Barton and Woodward (and other Nobel prize winners), subscribe [http://www.ch.ic.ac.uk/video/index.rss here]
# R. B. Woodward, F. Sondheimer, and D. Taub, ''The total Synthesis of Cortisone'', ''J. Am. Chem. Soc.'', '''1951''', ''73'', 4057 - 4057. {{DOI|10.1021/ja01152a551}}.
# P.-W. Phuan and M. C. Kozlowski, ''Control of the Conformational Equilibria in Aza-cis-Decalins: Structural Modification, Solvation, and Metal Chelation'', ''J. Org. Chem.'', '''2002''', ''67'', 6339 - 6346; {{DOI|10.1021/jo025544t}}

=== Menthone/''iso''menthone and Bridgehead enols: Thermodynamic vs Kinetic Control Part 1.===

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#[[Image:Menthone.gif|thumb|right|Menthone]] Beckmann (of rearrangement fame) in 1889 dissolved optically active levorotatory (-) (S,R)-menthone ([α]D -28°) in conc. sulfuric acid, followed by quenching on ice to give what Beckmann assumed was pure (and what we would nowadays call [[diastereomeric]]) (+) (R,R)-isomenthone, [α]D +28°. He suggested for the first time that such an isomerisation, involving epimerisation at the asymmetric centre next to the keto group, proceeded via an intermediate enol in which the tetrahedral asymmetric carbon becomes planar. But this famous (perhaps even notorious2) early example of a [[reaction mechanism]] makes an interesting assumption, which can be tested by molecular modelling.
# Two possible enols can be formed, only one of which allows the [S] asymmetric carbon to become planar and then protonate to the [R] epimer. This is the so called [[thermodynamic enol]]. The other, which leaves the [S]-centre untouched is the [[kinetic enol]]. Find out if simple molecular modelling correctly predicts that the thermodynamic enol is indeed the more stable of the two. '''Hint:''' Model the enol and '''not''' the ketone. Consider carefully any conformational isomers possible.
# Given that the optical rotation3 of pure (+)-isomenthone is now known to be [α]D +101° rather than +28°, we can infer that Beckmann's product contains only 43% isomenthone and hence still contains 57% of original menthone, corresponding to an equilibrium constant of K= 0.75. This can be related to a (free energy) difference using the equation ΔG = -RT ln K, or ΔG = 0.7 kJ/mol (menthone being lower in energy by this amount compared to isomenthone). Can this energy difference be verified using molecular mechanics modelling? Can you explain why menthone is the more stable? (For another hint, or possibly a fright, visit [http://chemistry.gsu.edu/glactone/modeling/Luise/organic/cychexon.html this page]).
|}

==== References and footnotes ====
# E. Beckmann, ''Annalen'', '''1889''', ''250'', 322. {{DOI|10.1002/jlac.18892500306}}.
# Many of Beckmann's misconceptions were corrected by O. Wallach, ''Annalen'', '''1893''', ''276'', 296. {{DOI|10.1002/jlac.18932760306}}. The notoriety is because the coincidence of equal but opposite optical rotations obtained in this experiment led Beckmann to believe that he had obtained the [[enantiomer]] of menthone, and not as we now know, the impure (R,R) [[diastereomer]]. It should be borne in mind that the concept of tetrahedral and asymmetric carbon was only 15 years old at this time (see [http://en.wikipedia.org/wiki/Jacobus_van_%27t_Hoff Jacobus Henricus van't Hoff] and [http://en.wikipedia.org/wiki/Achille_Le_Bel Joseph Achille Le Bel]). Nevertheless confusion over this aspect persisted for some time after, and was often evident in the writings of even very famous chemists of the time (and Beckmann was very famous)!.
#[http://en.wikipedia.org/wiki/Menthone Wikipedia article]
# From about 1890-1935, mechanistic organic chemistry was born. In the absence of UV, IR, NMR, MS and X-Ray techniques, the [http://en.wikipedia.org/wiki/Polarimeter polarimeter] occupied a pivotal role. Many of the great discoveries in reaction mechanisms (keto-enol tautomerism as seen here, [[Organic:tutorial:meerwein| carbocations]], the Walden inversion, etc) relied on polarimetric measurements.
# A notorious modern example of (unwanted) epimerisation of a ketone is [http://en.wikipedia.org/wiki/Thalidomide Thalidomide], where one epimer inhibits morning sickness in pregnant women, and the other epimer is teratogenic, causing fetal abnormalities. The equilibrium in this case does not require conc. sulfuric acid, but can occur at physiological pH.

== Additional Molecular modelling Coursework ==

Please feel free to try these problems in your own time, and to discuss these with your organic tutors and lecturers. Note also that the relevant lectures may occur in the spring as well as autumn terms.
=== Axial/Equatorial preferences in cyclohexane and cyclohexanone and Hydrogen Bonding ===
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#Construct a chair cyclohexane and replace firstly one of the [[axial]] hydrogens with the following groups: '''methyl''', '''t-butyl''', '''OH'''. Calculate the energy of the axial isomer.
# Then repeat (either by deleting/redrawing or by moving) for the equatorial forms. Compare the energies of the two isomers. Does any energy difference increase with the size of the group? Does OH fit into this in terms of size?
# [[Image:Thiomethylcyclohexanone.gif|right|thumb|thiomethyl cyclohexanone]]The dissolving metal reduction of cyclohexanones in a protic solvent (i.e. one capable of hydrogen bonding) is thermodynamically controlled and gives the more stable, equatorial alcohol. In fact, its probably the alkoxide that is the product, not the free alcohol. It is thought the alkoxide is actually a lot larger than the alcohol, accounting for the substantial equatorial preference. Can you think why its larger? [Ghemical cannot in fact model this, since the force field does not include parameters for the alkoxide anion].
# Determine the axial/equatorial preference of 2-methylthio-cyclohexanone (Hint: there are many conformations possible, and you should try a few to see if you can get the lowest).
|}
==== References and Footnotes ====

# A. H. Lewin and S. Winstein, ''NMR. Spectra and Conformational Analysis of 4-Alkylcyclohexanols'' ''J. Am. Chem. Soc.''; '''1962''', ''84'', 2464 - 2465; {{DOI|10.1021/ja00871a049}}
#F. R. Jensen and L. H. Gale, ''The Conformational Preference of the Bromo and Methyl Groups in Cyclohexane by IR Spectral Analysis'', ''J. Org. Chem.'', '''1960''', ''25'', 2075 - 2078. {{DOI|10.1021/jo01082a001}}
# K. B. Wiberg, J. D. Hammer, H. Castejon, W. F. Bailey, E. L. DeLeon, and R. M. Jarret, ''Conformational Studies in the Cyclohexane Series. 1. Experimental and Computational Investigation of Methyl, Ethyl, Isopropyl, and tert-Butylcyclohexanes'', ''J. Org. Chem.'', '''1999''', ''64'', 2085 - 2095; {{DOI|10.1021/jo990056f}}. The salient point here is that the [[enthalpy]] and [[entropy]] of this series differ in their trends.
# Just when you are starting to think that things are quite simple, along comes the observation: S. E. Biali, ''Axial monoalkyl cyclohexanes'', ''J. Org. Chem.'', '''1992''', ''57'', 2979 - 2980; {{DOI|10.1021/jo00037a001}}
# And this one with knobs on: ''In all-trans-1,2,3,4,5,6-hexaisopropylcyclohexane, all the alkyl groups are located at axial rather than equatorial positions: O. Golan, Z. Goren, and S. E. Biali, ''Axial-equatorial stability reversal in all-trans-polyalkylcyclohexanes'', ''J. Am. Chem. Soc.'', '''1990''', ''112'', 9300 - 9307. {{DOI|10.1021/ja00181a036}}.
#J. A. Anderson, K. Crager, Kelly, L.Fedoroff, G. S. Tschumper, Gregory S. ''Anchoring the potential energy surface of the cyclic water trimer.'' ''J. Chem. Physics'', '''2004''', ''121'', 11023-11029. {{DOI|10.1063/1.1799931}}.
#R. R. Fraser, N. C. Faibish, ''On the purported axial preference in 2-methylthio- and 2-methoxycyclohexanones: steric effects versus orbital interactions'', ''Can. J. Chem.'', '''1995''', ''73'', 88-94.
=== How to induce room temperature hydrolysis of a peptide ===
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[[Image:amide-cleavage.png|thumb|right|Peptide hydrolysis]] This introduces a further example of how simple conformational analysis can quickly rationalize kinetic behaviour. At neutral pH and 25° the half life for hydrolysis of a peptide bond is around 500 years (and thank goodness, or we would ourselves all rapidly hydrolise to a mush!). Some enzymes however can achieve this in less than 1 second, an acceleration of 1013! Organic chemists are not quite so clever, but they can achieve room temperature hydrolysis of a peptide in 21 minutes by careful conformational design. The two isomers shown on the right differ only in their stereochemistry, one hydrolysing quickly, the other slowly. Build a model of each compound, and calculate two isomers for each, varying in whether the ring N-substituent is oriented axial or equatorial with respect to the decalin ring. On the basis of your two pairs of energies, can you rationalise the observed kinetic behaviour? Do you know why both of these compounds take very much less than 500 years to hydrolise the peptide bond?

'''Hint1:''' Use the chair-chair conformation for cis-decalin as your template for constructing this system.

'''Hint2:''' When constructing your models, think if there are any hydrogen bonds that might stabilize the structure!

'''Hint3:''' Hydrolysis can only occur when the OH group can approach the carbonyl of the peptide bond close enough to react, and at the right angle of approach.
|}

==== Reference ====

# M. Fernandes, F. Fache, M. Rosen, P.-L. Nguyen, and D. E. Hansen, 'Rapid Cleavage of Unactivated, Unstrained Amide Bonds at Neutral pH', ''J. Org. Chem.,'' '''2008''', ASAP: {{DOI|10.1021/jo800706y}}

=== Caryophyllene: The phenomenon of Atropisomerism ===

# [[Image:caryophyllene-ketone.gif|thumb|right|Caryophyllene ketone]] [http://en.wikipedia.org/wiki/Caryophyllene Caryophyllene], a constituent of many essential oils, include clove oil, has a [[trans]] alkene contained in a 9-membered ring. One interesting property is that it has 4 [[diastereoisomers]] possible, originating from a total of three asymmetric centres present in the molecule. Two of these are conventional chiral centres, one is present in the form of a disymmetric trans double bond. To understand why such a bond can result in two configurations, one must appreciate that (concurrent) rotation about the two C-C single bonds adjacent to the alkene is in fact restricted, because to the hydrogen labelled Ha cannot easily pass by the edge of the 4-membered ring. Construct this molecule (in fact the ketone rather than the alkene) and optimize its geometry. Note in particular that the ring junction is ''trans'' and not ''cis''.
# You will find you may well have obtained one of two forms. In the first, the Ha hydrogen will be opposite the C=O group, in the other it will be adjacent to it. Record the energy of whatever form you got. At the end of the course, we will try to find the ''winner'' with the lowest energy (this is not as trivial as it sounds!).
# Next, take your structure, and try to ''flip'' the [[trans]] alkene bond around so that eg if the methyl were previously pointing up, now it will point down. You may find a combination of erasing/redrawing or of moving, will accomplish this. You may also find another trick useful, of deleting all hydrogens, and then re-sprouting them back on again. Re-optimise your structure and compare the energy with your first isomer.
# Another feature of this model is that you can judge which group is in the so-called shielded region of the carbonyl group magnetic anisotropy. Using this information, you can see if there are any anomalous 1H chemical shifts that might need explaining!

==== References ====
# M. Clericuzio, G. Alagona, C. Ghio, and L. Toma, ''Ab Initio and Density Functional Evaluations of the Molecular Conformations of -Caryophyllene and 6-Hydroxycaryophyllene'', ''J. Org. Chem.'' '''2000''', ''65'', 6910 - 6916. {{DOI|10.1021/jo000404+}}.
#[http://en.wikipedia.org/wiki/Caryophyllene Wikipedia article]
# For a recent application of this phenomenon, see P. C. Bulman Page, B. R. Buckley, S. D.R. Christie, M. Edgar, A. M. Poulton, M. R.J. Elsegood and V. McKee, ''A new paradigm in N-heterocyclic carbenoid ligands'', ''J. Organometallic Chem.'', '''2005''', ''690'', 6210-6216. D {{DOI|10.1016/j.jorganchem.2005.09.015}}.

=== Germacrene: Conformational analysis of medium sized rings ===

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# [[Image:Germacrene.gif|thumb|right|Germacrene and the thermal reaction product]]Germacrene is a natural product with a ten-membered ring; it has the triene structure shown. Assuming that it adopts a crown conformation, build a three-dimensional model.
# On heating, germacrene is converted into one of the stereoisomers of the divinylcyclohexane, via a [3,3] sigmatropic pericyclic reaction. Predict from your model for Germacrene whether the product will have the two vinyl groups [[cis]] or [[trans]] to one another.
|}

==== References ====

# K. Shimazaki, M. Mori, K. Okada, T. Chuman, H. Goto, K. Sakakibara and M. Hirota, ''Conformational analyses of periplanone analogs by molecular mechanics calculations'', '' J. Chem. Ecology'', '''1991''', ''17'', 779-88. {{DOI|10.1007/BF00994200}}.
# H. Shirahama, E. Sawa and T. Matsumoto, ''Conformational aspects of germacrene B. Are the germacrenes resolvable ?'', ''Tetrahedron Lett.'', '''1979''', ''20'', 2245-2246. {{DOI|10.1016/S0040-4039(01)93687-1}}. See also {{DOI|10.1039/P19750002332}} for an explanation of the selective epoxidation of germacrene.

=== Xestoquinone: Regio and Stereoselectivity in the Diels Alder reaction===

# [[Image:xestoquinone.gif|thumb|right|Xestoquinone precursor]] This compound is a precursor to a natural product called Xestoquinone. It has four alkene groups, which can individually be considered as the alkene component in a π2s + π4s [[Diels Alder]] [[cycloaddition]]. The pair of alkenes ''a+b'' or ''c+d'' can also act as the diene component in the π2s + π4s [[Diels Alder]] [[cycloaddition]]. Construct a model of the product of e.g. forming a bond between alkene ''a'' or alkene ''b'' and diene ''c+d'', and then reverse the addition by using either ''c'' or ''d'' adding to the diene ''a+b''. The stereochemistry of addition should always be [[suprafacial]], i.e. preserving the stereochemical relationships of the alkenes. You should very carefully check that this is so in your final model.
# Whilst you should stop at '''two''' models, it is possible to construct many more. For example, one might be able to add to either the ''top'' face of alkene ''b'' or to its ''bottom'' face. Identify the model with the lower energy, and save it for the end of the workshop. We will identify the isomer of lowest energy from everyone's results, this being a communal [[Monte Carlo]] experiment to find the [[global minimum]].

==== References ====

#[http://en.wikipedia.org/wiki/Diels-Alder_reaction Wikipedia article]
#For the original literature on this synthesis, see R. Carlini, K. Higgs, C. Older, S. Randhawa, and R. Rodrigo, ''Intramolecular Diels-Alder and Cope Reactions of o-Quinonoid Monoketals and Their Adducts: Efficient Syntheses of (±)-Xestoquinone and Heterocycles Related to Viridin'', ''J. Org. Chem.'', '''1997''', ''62'', 2330 - 2331. {{DOI|10.1021/jo970394l}} where you can check to see which isomers actually do form!

=== Aldol Reaction and anti-Bredt Rings ===

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# [[Image:Aldol.gif|thumb|right|Aldol Reaction]]When the diketone shown is treated with base, it undergoes an aldol condensation. Two obvious possibililties are elimination of the combination Ha and Oa, or of the alternative combination Hb and Ob. In fact, only a single product is formed. On the basis of energies for both products, can you predict which one is actually formed?
# Measure a few dihedral angles, ie to find out how planar the alkene present is. Does this suggest a reason why one isomer is less stable than the other?
# There is a third very remote structural possibility. If you have time, verify that this third product truly is unlikely.
|}

==== References ====
#[http://en.wikipedia.org/wiki/Bredt's_Rule Bredt's Rule]
# I. Novak, ''Molecular Modeling of Anti-Bredt Compounds'', ''J. Chem. Inf. Model.'', '''2005''', ''45'', 334 - 338. {{DOI|10.1021/ci0497354}}
# See also this article A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, ''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins'', ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}} in conjunction with Project 9.

=== Conformational Preference for asymmetric hydride reduction of a ketone ===

# [[Image:Felkin.gif|thumb|right|Asymmetric hydride reduction]]The hydride ([http://en.wikipedia.org/wiki/Lithium_aluminium_hydride BH4, AlH4, etc]) reduction of the ketone shown here is stereospecific, resulting in an alcohol with the stereochemistry shown (known as the [http://en.wikipedia.org/wiki/Chiral_induction Cram or the Felkin-Anh] rule). Construct a model of the ketone and establish which of at least two conformations is the lowest in energy.
# If the hydride anion is delivered from the least hindered position, is the conformation you have consistent with the stereochemistry shown for the product?
# You can see from Ref 4 that the situation can be far more complex, depending on many other factors.

====References ====
# [http://en.wikipedia.org/wiki/Chiral_induction Wikipedia article]
# D. J. Cram and D. R. Wilson, ''Studies in Stereochemistry. XXXII. Models for 1,2-Asymmetric Induction'', ''J. Am. Chem. Soc.'', '''1963''', ''85'', 1245 - 1249. {{DOI|10.1021/ja00892a008}}.
# Y. Yamamoto, K. Matsuoka, and H. Nemoto, ''Anti-Cram selective reduction of acyclic ketones via electron transfer initiated processes'', ''J. Am. Chem. Soc.'', '''1988''', ''110'', 4475 - 4476; {{DOI|10.1021/ja00221a093}}.
# A. Mengel and O. Reiser, ''Around and beyond Cram's Rule'', ''Chem. Rev.'', '''1999''', ''99'', 1191 - 1224. {{DOI|10.1021/cr980379w}}.

=== Enantiomers vs Diastereomers Part 2: NMR Coupling constants ===

#[[Image:karplus.gif|thumb|Axial-equatorial interconversion|right]]In Project 2.2 above, we saw how the energies of diastereomeric compounds could be compared with the corresponding enantiomers. In this extension, we show how molecular modelling can cast light on the conformation adopted by 2-ethyl-4-methyl-1-oxa-cyclopentane-3-carboxylic acid estimated using measured 1H NMR coupling constants. The (2S,3S,4S) diastereomer has couplings of 3JH2,H3 8.3 Hz and 3JH3,H4 9.8 Hz. Two possible conformations of this diastereomer are shown on the right. They differ in that one has Et axial, and Me/COOH equatorial, and the other Et equatorial and Me/COOH axial.
#[[Image:karplus.jpg|Karplus plot|thumb|left]]By calculating the geometries of both conformations, and measuring the dihedral angle H2-C-C-H3 and H3-C-C-H4, one can assess by using the Karplus equation (left, taken from Ref 2 and relevant for a cyclopentane, but the values for which might be modified by the presence of electronegative substituents), which conformation leads to the best agreement between the calculated angle and the measured coupling constants (Hint: on the basis of the predicted couplings, you should be able to eliminate one of the two conformations shown for this molecule).
#[[Image:5-circulene.gif|thumb|5-circulene|right]]In Project 2.2 we also introduced molecules such as helicenes and circulenes. The 1H NMR of the [5]-circulene shown to the right revealed a complex spectrum at δ 2.98 ppm and again at 3.75 ppm. On the face of it, the four protons labeled Ha and Hb should all be equivalent, and the spectrum should be a single peak, not two complex multiplets. Indeed, if the NMR is recorded at high temperatures, this is exactly what is observed. By constructing a model of the [5]-circulene shown, can you explain why at normal temperatures, the NMR spectrum is so complex? 
#[[Image:Lab_expt.jpg|thumb|Synthesis lab experiment|right]]A practical application of this technique is to determine the stereochemistry of the product of the reaction between E,E-2,4-hexadien-1-ol and maleic anhydride. You will have the 1H NMR spectrum of your sample recorded, and evident from that will be peak multiplicities of the various proton resonances. You should endeavour from your analysis to come up with a suggestion for the structure of compound '''Y''', and from this, estimates of the numerical values (but not the signs) of the 2J and 3J couplings visible. Now using the techniques described above, construct a model of your proposed structure for '''Y'''. Measure the dihedral angles for all the 3J couplings, and very approximately estimate what the corresponding 3J might be from the diagram above. Does this help you assign the stereochemistry of the product?
#'''Advanced topic''': Part of the spectroscopic analysis of the compound '''Y''' involves interpreting the IR spectrum. Theory can be used in fact to simulate the full IR spectrum. In section 5.3 below, you will find instructions on how to use the model you have calculated here to initiate a so called '''density functional''' calculation. This will provide you with the required IR simulation. Follow these instructions, and open the resulting .log file in Gaussview. Go to the '''Results''' menu and select '''vibrations'''. The IR spectrum will be displayed. Does it match the one you have recorded for yourself?

==== References ====

#M. Karplus, ''Vicinal Proton Coupling in Nuclear Magnetic Resonance'', '' J. Am. Chem. Soc.'', '''1963''', ''85'', 2870 - 2871; {{DOI|10.1021/ja00901a059}}
#A. Wu, D. Cremer, A. A. Auer, and J. Gauss, ''Extension of the Karplus Relationship for NMR Spin-Spin Coupling Constants to Nonplanar Ring Systems: Pseudorotation of Cyclopentane'', ''J. Phys. Chem. A,'', '''2002''', ''106'', 657 -667; {{DOI|10.1021/jp013160l}}
#C. A. Stortz and M. S. Maier, ''Configurational assignments of diastereomeric γ-lactones using vicinal H–H NMR coupling constants and molecular modelling'', ''J. Chem. Soc., Perkin Trans. 2'', '''2000''', 1832 - 1836. {{DOI|10.1039/b003862h}}
# A. H. Abdourazak, A. Sygula, and P. W. Rabideau ''Locking the bowl-shaped geometry of corannulene: cyclopentacorannulene'', ''J. Am. Chem. Soc.'', '''1993''', ''115'', 3010 - 3011. {{DOI|10.1021/ja00060a073}}

=== Bridgehead enols: Thermodynamic vs Kinetic Control Part 2.===
{|
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#[[Image:Bredt.gif|thumb|right|Brendanone]] The ketone Brendan-2-one shown right exhibits unusual behaviour.6 When treated with NaOD/MeOD, deuterium substitution occurs easily and rapidly only in position Hb. Enolisation must of necessity form a bridgehead double bond (''anti-Bredt''), but clearly one isomer is more stable than the other possible form. Does molecular modelling predict this correctly?
#The unusually facile enolisation of this ketone (given that it forms an anti-Bredt enol) can also be investigated by molecular modelling. '''Measure''' the dihedral angle between the C-Ha or C-Hb vector and the carbonyl group. Assuming that the ''ideal'' angle for proton removal is around 90°, which proton is better set up for abstraction? Might this be kinetic rather than thermodynamic control?
#[[Image:Cortisone.gif|thumb|right|Cortisone]]One could also revisit Problem 2.3.3 above. Here, proton abstraction forms an enol which eventually epimerises the bridgehead position to form a ''trans'' ring junction. Why should this proton be particularly easy to remove? From what you have learnt above, would this be for kinetic or for thermodynamic reasons (or both?). Are all the relevant effects modelled using the mechanics approach or is consideration of the electrons also necessary?
|}
==== References and Footnotes====

# A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, {{doi-inline|10.1021/ja00837a043|''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins''}}, ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}}.

===Sulfonylation of Naphthalene: Thermodynamic vs Kinetic Control Part 3.===

[[Image:Sulfonylation.gif|right|thumb|Sulfonylation of naphthalene]]The sulfonylation of naphthalene using sulfuric acid is a good example of a mechanism combining both steric and electronic influences. The Molecular mechanics method intrinsic to the Ghemical program can only model the former, and not the latter. It is a worthwhile exercise to establish whether this anticipated deficiency does indeed lead to a model which only partially explains experiment.

It has been known for some time that treating naphthalene with sulfuric acids at low temperatures produces mostly substitution at the 1-position of the naphthalene. Heating the reaction mixture, or conducting the reaction at elevated temperatures produces mostly the 2-isomer. This is indeed a classic example of [[kinetic]] vs [[thermodynamic]] control, the 1-isomer being the kinetic one and the 2-isomer the thermodynamic one. To model the kinetic reaction, we have to inspect the [[transition state]] for the reaction, and here we can approximate this by the [[Wheland Intermediate]]. To model the thermodynamic reaction, we have to inspect the product (rather than the transition state) for the reaction.

#Build models for all four species shown in the diagram on the right. For the two products, define ''conjugated'' bond types for all the ring bonds, and define the sulfonyl group with two S=O double bonds and one S-O single bond. Take care to optimise the conformation of the sulfonyl group with respect to the aromatic ring. For the two Wheland intermediates, the limitations of Ghemical will force us to ''cheat''. Ghemical does not have parameters for a carbocation. So define the C2-C3 bond as conjugated (for the 1-Wheland intermediate). When you '''add hydrogens''' it will in fact add a second hydrogen to C2. Delete this one hydrogen. Ghemical will calculated the energy regardless of not knowing C2 is actually a carbonium ion! For the 2-Wheland intermediate, ensure that you use '''exactly''' the same number of ''conjugated'' bond types as you did for the 1-isomer (the two models in a mechanics sense are only comparable if you have the same total number of bond types in each model). You will have to decide whether these (undoubted) approximations have produced reasonable models or not (is the naphthalene framework planar for example, as it should be?).
#Record the pairs of energies (two for the 1- and 2-products, and two for each preceeding transition (Wheland) state.
#By turning the spacefilling representation on, which of the two products has the least unfavourable steric interactions between the sulfonic acid group and any adjacent hydrogens? Does this match with their relative energies?
#Do any unfavourable steric interactions observed in the product(s) also exist in the Wheland intermediates (as models for the transition states)?
#The relative stability of the Wheland intermediates is always assumed to be an '''electronic''' phenomenon. The conventional explanation is that the 1-Wheland isomer is stablized by both one aromatic ring '''and''' an allyl cation conjugated to it. The 2-Wheland isomer is stabilised by one aromatic ring conjugated to a secondary carbocation and an alkene. This type of ''cross conjugation'' is conventionally assumed to be less favourable. Does a purely mechanical approach to this problem reproduce this expectation? Or is this ''mechanical'' approximation to an ''electronic'' model too severe? It seems a good point to stop this course, since the next time you will build models, it will indeed be using methods which properly approximate the electronic components.
====References====

#R. Lantz, ''Mechanism of the monosulfonation of naphthalene'', ''Compt. Rend''. '''1935''', ''201'', 149-52.
#G. W. Wheland, ''A Quantum Mechanical Investigation of the Orientation of Substituents in Aromatic Molecules'', ''J. Am. Chem. Soc.'' '''1942''', ''64'', 900 - 908; {{DOI|10.1021/ja01256a047}}
#C. A. Reed, N. L. P. Fackler, K-C. Kim, D. Stasko, D. R. Evans, P. D. W. Boyd, and C. E. F. Rickard, ''Isolation of Protonated Arenes (Wheland Intermediates) with BArF and Carborane Anions. A Novel Crystalline Superacid'', ''J. Am. Chem. Soc.'' '''1999''', ''121'', 6314 - 6315 {{DOI|10.1021/ja981861z}}

== Coursework not to be attempted at any time: Antimodelling Molecules ==

The following represent molecules that should '''not''' be modelled under any circumstances! You should instead attempt to '''NAME''' them.

[[Image:Contraceptive.gif|Contraceptive (NO in every conceivable position)]] [[Image:Paradise.gif|Paradise lost]] [[Image:Synoptic.gif|Synoptic]] [[Image:Cisters.gif|Cisters]] [[Image:Transisters.gif|Transisters]] [[Image:Metaphor.gif|Metaphor]] [[Image:Metastasis.gif|Metastasis]] [[Image:Cyclone.gif|Cyclone]] [[Image:Anticyclone.gif|Anticyclone]] [[Image:Arsole.gif|Arsole]] [[Image:Orthodox.gif|Orthodox]] [[Image:Synthesis.gif|Synthesis and Antithesis]] [[Image:Aphrodisiac.gif|Name this yourself. Does Meg Ryan spring to mind?]] [[Image:Cyclops.gif|Cyclops]] [[Image:Paradox.gif|Paradox]] [[Image:Transparent.gif|Transparent]] [[Image:Encyclopedia.gif|Encyclopedia]] [[Image:Maths.jpg|Find X]] [[Image:VanderMaxforce.jpg|150px|Max Whitby stuck to a strangely attractive Lamp Post]] [[Image:nanoballet.jpg|200px|Nanoballet dancer]] [[Image:NanoCossacks.jpg|200px|NanoCossacks]]
[[Image:Paralysis.png|500px|Paralysis]] [[Image:Mcdonalds.png|350px|Old McDonald's Molecule: ene-yne-ene-yne-one]]
[[Image:Silenedione.png|300px|Celine Dion]] [[Image:Sundial.png|350px|Sun Dial]]

If you know of any other antimodelling molecules, please add them here!

====Acknowledgements ====

Some of these cartoons are from [http://www.nearingzero.net/sci_chemistry.html here], and six are original. A superb collection of '''''silly names''''' is maintained
by [http://www.chm.bris.ac.uk/sillymolecules/sillymols.htm Paul May] [[Organic:Model_answers|.]] See {{DOI|10.1021/jo0349227}} for the nanoputians.

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[[Second_Year_Modelling_Workshop|Back to introduction]]
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File:Sundial.png

2010-10-15T15:33:04Z

Nm607:

Coursework

2010-10-15T15:29:54Z

Nm607: /* Coursework not to be attempted at any time: Antimodelling Molecules */

[[Second_Year_Modelling_Workshop|Back to introduction]]
----
== Molecular modelling Coursework to be attempted during Scheduled Sessions ==

These projects are arranged in increasing order of difficulty, and time taken to complete. You should do as many as you can in the 2 hour session allocated to you, and return to finish the rest if you wish at your convenience. At the end of the session, we will conduct a ''number auction''. For each project, the bidding will start with the first volunteer offering an energy for the system (or one of the isomers). If anyone has a lower energy for that molecule, they will then bid that energy. The winner will be the one with the lowest energy.

=== Conformational analysis I: Chair and Boat-like conformations of Cyclohexane ===
{|
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<jmol><jmolApplet><title>Chiralane</title><color>white</color>
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#Construct '''[[chair]]''' and '''[[boat]]'''-like '''[[conformation]]s''' of [[cyclohexane]]. Compare the energies of both forms.
#Check carefully if your boat really is a boat, or whether it has any apparent distorsion.
#Try changing one or more of the CH2 groups into an oxygen and see if that affects things.
#For the record, the point group symmetries of the various species which may be involved are D3d for the chair conformation, C2v for a boat geometry, and D2 for any twisted boat form. Is any of these forms '''chiral'''?
#The molecule on the left is called '''chiralane'''. Are its rings boats or chairs?
|}
====References ====
# The first suggestion of two forms for cyclohexane goes as far back as H. Sachse, ''Chem. Ber'', 1890, '''23''', 1363 and ''Z. Physik. Chem.'', 1892, 10, 203. This is nicely explained [http://www.chem.yale.edu/~chem125/125/history/Baeyer/Sachse.html here]. E. Mohr, ''J. Prakt. Chem.'', 1918, '''98''', 315 and ''Chem. Ber.'', 1922, '''55''', 230, translated Sachse's argument into a pictorial one.
# The article that put [[conformational analysis]] on the map: D. H. R. Barton and R. C. Cookson, ''The principles of conformational analysis'', ''Q. Rev. Chem. Soc.'', '''1956''', ''10'', 44. {{DOI|10.1039/QR9561000044}}
#[http://en.wikipedia.org/wiki/Chair_conformation Wikipedia article]
#D. A. Dixon and A. Komornicki, ''Ab initio conformational analysis of cyclohexane'', ''J. Phys. Chem.'', '''1990''', ''94'', 5630 - 5636; {{DOI|10.1021/j100377a041}}.
#A nice exploration of the potential energy surfaces for cyclohexane can be viewed [http://www.springer.com/carey-sundberg/cyclohex/cyclohex.php here].
# For a more modern application of this technique, see I. Columbus, R. E. Hoffman, and S. E. Biali, ''Stereochemistry and Conformational Anomalies of 1,2,3- and 1,2,3,4-Polycyclohexylcyclohexanes''. ''J. Am. Chem. Soc.'', '''1996''', ''118'', 6890 - 6896; {{DOI|10.1021/ja960380h}}.
# The second molecule shown in this section is called [6.6]chiralane. It is peculiar for having many six-membered saturated rings, all of them as twist-boats rather than chairs! (a chair has a plane of symmetry, a twist boat only axes, which of course allows it to be chiral). See [http://petitjeanmichel.free.fr/itoweb.petitjean.graphs.html#CHIR here] for more details.
# More detail on the conformation of rings (and acyclic systems) will be found in the [http://www.ch.ic.ac.uk/local/organic/conf/ lecture course] on the topic to be given in the spring term.

=== Enantiomers vs Diastereomers Part 1: Butanes and Helicenes. ===

This problem illustrates, using models, the difference between an enantiomer and a diastereomer.

#[[Image:diastereo.gif|thumb|right|2-bromo-3-chlorobutane]][[Image:pentahelicene.gif|thumb|right|Pentahelicene]]The compound 2-bromo-3-chlorobutane has two [[chiral]] centres, and four isomers (22) are therefore possible. Calculate all four isomers, and for each be careful to label each of the two stereo centres '''R''' or '''S''' as you go. For each of the four isomers '''R,R''', '''S,S''', '''R,S''', '''S,R''' you will have to think about whether you have obtained the lowest energy [[conformer]].
#Can your four energies be grouped in any way? You should think about the expected difference between '''enantiomers''', '''diastereomers''' and '''conformers'''.
{|
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#Construct some helicenes (pentahelicene or [5]helicene is shown on the right), using '''conjugated''' bonds for all the ring bonds. Benzene, naphthalene, phenanthrene and benzophenanthrene are in fact the first four members of this series. At what point in this series can you detect helicity cropping up? This is manifested by a non-planar helical wind of the molecule. If you do detect it, note how the wind is either left or right handed, ie the two forms are '''enantiomers''' of each other. Try displaying the molecule in '''spacefill mode''' (see above) to see if you can identify the source of the helicity. (Note: the smallest helicene which can be resolved experimentally into enantiomers is in fact [5]helicene]).
#The higher helicenes are well known (up to about [14]helicene) and amongst the ''most chiral'' molecules known (in terms of how much they rotate the plane of polarised light).
#[7]circulene is a known molecule, with a unique saddle-shaped structure, shown on the left (there is no real need for you to build this model, but do please do so if you are curious). [http://en.wikipedia.org/wiki/Graphene Graphene] is a related polymeric molecule, of much topical interest in the semi-conducting and other industries (Nobel Prize 2010).
|}
==== References ====

#[http://en.wikipedia.org/wiki/Diastereomer Wikipedia article on Diastereomers]
#[http://en.wikipedia.org/wiki/Helicene Wikipedia article on Helicenes and related molecules]
#R. H. Janke, G. Haufe, E.-U. Würthwein, and J. H. Borkent, ''Racemization Barriers of Helicenes: A Computational Study'', ''J. Am. Chem. Soc.'', '''1996''', ''118'' 6031 - 6035 {{DOI|10.1021/ja950774t}}

=== Conformational analysis II: ''cis'' and ''trans''-decalins, Steroids and Podcasts! ===
{|
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<jmol><jmolApplet><title>Elimination</title><color>white</color>
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<jmol><jmolApplet><title>Woodward</title><color>white</color>
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# [[Image:cis-decalin.gif|thumb|right|cis Decalin]]This is the famous molecule that started the whole molecular mechanics modelling ball rolling. [http://www.ch.ic.ac.uk/video/barton/barton1.pdf Barton] in 1948 sought to find out which [[conformation]] of ''cis''-decalin was the most stable (see [http://www.ch.ic.ac.uk/video/barton/index_qt.html here] for video). You should be able to find at least three conformations of this molecule. Try locating these, and conclude which is the most stable. Identify any [[chair]] rings and any [[boat]].
#Measure some dihedral angles to see if the [[staggered]] relationships hold (i.e. for such a relationship, the dihedral angle should be close to 60 degrees).
#A key step in Woodward's famous synthesis of [http://en.wikipedia.org/wiki/Cortisone cortisone] is a quinone+butadiene [[Diels-Alder]] reaction to give a cis-decalin (left), with an assumption that [[epimerisation]] to a trans-decalin is thermodynamically favourable. [[Image:Cortisone.gif|thumb|left|cis Cortisone]]Can you verify whether the trans-isomer is indeed more stable? Its not so obvious, since this compound has two extra double bonds in the rings and six sp2 centres which might perturb things.
#[[Image:App.gif|thumb|right|trans Decalin]]The two diastereomeric ''trans''-decalin tosylates react quite differently with NaBH4. Construct models for both isomers (use methoxy as a model for the Tosyl group) and from the [[antiperiplanar]] alignments of bonds that you can find in each isomer, can you make a connection to the reactivity of each form? Consider very carefully where you would put a lone pair located on the nitrogen (i.e. include the N-Lp "bond" in your antiperiplanar alignments) asuming the this atom is tetrahedral rather than planar. Does this lone pair play any part in either reaction in this position?. Note that the relative energy of the axial/equatorial N-Methyl group will not be an accurate reflection of any [[antiperiplanar]] alignments, since these are predominantly electronic in origin, and this mechanics method does not take these into account.
##'''Optional:''' The second (elimination) reaction is very slow compared to the first. Discuss with tutors why this might be so (for Hints, see [[organic:entropy|here]] or [[organic:ngp|here]]).
##'''Optional''': These reactions do not appear to occur for the corresponding ''cis''-decalins6. Why not?

|}

==== References and Footnotes ====
# D. H. R. Barton, ''Interactions between non-bonded atoms, and the structure of cis-decalin'', ''J. Chem. Soc.'', '''1948''', 340-342. {{DOI|10.1039/JR9480000340}}
#[http://en.wikipedia.org/wiki/Decalin Wikipedia article]
# For a modern application of mechanics to this molecule, see J. M. A. Baas, B. Van de Graaf, D. Tavernier, and P. Vanhee, ''Empirical force field calculations. 10. Conformational analysis of cis-decalin'', ''J. Am. Chem. Soc.'', '''1981''', ''103'', 5014 - 5021; {{DOI|10.1021/ja00407a007}}.
# For a video-Podcast of Barton and Woodward (and other Nobel prize winners), subscribe [http://www.ch.ic.ac.uk/video/index.rss here]
# R. B. Woodward, F. Sondheimer, and D. Taub, ''The total Synthesis of Cortisone'', ''J. Am. Chem. Soc.'', '''1951''', ''73'', 4057 - 4057. {{DOI|10.1021/ja01152a551}}.
# P.-W. Phuan and M. C. Kozlowski, ''Control of the Conformational Equilibria in Aza-cis-Decalins: Structural Modification, Solvation, and Metal Chelation'', ''J. Org. Chem.'', '''2002''', ''67'', 6339 - 6346; {{DOI|10.1021/jo025544t}}

=== Menthone/''iso''menthone and Bridgehead enols: Thermodynamic vs Kinetic Control Part 1.===

{|
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#[[Image:Menthone.gif|thumb|right|Menthone]] Beckmann (of rearrangement fame) in 1889 dissolved optically active levorotatory (-) (S,R)-menthone ([α]D -28°) in conc. sulfuric acid, followed by quenching on ice to give what Beckmann assumed was pure (and what we would nowadays call [[diastereomeric]]) (+) (R,R)-isomenthone, [α]D +28°. He suggested for the first time that such an isomerisation, involving epimerisation at the asymmetric centre next to the keto group, proceeded via an intermediate enol in which the tetrahedral asymmetric carbon becomes planar. But this famous (perhaps even notorious2) early example of a [[reaction mechanism]] makes an interesting assumption, which can be tested by molecular modelling.
# Two possible enols can be formed, only one of which allows the [S] asymmetric carbon to become planar and then protonate to the [R] epimer. This is the so called [[thermodynamic enol]]. The other, which leaves the [S]-centre untouched is the [[kinetic enol]]. Find out if simple molecular modelling correctly predicts that the thermodynamic enol is indeed the more stable of the two. '''Hint:''' Model the enol and '''not''' the ketone. Consider carefully any conformational isomers possible.
# Given that the optical rotation3 of pure (+)-isomenthone is now known to be [α]D +101° rather than +28°, we can infer that Beckmann's product contains only 43% isomenthone and hence still contains 57% of original menthone, corresponding to an equilibrium constant of K= 0.75. This can be related to a (free energy) difference using the equation ΔG = -RT ln K, or ΔG = 0.7 kJ/mol (menthone being lower in energy by this amount compared to isomenthone). Can this energy difference be verified using molecular mechanics modelling? Can you explain why menthone is the more stable? (For another hint, or possibly a fright, visit [http://chemistry.gsu.edu/glactone/modeling/Luise/organic/cychexon.html this page]).
|}

==== References and footnotes ====
# E. Beckmann, ''Annalen'', '''1889''', ''250'', 322. {{DOI|10.1002/jlac.18892500306}}.
# Many of Beckmann's misconceptions were corrected by O. Wallach, ''Annalen'', '''1893''', ''276'', 296. {{DOI|10.1002/jlac.18932760306}}. The notoriety is because the coincidence of equal but opposite optical rotations obtained in this experiment led Beckmann to believe that he had obtained the [[enantiomer]] of menthone, and not as we now know, the impure (R,R) [[diastereomer]]. It should be borne in mind that the concept of tetrahedral and asymmetric carbon was only 15 years old at this time (see [http://en.wikipedia.org/wiki/Jacobus_van_%27t_Hoff Jacobus Henricus van't Hoff] and [http://en.wikipedia.org/wiki/Achille_Le_Bel Joseph Achille Le Bel]). Nevertheless confusion over this aspect persisted for some time after, and was often evident in the writings of even very famous chemists of the time (and Beckmann was very famous)!.
#[http://en.wikipedia.org/wiki/Menthone Wikipedia article]
# From about 1890-1935, mechanistic organic chemistry was born. In the absence of UV, IR, NMR, MS and X-Ray techniques, the [http://en.wikipedia.org/wiki/Polarimeter polarimeter] occupied a pivotal role. Many of the great discoveries in reaction mechanisms (keto-enol tautomerism as seen here, [[Organic:tutorial:meerwein| carbocations]], the Walden inversion, etc) relied on polarimetric measurements.
# A notorious modern example of (unwanted) epimerisation of a ketone is [http://en.wikipedia.org/wiki/Thalidomide Thalidomide], where one epimer inhibits morning sickness in pregnant women, and the other epimer is teratogenic, causing fetal abnormalities. The equilibrium in this case does not require conc. sulfuric acid, but can occur at physiological pH.

== Additional Molecular modelling Coursework ==

Please feel free to try these problems in your own time, and to discuss these with your organic tutors and lecturers. Note also that the relevant lectures may occur in the spring as well as autumn terms.
=== Axial/Equatorial preferences in cyclohexane and cyclohexanone and Hydrogen Bonding ===
{|
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#Construct a chair cyclohexane and replace firstly one of the [[axial]] hydrogens with the following groups: '''methyl''', '''t-butyl''', '''OH'''. Calculate the energy of the axial isomer.
# Then repeat (either by deleting/redrawing or by moving) for the equatorial forms. Compare the energies of the two isomers. Does any energy difference increase with the size of the group? Does OH fit into this in terms of size?
# [[Image:Thiomethylcyclohexanone.gif|right|thumb|thiomethyl cyclohexanone]]The dissolving metal reduction of cyclohexanones in a protic solvent (i.e. one capable of hydrogen bonding) is thermodynamically controlled and gives the more stable, equatorial alcohol. In fact, its probably the alkoxide that is the product, not the free alcohol. It is thought the alkoxide is actually a lot larger than the alcohol, accounting for the substantial equatorial preference. Can you think why its larger? [Ghemical cannot in fact model this, since the force field does not include parameters for the alkoxide anion].
# Determine the axial/equatorial preference of 2-methylthio-cyclohexanone (Hint: there are many conformations possible, and you should try a few to see if you can get the lowest).
|}
==== References and Footnotes ====

# A. H. Lewin and S. Winstein, ''NMR. Spectra and Conformational Analysis of 4-Alkylcyclohexanols'' ''J. Am. Chem. Soc.''; '''1962''', ''84'', 2464 - 2465; {{DOI|10.1021/ja00871a049}}
#F. R. Jensen and L. H. Gale, ''The Conformational Preference of the Bromo and Methyl Groups in Cyclohexane by IR Spectral Analysis'', ''J. Org. Chem.'', '''1960''', ''25'', 2075 - 2078. {{DOI|10.1021/jo01082a001}}
# K. B. Wiberg, J. D. Hammer, H. Castejon, W. F. Bailey, E. L. DeLeon, and R. M. Jarret, ''Conformational Studies in the Cyclohexane Series. 1. Experimental and Computational Investigation of Methyl, Ethyl, Isopropyl, and tert-Butylcyclohexanes'', ''J. Org. Chem.'', '''1999''', ''64'', 2085 - 2095; {{DOI|10.1021/jo990056f}}. The salient point here is that the [[enthalpy]] and [[entropy]] of this series differ in their trends.
# Just when you are starting to think that things are quite simple, along comes the observation: S. E. Biali, ''Axial monoalkyl cyclohexanes'', ''J. Org. Chem.'', '''1992''', ''57'', 2979 - 2980; {{DOI|10.1021/jo00037a001}}
# And this one with knobs on: ''In all-trans-1,2,3,4,5,6-hexaisopropylcyclohexane, all the alkyl groups are located at axial rather than equatorial positions: O. Golan, Z. Goren, and S. E. Biali, ''Axial-equatorial stability reversal in all-trans-polyalkylcyclohexanes'', ''J. Am. Chem. Soc.'', '''1990''', ''112'', 9300 - 9307. {{DOI|10.1021/ja00181a036}}.
#J. A. Anderson, K. Crager, Kelly, L.Fedoroff, G. S. Tschumper, Gregory S. ''Anchoring the potential energy surface of the cyclic water trimer.'' ''J. Chem. Physics'', '''2004''', ''121'', 11023-11029. {{DOI|10.1063/1.1799931}}.
#R. R. Fraser, N. C. Faibish, ''On the purported axial preference in 2-methylthio- and 2-methoxycyclohexanones: steric effects versus orbital interactions'', ''Can. J. Chem.'', '''1995''', ''73'', 88-94.
=== How to induce room temperature hydrolysis of a peptide ===
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<uploadedFileContents>peptide-13.3.mol</uploadedFileContents>
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[[Image:amide-cleavage.png|thumb|right|Peptide hydrolysis]] This introduces a further example of how simple conformational analysis can quickly rationalize kinetic behaviour. At neutral pH and 25° the half life for hydrolysis of a peptide bond is around 500 years (and thank goodness, or we would ourselves all rapidly hydrolise to a mush!). Some enzymes however can achieve this in less than 1 second, an acceleration of 1013! Organic chemists are not quite so clever, but they can achieve room temperature hydrolysis of a peptide in 21 minutes by careful conformational design. The two isomers shown on the right differ only in their stereochemistry, one hydrolysing quickly, the other slowly. Build a model of each compound, and calculate two isomers for each, varying in whether the ring N-substituent is oriented axial or equatorial with respect to the decalin ring. On the basis of your two pairs of energies, can you rationalise the observed kinetic behaviour? Do you know why both of these compounds take very much less than 500 years to hydrolise the peptide bond?

'''Hint1:''' Use the chair-chair conformation for cis-decalin as your template for constructing this system.

'''Hint2:''' When constructing your models, think if there are any hydrogen bonds that might stabilize the structure!

'''Hint3:''' Hydrolysis can only occur when the OH group can approach the carbonyl of the peptide bond close enough to react, and at the right angle of approach.
|}

==== Reference ====

# M. Fernandes, F. Fache, M. Rosen, P.-L. Nguyen, and D. E. Hansen, 'Rapid Cleavage of Unactivated, Unstrained Amide Bonds at Neutral pH', ''J. Org. Chem.,'' '''2008''', ASAP: {{DOI|10.1021/jo800706y}}

=== Caryophyllene: The phenomenon of Atropisomerism ===

# [[Image:caryophyllene-ketone.gif|thumb|right|Caryophyllene ketone]] [http://en.wikipedia.org/wiki/Caryophyllene Caryophyllene], a constituent of many essential oils, include clove oil, has a [[trans]] alkene contained in a 9-membered ring. One interesting property is that it has 4 [[diastereoisomers]] possible, originating from a total of three asymmetric centres present in the molecule. Two of these are conventional chiral centres, one is present in the form of a disymmetric trans double bond. To understand why such a bond can result in two configurations, one must appreciate that (concurrent) rotation about the two C-C single bonds adjacent to the alkene is in fact restricted, because to the hydrogen labelled Ha cannot easily pass by the edge of the 4-membered ring. Construct this molecule (in fact the ketone rather than the alkene) and optimize its geometry. Note in particular that the ring junction is ''trans'' and not ''cis''.
# You will find you may well have obtained one of two forms. In the first, the Ha hydrogen will be opposite the C=O group, in the other it will be adjacent to it. Record the energy of whatever form you got. At the end of the course, we will try to find the ''winner'' with the lowest energy (this is not as trivial as it sounds!).
# Next, take your structure, and try to ''flip'' the [[trans]] alkene bond around so that eg if the methyl were previously pointing up, now it will point down. You may find a combination of erasing/redrawing or of moving, will accomplish this. You may also find another trick useful, of deleting all hydrogens, and then re-sprouting them back on again. Re-optimise your structure and compare the energy with your first isomer.
# Another feature of this model is that you can judge which group is in the so-called shielded region of the carbonyl group magnetic anisotropy. Using this information, you can see if there are any anomalous 1H chemical shifts that might need explaining!

==== References ====
# M. Clericuzio, G. Alagona, C. Ghio, and L. Toma, ''Ab Initio and Density Functional Evaluations of the Molecular Conformations of -Caryophyllene and 6-Hydroxycaryophyllene'', ''J. Org. Chem.'' '''2000''', ''65'', 6910 - 6916. {{DOI|10.1021/jo000404+}}.
#[http://en.wikipedia.org/wiki/Caryophyllene Wikipedia article]
# For a recent application of this phenomenon, see P. C. Bulman Page, B. R. Buckley, S. D.R. Christie, M. Edgar, A. M. Poulton, M. R.J. Elsegood and V. McKee, ''A new paradigm in N-heterocyclic carbenoid ligands'', ''J. Organometallic Chem.'', '''2005''', ''690'', 6210-6216. D {{DOI|10.1016/j.jorganchem.2005.09.015}}.

=== Germacrene: Conformational analysis of medium sized rings ===

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# [[Image:Germacrene.gif|thumb|right|Germacrene and the thermal reaction product]]Germacrene is a natural product with a ten-membered ring; it has the triene structure shown. Assuming that it adopts a crown conformation, build a three-dimensional model.
# On heating, germacrene is converted into one of the stereoisomers of the divinylcyclohexane, via a [3,3] sigmatropic pericyclic reaction. Predict from your model for Germacrene whether the product will have the two vinyl groups [[cis]] or [[trans]] to one another.
|}

==== References ====

# K. Shimazaki, M. Mori, K. Okada, T. Chuman, H. Goto, K. Sakakibara and M. Hirota, ''Conformational analyses of periplanone analogs by molecular mechanics calculations'', '' J. Chem. Ecology'', '''1991''', ''17'', 779-88. {{DOI|10.1007/BF00994200}}.
# H. Shirahama, E. Sawa and T. Matsumoto, ''Conformational aspects of germacrene B. Are the germacrenes resolvable ?'', ''Tetrahedron Lett.'', '''1979''', ''20'', 2245-2246. {{DOI|10.1016/S0040-4039(01)93687-1}}. See also {{DOI|10.1039/P19750002332}} for an explanation of the selective epoxidation of germacrene.

=== Xestoquinone: Regio and Stereoselectivity in the Diels Alder reaction===

# [[Image:xestoquinone.gif|thumb|right|Xestoquinone precursor]] This compound is a precursor to a natural product called Xestoquinone. It has four alkene groups, which can individually be considered as the alkene component in a π2s + π4s [[Diels Alder]] [[cycloaddition]]. The pair of alkenes ''a+b'' or ''c+d'' can also act as the diene component in the π2s + π4s [[Diels Alder]] [[cycloaddition]]. Construct a model of the product of e.g. forming a bond between alkene ''a'' or alkene ''b'' and diene ''c+d'', and then reverse the addition by using either ''c'' or ''d'' adding to the diene ''a+b''. The stereochemistry of addition should always be [[suprafacial]], i.e. preserving the stereochemical relationships of the alkenes. You should very carefully check that this is so in your final model.
# Whilst you should stop at '''two''' models, it is possible to construct many more. For example, one might be able to add to either the ''top'' face of alkene ''b'' or to its ''bottom'' face. Identify the model with the lower energy, and save it for the end of the workshop. We will identify the isomer of lowest energy from everyone's results, this being a communal [[Monte Carlo]] experiment to find the [[global minimum]].

==== References ====

#[http://en.wikipedia.org/wiki/Diels-Alder_reaction Wikipedia article]
#For the original literature on this synthesis, see R. Carlini, K. Higgs, C. Older, S. Randhawa, and R. Rodrigo, ''Intramolecular Diels-Alder and Cope Reactions of o-Quinonoid Monoketals and Their Adducts: Efficient Syntheses of (±)-Xestoquinone and Heterocycles Related to Viridin'', ''J. Org. Chem.'', '''1997''', ''62'', 2330 - 2331. {{DOI|10.1021/jo970394l}} where you can check to see which isomers actually do form!

=== Aldol Reaction and anti-Bredt Rings ===

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# [[Image:Aldol.gif|thumb|right|Aldol Reaction]]When the diketone shown is treated with base, it undergoes an aldol condensation. Two obvious possibililties are elimination of the combination Ha and Oa, or of the alternative combination Hb and Ob. In fact, only a single product is formed. On the basis of energies for both products, can you predict which one is actually formed?
# Measure a few dihedral angles, ie to find out how planar the alkene present is. Does this suggest a reason why one isomer is less stable than the other?
# There is a third very remote structural possibility. If you have time, verify that this third product truly is unlikely.
|}

==== References ====
#[http://en.wikipedia.org/wiki/Bredt's_Rule Bredt's Rule]
# I. Novak, ''Molecular Modeling of Anti-Bredt Compounds'', ''J. Chem. Inf. Model.'', '''2005''', ''45'', 334 - 338. {{DOI|10.1021/ci0497354}}
# See also this article A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, ''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins'', ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}} in conjunction with Project 9.

=== Conformational Preference for asymmetric hydride reduction of a ketone ===

# [[Image:Felkin.gif|thumb|right|Asymmetric hydride reduction]]The hydride ([http://en.wikipedia.org/wiki/Lithium_aluminium_hydride BH4, AlH4, etc]) reduction of the ketone shown here is stereospecific, resulting in an alcohol with the stereochemistry shown (known as the [http://en.wikipedia.org/wiki/Chiral_induction Cram or the Felkin-Anh] rule). Construct a model of the ketone and establish which of at least two conformations is the lowest in energy.
# If the hydride anion is delivered from the least hindered position, is the conformation you have consistent with the stereochemistry shown for the product?
# You can see from Ref 4 that the situation can be far more complex, depending on many other factors.

====References ====
# [http://en.wikipedia.org/wiki/Chiral_induction Wikipedia article]
# D. J. Cram and D. R. Wilson, ''Studies in Stereochemistry. XXXII. Models for 1,2-Asymmetric Induction'', ''J. Am. Chem. Soc.'', '''1963''', ''85'', 1245 - 1249. {{DOI|10.1021/ja00892a008}}.
# Y. Yamamoto, K. Matsuoka, and H. Nemoto, ''Anti-Cram selective reduction of acyclic ketones via electron transfer initiated processes'', ''J. Am. Chem. Soc.'', '''1988''', ''110'', 4475 - 4476; {{DOI|10.1021/ja00221a093}}.
# A. Mengel and O. Reiser, ''Around and beyond Cram's Rule'', ''Chem. Rev.'', '''1999''', ''99'', 1191 - 1224. {{DOI|10.1021/cr980379w}}.

=== Enantiomers vs Diastereomers Part 2: NMR Coupling constants ===

#[[Image:karplus.gif|thumb|Axial-equatorial interconversion|right]]In Project 2.2 above, we saw how the energies of diastereomeric compounds could be compared with the corresponding enantiomers. In this extension, we show how molecular modelling can cast light on the conformation adopted by 2-ethyl-4-methyl-1-oxa-cyclopentane-3-carboxylic acid estimated using measured 1H NMR coupling constants. The (2S,3S,4S) diastereomer has couplings of 3JH2,H3 8.3 Hz and 3JH3,H4 9.8 Hz. Two possible conformations of this diastereomer are shown on the right. They differ in that one has Et axial, and Me/COOH equatorial, and the other Et equatorial and Me/COOH axial.
#[[Image:karplus.jpg|Karplus plot|thumb|left]]By calculating the geometries of both conformations, and measuring the dihedral angle H2-C-C-H3 and H3-C-C-H4, one can assess by using the Karplus equation (left, taken from Ref 2 and relevant for a cyclopentane, but the values for which might be modified by the presence of electronegative substituents), which conformation leads to the best agreement between the calculated angle and the measured coupling constants (Hint: on the basis of the predicted couplings, you should be able to eliminate one of the two conformations shown for this molecule).
#[[Image:5-circulene.gif|thumb|5-circulene|right]]In Project 2.2 we also introduced molecules such as helicenes and circulenes. The 1H NMR of the [5]-circulene shown to the right revealed a complex spectrum at δ 2.98 ppm and again at 3.75 ppm. On the face of it, the four protons labeled Ha and Hb should all be equivalent, and the spectrum should be a single peak, not two complex multiplets. Indeed, if the NMR is recorded at high temperatures, this is exactly what is observed. By constructing a model of the [5]-circulene shown, can you explain why at normal temperatures, the NMR spectrum is so complex? 
#[[Image:Lab_expt.jpg|thumb|Synthesis lab experiment|right]]A practical application of this technique is to determine the stereochemistry of the product of the reaction between E,E-2,4-hexadien-1-ol and maleic anhydride. You will have the 1H NMR spectrum of your sample recorded, and evident from that will be peak multiplicities of the various proton resonances. You should endeavour from your analysis to come up with a suggestion for the structure of compound '''Y''', and from this, estimates of the numerical values (but not the signs) of the 2J and 3J couplings visible. Now using the techniques described above, construct a model of your proposed structure for '''Y'''. Measure the dihedral angles for all the 3J couplings, and very approximately estimate what the corresponding 3J might be from the diagram above. Does this help you assign the stereochemistry of the product?
#'''Advanced topic''': Part of the spectroscopic analysis of the compound '''Y''' involves interpreting the IR spectrum. Theory can be used in fact to simulate the full IR spectrum. In section 5.3 below, you will find instructions on how to use the model you have calculated here to initiate a so called '''density functional''' calculation. This will provide you with the required IR simulation. Follow these instructions, and open the resulting .log file in Gaussview. Go to the '''Results''' menu and select '''vibrations'''. The IR spectrum will be displayed. Does it match the one you have recorded for yourself?

==== References ====

#M. Karplus, ''Vicinal Proton Coupling in Nuclear Magnetic Resonance'', '' J. Am. Chem. Soc.'', '''1963''', ''85'', 2870 - 2871; {{DOI|10.1021/ja00901a059}}
#A. Wu, D. Cremer, A. A. Auer, and J. Gauss, ''Extension of the Karplus Relationship for NMR Spin-Spin Coupling Constants to Nonplanar Ring Systems: Pseudorotation of Cyclopentane'', ''J. Phys. Chem. A,'', '''2002''', ''106'', 657 -667; {{DOI|10.1021/jp013160l}}
#C. A. Stortz and M. S. Maier, ''Configurational assignments of diastereomeric γ-lactones using vicinal H–H NMR coupling constants and molecular modelling'', ''J. Chem. Soc., Perkin Trans. 2'', '''2000''', 1832 - 1836. {{DOI|10.1039/b003862h}}
# A. H. Abdourazak, A. Sygula, and P. W. Rabideau ''Locking the bowl-shaped geometry of corannulene: cyclopentacorannulene'', ''J. Am. Chem. Soc.'', '''1993''', ''115'', 3010 - 3011. {{DOI|10.1021/ja00060a073}}

=== Bridgehead enols: Thermodynamic vs Kinetic Control Part 2.===
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#[[Image:Bredt.gif|thumb|right|Brendanone]] The ketone Brendan-2-one shown right exhibits unusual behaviour.6 When treated with NaOD/MeOD, deuterium substitution occurs easily and rapidly only in position Hb. Enolisation must of necessity form a bridgehead double bond (''anti-Bredt''), but clearly one isomer is more stable than the other possible form. Does molecular modelling predict this correctly?
#The unusually facile enolisation of this ketone (given that it forms an anti-Bredt enol) can also be investigated by molecular modelling. '''Measure''' the dihedral angle between the C-Ha or C-Hb vector and the carbonyl group. Assuming that the ''ideal'' angle for proton removal is around 90°, which proton is better set up for abstraction? Might this be kinetic rather than thermodynamic control?
#[[Image:Cortisone.gif|thumb|right|Cortisone]]One could also revisit Problem 2.3.3 above. Here, proton abstraction forms an enol which eventually epimerises the bridgehead position to form a ''trans'' ring junction. Why should this proton be particularly easy to remove? From what you have learnt above, would this be for kinetic or for thermodynamic reasons (or both?). Are all the relevant effects modelled using the mechanics approach or is consideration of the electrons also necessary?
|}
==== References and Footnotes====

# A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, {{doi-inline|10.1021/ja00837a043|''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins''}}, ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}}.

===Sulfonylation of Naphthalene: Thermodynamic vs Kinetic Control Part 3.===

[[Image:Sulfonylation.gif|right|thumb|Sulfonylation of naphthalene]]The sulfonylation of naphthalene using sulfuric acid is a good example of a mechanism combining both steric and electronic influences. The Molecular mechanics method intrinsic to the Ghemical program can only model the former, and not the latter. It is a worthwhile exercise to establish whether this anticipated deficiency does indeed lead to a model which only partially explains experiment.

It has been known for some time that treating naphthalene with sulfuric acids at low temperatures produces mostly substitution at the 1-position of the naphthalene. Heating the reaction mixture, or conducting the reaction at elevated temperatures produces mostly the 2-isomer. This is indeed a classic example of [[kinetic]] vs [[thermodynamic]] control, the 1-isomer being the kinetic one and the 2-isomer the thermodynamic one. To model the kinetic reaction, we have to inspect the [[transition state]] for the reaction, and here we can approximate this by the [[Wheland Intermediate]]. To model the thermodynamic reaction, we have to inspect the product (rather than the transition state) for the reaction.

#Build models for all four species shown in the diagram on the right. For the two products, define ''conjugated'' bond types for all the ring bonds, and define the sulfonyl group with two S=O double bonds and one S-O single bond. Take care to optimise the conformation of the sulfonyl group with respect to the aromatic ring. For the two Wheland intermediates, the limitations of Ghemical will force us to ''cheat''. Ghemical does not have parameters for a carbocation. So define the C2-C3 bond as conjugated (for the 1-Wheland intermediate). When you '''add hydrogens''' it will in fact add a second hydrogen to C2. Delete this one hydrogen. Ghemical will calculated the energy regardless of not knowing C2 is actually a carbonium ion! For the 2-Wheland intermediate, ensure that you use '''exactly''' the same number of ''conjugated'' bond types as you did for the 1-isomer (the two models in a mechanics sense are only comparable if you have the same total number of bond types in each model). You will have to decide whether these (undoubted) approximations have produced reasonable models or not (is the naphthalene framework planar for example, as it should be?).
#Record the pairs of energies (two for the 1- and 2-products, and two for each preceeding transition (Wheland) state.
#By turning the spacefilling representation on, which of the two products has the least unfavourable steric interactions between the sulfonic acid group and any adjacent hydrogens? Does this match with their relative energies?
#Do any unfavourable steric interactions observed in the product(s) also exist in the Wheland intermediates (as models for the transition states)?
#The relative stability of the Wheland intermediates is always assumed to be an '''electronic''' phenomenon. The conventional explanation is that the 1-Wheland isomer is stablized by both one aromatic ring '''and''' an allyl cation conjugated to it. The 2-Wheland isomer is stabilised by one aromatic ring conjugated to a secondary carbocation and an alkene. This type of ''cross conjugation'' is conventionally assumed to be less favourable. Does a purely mechanical approach to this problem reproduce this expectation? Or is this ''mechanical'' approximation to an ''electronic'' model too severe? It seems a good point to stop this course, since the next time you will build models, it will indeed be using methods which properly approximate the electronic components.
====References====

#R. Lantz, ''Mechanism of the monosulfonation of naphthalene'', ''Compt. Rend''. '''1935''', ''201'', 149-52.
#G. W. Wheland, ''A Quantum Mechanical Investigation of the Orientation of Substituents in Aromatic Molecules'', ''J. Am. Chem. Soc.'' '''1942''', ''64'', 900 - 908; {{DOI|10.1021/ja01256a047}}
#C. A. Reed, N. L. P. Fackler, K-C. Kim, D. Stasko, D. R. Evans, P. D. W. Boyd, and C. E. F. Rickard, ''Isolation of Protonated Arenes (Wheland Intermediates) with BArF and Carborane Anions. A Novel Crystalline Superacid'', ''J. Am. Chem. Soc.'' '''1999''', ''121'', 6314 - 6315 {{DOI|10.1021/ja981861z}}

== Coursework not to be attempted at any time: Antimodelling Molecules ==

The following represent molecules that should '''not''' be modelled under any circumstances! You should instead attempt to '''NAME''' them.

[[Image:Contraceptive.gif|Contraceptive (NO in every conceivable position)]] [[Image:Paradise.gif|Paradise lost]] [[Image:Synoptic.gif|Synoptic]] [[Image:Cisters.gif|Cisters]] [[Image:Transisters.gif|Transisters]] [[Image:Metaphor.gif|Metaphor]] [[Image:Metastasis.gif|Metastasis]] [[Image:Cyclone.gif|Cyclone]] [[Image:Anticyclone.gif|Anticyclone]] [[Image:Arsole.gif|Arsole]] [[Image:Orthodox.gif|Orthodox]] [[Image:Synthesis.gif|Synthesis and Antithesis]] [[Image:Aphrodisiac.gif|Name this yourself. Does Meg Ryan spring to mind?]] [[Image:Cyclops.gif|Cyclops]] [[Image:Paradox.gif|Paradox]] [[Image:Transparent.gif|Transparent]] [[Image:Encyclopedia.gif|Encyclopedia]] [[Image:Maths.jpg|Find X]] [[Image:VanderMaxforce.jpg|150px|Max Whitby stuck to a strangely attractive Lamp Post]] [[Image:nanoballet.jpg|200px|Nanoballet dancer]] [[Image:NanoCossacks.jpg|200px|NanoCossacks]]
[[Image:Paralysis.png|500px|Paralysis]] [[Image:Mcdonalds.png|350px|Old McDonald's Molecule: ene-yne-ene-yne-one]]
[[Image:Silenedione.png|3000px|Celine Dion]]

If you know of any other antimodelling molecules, please add them here!

====Acknowledgements ====

Some of these cartoons are from [http://www.nearingzero.net/sci_chemistry.html here], and six are original. A superb collection of '''''silly names''''' is maintained
by [http://www.chm.bris.ac.uk/sillymolecules/sillymols.htm Paul May] [[Organic:Model_answers|.]] See {{DOI|10.1021/jo0349227}} for the nanoputians.

----
[[Second_Year_Modelling_Workshop|Back to introduction]]
----

Coursework

2010-10-15T15:28:57Z

Nm607: /* Coursework not to be attempted at any time: Antimodelling Molecules */

[[Second_Year_Modelling_Workshop|Back to introduction]]
----
== Molecular modelling Coursework to be attempted during Scheduled Sessions ==

These projects are arranged in increasing order of difficulty, and time taken to complete. You should do as many as you can in the 2 hour session allocated to you, and return to finish the rest if you wish at your convenience. At the end of the session, we will conduct a ''number auction''. For each project, the bidding will start with the first volunteer offering an energy for the system (or one of the isomers). If anyone has a lower energy for that molecule, they will then bid that energy. The winner will be the one with the lowest energy.

=== Conformational analysis I: Chair and Boat-like conformations of Cyclohexane ===
{|
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#Construct '''[[chair]]''' and '''[[boat]]'''-like '''[[conformation]]s''' of [[cyclohexane]]. Compare the energies of both forms.
#Check carefully if your boat really is a boat, or whether it has any apparent distorsion.
#Try changing one or more of the CH2 groups into an oxygen and see if that affects things.
#For the record, the point group symmetries of the various species which may be involved are D3d for the chair conformation, C2v for a boat geometry, and D2 for any twisted boat form. Is any of these forms '''chiral'''?
#The molecule on the left is called '''chiralane'''. Are its rings boats or chairs?
|}
====References ====
# The first suggestion of two forms for cyclohexane goes as far back as H. Sachse, ''Chem. Ber'', 1890, '''23''', 1363 and ''Z. Physik. Chem.'', 1892, 10, 203. This is nicely explained [http://www.chem.yale.edu/~chem125/125/history/Baeyer/Sachse.html here]. E. Mohr, ''J. Prakt. Chem.'', 1918, '''98''', 315 and ''Chem. Ber.'', 1922, '''55''', 230, translated Sachse's argument into a pictorial one.
# The article that put [[conformational analysis]] on the map: D. H. R. Barton and R. C. Cookson, ''The principles of conformational analysis'', ''Q. Rev. Chem. Soc.'', '''1956''', ''10'', 44. {{DOI|10.1039/QR9561000044}}
#[http://en.wikipedia.org/wiki/Chair_conformation Wikipedia article]
#D. A. Dixon and A. Komornicki, ''Ab initio conformational analysis of cyclohexane'', ''J. Phys. Chem.'', '''1990''', ''94'', 5630 - 5636; {{DOI|10.1021/j100377a041}}.
#A nice exploration of the potential energy surfaces for cyclohexane can be viewed [http://www.springer.com/carey-sundberg/cyclohex/cyclohex.php here].
# For a more modern application of this technique, see I. Columbus, R. E. Hoffman, and S. E. Biali, ''Stereochemistry and Conformational Anomalies of 1,2,3- and 1,2,3,4-Polycyclohexylcyclohexanes''. ''J. Am. Chem. Soc.'', '''1996''', ''118'', 6890 - 6896; {{DOI|10.1021/ja960380h}}.
# The second molecule shown in this section is called [6.6]chiralane. It is peculiar for having many six-membered saturated rings, all of them as twist-boats rather than chairs! (a chair has a plane of symmetry, a twist boat only axes, which of course allows it to be chiral). See [http://petitjeanmichel.free.fr/itoweb.petitjean.graphs.html#CHIR here] for more details.
# More detail on the conformation of rings (and acyclic systems) will be found in the [http://www.ch.ic.ac.uk/local/organic/conf/ lecture course] on the topic to be given in the spring term.

=== Enantiomers vs Diastereomers Part 1: Butanes and Helicenes. ===

This problem illustrates, using models, the difference between an enantiomer and a diastereomer.

#[[Image:diastereo.gif|thumb|right|2-bromo-3-chlorobutane]][[Image:pentahelicene.gif|thumb|right|Pentahelicene]]The compound 2-bromo-3-chlorobutane has two [[chiral]] centres, and four isomers (22) are therefore possible. Calculate all four isomers, and for each be careful to label each of the two stereo centres '''R''' or '''S''' as you go. For each of the four isomers '''R,R''', '''S,S''', '''R,S''', '''S,R''' you will have to think about whether you have obtained the lowest energy [[conformer]].
#Can your four energies be grouped in any way? You should think about the expected difference between '''enantiomers''', '''diastereomers''' and '''conformers'''.
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#Construct some helicenes (pentahelicene or [5]helicene is shown on the right), using '''conjugated''' bonds for all the ring bonds. Benzene, naphthalene, phenanthrene and benzophenanthrene are in fact the first four members of this series. At what point in this series can you detect helicity cropping up? This is manifested by a non-planar helical wind of the molecule. If you do detect it, note how the wind is either left or right handed, ie the two forms are '''enantiomers''' of each other. Try displaying the molecule in '''spacefill mode''' (see above) to see if you can identify the source of the helicity. (Note: the smallest helicene which can be resolved experimentally into enantiomers is in fact [5]helicene]).
#The higher helicenes are well known (up to about [14]helicene) and amongst the ''most chiral'' molecules known (in terms of how much they rotate the plane of polarised light).
#[7]circulene is a known molecule, with a unique saddle-shaped structure, shown on the left (there is no real need for you to build this model, but do please do so if you are curious). [http://en.wikipedia.org/wiki/Graphene Graphene] is a related polymeric molecule, of much topical interest in the semi-conducting and other industries (Nobel Prize 2010).
|}
==== References ====

#[http://en.wikipedia.org/wiki/Diastereomer Wikipedia article on Diastereomers]
#[http://en.wikipedia.org/wiki/Helicene Wikipedia article on Helicenes and related molecules]
#R. H. Janke, G. Haufe, E.-U. Würthwein, and J. H. Borkent, ''Racemization Barriers of Helicenes: A Computational Study'', ''J. Am. Chem. Soc.'', '''1996''', ''118'' 6031 - 6035 {{DOI|10.1021/ja950774t}}

=== Conformational analysis II: ''cis'' and ''trans''-decalins, Steroids and Podcasts! ===
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# [[Image:cis-decalin.gif|thumb|right|cis Decalin]]This is the famous molecule that started the whole molecular mechanics modelling ball rolling. [http://www.ch.ic.ac.uk/video/barton/barton1.pdf Barton] in 1948 sought to find out which [[conformation]] of ''cis''-decalin was the most stable (see [http://www.ch.ic.ac.uk/video/barton/index_qt.html here] for video). You should be able to find at least three conformations of this molecule. Try locating these, and conclude which is the most stable. Identify any [[chair]] rings and any [[boat]].
#Measure some dihedral angles to see if the [[staggered]] relationships hold (i.e. for such a relationship, the dihedral angle should be close to 60 degrees).
#A key step in Woodward's famous synthesis of [http://en.wikipedia.org/wiki/Cortisone cortisone] is a quinone+butadiene [[Diels-Alder]] reaction to give a cis-decalin (left), with an assumption that [[epimerisation]] to a trans-decalin is thermodynamically favourable. [[Image:Cortisone.gif|thumb|left|cis Cortisone]]Can you verify whether the trans-isomer is indeed more stable? Its not so obvious, since this compound has two extra double bonds in the rings and six sp2 centres which might perturb things.
#[[Image:App.gif|thumb|right|trans Decalin]]The two diastereomeric ''trans''-decalin tosylates react quite differently with NaBH4. Construct models for both isomers (use methoxy as a model for the Tosyl group) and from the [[antiperiplanar]] alignments of bonds that you can find in each isomer, can you make a connection to the reactivity of each form? Consider very carefully where you would put a lone pair located on the nitrogen (i.e. include the N-Lp "bond" in your antiperiplanar alignments) asuming the this atom is tetrahedral rather than planar. Does this lone pair play any part in either reaction in this position?. Note that the relative energy of the axial/equatorial N-Methyl group will not be an accurate reflection of any [[antiperiplanar]] alignments, since these are predominantly electronic in origin, and this mechanics method does not take these into account.
##'''Optional:''' The second (elimination) reaction is very slow compared to the first. Discuss with tutors why this might be so (for Hints, see [[organic:entropy|here]] or [[organic:ngp|here]]).
##'''Optional''': These reactions do not appear to occur for the corresponding ''cis''-decalins6. Why not?

|}

==== References and Footnotes ====
# D. H. R. Barton, ''Interactions between non-bonded atoms, and the structure of cis-decalin'', ''J. Chem. Soc.'', '''1948''', 340-342. {{DOI|10.1039/JR9480000340}}
#[http://en.wikipedia.org/wiki/Decalin Wikipedia article]
# For a modern application of mechanics to this molecule, see J. M. A. Baas, B. Van de Graaf, D. Tavernier, and P. Vanhee, ''Empirical force field calculations. 10. Conformational analysis of cis-decalin'', ''J. Am. Chem. Soc.'', '''1981''', ''103'', 5014 - 5021; {{DOI|10.1021/ja00407a007}}.
# For a video-Podcast of Barton and Woodward (and other Nobel prize winners), subscribe [http://www.ch.ic.ac.uk/video/index.rss here]
# R. B. Woodward, F. Sondheimer, and D. Taub, ''The total Synthesis of Cortisone'', ''J. Am. Chem. Soc.'', '''1951''', ''73'', 4057 - 4057. {{DOI|10.1021/ja01152a551}}.
# P.-W. Phuan and M. C. Kozlowski, ''Control of the Conformational Equilibria in Aza-cis-Decalins: Structural Modification, Solvation, and Metal Chelation'', ''J. Org. Chem.'', '''2002''', ''67'', 6339 - 6346; {{DOI|10.1021/jo025544t}}

=== Menthone/''iso''menthone and Bridgehead enols: Thermodynamic vs Kinetic Control Part 1.===

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#[[Image:Menthone.gif|thumb|right|Menthone]] Beckmann (of rearrangement fame) in 1889 dissolved optically active levorotatory (-) (S,R)-menthone ([α]D -28°) in conc. sulfuric acid, followed by quenching on ice to give what Beckmann assumed was pure (and what we would nowadays call [[diastereomeric]]) (+) (R,R)-isomenthone, [α]D +28°. He suggested for the first time that such an isomerisation, involving epimerisation at the asymmetric centre next to the keto group, proceeded via an intermediate enol in which the tetrahedral asymmetric carbon becomes planar. But this famous (perhaps even notorious2) early example of a [[reaction mechanism]] makes an interesting assumption, which can be tested by molecular modelling.
# Two possible enols can be formed, only one of which allows the [S] asymmetric carbon to become planar and then protonate to the [R] epimer. This is the so called [[thermodynamic enol]]. The other, which leaves the [S]-centre untouched is the [[kinetic enol]]. Find out if simple molecular modelling correctly predicts that the thermodynamic enol is indeed the more stable of the two. '''Hint:''' Model the enol and '''not''' the ketone. Consider carefully any conformational isomers possible.
# Given that the optical rotation3 of pure (+)-isomenthone is now known to be [α]D +101° rather than +28°, we can infer that Beckmann's product contains only 43% isomenthone and hence still contains 57% of original menthone, corresponding to an equilibrium constant of K= 0.75. This can be related to a (free energy) difference using the equation ΔG = -RT ln K, or ΔG = 0.7 kJ/mol (menthone being lower in energy by this amount compared to isomenthone). Can this energy difference be verified using molecular mechanics modelling? Can you explain why menthone is the more stable? (For another hint, or possibly a fright, visit [http://chemistry.gsu.edu/glactone/modeling/Luise/organic/cychexon.html this page]).
|}

==== References and footnotes ====
# E. Beckmann, ''Annalen'', '''1889''', ''250'', 322. {{DOI|10.1002/jlac.18892500306}}.
# Many of Beckmann's misconceptions were corrected by O. Wallach, ''Annalen'', '''1893''', ''276'', 296. {{DOI|10.1002/jlac.18932760306}}. The notoriety is because the coincidence of equal but opposite optical rotations obtained in this experiment led Beckmann to believe that he had obtained the [[enantiomer]] of menthone, and not as we now know, the impure (R,R) [[diastereomer]]. It should be borne in mind that the concept of tetrahedral and asymmetric carbon was only 15 years old at this time (see [http://en.wikipedia.org/wiki/Jacobus_van_%27t_Hoff Jacobus Henricus van't Hoff] and [http://en.wikipedia.org/wiki/Achille_Le_Bel Joseph Achille Le Bel]). Nevertheless confusion over this aspect persisted for some time after, and was often evident in the writings of even very famous chemists of the time (and Beckmann was very famous)!.
#[http://en.wikipedia.org/wiki/Menthone Wikipedia article]
# From about 1890-1935, mechanistic organic chemistry was born. In the absence of UV, IR, NMR, MS and X-Ray techniques, the [http://en.wikipedia.org/wiki/Polarimeter polarimeter] occupied a pivotal role. Many of the great discoveries in reaction mechanisms (keto-enol tautomerism as seen here, [[Organic:tutorial:meerwein| carbocations]], the Walden inversion, etc) relied on polarimetric measurements.
# A notorious modern example of (unwanted) epimerisation of a ketone is [http://en.wikipedia.org/wiki/Thalidomide Thalidomide], where one epimer inhibits morning sickness in pregnant women, and the other epimer is teratogenic, causing fetal abnormalities. The equilibrium in this case does not require conc. sulfuric acid, but can occur at physiological pH.

== Additional Molecular modelling Coursework ==

Please feel free to try these problems in your own time, and to discuss these with your organic tutors and lecturers. Note also that the relevant lectures may occur in the spring as well as autumn terms.
=== Axial/Equatorial preferences in cyclohexane and cyclohexanone and Hydrogen Bonding ===
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#Construct a chair cyclohexane and replace firstly one of the [[axial]] hydrogens with the following groups: '''methyl''', '''t-butyl''', '''OH'''. Calculate the energy of the axial isomer.
# Then repeat (either by deleting/redrawing or by moving) for the equatorial forms. Compare the energies of the two isomers. Does any energy difference increase with the size of the group? Does OH fit into this in terms of size?
# [[Image:Thiomethylcyclohexanone.gif|right|thumb|thiomethyl cyclohexanone]]The dissolving metal reduction of cyclohexanones in a protic solvent (i.e. one capable of hydrogen bonding) is thermodynamically controlled and gives the more stable, equatorial alcohol. In fact, its probably the alkoxide that is the product, not the free alcohol. It is thought the alkoxide is actually a lot larger than the alcohol, accounting for the substantial equatorial preference. Can you think why its larger? [Ghemical cannot in fact model this, since the force field does not include parameters for the alkoxide anion].
# Determine the axial/equatorial preference of 2-methylthio-cyclohexanone (Hint: there are many conformations possible, and you should try a few to see if you can get the lowest).
|}
==== References and Footnotes ====

# A. H. Lewin and S. Winstein, ''NMR. Spectra and Conformational Analysis of 4-Alkylcyclohexanols'' ''J. Am. Chem. Soc.''; '''1962''', ''84'', 2464 - 2465; {{DOI|10.1021/ja00871a049}}
#F. R. Jensen and L. H. Gale, ''The Conformational Preference of the Bromo and Methyl Groups in Cyclohexane by IR Spectral Analysis'', ''J. Org. Chem.'', '''1960''', ''25'', 2075 - 2078. {{DOI|10.1021/jo01082a001}}
# K. B. Wiberg, J. D. Hammer, H. Castejon, W. F. Bailey, E. L. DeLeon, and R. M. Jarret, ''Conformational Studies in the Cyclohexane Series. 1. Experimental and Computational Investigation of Methyl, Ethyl, Isopropyl, and tert-Butylcyclohexanes'', ''J. Org. Chem.'', '''1999''', ''64'', 2085 - 2095; {{DOI|10.1021/jo990056f}}. The salient point here is that the [[enthalpy]] and [[entropy]] of this series differ in their trends.
# Just when you are starting to think that things are quite simple, along comes the observation: S. E. Biali, ''Axial monoalkyl cyclohexanes'', ''J. Org. Chem.'', '''1992''', ''57'', 2979 - 2980; {{DOI|10.1021/jo00037a001}}
# And this one with knobs on: ''In all-trans-1,2,3,4,5,6-hexaisopropylcyclohexane, all the alkyl groups are located at axial rather than equatorial positions: O. Golan, Z. Goren, and S. E. Biali, ''Axial-equatorial stability reversal in all-trans-polyalkylcyclohexanes'', ''J. Am. Chem. Soc.'', '''1990''', ''112'', 9300 - 9307. {{DOI|10.1021/ja00181a036}}.
#J. A. Anderson, K. Crager, Kelly, L.Fedoroff, G. S. Tschumper, Gregory S. ''Anchoring the potential energy surface of the cyclic water trimer.'' ''J. Chem. Physics'', '''2004''', ''121'', 11023-11029. {{DOI|10.1063/1.1799931}}.
#R. R. Fraser, N. C. Faibish, ''On the purported axial preference in 2-methylthio- and 2-methoxycyclohexanones: steric effects versus orbital interactions'', ''Can. J. Chem.'', '''1995''', ''73'', 88-94.
=== How to induce room temperature hydrolysis of a peptide ===
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[[Image:amide-cleavage.png|thumb|right|Peptide hydrolysis]] This introduces a further example of how simple conformational analysis can quickly rationalize kinetic behaviour. At neutral pH and 25° the half life for hydrolysis of a peptide bond is around 500 years (and thank goodness, or we would ourselves all rapidly hydrolise to a mush!). Some enzymes however can achieve this in less than 1 second, an acceleration of 1013! Organic chemists are not quite so clever, but they can achieve room temperature hydrolysis of a peptide in 21 minutes by careful conformational design. The two isomers shown on the right differ only in their stereochemistry, one hydrolysing quickly, the other slowly. Build a model of each compound, and calculate two isomers for each, varying in whether the ring N-substituent is oriented axial or equatorial with respect to the decalin ring. On the basis of your two pairs of energies, can you rationalise the observed kinetic behaviour? Do you know why both of these compounds take very much less than 500 years to hydrolise the peptide bond?

'''Hint1:''' Use the chair-chair conformation for cis-decalin as your template for constructing this system.

'''Hint2:''' When constructing your models, think if there are any hydrogen bonds that might stabilize the structure!

'''Hint3:''' Hydrolysis can only occur when the OH group can approach the carbonyl of the peptide bond close enough to react, and at the right angle of approach.
|}

==== Reference ====

# M. Fernandes, F. Fache, M. Rosen, P.-L. Nguyen, and D. E. Hansen, 'Rapid Cleavage of Unactivated, Unstrained Amide Bonds at Neutral pH', ''J. Org. Chem.,'' '''2008''', ASAP: {{DOI|10.1021/jo800706y}}

=== Caryophyllene: The phenomenon of Atropisomerism ===

# [[Image:caryophyllene-ketone.gif|thumb|right|Caryophyllene ketone]] [http://en.wikipedia.org/wiki/Caryophyllene Caryophyllene], a constituent of many essential oils, include clove oil, has a [[trans]] alkene contained in a 9-membered ring. One interesting property is that it has 4 [[diastereoisomers]] possible, originating from a total of three asymmetric centres present in the molecule. Two of these are conventional chiral centres, one is present in the form of a disymmetric trans double bond. To understand why such a bond can result in two configurations, one must appreciate that (concurrent) rotation about the two C-C single bonds adjacent to the alkene is in fact restricted, because to the hydrogen labelled Ha cannot easily pass by the edge of the 4-membered ring. Construct this molecule (in fact the ketone rather than the alkene) and optimize its geometry. Note in particular that the ring junction is ''trans'' and not ''cis''.
# You will find you may well have obtained one of two forms. In the first, the Ha hydrogen will be opposite the C=O group, in the other it will be adjacent to it. Record the energy of whatever form you got. At the end of the course, we will try to find the ''winner'' with the lowest energy (this is not as trivial as it sounds!).
# Next, take your structure, and try to ''flip'' the [[trans]] alkene bond around so that eg if the methyl were previously pointing up, now it will point down. You may find a combination of erasing/redrawing or of moving, will accomplish this. You may also find another trick useful, of deleting all hydrogens, and then re-sprouting them back on again. Re-optimise your structure and compare the energy with your first isomer.
# Another feature of this model is that you can judge which group is in the so-called shielded region of the carbonyl group magnetic anisotropy. Using this information, you can see if there are any anomalous 1H chemical shifts that might need explaining!

==== References ====
# M. Clericuzio, G. Alagona, C. Ghio, and L. Toma, ''Ab Initio and Density Functional Evaluations of the Molecular Conformations of -Caryophyllene and 6-Hydroxycaryophyllene'', ''J. Org. Chem.'' '''2000''', ''65'', 6910 - 6916. {{DOI|10.1021/jo000404+}}.
#[http://en.wikipedia.org/wiki/Caryophyllene Wikipedia article]
# For a recent application of this phenomenon, see P. C. Bulman Page, B. R. Buckley, S. D.R. Christie, M. Edgar, A. M. Poulton, M. R.J. Elsegood and V. McKee, ''A new paradigm in N-heterocyclic carbenoid ligands'', ''J. Organometallic Chem.'', '''2005''', ''690'', 6210-6216. D {{DOI|10.1016/j.jorganchem.2005.09.015}}.

=== Germacrene: Conformational analysis of medium sized rings ===

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# [[Image:Germacrene.gif|thumb|right|Germacrene and the thermal reaction product]]Germacrene is a natural product with a ten-membered ring; it has the triene structure shown. Assuming that it adopts a crown conformation, build a three-dimensional model.
# On heating, germacrene is converted into one of the stereoisomers of the divinylcyclohexane, via a [3,3] sigmatropic pericyclic reaction. Predict from your model for Germacrene whether the product will have the two vinyl groups [[cis]] or [[trans]] to one another.
|}

==== References ====

# K. Shimazaki, M. Mori, K. Okada, T. Chuman, H. Goto, K. Sakakibara and M. Hirota, ''Conformational analyses of periplanone analogs by molecular mechanics calculations'', '' J. Chem. Ecology'', '''1991''', ''17'', 779-88. {{DOI|10.1007/BF00994200}}.
# H. Shirahama, E. Sawa and T. Matsumoto, ''Conformational aspects of germacrene B. Are the germacrenes resolvable ?'', ''Tetrahedron Lett.'', '''1979''', ''20'', 2245-2246. {{DOI|10.1016/S0040-4039(01)93687-1}}. See also {{DOI|10.1039/P19750002332}} for an explanation of the selective epoxidation of germacrene.

=== Xestoquinone: Regio and Stereoselectivity in the Diels Alder reaction===

# [[Image:xestoquinone.gif|thumb|right|Xestoquinone precursor]] This compound is a precursor to a natural product called Xestoquinone. It has four alkene groups, which can individually be considered as the alkene component in a π2s + π4s [[Diels Alder]] [[cycloaddition]]. The pair of alkenes ''a+b'' or ''c+d'' can also act as the diene component in the π2s + π4s [[Diels Alder]] [[cycloaddition]]. Construct a model of the product of e.g. forming a bond between alkene ''a'' or alkene ''b'' and diene ''c+d'', and then reverse the addition by using either ''c'' or ''d'' adding to the diene ''a+b''. The stereochemistry of addition should always be [[suprafacial]], i.e. preserving the stereochemical relationships of the alkenes. You should very carefully check that this is so in your final model.
# Whilst you should stop at '''two''' models, it is possible to construct many more. For example, one might be able to add to either the ''top'' face of alkene ''b'' or to its ''bottom'' face. Identify the model with the lower energy, and save it for the end of the workshop. We will identify the isomer of lowest energy from everyone's results, this being a communal [[Monte Carlo]] experiment to find the [[global minimum]].

==== References ====

#[http://en.wikipedia.org/wiki/Diels-Alder_reaction Wikipedia article]
#For the original literature on this synthesis, see R. Carlini, K. Higgs, C. Older, S. Randhawa, and R. Rodrigo, ''Intramolecular Diels-Alder and Cope Reactions of o-Quinonoid Monoketals and Their Adducts: Efficient Syntheses of (±)-Xestoquinone and Heterocycles Related to Viridin'', ''J. Org. Chem.'', '''1997''', ''62'', 2330 - 2331. {{DOI|10.1021/jo970394l}} where you can check to see which isomers actually do form!

=== Aldol Reaction and anti-Bredt Rings ===

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# [[Image:Aldol.gif|thumb|right|Aldol Reaction]]When the diketone shown is treated with base, it undergoes an aldol condensation. Two obvious possibililties are elimination of the combination Ha and Oa, or of the alternative combination Hb and Ob. In fact, only a single product is formed. On the basis of energies for both products, can you predict which one is actually formed?
# Measure a few dihedral angles, ie to find out how planar the alkene present is. Does this suggest a reason why one isomer is less stable than the other?
# There is a third very remote structural possibility. If you have time, verify that this third product truly is unlikely.
|}

==== References ====
#[http://en.wikipedia.org/wiki/Bredt's_Rule Bredt's Rule]
# I. Novak, ''Molecular Modeling of Anti-Bredt Compounds'', ''J. Chem. Inf. Model.'', '''2005''', ''45'', 334 - 338. {{DOI|10.1021/ci0497354}}
# See also this article A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, ''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins'', ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}} in conjunction with Project 9.

=== Conformational Preference for asymmetric hydride reduction of a ketone ===

# [[Image:Felkin.gif|thumb|right|Asymmetric hydride reduction]]The hydride ([http://en.wikipedia.org/wiki/Lithium_aluminium_hydride BH4, AlH4, etc]) reduction of the ketone shown here is stereospecific, resulting in an alcohol with the stereochemistry shown (known as the [http://en.wikipedia.org/wiki/Chiral_induction Cram or the Felkin-Anh] rule). Construct a model of the ketone and establish which of at least two conformations is the lowest in energy.
# If the hydride anion is delivered from the least hindered position, is the conformation you have consistent with the stereochemistry shown for the product?
# You can see from Ref 4 that the situation can be far more complex, depending on many other factors.

====References ====
# [http://en.wikipedia.org/wiki/Chiral_induction Wikipedia article]
# D. J. Cram and D. R. Wilson, ''Studies in Stereochemistry. XXXII. Models for 1,2-Asymmetric Induction'', ''J. Am. Chem. Soc.'', '''1963''', ''85'', 1245 - 1249. {{DOI|10.1021/ja00892a008}}.
# Y. Yamamoto, K. Matsuoka, and H. Nemoto, ''Anti-Cram selective reduction of acyclic ketones via electron transfer initiated processes'', ''J. Am. Chem. Soc.'', '''1988''', ''110'', 4475 - 4476; {{DOI|10.1021/ja00221a093}}.
# A. Mengel and O. Reiser, ''Around and beyond Cram's Rule'', ''Chem. Rev.'', '''1999''', ''99'', 1191 - 1224. {{DOI|10.1021/cr980379w}}.

=== Enantiomers vs Diastereomers Part 2: NMR Coupling constants ===

#[[Image:karplus.gif|thumb|Axial-equatorial interconversion|right]]In Project 2.2 above, we saw how the energies of diastereomeric compounds could be compared with the corresponding enantiomers. In this extension, we show how molecular modelling can cast light on the conformation adopted by 2-ethyl-4-methyl-1-oxa-cyclopentane-3-carboxylic acid estimated using measured 1H NMR coupling constants. The (2S,3S,4S) diastereomer has couplings of 3JH2,H3 8.3 Hz and 3JH3,H4 9.8 Hz. Two possible conformations of this diastereomer are shown on the right. They differ in that one has Et axial, and Me/COOH equatorial, and the other Et equatorial and Me/COOH axial.
#[[Image:karplus.jpg|Karplus plot|thumb|left]]By calculating the geometries of both conformations, and measuring the dihedral angle H2-C-C-H3 and H3-C-C-H4, one can assess by using the Karplus equation (left, taken from Ref 2 and relevant for a cyclopentane, but the values for which might be modified by the presence of electronegative substituents), which conformation leads to the best agreement between the calculated angle and the measured coupling constants (Hint: on the basis of the predicted couplings, you should be able to eliminate one of the two conformations shown for this molecule).
#[[Image:5-circulene.gif|thumb|5-circulene|right]]In Project 2.2 we also introduced molecules such as helicenes and circulenes. The 1H NMR of the [5]-circulene shown to the right revealed a complex spectrum at δ 2.98 ppm and again at 3.75 ppm. On the face of it, the four protons labeled Ha and Hb should all be equivalent, and the spectrum should be a single peak, not two complex multiplets. Indeed, if the NMR is recorded at high temperatures, this is exactly what is observed. By constructing a model of the [5]-circulene shown, can you explain why at normal temperatures, the NMR spectrum is so complex? 
#[[Image:Lab_expt.jpg|thumb|Synthesis lab experiment|right]]A practical application of this technique is to determine the stereochemistry of the product of the reaction between E,E-2,4-hexadien-1-ol and maleic anhydride. You will have the 1H NMR spectrum of your sample recorded, and evident from that will be peak multiplicities of the various proton resonances. You should endeavour from your analysis to come up with a suggestion for the structure of compound '''Y''', and from this, estimates of the numerical values (but not the signs) of the 2J and 3J couplings visible. Now using the techniques described above, construct a model of your proposed structure for '''Y'''. Measure the dihedral angles for all the 3J couplings, and very approximately estimate what the corresponding 3J might be from the diagram above. Does this help you assign the stereochemistry of the product?
#'''Advanced topic''': Part of the spectroscopic analysis of the compound '''Y''' involves interpreting the IR spectrum. Theory can be used in fact to simulate the full IR spectrum. In section 5.3 below, you will find instructions on how to use the model you have calculated here to initiate a so called '''density functional''' calculation. This will provide you with the required IR simulation. Follow these instructions, and open the resulting .log file in Gaussview. Go to the '''Results''' menu and select '''vibrations'''. The IR spectrum will be displayed. Does it match the one you have recorded for yourself?

==== References ====

#M. Karplus, ''Vicinal Proton Coupling in Nuclear Magnetic Resonance'', '' J. Am. Chem. Soc.'', '''1963''', ''85'', 2870 - 2871; {{DOI|10.1021/ja00901a059}}
#A. Wu, D. Cremer, A. A. Auer, and J. Gauss, ''Extension of the Karplus Relationship for NMR Spin-Spin Coupling Constants to Nonplanar Ring Systems: Pseudorotation of Cyclopentane'', ''J. Phys. Chem. A,'', '''2002''', ''106'', 657 -667; {{DOI|10.1021/jp013160l}}
#C. A. Stortz and M. S. Maier, ''Configurational assignments of diastereomeric γ-lactones using vicinal H–H NMR coupling constants and molecular modelling'', ''J. Chem. Soc., Perkin Trans. 2'', '''2000''', 1832 - 1836. {{DOI|10.1039/b003862h}}
# A. H. Abdourazak, A. Sygula, and P. W. Rabideau ''Locking the bowl-shaped geometry of corannulene: cyclopentacorannulene'', ''J. Am. Chem. Soc.'', '''1993''', ''115'', 3010 - 3011. {{DOI|10.1021/ja00060a073}}

=== Bridgehead enols: Thermodynamic vs Kinetic Control Part 2.===
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#[[Image:Bredt.gif|thumb|right|Brendanone]] The ketone Brendan-2-one shown right exhibits unusual behaviour.6 When treated with NaOD/MeOD, deuterium substitution occurs easily and rapidly only in position Hb. Enolisation must of necessity form a bridgehead double bond (''anti-Bredt''), but clearly one isomer is more stable than the other possible form. Does molecular modelling predict this correctly?
#The unusually facile enolisation of this ketone (given that it forms an anti-Bredt enol) can also be investigated by molecular modelling. '''Measure''' the dihedral angle between the C-Ha or C-Hb vector and the carbonyl group. Assuming that the ''ideal'' angle for proton removal is around 90°, which proton is better set up for abstraction? Might this be kinetic rather than thermodynamic control?
#[[Image:Cortisone.gif|thumb|right|Cortisone]]One could also revisit Problem 2.3.3 above. Here, proton abstraction forms an enol which eventually epimerises the bridgehead position to form a ''trans'' ring junction. Why should this proton be particularly easy to remove? From what you have learnt above, would this be for kinetic or for thermodynamic reasons (or both?). Are all the relevant effects modelled using the mechanics approach or is consideration of the electrons also necessary?
|}
==== References and Footnotes====

# A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, {{doi-inline|10.1021/ja00837a043|''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins''}}, ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}}.

===Sulfonylation of Naphthalene: Thermodynamic vs Kinetic Control Part 3.===

[[Image:Sulfonylation.gif|right|thumb|Sulfonylation of naphthalene]]The sulfonylation of naphthalene using sulfuric acid is a good example of a mechanism combining both steric and electronic influences. The Molecular mechanics method intrinsic to the Ghemical program can only model the former, and not the latter. It is a worthwhile exercise to establish whether this anticipated deficiency does indeed lead to a model which only partially explains experiment.

It has been known for some time that treating naphthalene with sulfuric acids at low temperatures produces mostly substitution at the 1-position of the naphthalene. Heating the reaction mixture, or conducting the reaction at elevated temperatures produces mostly the 2-isomer. This is indeed a classic example of [[kinetic]] vs [[thermodynamic]] control, the 1-isomer being the kinetic one and the 2-isomer the thermodynamic one. To model the kinetic reaction, we have to inspect the [[transition state]] for the reaction, and here we can approximate this by the [[Wheland Intermediate]]. To model the thermodynamic reaction, we have to inspect the product (rather than the transition state) for the reaction.

#Build models for all four species shown in the diagram on the right. For the two products, define ''conjugated'' bond types for all the ring bonds, and define the sulfonyl group with two S=O double bonds and one S-O single bond. Take care to optimise the conformation of the sulfonyl group with respect to the aromatic ring. For the two Wheland intermediates, the limitations of Ghemical will force us to ''cheat''. Ghemical does not have parameters for a carbocation. So define the C2-C3 bond as conjugated (for the 1-Wheland intermediate). When you '''add hydrogens''' it will in fact add a second hydrogen to C2. Delete this one hydrogen. Ghemical will calculated the energy regardless of not knowing C2 is actually a carbonium ion! For the 2-Wheland intermediate, ensure that you use '''exactly''' the same number of ''conjugated'' bond types as you did for the 1-isomer (the two models in a mechanics sense are only comparable if you have the same total number of bond types in each model). You will have to decide whether these (undoubted) approximations have produced reasonable models or not (is the naphthalene framework planar for example, as it should be?).
#Record the pairs of energies (two for the 1- and 2-products, and two for each preceeding transition (Wheland) state.
#By turning the spacefilling representation on, which of the two products has the least unfavourable steric interactions between the sulfonic acid group and any adjacent hydrogens? Does this match with their relative energies?
#Do any unfavourable steric interactions observed in the product(s) also exist in the Wheland intermediates (as models for the transition states)?
#The relative stability of the Wheland intermediates is always assumed to be an '''electronic''' phenomenon. The conventional explanation is that the 1-Wheland isomer is stablized by both one aromatic ring '''and''' an allyl cation conjugated to it. The 2-Wheland isomer is stabilised by one aromatic ring conjugated to a secondary carbocation and an alkene. This type of ''cross conjugation'' is conventionally assumed to be less favourable. Does a purely mechanical approach to this problem reproduce this expectation? Or is this ''mechanical'' approximation to an ''electronic'' model too severe? It seems a good point to stop this course, since the next time you will build models, it will indeed be using methods which properly approximate the electronic components.
====References====

#R. Lantz, ''Mechanism of the monosulfonation of naphthalene'', ''Compt. Rend''. '''1935''', ''201'', 149-52.
#G. W. Wheland, ''A Quantum Mechanical Investigation of the Orientation of Substituents in Aromatic Molecules'', ''J. Am. Chem. Soc.'' '''1942''', ''64'', 900 - 908; {{DOI|10.1021/ja01256a047}}
#C. A. Reed, N. L. P. Fackler, K-C. Kim, D. Stasko, D. R. Evans, P. D. W. Boyd, and C. E. F. Rickard, ''Isolation of Protonated Arenes (Wheland Intermediates) with BArF and Carborane Anions. A Novel Crystalline Superacid'', ''J. Am. Chem. Soc.'' '''1999''', ''121'', 6314 - 6315 {{DOI|10.1021/ja981861z}}

== Coursework not to be attempted at any time: Antimodelling Molecules ==

The following represent molecules that should '''not''' be modelled under any circumstances! You should instead attempt to '''NAME''' them.

[[Image:Contraceptive.gif|Contraceptive (NO in every conceivable position)]] [[Image:Paradise.gif|Paradise lost]] [[Image:Synoptic.gif|Synoptic]] [[Image:Cisters.gif|Cisters]] [[Image:Transisters.gif|Transisters]] [[Image:Metaphor.gif|Metaphor]] [[Image:Metastasis.gif|Metastasis]] [[Image:Cyclone.gif|Cyclone]] [[Image:Anticyclone.gif|Anticyclone]] [[Image:Arsole.gif|Arsole]] [[Image:Orthodox.gif|Orthodox]] [[Image:Synthesis.gif|Synthesis and Antithesis]] [[Image:Aphrodisiac.gif|Name this yourself. Does Meg Ryan spring to mind?]] [[Image:Cyclops.gif|Cyclops]] [[Image:Paradox.gif|Paradox]] [[Image:Transparent.gif|Transparent]] [[Image:Encyclopedia.gif|Encyclopedia]] [[Image:Maths.jpg|Find X]] [[Image:VanderMaxforce.jpg|150px|Max Whitby stuck to a strangely attractive Lamp Post]] [[Image:nanoballet.jpg|200px|Nanoballet dancer]] [[Image:NanoCossacks.jpg|200px|NanoCossacks]]
[[Image:Paralysis.png|500px|Paralysis]] [[Image:Mcdonalds.png|350px|Old McDonald's Molecule: ene-yne-ene-yne-one]]
[[Image:Silenedione.png|350px|Celine Dion]]

If you know of any other antimodelling molecules, please add them here!

====Acknowledgements ====

Some of these cartoons are from [http://www.nearingzero.net/sci_chemistry.html here], and six are original. A superb collection of '''''silly names''''' is maintained
by [http://www.chm.bris.ac.uk/sillymolecules/sillymols.htm Paul May] [[Organic:Model_answers|.]] See {{DOI|10.1021/jo0349227}} for the nanoputians.

----
[[Second_Year_Modelling_Workshop|Back to introduction]]
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Coursework

2010-10-15T15:27:49Z

Nm607: /* Coursework not to be attempted at any time: Antimodelling Molecules */

[[Second_Year_Modelling_Workshop|Back to introduction]]
----
== Molecular modelling Coursework to be attempted during Scheduled Sessions ==

These projects are arranged in increasing order of difficulty, and time taken to complete. You should do as many as you can in the 2 hour session allocated to you, and return to finish the rest if you wish at your convenience. At the end of the session, we will conduct a ''number auction''. For each project, the bidding will start with the first volunteer offering an energy for the system (or one of the isomers). If anyone has a lower energy for that molecule, they will then bid that energy. The winner will be the one with the lowest energy.

=== Conformational analysis I: Chair and Boat-like conformations of Cyclohexane ===
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#Construct '''[[chair]]''' and '''[[boat]]'''-like '''[[conformation]]s''' of [[cyclohexane]]. Compare the energies of both forms.
#Check carefully if your boat really is a boat, or whether it has any apparent distorsion.
#Try changing one or more of the CH2 groups into an oxygen and see if that affects things.
#For the record, the point group symmetries of the various species which may be involved are D3d for the chair conformation, C2v for a boat geometry, and D2 for any twisted boat form. Is any of these forms '''chiral'''?
#The molecule on the left is called '''chiralane'''. Are its rings boats or chairs?
|}
====References ====
# The first suggestion of two forms for cyclohexane goes as far back as H. Sachse, ''Chem. Ber'', 1890, '''23''', 1363 and ''Z. Physik. Chem.'', 1892, 10, 203. This is nicely explained [http://www.chem.yale.edu/~chem125/125/history/Baeyer/Sachse.html here]. E. Mohr, ''J. Prakt. Chem.'', 1918, '''98''', 315 and ''Chem. Ber.'', 1922, '''55''', 230, translated Sachse's argument into a pictorial one.
# The article that put [[conformational analysis]] on the map: D. H. R. Barton and R. C. Cookson, ''The principles of conformational analysis'', ''Q. Rev. Chem. Soc.'', '''1956''', ''10'', 44. {{DOI|10.1039/QR9561000044}}
#[http://en.wikipedia.org/wiki/Chair_conformation Wikipedia article]
#D. A. Dixon and A. Komornicki, ''Ab initio conformational analysis of cyclohexane'', ''J. Phys. Chem.'', '''1990''', ''94'', 5630 - 5636; {{DOI|10.1021/j100377a041}}.
#A nice exploration of the potential energy surfaces for cyclohexane can be viewed [http://www.springer.com/carey-sundberg/cyclohex/cyclohex.php here].
# For a more modern application of this technique, see I. Columbus, R. E. Hoffman, and S. E. Biali, ''Stereochemistry and Conformational Anomalies of 1,2,3- and 1,2,3,4-Polycyclohexylcyclohexanes''. ''J. Am. Chem. Soc.'', '''1996''', ''118'', 6890 - 6896; {{DOI|10.1021/ja960380h}}.
# The second molecule shown in this section is called [6.6]chiralane. It is peculiar for having many six-membered saturated rings, all of them as twist-boats rather than chairs! (a chair has a plane of symmetry, a twist boat only axes, which of course allows it to be chiral). See [http://petitjeanmichel.free.fr/itoweb.petitjean.graphs.html#CHIR here] for more details.
# More detail on the conformation of rings (and acyclic systems) will be found in the [http://www.ch.ic.ac.uk/local/organic/conf/ lecture course] on the topic to be given in the spring term.

=== Enantiomers vs Diastereomers Part 1: Butanes and Helicenes. ===

This problem illustrates, using models, the difference between an enantiomer and a diastereomer.

#[[Image:diastereo.gif|thumb|right|2-bromo-3-chlorobutane]][[Image:pentahelicene.gif|thumb|right|Pentahelicene]]The compound 2-bromo-3-chlorobutane has two [[chiral]] centres, and four isomers (22) are therefore possible. Calculate all four isomers, and for each be careful to label each of the two stereo centres '''R''' or '''S''' as you go. For each of the four isomers '''R,R''', '''S,S''', '''R,S''', '''S,R''' you will have to think about whether you have obtained the lowest energy [[conformer]].
#Can your four energies be grouped in any way? You should think about the expected difference between '''enantiomers''', '''diastereomers''' and '''conformers'''.
{|
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#Construct some helicenes (pentahelicene or [5]helicene is shown on the right), using '''conjugated''' bonds for all the ring bonds. Benzene, naphthalene, phenanthrene and benzophenanthrene are in fact the first four members of this series. At what point in this series can you detect helicity cropping up? This is manifested by a non-planar helical wind of the molecule. If you do detect it, note how the wind is either left or right handed, ie the two forms are '''enantiomers''' of each other. Try displaying the molecule in '''spacefill mode''' (see above) to see if you can identify the source of the helicity. (Note: the smallest helicene which can be resolved experimentally into enantiomers is in fact [5]helicene]).
#The higher helicenes are well known (up to about [14]helicene) and amongst the ''most chiral'' molecules known (in terms of how much they rotate the plane of polarised light).
#[7]circulene is a known molecule, with a unique saddle-shaped structure, shown on the left (there is no real need for you to build this model, but do please do so if you are curious). [http://en.wikipedia.org/wiki/Graphene Graphene] is a related polymeric molecule, of much topical interest in the semi-conducting and other industries (Nobel Prize 2010).
|}
==== References ====

#[http://en.wikipedia.org/wiki/Diastereomer Wikipedia article on Diastereomers]
#[http://en.wikipedia.org/wiki/Helicene Wikipedia article on Helicenes and related molecules]
#R. H. Janke, G. Haufe, E.-U. Würthwein, and J. H. Borkent, ''Racemization Barriers of Helicenes: A Computational Study'', ''J. Am. Chem. Soc.'', '''1996''', ''118'' 6031 - 6035 {{DOI|10.1021/ja950774t}}

=== Conformational analysis II: ''cis'' and ''trans''-decalins, Steroids and Podcasts! ===
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# [[Image:cis-decalin.gif|thumb|right|cis Decalin]]This is the famous molecule that started the whole molecular mechanics modelling ball rolling. [http://www.ch.ic.ac.uk/video/barton/barton1.pdf Barton] in 1948 sought to find out which [[conformation]] of ''cis''-decalin was the most stable (see [http://www.ch.ic.ac.uk/video/barton/index_qt.html here] for video). You should be able to find at least three conformations of this molecule. Try locating these, and conclude which is the most stable. Identify any [[chair]] rings and any [[boat]].
#Measure some dihedral angles to see if the [[staggered]] relationships hold (i.e. for such a relationship, the dihedral angle should be close to 60 degrees).
#A key step in Woodward's famous synthesis of [http://en.wikipedia.org/wiki/Cortisone cortisone] is a quinone+butadiene [[Diels-Alder]] reaction to give a cis-decalin (left), with an assumption that [[epimerisation]] to a trans-decalin is thermodynamically favourable. [[Image:Cortisone.gif|thumb|left|cis Cortisone]]Can you verify whether the trans-isomer is indeed more stable? Its not so obvious, since this compound has two extra double bonds in the rings and six sp2 centres which might perturb things.
#[[Image:App.gif|thumb|right|trans Decalin]]The two diastereomeric ''trans''-decalin tosylates react quite differently with NaBH4. Construct models for both isomers (use methoxy as a model for the Tosyl group) and from the [[antiperiplanar]] alignments of bonds that you can find in each isomer, can you make a connection to the reactivity of each form? Consider very carefully where you would put a lone pair located on the nitrogen (i.e. include the N-Lp "bond" in your antiperiplanar alignments) asuming the this atom is tetrahedral rather than planar. Does this lone pair play any part in either reaction in this position?. Note that the relative energy of the axial/equatorial N-Methyl group will not be an accurate reflection of any [[antiperiplanar]] alignments, since these are predominantly electronic in origin, and this mechanics method does not take these into account.
##'''Optional:''' The second (elimination) reaction is very slow compared to the first. Discuss with tutors why this might be so (for Hints, see [[organic:entropy|here]] or [[organic:ngp|here]]).
##'''Optional''': These reactions do not appear to occur for the corresponding ''cis''-decalins6. Why not?

|}

==== References and Footnotes ====
# D. H. R. Barton, ''Interactions between non-bonded atoms, and the structure of cis-decalin'', ''J. Chem. Soc.'', '''1948''', 340-342. {{DOI|10.1039/JR9480000340}}
#[http://en.wikipedia.org/wiki/Decalin Wikipedia article]
# For a modern application of mechanics to this molecule, see J. M. A. Baas, B. Van de Graaf, D. Tavernier, and P. Vanhee, ''Empirical force field calculations. 10. Conformational analysis of cis-decalin'', ''J. Am. Chem. Soc.'', '''1981''', ''103'', 5014 - 5021; {{DOI|10.1021/ja00407a007}}.
# For a video-Podcast of Barton and Woodward (and other Nobel prize winners), subscribe [http://www.ch.ic.ac.uk/video/index.rss here]
# R. B. Woodward, F. Sondheimer, and D. Taub, ''The total Synthesis of Cortisone'', ''J. Am. Chem. Soc.'', '''1951''', ''73'', 4057 - 4057. {{DOI|10.1021/ja01152a551}}.
# P.-W. Phuan and M. C. Kozlowski, ''Control of the Conformational Equilibria in Aza-cis-Decalins: Structural Modification, Solvation, and Metal Chelation'', ''J. Org. Chem.'', '''2002''', ''67'', 6339 - 6346; {{DOI|10.1021/jo025544t}}

=== Menthone/''iso''menthone and Bridgehead enols: Thermodynamic vs Kinetic Control Part 1.===

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#[[Image:Menthone.gif|thumb|right|Menthone]] Beckmann (of rearrangement fame) in 1889 dissolved optically active levorotatory (-) (S,R)-menthone ([α]D -28°) in conc. sulfuric acid, followed by quenching on ice to give what Beckmann assumed was pure (and what we would nowadays call [[diastereomeric]]) (+) (R,R)-isomenthone, [α]D +28°. He suggested for the first time that such an isomerisation, involving epimerisation at the asymmetric centre next to the keto group, proceeded via an intermediate enol in which the tetrahedral asymmetric carbon becomes planar. But this famous (perhaps even notorious2) early example of a [[reaction mechanism]] makes an interesting assumption, which can be tested by molecular modelling.
# Two possible enols can be formed, only one of which allows the [S] asymmetric carbon to become planar and then protonate to the [R] epimer. This is the so called [[thermodynamic enol]]. The other, which leaves the [S]-centre untouched is the [[kinetic enol]]. Find out if simple molecular modelling correctly predicts that the thermodynamic enol is indeed the more stable of the two. '''Hint:''' Model the enol and '''not''' the ketone. Consider carefully any conformational isomers possible.
# Given that the optical rotation3 of pure (+)-isomenthone is now known to be [α]D +101° rather than +28°, we can infer that Beckmann's product contains only 43% isomenthone and hence still contains 57% of original menthone, corresponding to an equilibrium constant of K= 0.75. This can be related to a (free energy) difference using the equation ΔG = -RT ln K, or ΔG = 0.7 kJ/mol (menthone being lower in energy by this amount compared to isomenthone). Can this energy difference be verified using molecular mechanics modelling? Can you explain why menthone is the more stable? (For another hint, or possibly a fright, visit [http://chemistry.gsu.edu/glactone/modeling/Luise/organic/cychexon.html this page]).
|}

==== References and footnotes ====
# E. Beckmann, ''Annalen'', '''1889''', ''250'', 322. {{DOI|10.1002/jlac.18892500306}}.
# Many of Beckmann's misconceptions were corrected by O. Wallach, ''Annalen'', '''1893''', ''276'', 296. {{DOI|10.1002/jlac.18932760306}}. The notoriety is because the coincidence of equal but opposite optical rotations obtained in this experiment led Beckmann to believe that he had obtained the [[enantiomer]] of menthone, and not as we now know, the impure (R,R) [[diastereomer]]. It should be borne in mind that the concept of tetrahedral and asymmetric carbon was only 15 years old at this time (see [http://en.wikipedia.org/wiki/Jacobus_van_%27t_Hoff Jacobus Henricus van't Hoff] and [http://en.wikipedia.org/wiki/Achille_Le_Bel Joseph Achille Le Bel]). Nevertheless confusion over this aspect persisted for some time after, and was often evident in the writings of even very famous chemists of the time (and Beckmann was very famous)!.
#[http://en.wikipedia.org/wiki/Menthone Wikipedia article]
# From about 1890-1935, mechanistic organic chemistry was born. In the absence of UV, IR, NMR, MS and X-Ray techniques, the [http://en.wikipedia.org/wiki/Polarimeter polarimeter] occupied a pivotal role. Many of the great discoveries in reaction mechanisms (keto-enol tautomerism as seen here, [[Organic:tutorial:meerwein| carbocations]], the Walden inversion, etc) relied on polarimetric measurements.
# A notorious modern example of (unwanted) epimerisation of a ketone is [http://en.wikipedia.org/wiki/Thalidomide Thalidomide], where one epimer inhibits morning sickness in pregnant women, and the other epimer is teratogenic, causing fetal abnormalities. The equilibrium in this case does not require conc. sulfuric acid, but can occur at physiological pH.

== Additional Molecular modelling Coursework ==

Please feel free to try these problems in your own time, and to discuss these with your organic tutors and lecturers. Note also that the relevant lectures may occur in the spring as well as autumn terms.
=== Axial/Equatorial preferences in cyclohexane and cyclohexanone and Hydrogen Bonding ===
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#Construct a chair cyclohexane and replace firstly one of the [[axial]] hydrogens with the following groups: '''methyl''', '''t-butyl''', '''OH'''. Calculate the energy of the axial isomer.
# Then repeat (either by deleting/redrawing or by moving) for the equatorial forms. Compare the energies of the two isomers. Does any energy difference increase with the size of the group? Does OH fit into this in terms of size?
# [[Image:Thiomethylcyclohexanone.gif|right|thumb|thiomethyl cyclohexanone]]The dissolving metal reduction of cyclohexanones in a protic solvent (i.e. one capable of hydrogen bonding) is thermodynamically controlled and gives the more stable, equatorial alcohol. In fact, its probably the alkoxide that is the product, not the free alcohol. It is thought the alkoxide is actually a lot larger than the alcohol, accounting for the substantial equatorial preference. Can you think why its larger? [Ghemical cannot in fact model this, since the force field does not include parameters for the alkoxide anion].
# Determine the axial/equatorial preference of 2-methylthio-cyclohexanone (Hint: there are many conformations possible, and you should try a few to see if you can get the lowest).
|}
==== References and Footnotes ====

# A. H. Lewin and S. Winstein, ''NMR. Spectra and Conformational Analysis of 4-Alkylcyclohexanols'' ''J. Am. Chem. Soc.''; '''1962''', ''84'', 2464 - 2465; {{DOI|10.1021/ja00871a049}}
#F. R. Jensen and L. H. Gale, ''The Conformational Preference of the Bromo and Methyl Groups in Cyclohexane by IR Spectral Analysis'', ''J. Org. Chem.'', '''1960''', ''25'', 2075 - 2078. {{DOI|10.1021/jo01082a001}}
# K. B. Wiberg, J. D. Hammer, H. Castejon, W. F. Bailey, E. L. DeLeon, and R. M. Jarret, ''Conformational Studies in the Cyclohexane Series. 1. Experimental and Computational Investigation of Methyl, Ethyl, Isopropyl, and tert-Butylcyclohexanes'', ''J. Org. Chem.'', '''1999''', ''64'', 2085 - 2095; {{DOI|10.1021/jo990056f}}. The salient point here is that the [[enthalpy]] and [[entropy]] of this series differ in their trends.
# Just when you are starting to think that things are quite simple, along comes the observation: S. E. Biali, ''Axial monoalkyl cyclohexanes'', ''J. Org. Chem.'', '''1992''', ''57'', 2979 - 2980; {{DOI|10.1021/jo00037a001}}
# And this one with knobs on: ''In all-trans-1,2,3,4,5,6-hexaisopropylcyclohexane, all the alkyl groups are located at axial rather than equatorial positions: O. Golan, Z. Goren, and S. E. Biali, ''Axial-equatorial stability reversal in all-trans-polyalkylcyclohexanes'', ''J. Am. Chem. Soc.'', '''1990''', ''112'', 9300 - 9307. {{DOI|10.1021/ja00181a036}}.
#J. A. Anderson, K. Crager, Kelly, L.Fedoroff, G. S. Tschumper, Gregory S. ''Anchoring the potential energy surface of the cyclic water trimer.'' ''J. Chem. Physics'', '''2004''', ''121'', 11023-11029. {{DOI|10.1063/1.1799931}}.
#R. R. Fraser, N. C. Faibish, ''On the purported axial preference in 2-methylthio- and 2-methoxycyclohexanones: steric effects versus orbital interactions'', ''Can. J. Chem.'', '''1995''', ''73'', 88-94.
=== How to induce room temperature hydrolysis of a peptide ===
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<uploadedFileContents>peptide-13.3.mol</uploadedFileContents>
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[[Image:amide-cleavage.png|thumb|right|Peptide hydrolysis]] This introduces a further example of how simple conformational analysis can quickly rationalize kinetic behaviour. At neutral pH and 25° the half life for hydrolysis of a peptide bond is around 500 years (and thank goodness, or we would ourselves all rapidly hydrolise to a mush!). Some enzymes however can achieve this in less than 1 second, an acceleration of 1013! Organic chemists are not quite so clever, but they can achieve room temperature hydrolysis of a peptide in 21 minutes by careful conformational design. The two isomers shown on the right differ only in their stereochemistry, one hydrolysing quickly, the other slowly. Build a model of each compound, and calculate two isomers for each, varying in whether the ring N-substituent is oriented axial or equatorial with respect to the decalin ring. On the basis of your two pairs of energies, can you rationalise the observed kinetic behaviour? Do you know why both of these compounds take very much less than 500 years to hydrolise the peptide bond?

'''Hint1:''' Use the chair-chair conformation for cis-decalin as your template for constructing this system.

'''Hint2:''' When constructing your models, think if there are any hydrogen bonds that might stabilize the structure!

'''Hint3:''' Hydrolysis can only occur when the OH group can approach the carbonyl of the peptide bond close enough to react, and at the right angle of approach.
|}

==== Reference ====

# M. Fernandes, F. Fache, M. Rosen, P.-L. Nguyen, and D. E. Hansen, 'Rapid Cleavage of Unactivated, Unstrained Amide Bonds at Neutral pH', ''J. Org. Chem.,'' '''2008''', ASAP: {{DOI|10.1021/jo800706y}}

=== Caryophyllene: The phenomenon of Atropisomerism ===

# [[Image:caryophyllene-ketone.gif|thumb|right|Caryophyllene ketone]] [http://en.wikipedia.org/wiki/Caryophyllene Caryophyllene], a constituent of many essential oils, include clove oil, has a [[trans]] alkene contained in a 9-membered ring. One interesting property is that it has 4 [[diastereoisomers]] possible, originating from a total of three asymmetric centres present in the molecule. Two of these are conventional chiral centres, one is present in the form of a disymmetric trans double bond. To understand why such a bond can result in two configurations, one must appreciate that (concurrent) rotation about the two C-C single bonds adjacent to the alkene is in fact restricted, because to the hydrogen labelled Ha cannot easily pass by the edge of the 4-membered ring. Construct this molecule (in fact the ketone rather than the alkene) and optimize its geometry. Note in particular that the ring junction is ''trans'' and not ''cis''.
# You will find you may well have obtained one of two forms. In the first, the Ha hydrogen will be opposite the C=O group, in the other it will be adjacent to it. Record the energy of whatever form you got. At the end of the course, we will try to find the ''winner'' with the lowest energy (this is not as trivial as it sounds!).
# Next, take your structure, and try to ''flip'' the [[trans]] alkene bond around so that eg if the methyl were previously pointing up, now it will point down. You may find a combination of erasing/redrawing or of moving, will accomplish this. You may also find another trick useful, of deleting all hydrogens, and then re-sprouting them back on again. Re-optimise your structure and compare the energy with your first isomer.
# Another feature of this model is that you can judge which group is in the so-called shielded region of the carbonyl group magnetic anisotropy. Using this information, you can see if there are any anomalous 1H chemical shifts that might need explaining!

==== References ====
# M. Clericuzio, G. Alagona, C. Ghio, and L. Toma, ''Ab Initio and Density Functional Evaluations of the Molecular Conformations of -Caryophyllene and 6-Hydroxycaryophyllene'', ''J. Org. Chem.'' '''2000''', ''65'', 6910 - 6916. {{DOI|10.1021/jo000404+}}.
#[http://en.wikipedia.org/wiki/Caryophyllene Wikipedia article]
# For a recent application of this phenomenon, see P. C. Bulman Page, B. R. Buckley, S. D.R. Christie, M. Edgar, A. M. Poulton, M. R.J. Elsegood and V. McKee, ''A new paradigm in N-heterocyclic carbenoid ligands'', ''J. Organometallic Chem.'', '''2005''', ''690'', 6210-6216. D {{DOI|10.1016/j.jorganchem.2005.09.015}}.

=== Germacrene: Conformational analysis of medium sized rings ===

{|
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# [[Image:Germacrene.gif|thumb|right|Germacrene and the thermal reaction product]]Germacrene is a natural product with a ten-membered ring; it has the triene structure shown. Assuming that it adopts a crown conformation, build a three-dimensional model.
# On heating, germacrene is converted into one of the stereoisomers of the divinylcyclohexane, via a [3,3] sigmatropic pericyclic reaction. Predict from your model for Germacrene whether the product will have the two vinyl groups [[cis]] or [[trans]] to one another.
|}

==== References ====

# K. Shimazaki, M. Mori, K. Okada, T. Chuman, H. Goto, K. Sakakibara and M. Hirota, ''Conformational analyses of periplanone analogs by molecular mechanics calculations'', '' J. Chem. Ecology'', '''1991''', ''17'', 779-88. {{DOI|10.1007/BF00994200}}.
# H. Shirahama, E. Sawa and T. Matsumoto, ''Conformational aspects of germacrene B. Are the germacrenes resolvable ?'', ''Tetrahedron Lett.'', '''1979''', ''20'', 2245-2246. {{DOI|10.1016/S0040-4039(01)93687-1}}. See also {{DOI|10.1039/P19750002332}} for an explanation of the selective epoxidation of germacrene.

=== Xestoquinone: Regio and Stereoselectivity in the Diels Alder reaction===

# [[Image:xestoquinone.gif|thumb|right|Xestoquinone precursor]] This compound is a precursor to a natural product called Xestoquinone. It has four alkene groups, which can individually be considered as the alkene component in a π2s + π4s [[Diels Alder]] [[cycloaddition]]. The pair of alkenes ''a+b'' or ''c+d'' can also act as the diene component in the π2s + π4s [[Diels Alder]] [[cycloaddition]]. Construct a model of the product of e.g. forming a bond between alkene ''a'' or alkene ''b'' and diene ''c+d'', and then reverse the addition by using either ''c'' or ''d'' adding to the diene ''a+b''. The stereochemistry of addition should always be [[suprafacial]], i.e. preserving the stereochemical relationships of the alkenes. You should very carefully check that this is so in your final model.
# Whilst you should stop at '''two''' models, it is possible to construct many more. For example, one might be able to add to either the ''top'' face of alkene ''b'' or to its ''bottom'' face. Identify the model with the lower energy, and save it for the end of the workshop. We will identify the isomer of lowest energy from everyone's results, this being a communal [[Monte Carlo]] experiment to find the [[global minimum]].

==== References ====

#[http://en.wikipedia.org/wiki/Diels-Alder_reaction Wikipedia article]
#For the original literature on this synthesis, see R. Carlini, K. Higgs, C. Older, S. Randhawa, and R. Rodrigo, ''Intramolecular Diels-Alder and Cope Reactions of o-Quinonoid Monoketals and Their Adducts: Efficient Syntheses of (±)-Xestoquinone and Heterocycles Related to Viridin'', ''J. Org. Chem.'', '''1997''', ''62'', 2330 - 2331. {{DOI|10.1021/jo970394l}} where you can check to see which isomers actually do form!

=== Aldol Reaction and anti-Bredt Rings ===

{|
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# [[Image:Aldol.gif|thumb|right|Aldol Reaction]]When the diketone shown is treated with base, it undergoes an aldol condensation. Two obvious possibililties are elimination of the combination Ha and Oa, or of the alternative combination Hb and Ob. In fact, only a single product is formed. On the basis of energies for both products, can you predict which one is actually formed?
# Measure a few dihedral angles, ie to find out how planar the alkene present is. Does this suggest a reason why one isomer is less stable than the other?
# There is a third very remote structural possibility. If you have time, verify that this third product truly is unlikely.
|}

==== References ====
#[http://en.wikipedia.org/wiki/Bredt's_Rule Bredt's Rule]
# I. Novak, ''Molecular Modeling of Anti-Bredt Compounds'', ''J. Chem. Inf. Model.'', '''2005''', ''45'', 334 - 338. {{DOI|10.1021/ci0497354}}
# See also this article A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, ''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins'', ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}} in conjunction with Project 9.

=== Conformational Preference for asymmetric hydride reduction of a ketone ===

# [[Image:Felkin.gif|thumb|right|Asymmetric hydride reduction]]The hydride ([http://en.wikipedia.org/wiki/Lithium_aluminium_hydride BH4, AlH4, etc]) reduction of the ketone shown here is stereospecific, resulting in an alcohol with the stereochemistry shown (known as the [http://en.wikipedia.org/wiki/Chiral_induction Cram or the Felkin-Anh] rule). Construct a model of the ketone and establish which of at least two conformations is the lowest in energy.
# If the hydride anion is delivered from the least hindered position, is the conformation you have consistent with the stereochemistry shown for the product?
# You can see from Ref 4 that the situation can be far more complex, depending on many other factors.

====References ====
# [http://en.wikipedia.org/wiki/Chiral_induction Wikipedia article]
# D. J. Cram and D. R. Wilson, ''Studies in Stereochemistry. XXXII. Models for 1,2-Asymmetric Induction'', ''J. Am. Chem. Soc.'', '''1963''', ''85'', 1245 - 1249. {{DOI|10.1021/ja00892a008}}.
# Y. Yamamoto, K. Matsuoka, and H. Nemoto, ''Anti-Cram selective reduction of acyclic ketones via electron transfer initiated processes'', ''J. Am. Chem. Soc.'', '''1988''', ''110'', 4475 - 4476; {{DOI|10.1021/ja00221a093}}.
# A. Mengel and O. Reiser, ''Around and beyond Cram's Rule'', ''Chem. Rev.'', '''1999''', ''99'', 1191 - 1224. {{DOI|10.1021/cr980379w}}.

=== Enantiomers vs Diastereomers Part 2: NMR Coupling constants ===

#[[Image:karplus.gif|thumb|Axial-equatorial interconversion|right]]In Project 2.2 above, we saw how the energies of diastereomeric compounds could be compared with the corresponding enantiomers. In this extension, we show how molecular modelling can cast light on the conformation adopted by 2-ethyl-4-methyl-1-oxa-cyclopentane-3-carboxylic acid estimated using measured 1H NMR coupling constants. The (2S,3S,4S) diastereomer has couplings of 3JH2,H3 8.3 Hz and 3JH3,H4 9.8 Hz. Two possible conformations of this diastereomer are shown on the right. They differ in that one has Et axial, and Me/COOH equatorial, and the other Et equatorial and Me/COOH axial.
#[[Image:karplus.jpg|Karplus plot|thumb|left]]By calculating the geometries of both conformations, and measuring the dihedral angle H2-C-C-H3 and H3-C-C-H4, one can assess by using the Karplus equation (left, taken from Ref 2 and relevant for a cyclopentane, but the values for which might be modified by the presence of electronegative substituents), which conformation leads to the best agreement between the calculated angle and the measured coupling constants (Hint: on the basis of the predicted couplings, you should be able to eliminate one of the two conformations shown for this molecule).
#[[Image:5-circulene.gif|thumb|5-circulene|right]]In Project 2.2 we also introduced molecules such as helicenes and circulenes. The 1H NMR of the [5]-circulene shown to the right revealed a complex spectrum at δ 2.98 ppm and again at 3.75 ppm. On the face of it, the four protons labeled Ha and Hb should all be equivalent, and the spectrum should be a single peak, not two complex multiplets. Indeed, if the NMR is recorded at high temperatures, this is exactly what is observed. By constructing a model of the [5]-circulene shown, can you explain why at normal temperatures, the NMR spectrum is so complex? 
#[[Image:Lab_expt.jpg|thumb|Synthesis lab experiment|right]]A practical application of this technique is to determine the stereochemistry of the product of the reaction between E,E-2,4-hexadien-1-ol and maleic anhydride. You will have the 1H NMR spectrum of your sample recorded, and evident from that will be peak multiplicities of the various proton resonances. You should endeavour from your analysis to come up with a suggestion for the structure of compound '''Y''', and from this, estimates of the numerical values (but not the signs) of the 2J and 3J couplings visible. Now using the techniques described above, construct a model of your proposed structure for '''Y'''. Measure the dihedral angles for all the 3J couplings, and very approximately estimate what the corresponding 3J might be from the diagram above. Does this help you assign the stereochemistry of the product?
#'''Advanced topic''': Part of the spectroscopic analysis of the compound '''Y''' involves interpreting the IR spectrum. Theory can be used in fact to simulate the full IR spectrum. In section 5.3 below, you will find instructions on how to use the model you have calculated here to initiate a so called '''density functional''' calculation. This will provide you with the required IR simulation. Follow these instructions, and open the resulting .log file in Gaussview. Go to the '''Results''' menu and select '''vibrations'''. The IR spectrum will be displayed. Does it match the one you have recorded for yourself?

==== References ====

#M. Karplus, ''Vicinal Proton Coupling in Nuclear Magnetic Resonance'', '' J. Am. Chem. Soc.'', '''1963''', ''85'', 2870 - 2871; {{DOI|10.1021/ja00901a059}}
#A. Wu, D. Cremer, A. A. Auer, and J. Gauss, ''Extension of the Karplus Relationship for NMR Spin-Spin Coupling Constants to Nonplanar Ring Systems: Pseudorotation of Cyclopentane'', ''J. Phys. Chem. A,'', '''2002''', ''106'', 657 -667; {{DOI|10.1021/jp013160l}}
#C. A. Stortz and M. S. Maier, ''Configurational assignments of diastereomeric γ-lactones using vicinal H–H NMR coupling constants and molecular modelling'', ''J. Chem. Soc., Perkin Trans. 2'', '''2000''', 1832 - 1836. {{DOI|10.1039/b003862h}}
# A. H. Abdourazak, A. Sygula, and P. W. Rabideau ''Locking the bowl-shaped geometry of corannulene: cyclopentacorannulene'', ''J. Am. Chem. Soc.'', '''1993''', ''115'', 3010 - 3011. {{DOI|10.1021/ja00060a073}}

=== Bridgehead enols: Thermodynamic vs Kinetic Control Part 2.===
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#[[Image:Bredt.gif|thumb|right|Brendanone]] The ketone Brendan-2-one shown right exhibits unusual behaviour.6 When treated with NaOD/MeOD, deuterium substitution occurs easily and rapidly only in position Hb. Enolisation must of necessity form a bridgehead double bond (''anti-Bredt''), but clearly one isomer is more stable than the other possible form. Does molecular modelling predict this correctly?
#The unusually facile enolisation of this ketone (given that it forms an anti-Bredt enol) can also be investigated by molecular modelling. '''Measure''' the dihedral angle between the C-Ha or C-Hb vector and the carbonyl group. Assuming that the ''ideal'' angle for proton removal is around 90°, which proton is better set up for abstraction? Might this be kinetic rather than thermodynamic control?
#[[Image:Cortisone.gif|thumb|right|Cortisone]]One could also revisit Problem 2.3.3 above. Here, proton abstraction forms an enol which eventually epimerises the bridgehead position to form a ''trans'' ring junction. Why should this proton be particularly easy to remove? From what you have learnt above, would this be for kinetic or for thermodynamic reasons (or both?). Are all the relevant effects modelled using the mechanics approach or is consideration of the electrons also necessary?
|}
==== References and Footnotes====

# A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, {{doi-inline|10.1021/ja00837a043|''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins''}}, ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}}.

===Sulfonylation of Naphthalene: Thermodynamic vs Kinetic Control Part 3.===

[[Image:Sulfonylation.gif|right|thumb|Sulfonylation of naphthalene]]The sulfonylation of naphthalene using sulfuric acid is a good example of a mechanism combining both steric and electronic influences. The Molecular mechanics method intrinsic to the Ghemical program can only model the former, and not the latter. It is a worthwhile exercise to establish whether this anticipated deficiency does indeed lead to a model which only partially explains experiment.

It has been known for some time that treating naphthalene with sulfuric acids at low temperatures produces mostly substitution at the 1-position of the naphthalene. Heating the reaction mixture, or conducting the reaction at elevated temperatures produces mostly the 2-isomer. This is indeed a classic example of [[kinetic]] vs [[thermodynamic]] control, the 1-isomer being the kinetic one and the 2-isomer the thermodynamic one. To model the kinetic reaction, we have to inspect the [[transition state]] for the reaction, and here we can approximate this by the [[Wheland Intermediate]]. To model the thermodynamic reaction, we have to inspect the product (rather than the transition state) for the reaction.

#Build models for all four species shown in the diagram on the right. For the two products, define ''conjugated'' bond types for all the ring bonds, and define the sulfonyl group with two S=O double bonds and one S-O single bond. Take care to optimise the conformation of the sulfonyl group with respect to the aromatic ring. For the two Wheland intermediates, the limitations of Ghemical will force us to ''cheat''. Ghemical does not have parameters for a carbocation. So define the C2-C3 bond as conjugated (for the 1-Wheland intermediate). When you '''add hydrogens''' it will in fact add a second hydrogen to C2. Delete this one hydrogen. Ghemical will calculated the energy regardless of not knowing C2 is actually a carbonium ion! For the 2-Wheland intermediate, ensure that you use '''exactly''' the same number of ''conjugated'' bond types as you did for the 1-isomer (the two models in a mechanics sense are only comparable if you have the same total number of bond types in each model). You will have to decide whether these (undoubted) approximations have produced reasonable models or not (is the naphthalene framework planar for example, as it should be?).
#Record the pairs of energies (two for the 1- and 2-products, and two for each preceeding transition (Wheland) state.
#By turning the spacefilling representation on, which of the two products has the least unfavourable steric interactions between the sulfonic acid group and any adjacent hydrogens? Does this match with their relative energies?
#Do any unfavourable steric interactions observed in the product(s) also exist in the Wheland intermediates (as models for the transition states)?
#The relative stability of the Wheland intermediates is always assumed to be an '''electronic''' phenomenon. The conventional explanation is that the 1-Wheland isomer is stablized by both one aromatic ring '''and''' an allyl cation conjugated to it. The 2-Wheland isomer is stabilised by one aromatic ring conjugated to a secondary carbocation and an alkene. This type of ''cross conjugation'' is conventionally assumed to be less favourable. Does a purely mechanical approach to this problem reproduce this expectation? Or is this ''mechanical'' approximation to an ''electronic'' model too severe? It seems a good point to stop this course, since the next time you will build models, it will indeed be using methods which properly approximate the electronic components.
====References====

#R. Lantz, ''Mechanism of the monosulfonation of naphthalene'', ''Compt. Rend''. '''1935''', ''201'', 149-52.
#G. W. Wheland, ''A Quantum Mechanical Investigation of the Orientation of Substituents in Aromatic Molecules'', ''J. Am. Chem. Soc.'' '''1942''', ''64'', 900 - 908; {{DOI|10.1021/ja01256a047}}
#C. A. Reed, N. L. P. Fackler, K-C. Kim, D. Stasko, D. R. Evans, P. D. W. Boyd, and C. E. F. Rickard, ''Isolation of Protonated Arenes (Wheland Intermediates) with BArF and Carborane Anions. A Novel Crystalline Superacid'', ''J. Am. Chem. Soc.'' '''1999''', ''121'', 6314 - 6315 {{DOI|10.1021/ja981861z}}

== Coursework not to be attempted at any time: Antimodelling Molecules ==

The following represent molecules that should '''not''' be modelled under any circumstances! You should instead attempt to '''NAME''' them.

[[Image:Contraceptive.gif|Contraceptive (NO in every conceivable position)]] [[Image:Paradise.gif|Paradise lost]] [[Image:Synoptic.gif|Synoptic]] [[Image:Cisters.gif|Cisters]] [[Image:Transisters.gif|Transisters]] [[Image:Metaphor.gif|Metaphor]] [[Image:Metastasis.gif|Metastasis]] [[Image:Cyclone.gif|Cyclone]] [[Image:Anticyclone.gif|Anticyclone]] [[Image:Arsole.gif|Arsole]] [[Image:Orthodox.gif|Orthodox]] [[Image:Synthesis.gif|Synthesis and Antithesis]] [[Image:Aphrodisiac.gif|Name this yourself. Does Meg Ryan spring to mind?]] [[Image:Cyclops.gif|Cyclops]] [[Image:Paradox.gif|Paradox]] [[Image:Transparent.gif|Transparent]] [[Image:Encyclopedia.gif|Encyclopedia]] [[Image:Maths.jpg|Find X]] [[Image:VanderMaxforce.jpg|150px|Max Whitby stuck to a strangely attractive Lamp Post]] [[Image:nanoballet.jpg|200px|Nanoballet dancer]] [[Image:NanoCossacks.jpg|200px|NanoCossacks]]
[[Image:Paralysis.png|500px|Paralysis]] [[Image:Mcdonalds.png|500px|Old McDonald's Molecule: ene-yne-ene-yne-one]]
[[Image:Silenedione.png|500px|Celine Dion]]

If you know of any other antimodelling molecules, please add them here!

====Acknowledgements ====

Some of these cartoons are from [http://www.nearingzero.net/sci_chemistry.html here], and six are original. A superb collection of '''''silly names''''' is maintained
by [http://www.chm.bris.ac.uk/sillymolecules/sillymols.htm Paul May] [[Organic:Model_answers|.]] See {{DOI|10.1021/jo0349227}} for the nanoputians.

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[[Second_Year_Modelling_Workshop|Back to introduction]]
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File:Silenedione.png

2010-10-15T15:26:01Z

Nm607:

File:Mcdonalds.png

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Nm607:

Coursework

2010-10-15T14:33:08Z

Nm607: /* Coursework not to be attempted at any time: Antimodelling Molecules */

[[Second_Year_Modelling_Workshop|Back to introduction]]
----
== Molecular modelling Coursework to be attempted during Scheduled Sessions ==

These projects are arranged in increasing order of difficulty, and time taken to complete. You should do as many as you can in the 2 hour session allocated to you, and return to finish the rest if you wish at your convenience. At the end of the session, we will conduct a ''number auction''. For each project, the bidding will start with the first volunteer offering an energy for the system (or one of the isomers). If anyone has a lower energy for that molecule, they will then bid that energy. The winner will be the one with the lowest energy.

=== Conformational analysis I: Chair and Boat-like conformations of Cyclohexane ===
{|
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#Construct '''[[chair]]''' and '''[[boat]]'''-like '''[[conformation]]s''' of [[cyclohexane]]. Compare the energies of both forms.
#Check carefully if your boat really is a boat, or whether it has any apparent distorsion.
#Try changing one or more of the CH2 groups into an oxygen and see if that affects things.
#For the record, the point group symmetries of the various species which may be involved are D3d for the chair conformation, C2v for a boat geometry, and D2 for any twisted boat form. Is any of these forms '''chiral'''?
#The molecule on the left is called '''chiralane'''. Are its rings boats or chairs?
|}
====References ====
# The first suggestion of two forms for cyclohexane goes as far back as H. Sachse, ''Chem. Ber'', 1890, '''23''', 1363 and ''Z. Physik. Chem.'', 1892, 10, 203. This is nicely explained [http://www.chem.yale.edu/~chem125/125/history/Baeyer/Sachse.html here]. E. Mohr, ''J. Prakt. Chem.'', 1918, '''98''', 315 and ''Chem. Ber.'', 1922, '''55''', 230, translated Sachse's argument into a pictorial one.
# The article that put [[conformational analysis]] on the map: D. H. R. Barton and R. C. Cookson, ''The principles of conformational analysis'', ''Q. Rev. Chem. Soc.'', '''1956''', ''10'', 44. {{DOI|10.1039/QR9561000044}}
#[http://en.wikipedia.org/wiki/Chair_conformation Wikipedia article]
#D. A. Dixon and A. Komornicki, ''Ab initio conformational analysis of cyclohexane'', ''J. Phys. Chem.'', '''1990''', ''94'', 5630 - 5636; {{DOI|10.1021/j100377a041}}.
#A nice exploration of the potential energy surfaces for cyclohexane can be viewed [http://www.springer.com/carey-sundberg/cyclohex/cyclohex.php here].
# For a more modern application of this technique, see I. Columbus, R. E. Hoffman, and S. E. Biali, ''Stereochemistry and Conformational Anomalies of 1,2,3- and 1,2,3,4-Polycyclohexylcyclohexanes''. ''J. Am. Chem. Soc.'', '''1996''', ''118'', 6890 - 6896; {{DOI|10.1021/ja960380h}}.
# The second molecule shown in this section is called [6.6]chiralane. It is peculiar for having many six-membered saturated rings, all of them as twist-boats rather than chairs! (a chair has a plane of symmetry, a twist boat only axes, which of course allows it to be chiral). See [http://petitjeanmichel.free.fr/itoweb.petitjean.graphs.html#CHIR here] for more details.
# More detail on the conformation of rings (and acyclic systems) will be found in the [http://www.ch.ic.ac.uk/local/organic/conf/ lecture course] on the topic to be given in the spring term.

=== Enantiomers vs Diastereomers Part 1: Butanes and Helicenes. ===

This problem illustrates, using models, the difference between an enantiomer and a diastereomer.

#[[Image:diastereo.gif|thumb|right|2-bromo-3-chlorobutane]][[Image:pentahelicene.gif|thumb|right|Pentahelicene]]The compound 2-bromo-3-chlorobutane has two [[chiral]] centres, and four isomers (22) are therefore possible. Calculate all four isomers, and for each be careful to label each of the two stereo centres '''R''' or '''S''' as you go. For each of the four isomers '''R,R''', '''S,S''', '''R,S''', '''S,R''' you will have to think about whether you have obtained the lowest energy [[conformer]].
#Can your four energies be grouped in any way? You should think about the expected difference between '''enantiomers''', '''diastereomers''' and '''conformers'''.
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#Construct some helicenes (pentahelicene or [5]helicene is shown on the right), using '''conjugated''' bonds for all the ring bonds. Benzene, naphthalene, phenanthrene and benzophenanthrene are in fact the first four members of this series. At what point in this series can you detect helicity cropping up? This is manifested by a non-planar helical wind of the molecule. If you do detect it, note how the wind is either left or right handed, ie the two forms are '''enantiomers''' of each other. Try displaying the molecule in '''spacefill mode''' (see above) to see if you can identify the source of the helicity. (Note: the smallest helicene which can be resolved experimentally into enantiomers is in fact [5]helicene]).
#The higher helicenes are well known (up to about [14]helicene) and amongst the ''most chiral'' molecules known (in terms of how much they rotate the plane of polarised light).
#[7]circulene is a known molecule, with a unique saddle-shaped structure, shown on the left (there is no real need for you to build this model, but do please do so if you are curious). [http://en.wikipedia.org/wiki/Graphene Graphene] is a related polymeric molecule, of much topical interest in the semi-conducting and other industries (Nobel Prize 2010).
|}
==== References ====

#[http://en.wikipedia.org/wiki/Diastereomer Wikipedia article on Diastereomers]
#[http://en.wikipedia.org/wiki/Helicene Wikipedia article on Helicenes and related molecules]
#R. H. Janke, G. Haufe, E.-U. Würthwein, and J. H. Borkent, ''Racemization Barriers of Helicenes: A Computational Study'', ''J. Am. Chem. Soc.'', '''1996''', ''118'' 6031 - 6035 {{DOI|10.1021/ja950774t}}

=== Conformational analysis II: ''cis'' and ''trans''-decalins, Steroids and Podcasts! ===
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# [[Image:cis-decalin.gif|thumb|right|cis Decalin]]This is the famous molecule that started the whole molecular mechanics modelling ball rolling. [http://www.ch.ic.ac.uk/video/barton/barton1.pdf Barton] in 1948 sought to find out which [[conformation]] of ''cis''-decalin was the most stable (see [http://www.ch.ic.ac.uk/video/barton/index_qt.html here] for video). You should be able to find at least three conformations of this molecule. Try locating these, and conclude which is the most stable. Identify any [[chair]] rings and any [[boat]].
#Measure some dihedral angles to see if the [[staggered]] relationships hold (i.e. for such a relationship, the dihedral angle should be close to 60 degrees).
#A key step in Woodward's famous synthesis of [http://en.wikipedia.org/wiki/Cortisone cortisone] is a quinone+butadiene [[Diels-Alder]] reaction to give a cis-decalin (left), with an assumption that [[epimerisation]] to a trans-decalin is thermodynamically favourable. [[Image:Cortisone.gif|thumb|left|cis Cortisone]]Can you verify whether the trans-isomer is indeed more stable? Its not so obvious, since this compound has two extra double bonds in the rings and six sp2 centres which might perturb things.
#[[Image:App.gif|thumb|right|trans Decalin]]The two diastereomeric ''trans''-decalin tosylates react quite differently with NaBH4. Construct models for both isomers (use methoxy as a model for the Tosyl group) and from the [[antiperiplanar]] alignments of bonds that you can find in each isomer, can you make a connection to the reactivity of each form? Consider very carefully where you would put a lone pair located on the nitrogen (i.e. include the N-Lp "bond" in your antiperiplanar alignments) asuming the this atom is tetrahedral rather than planar. Does this lone pair play any part in either reaction in this position?. Note that the relative energy of the axial/equatorial N-Methyl group will not be an accurate reflection of any [[antiperiplanar]] alignments, since these are predominantly electronic in origin, and this mechanics method does not take these into account.
##'''Optional:''' The second (elimination) reaction is very slow compared to the first. Discuss with tutors why this might be so (for Hints, see [[organic:entropy|here]] or [[organic:ngp|here]]).
##'''Optional''': These reactions do not appear to occur for the corresponding ''cis''-decalins6. Why not?

|}

==== References and Footnotes ====
# D. H. R. Barton, ''Interactions between non-bonded atoms, and the structure of cis-decalin'', ''J. Chem. Soc.'', '''1948''', 340-342. {{DOI|10.1039/JR9480000340}}
#[http://en.wikipedia.org/wiki/Decalin Wikipedia article]
# For a modern application of mechanics to this molecule, see J. M. A. Baas, B. Van de Graaf, D. Tavernier, and P. Vanhee, ''Empirical force field calculations. 10. Conformational analysis of cis-decalin'', ''J. Am. Chem. Soc.'', '''1981''', ''103'', 5014 - 5021; {{DOI|10.1021/ja00407a007}}.
# For a video-Podcast of Barton and Woodward (and other Nobel prize winners), subscribe [http://www.ch.ic.ac.uk/video/index.rss here]
# R. B. Woodward, F. Sondheimer, and D. Taub, ''The total Synthesis of Cortisone'', ''J. Am. Chem. Soc.'', '''1951''', ''73'', 4057 - 4057. {{DOI|10.1021/ja01152a551}}.
# P.-W. Phuan and M. C. Kozlowski, ''Control of the Conformational Equilibria in Aza-cis-Decalins: Structural Modification, Solvation, and Metal Chelation'', ''J. Org. Chem.'', '''2002''', ''67'', 6339 - 6346; {{DOI|10.1021/jo025544t}}

=== Menthone/''iso''menthone and Bridgehead enols: Thermodynamic vs Kinetic Control Part 1.===

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#[[Image:Menthone.gif|thumb|right|Menthone]] Beckmann (of rearrangement fame) in 1889 dissolved optically active levorotatory (-) (S,R)-menthone ([α]D -28°) in conc. sulfuric acid, followed by quenching on ice to give what Beckmann assumed was pure (and what we would nowadays call [[diastereomeric]]) (+) (R,R)-isomenthone, [α]D +28°. He suggested for the first time that such an isomerisation, involving epimerisation at the asymmetric centre next to the keto group, proceeded via an intermediate enol in which the tetrahedral asymmetric carbon becomes planar. But this famous (perhaps even notorious2) early example of a [[reaction mechanism]] makes an interesting assumption, which can be tested by molecular modelling.
# Two possible enols can be formed, only one of which allows the [S] asymmetric carbon to become planar and then protonate to the [R] epimer. This is the so called [[thermodynamic enol]]. The other, which leaves the [S]-centre untouched is the [[kinetic enol]]. Find out if simple molecular modelling correctly predicts that the thermodynamic enol is indeed the more stable of the two. '''Hint:''' Model the enol and '''not''' the ketone. Consider carefully any conformational isomers possible.
# Given that the optical rotation3 of pure (+)-isomenthone is now known to be [α]D +101° rather than +28°, we can infer that Beckmann's product contains only 43% isomenthone and hence still contains 57% of original menthone, corresponding to an equilibrium constant of K= 0.75. This can be related to a (free energy) difference using the equation ΔG = -RT ln K, or ΔG = 0.7 kJ/mol (menthone being lower in energy by this amount compared to isomenthone). Can this energy difference be verified using molecular mechanics modelling? Can you explain why menthone is the more stable? (For another hint, or possibly a fright, visit [http://chemistry.gsu.edu/glactone/modeling/Luise/organic/cychexon.html this page]).
|}

==== References and footnotes ====
# E. Beckmann, ''Annalen'', '''1889''', ''250'', 322. {{DOI|10.1002/jlac.18892500306}}.
# Many of Beckmann's misconceptions were corrected by O. Wallach, ''Annalen'', '''1893''', ''276'', 296. {{DOI|10.1002/jlac.18932760306}}. The notoriety is because the coincidence of equal but opposite optical rotations obtained in this experiment led Beckmann to believe that he had obtained the [[enantiomer]] of menthone, and not as we now know, the impure (R,R) [[diastereomer]]. It should be borne in mind that the concept of tetrahedral and asymmetric carbon was only 15 years old at this time (see [http://en.wikipedia.org/wiki/Jacobus_van_%27t_Hoff Jacobus Henricus van't Hoff] and [http://en.wikipedia.org/wiki/Achille_Le_Bel Joseph Achille Le Bel]). Nevertheless confusion over this aspect persisted for some time after, and was often evident in the writings of even very famous chemists of the time (and Beckmann was very famous)!.
#[http://en.wikipedia.org/wiki/Menthone Wikipedia article]
# From about 1890-1935, mechanistic organic chemistry was born. In the absence of UV, IR, NMR, MS and X-Ray techniques, the [http://en.wikipedia.org/wiki/Polarimeter polarimeter] occupied a pivotal role. Many of the great discoveries in reaction mechanisms (keto-enol tautomerism as seen here, [[Organic:tutorial:meerwein| carbocations]], the Walden inversion, etc) relied on polarimetric measurements.
# A notorious modern example of (unwanted) epimerisation of a ketone is [http://en.wikipedia.org/wiki/Thalidomide Thalidomide], where one epimer inhibits morning sickness in pregnant women, and the other epimer is teratogenic, causing fetal abnormalities. The equilibrium in this case does not require conc. sulfuric acid, but can occur at physiological pH.

== Additional Molecular modelling Coursework ==

Please feel free to try these problems in your own time, and to discuss these with your organic tutors and lecturers. Note also that the relevant lectures may occur in the spring as well as autumn terms.
=== Axial/Equatorial preferences in cyclohexane and cyclohexanone and Hydrogen Bonding ===
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#Construct a chair cyclohexane and replace firstly one of the [[axial]] hydrogens with the following groups: '''methyl''', '''t-butyl''', '''OH'''. Calculate the energy of the axial isomer.
# Then repeat (either by deleting/redrawing or by moving) for the equatorial forms. Compare the energies of the two isomers. Does any energy difference increase with the size of the group? Does OH fit into this in terms of size?
# [[Image:Thiomethylcyclohexanone.gif|right|thumb|thiomethyl cyclohexanone]]The dissolving metal reduction of cyclohexanones in a protic solvent (i.e. one capable of hydrogen bonding) is thermodynamically controlled and gives the more stable, equatorial alcohol. In fact, its probably the alkoxide that is the product, not the free alcohol. It is thought the alkoxide is actually a lot larger than the alcohol, accounting for the substantial equatorial preference. Can you think why its larger? [Ghemical cannot in fact model this, since the force field does not include parameters for the alkoxide anion].
# Determine the axial/equatorial preference of 2-methylthio-cyclohexanone (Hint: there are many conformations possible, and you should try a few to see if you can get the lowest).
|}
==== References and Footnotes ====

# A. H. Lewin and S. Winstein, ''NMR. Spectra and Conformational Analysis of 4-Alkylcyclohexanols'' ''J. Am. Chem. Soc.''; '''1962''', ''84'', 2464 - 2465; {{DOI|10.1021/ja00871a049}}
#F. R. Jensen and L. H. Gale, ''The Conformational Preference of the Bromo and Methyl Groups in Cyclohexane by IR Spectral Analysis'', ''J. Org. Chem.'', '''1960''', ''25'', 2075 - 2078. {{DOI|10.1021/jo01082a001}}
# K. B. Wiberg, J. D. Hammer, H. Castejon, W. F. Bailey, E. L. DeLeon, and R. M. Jarret, ''Conformational Studies in the Cyclohexane Series. 1. Experimental and Computational Investigation of Methyl, Ethyl, Isopropyl, and tert-Butylcyclohexanes'', ''J. Org. Chem.'', '''1999''', ''64'', 2085 - 2095; {{DOI|10.1021/jo990056f}}. The salient point here is that the [[enthalpy]] and [[entropy]] of this series differ in their trends.
# Just when you are starting to think that things are quite simple, along comes the observation: S. E. Biali, ''Axial monoalkyl cyclohexanes'', ''J. Org. Chem.'', '''1992''', ''57'', 2979 - 2980; {{DOI|10.1021/jo00037a001}}
# And this one with knobs on: ''In all-trans-1,2,3,4,5,6-hexaisopropylcyclohexane, all the alkyl groups are located at axial rather than equatorial positions: O. Golan, Z. Goren, and S. E. Biali, ''Axial-equatorial stability reversal in all-trans-polyalkylcyclohexanes'', ''J. Am. Chem. Soc.'', '''1990''', ''112'', 9300 - 9307. {{DOI|10.1021/ja00181a036}}.
#J. A. Anderson, K. Crager, Kelly, L.Fedoroff, G. S. Tschumper, Gregory S. ''Anchoring the potential energy surface of the cyclic water trimer.'' ''J. Chem. Physics'', '''2004''', ''121'', 11023-11029. {{DOI|10.1063/1.1799931}}.
#R. R. Fraser, N. C. Faibish, ''On the purported axial preference in 2-methylthio- and 2-methoxycyclohexanones: steric effects versus orbital interactions'', ''Can. J. Chem.'', '''1995''', ''73'', 88-94.
=== How to induce room temperature hydrolysis of a peptide ===
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[[Image:amide-cleavage.png|thumb|right|Peptide hydrolysis]] This introduces a further example of how simple conformational analysis can quickly rationalize kinetic behaviour. At neutral pH and 25° the half life for hydrolysis of a peptide bond is around 500 years (and thank goodness, or we would ourselves all rapidly hydrolise to a mush!). Some enzymes however can achieve this in less than 1 second, an acceleration of 1013! Organic chemists are not quite so clever, but they can achieve room temperature hydrolysis of a peptide in 21 minutes by careful conformational design. The two isomers shown on the right differ only in their stereochemistry, one hydrolysing quickly, the other slowly. Build a model of each compound, and calculate two isomers for each, varying in whether the ring N-substituent is oriented axial or equatorial with respect to the decalin ring. On the basis of your two pairs of energies, can you rationalise the observed kinetic behaviour? Do you know why both of these compounds take very much less than 500 years to hydrolise the peptide bond?

'''Hint1:''' Use the chair-chair conformation for cis-decalin as your template for constructing this system.

'''Hint2:''' When constructing your models, think if there are any hydrogen bonds that might stabilize the structure!

'''Hint3:''' Hydrolysis can only occur when the OH group can approach the carbonyl of the peptide bond close enough to react, and at the right angle of approach.
|}

==== Reference ====

# M. Fernandes, F. Fache, M. Rosen, P.-L. Nguyen, and D. E. Hansen, 'Rapid Cleavage of Unactivated, Unstrained Amide Bonds at Neutral pH', ''J. Org. Chem.,'' '''2008''', ASAP: {{DOI|10.1021/jo800706y}}

=== Caryophyllene: The phenomenon of Atropisomerism ===

# [[Image:caryophyllene-ketone.gif|thumb|right|Caryophyllene ketone]] [http://en.wikipedia.org/wiki/Caryophyllene Caryophyllene], a constituent of many essential oils, include clove oil, has a [[trans]] alkene contained in a 9-membered ring. One interesting property is that it has 4 [[diastereoisomers]] possible, originating from a total of three asymmetric centres present in the molecule. Two of these are conventional chiral centres, one is present in the form of a disymmetric trans double bond. To understand why such a bond can result in two configurations, one must appreciate that (concurrent) rotation about the two C-C single bonds adjacent to the alkene is in fact restricted, because to the hydrogen labelled Ha cannot easily pass by the edge of the 4-membered ring. Construct this molecule (in fact the ketone rather than the alkene) and optimize its geometry. Note in particular that the ring junction is ''trans'' and not ''cis''.
# You will find you may well have obtained one of two forms. In the first, the Ha hydrogen will be opposite the C=O group, in the other it will be adjacent to it. Record the energy of whatever form you got. At the end of the course, we will try to find the ''winner'' with the lowest energy (this is not as trivial as it sounds!).
# Next, take your structure, and try to ''flip'' the [[trans]] alkene bond around so that eg if the methyl were previously pointing up, now it will point down. You may find a combination of erasing/redrawing or of moving, will accomplish this. You may also find another trick useful, of deleting all hydrogens, and then re-sprouting them back on again. Re-optimise your structure and compare the energy with your first isomer.
# Another feature of this model is that you can judge which group is in the so-called shielded region of the carbonyl group magnetic anisotropy. Using this information, you can see if there are any anomalous 1H chemical shifts that might need explaining!

==== References ====
# M. Clericuzio, G. Alagona, C. Ghio, and L. Toma, ''Ab Initio and Density Functional Evaluations of the Molecular Conformations of -Caryophyllene and 6-Hydroxycaryophyllene'', ''J. Org. Chem.'' '''2000''', ''65'', 6910 - 6916. {{DOI|10.1021/jo000404+}}.
#[http://en.wikipedia.org/wiki/Caryophyllene Wikipedia article]
# For a recent application of this phenomenon, see P. C. Bulman Page, B. R. Buckley, S. D.R. Christie, M. Edgar, A. M. Poulton, M. R.J. Elsegood and V. McKee, ''A new paradigm in N-heterocyclic carbenoid ligands'', ''J. Organometallic Chem.'', '''2005''', ''690'', 6210-6216. D {{DOI|10.1016/j.jorganchem.2005.09.015}}.

=== Germacrene: Conformational analysis of medium sized rings ===

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# [[Image:Germacrene.gif|thumb|right|Germacrene and the thermal reaction product]]Germacrene is a natural product with a ten-membered ring; it has the triene structure shown. Assuming that it adopts a crown conformation, build a three-dimensional model.
# On heating, germacrene is converted into one of the stereoisomers of the divinylcyclohexane, via a [3,3] sigmatropic pericyclic reaction. Predict from your model for Germacrene whether the product will have the two vinyl groups [[cis]] or [[trans]] to one another.
|}

==== References ====

# K. Shimazaki, M. Mori, K. Okada, T. Chuman, H. Goto, K. Sakakibara and M. Hirota, ''Conformational analyses of periplanone analogs by molecular mechanics calculations'', '' J. Chem. Ecology'', '''1991''', ''17'', 779-88. {{DOI|10.1007/BF00994200}}.
# H. Shirahama, E. Sawa and T. Matsumoto, ''Conformational aspects of germacrene B. Are the germacrenes resolvable ?'', ''Tetrahedron Lett.'', '''1979''', ''20'', 2245-2246. {{DOI|10.1016/S0040-4039(01)93687-1}}. See also {{DOI|10.1039/P19750002332}} for an explanation of the selective epoxidation of germacrene.

=== Xestoquinone: Regio and Stereoselectivity in the Diels Alder reaction===

# [[Image:xestoquinone.gif|thumb|right|Xestoquinone precursor]] This compound is a precursor to a natural product called Xestoquinone. It has four alkene groups, which can individually be considered as the alkene component in a π2s + π4s [[Diels Alder]] [[cycloaddition]]. The pair of alkenes ''a+b'' or ''c+d'' can also act as the diene component in the π2s + π4s [[Diels Alder]] [[cycloaddition]]. Construct a model of the product of e.g. forming a bond between alkene ''a'' or alkene ''b'' and diene ''c+d'', and then reverse the addition by using either ''c'' or ''d'' adding to the diene ''a+b''. The stereochemistry of addition should always be [[suprafacial]], i.e. preserving the stereochemical relationships of the alkenes. You should very carefully check that this is so in your final model.
# Whilst you should stop at '''two''' models, it is possible to construct many more. For example, one might be able to add to either the ''top'' face of alkene ''b'' or to its ''bottom'' face. Identify the model with the lower energy, and save it for the end of the workshop. We will identify the isomer of lowest energy from everyone's results, this being a communal [[Monte Carlo]] experiment to find the [[global minimum]].

==== References ====

#[http://en.wikipedia.org/wiki/Diels-Alder_reaction Wikipedia article]
#For the original literature on this synthesis, see R. Carlini, K. Higgs, C. Older, S. Randhawa, and R. Rodrigo, ''Intramolecular Diels-Alder and Cope Reactions of o-Quinonoid Monoketals and Their Adducts: Efficient Syntheses of (±)-Xestoquinone and Heterocycles Related to Viridin'', ''J. Org. Chem.'', '''1997''', ''62'', 2330 - 2331. {{DOI|10.1021/jo970394l}} where you can check to see which isomers actually do form!

=== Aldol Reaction and anti-Bredt Rings ===

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# [[Image:Aldol.gif|thumb|right|Aldol Reaction]]When the diketone shown is treated with base, it undergoes an aldol condensation. Two obvious possibililties are elimination of the combination Ha and Oa, or of the alternative combination Hb and Ob. In fact, only a single product is formed. On the basis of energies for both products, can you predict which one is actually formed?
# Measure a few dihedral angles, ie to find out how planar the alkene present is. Does this suggest a reason why one isomer is less stable than the other?
# There is a third very remote structural possibility. If you have time, verify that this third product truly is unlikely.
|}

==== References ====
#[http://en.wikipedia.org/wiki/Bredt's_Rule Bredt's Rule]
# I. Novak, ''Molecular Modeling of Anti-Bredt Compounds'', ''J. Chem. Inf. Model.'', '''2005''', ''45'', 334 - 338. {{DOI|10.1021/ci0497354}}
# See also this article A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, ''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins'', ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}} in conjunction with Project 9.

=== Conformational Preference for asymmetric hydride reduction of a ketone ===

# [[Image:Felkin.gif|thumb|right|Asymmetric hydride reduction]]The hydride ([http://en.wikipedia.org/wiki/Lithium_aluminium_hydride BH4, AlH4, etc]) reduction of the ketone shown here is stereospecific, resulting in an alcohol with the stereochemistry shown (known as the [http://en.wikipedia.org/wiki/Chiral_induction Cram or the Felkin-Anh] rule). Construct a model of the ketone and establish which of at least two conformations is the lowest in energy.
# If the hydride anion is delivered from the least hindered position, is the conformation you have consistent with the stereochemistry shown for the product?
# You can see from Ref 4 that the situation can be far more complex, depending on many other factors.

====References ====
# [http://en.wikipedia.org/wiki/Chiral_induction Wikipedia article]
# D. J. Cram and D. R. Wilson, ''Studies in Stereochemistry. XXXII. Models for 1,2-Asymmetric Induction'', ''J. Am. Chem. Soc.'', '''1963''', ''85'', 1245 - 1249. {{DOI|10.1021/ja00892a008}}.
# Y. Yamamoto, K. Matsuoka, and H. Nemoto, ''Anti-Cram selective reduction of acyclic ketones via electron transfer initiated processes'', ''J. Am. Chem. Soc.'', '''1988''', ''110'', 4475 - 4476; {{DOI|10.1021/ja00221a093}}.
# A. Mengel and O. Reiser, ''Around and beyond Cram's Rule'', ''Chem. Rev.'', '''1999''', ''99'', 1191 - 1224. {{DOI|10.1021/cr980379w}}.

=== Enantiomers vs Diastereomers Part 2: NMR Coupling constants ===

#[[Image:karplus.gif|thumb|Axial-equatorial interconversion|right]]In Project 2.2 above, we saw how the energies of diastereomeric compounds could be compared with the corresponding enantiomers. In this extension, we show how molecular modelling can cast light on the conformation adopted by 2-ethyl-4-methyl-1-oxa-cyclopentane-3-carboxylic acid estimated using measured 1H NMR coupling constants. The (2S,3S,4S) diastereomer has couplings of 3JH2,H3 8.3 Hz and 3JH3,H4 9.8 Hz. Two possible conformations of this diastereomer are shown on the right. They differ in that one has Et axial, and Me/COOH equatorial, and the other Et equatorial and Me/COOH axial.
#[[Image:karplus.jpg|Karplus plot|thumb|left]]By calculating the geometries of both conformations, and measuring the dihedral angle H2-C-C-H3 and H3-C-C-H4, one can assess by using the Karplus equation (left, taken from Ref 2 and relevant for a cyclopentane, but the values for which might be modified by the presence of electronegative substituents), which conformation leads to the best agreement between the calculated angle and the measured coupling constants (Hint: on the basis of the predicted couplings, you should be able to eliminate one of the two conformations shown for this molecule).
#[[Image:5-circulene.gif|thumb|5-circulene|right]]In Project 2.2 we also introduced molecules such as helicenes and circulenes. The 1H NMR of the [5]-circulene shown to the right revealed a complex spectrum at δ 2.98 ppm and again at 3.75 ppm. On the face of it, the four protons labeled Ha and Hb should all be equivalent, and the spectrum should be a single peak, not two complex multiplets. Indeed, if the NMR is recorded at high temperatures, this is exactly what is observed. By constructing a model of the [5]-circulene shown, can you explain why at normal temperatures, the NMR spectrum is so complex? 
#[[Image:Lab_expt.jpg|thumb|Synthesis lab experiment|right]]A practical application of this technique is to determine the stereochemistry of the product of the reaction between E,E-2,4-hexadien-1-ol and maleic anhydride. You will have the 1H NMR spectrum of your sample recorded, and evident from that will be peak multiplicities of the various proton resonances. You should endeavour from your analysis to come up with a suggestion for the structure of compound '''Y''', and from this, estimates of the numerical values (but not the signs) of the 2J and 3J couplings visible. Now using the techniques described above, construct a model of your proposed structure for '''Y'''. Measure the dihedral angles for all the 3J couplings, and very approximately estimate what the corresponding 3J might be from the diagram above. Does this help you assign the stereochemistry of the product?
#'''Advanced topic''': Part of the spectroscopic analysis of the compound '''Y''' involves interpreting the IR spectrum. Theory can be used in fact to simulate the full IR spectrum. In section 5.3 below, you will find instructions on how to use the model you have calculated here to initiate a so called '''density functional''' calculation. This will provide you with the required IR simulation. Follow these instructions, and open the resulting .log file in Gaussview. Go to the '''Results''' menu and select '''vibrations'''. The IR spectrum will be displayed. Does it match the one you have recorded for yourself?

==== References ====

#M. Karplus, ''Vicinal Proton Coupling in Nuclear Magnetic Resonance'', '' J. Am. Chem. Soc.'', '''1963''', ''85'', 2870 - 2871; {{DOI|10.1021/ja00901a059}}
#A. Wu, D. Cremer, A. A. Auer, and J. Gauss, ''Extension of the Karplus Relationship for NMR Spin-Spin Coupling Constants to Nonplanar Ring Systems: Pseudorotation of Cyclopentane'', ''J. Phys. Chem. A,'', '''2002''', ''106'', 657 -667; {{DOI|10.1021/jp013160l}}
#C. A. Stortz and M. S. Maier, ''Configurational assignments of diastereomeric γ-lactones using vicinal H–H NMR coupling constants and molecular modelling'', ''J. Chem. Soc., Perkin Trans. 2'', '''2000''', 1832 - 1836. {{DOI|10.1039/b003862h}}
# A. H. Abdourazak, A. Sygula, and P. W. Rabideau ''Locking the bowl-shaped geometry of corannulene: cyclopentacorannulene'', ''J. Am. Chem. Soc.'', '''1993''', ''115'', 3010 - 3011. {{DOI|10.1021/ja00060a073}}

=== Bridgehead enols: Thermodynamic vs Kinetic Control Part 2.===
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#[[Image:Bredt.gif|thumb|right|Brendanone]] The ketone Brendan-2-one shown right exhibits unusual behaviour.6 When treated with NaOD/MeOD, deuterium substitution occurs easily and rapidly only in position Hb. Enolisation must of necessity form a bridgehead double bond (''anti-Bredt''), but clearly one isomer is more stable than the other possible form. Does molecular modelling predict this correctly?
#The unusually facile enolisation of this ketone (given that it forms an anti-Bredt enol) can also be investigated by molecular modelling. '''Measure''' the dihedral angle between the C-Ha or C-Hb vector and the carbonyl group. Assuming that the ''ideal'' angle for proton removal is around 90°, which proton is better set up for abstraction? Might this be kinetic rather than thermodynamic control?
#[[Image:Cortisone.gif|thumb|right|Cortisone]]One could also revisit Problem 2.3.3 above. Here, proton abstraction forms an enol which eventually epimerises the bridgehead position to form a ''trans'' ring junction. Why should this proton be particularly easy to remove? From what you have learnt above, would this be for kinetic or for thermodynamic reasons (or both?). Are all the relevant effects modelled using the mechanics approach or is consideration of the electrons also necessary?
|}
==== References and Footnotes====

# A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, {{doi-inline|10.1021/ja00837a043|''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins''}}, ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}}.

===Sulfonylation of Naphthalene: Thermodynamic vs Kinetic Control Part 3.===

[[Image:Sulfonylation.gif|right|thumb|Sulfonylation of naphthalene]]The sulfonylation of naphthalene using sulfuric acid is a good example of a mechanism combining both steric and electronic influences. The Molecular mechanics method intrinsic to the Ghemical program can only model the former, and not the latter. It is a worthwhile exercise to establish whether this anticipated deficiency does indeed lead to a model which only partially explains experiment.

It has been known for some time that treating naphthalene with sulfuric acids at low temperatures produces mostly substitution at the 1-position of the naphthalene. Heating the reaction mixture, or conducting the reaction at elevated temperatures produces mostly the 2-isomer. This is indeed a classic example of [[kinetic]] vs [[thermodynamic]] control, the 1-isomer being the kinetic one and the 2-isomer the thermodynamic one. To model the kinetic reaction, we have to inspect the [[transition state]] for the reaction, and here we can approximate this by the [[Wheland Intermediate]]. To model the thermodynamic reaction, we have to inspect the product (rather than the transition state) for the reaction.

#Build models for all four species shown in the diagram on the right. For the two products, define ''conjugated'' bond types for all the ring bonds, and define the sulfonyl group with two S=O double bonds and one S-O single bond. Take care to optimise the conformation of the sulfonyl group with respect to the aromatic ring. For the two Wheland intermediates, the limitations of Ghemical will force us to ''cheat''. Ghemical does not have parameters for a carbocation. So define the C2-C3 bond as conjugated (for the 1-Wheland intermediate). When you '''add hydrogens''' it will in fact add a second hydrogen to C2. Delete this one hydrogen. Ghemical will calculated the energy regardless of not knowing C2 is actually a carbonium ion! For the 2-Wheland intermediate, ensure that you use '''exactly''' the same number of ''conjugated'' bond types as you did for the 1-isomer (the two models in a mechanics sense are only comparable if you have the same total number of bond types in each model). You will have to decide whether these (undoubted) approximations have produced reasonable models or not (is the naphthalene framework planar for example, as it should be?).
#Record the pairs of energies (two for the 1- and 2-products, and two for each preceeding transition (Wheland) state.
#By turning the spacefilling representation on, which of the two products has the least unfavourable steric interactions between the sulfonic acid group and any adjacent hydrogens? Does this match with their relative energies?
#Do any unfavourable steric interactions observed in the product(s) also exist in the Wheland intermediates (as models for the transition states)?
#The relative stability of the Wheland intermediates is always assumed to be an '''electronic''' phenomenon. The conventional explanation is that the 1-Wheland isomer is stablized by both one aromatic ring '''and''' an allyl cation conjugated to it. The 2-Wheland isomer is stabilised by one aromatic ring conjugated to a secondary carbocation and an alkene. This type of ''cross conjugation'' is conventionally assumed to be less favourable. Does a purely mechanical approach to this problem reproduce this expectation? Or is this ''mechanical'' approximation to an ''electronic'' model too severe? It seems a good point to stop this course, since the next time you will build models, it will indeed be using methods which properly approximate the electronic components.
====References====

#R. Lantz, ''Mechanism of the monosulfonation of naphthalene'', ''Compt. Rend''. '''1935''', ''201'', 149-52.
#G. W. Wheland, ''A Quantum Mechanical Investigation of the Orientation of Substituents in Aromatic Molecules'', ''J. Am. Chem. Soc.'' '''1942''', ''64'', 900 - 908; {{DOI|10.1021/ja01256a047}}
#C. A. Reed, N. L. P. Fackler, K-C. Kim, D. Stasko, D. R. Evans, P. D. W. Boyd, and C. E. F. Rickard, ''Isolation of Protonated Arenes (Wheland Intermediates) with BArF and Carborane Anions. A Novel Crystalline Superacid'', ''J. Am. Chem. Soc.'' '''1999''', ''121'', 6314 - 6315 {{DOI|10.1021/ja981861z}}

== Coursework not to be attempted at any time: Antimodelling Molecules ==

The following represent molecules that should '''not''' be modelled under any circumstances! You should instead attempt to '''NAME''' them.

[[Image:Contraceptive.gif|Contraceptive (NO in every conceivable position)]] [[Image:Paradise.gif|Paradise lost]] [[Image:Synoptic.gif|Synoptic]] [[Image:Cisters.gif|Cisters]] [[Image:Transisters.gif|Transisters]] [[Image:Metaphor.gif|Metaphor]] [[Image:Metastasis.gif|Metastasis]] [[Image:Cyclone.gif|Cyclone]] [[Image:Anticyclone.gif|Anticyclone]] [[Image:Arsole.gif|Arsole]] [[Image:Orthodox.gif|Orthodox]] [[Image:Synthesis.gif|Synthesis and Antithesis]] [[Image:Aphrodisiac.gif|Name this yourself. Does Meg Ryan spring to mind?]] [[Image:Cyclops.gif|Cyclops]] [[Image:Paradox.gif|Paradox]] [[Image:Transparent.gif|Transparent]] [[Image:Encyclopedia.gif|Encyclopedia]] [[Image:Maths.jpg|Find X]] [[Image:VanderMaxforce.jpg|150px|Max Whitby stuck to a strangely attractive Lamp Post]] [[Image:nanoballet.jpg|200px|Nanoballet dancer]] [[Image:NanoCossacks.jpg|200px|NanoCossacks]]
[[Image:Paralysis.png|500px|Paralysis]]

If you know of any other antimodelling molecules, please add them here!

====Acknowledgements ====

Some of these cartoons are from [http://www.nearingzero.net/sci_chemistry.html here], and six are original. A superb collection of '''''silly names''''' is maintained
by [http://www.chm.bris.ac.uk/sillymolecules/sillymols.htm Paul May] [[Organic:Model_answers|.]] See {{DOI|10.1021/jo0349227}} for the nanoputians.

----
[[Second_Year_Modelling_Workshop|Back to introduction]]
----

Coursework

2010-10-15T14:32:57Z

Nm607: /* Coursework not to be attempted at any time: Antimodelling Molecules */

[[Second_Year_Modelling_Workshop|Back to introduction]]
----
== Molecular modelling Coursework to be attempted during Scheduled Sessions ==

These projects are arranged in increasing order of difficulty, and time taken to complete. You should do as many as you can in the 2 hour session allocated to you, and return to finish the rest if you wish at your convenience. At the end of the session, we will conduct a ''number auction''. For each project, the bidding will start with the first volunteer offering an energy for the system (or one of the isomers). If anyone has a lower energy for that molecule, they will then bid that energy. The winner will be the one with the lowest energy.

=== Conformational analysis I: Chair and Boat-like conformations of Cyclohexane ===
{|
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#Construct '''[[chair]]''' and '''[[boat]]'''-like '''[[conformation]]s''' of [[cyclohexane]]. Compare the energies of both forms.
#Check carefully if your boat really is a boat, or whether it has any apparent distorsion.
#Try changing one or more of the CH2 groups into an oxygen and see if that affects things.
#For the record, the point group symmetries of the various species which may be involved are D3d for the chair conformation, C2v for a boat geometry, and D2 for any twisted boat form. Is any of these forms '''chiral'''?
#The molecule on the left is called '''chiralane'''. Are its rings boats or chairs?
|}
====References ====
# The first suggestion of two forms for cyclohexane goes as far back as H. Sachse, ''Chem. Ber'', 1890, '''23''', 1363 and ''Z. Physik. Chem.'', 1892, 10, 203. This is nicely explained [http://www.chem.yale.edu/~chem125/125/history/Baeyer/Sachse.html here]. E. Mohr, ''J. Prakt. Chem.'', 1918, '''98''', 315 and ''Chem. Ber.'', 1922, '''55''', 230, translated Sachse's argument into a pictorial one.
# The article that put [[conformational analysis]] on the map: D. H. R. Barton and R. C. Cookson, ''The principles of conformational analysis'', ''Q. Rev. Chem. Soc.'', '''1956''', ''10'', 44. {{DOI|10.1039/QR9561000044}}
#[http://en.wikipedia.org/wiki/Chair_conformation Wikipedia article]
#D. A. Dixon and A. Komornicki, ''Ab initio conformational analysis of cyclohexane'', ''J. Phys. Chem.'', '''1990''', ''94'', 5630 - 5636; {{DOI|10.1021/j100377a041}}.
#A nice exploration of the potential energy surfaces for cyclohexane can be viewed [http://www.springer.com/carey-sundberg/cyclohex/cyclohex.php here].
# For a more modern application of this technique, see I. Columbus, R. E. Hoffman, and S. E. Biali, ''Stereochemistry and Conformational Anomalies of 1,2,3- and 1,2,3,4-Polycyclohexylcyclohexanes''. ''J. Am. Chem. Soc.'', '''1996''', ''118'', 6890 - 6896; {{DOI|10.1021/ja960380h}}.
# The second molecule shown in this section is called [6.6]chiralane. It is peculiar for having many six-membered saturated rings, all of them as twist-boats rather than chairs! (a chair has a plane of symmetry, a twist boat only axes, which of course allows it to be chiral). See [http://petitjeanmichel.free.fr/itoweb.petitjean.graphs.html#CHIR here] for more details.
# More detail on the conformation of rings (and acyclic systems) will be found in the [http://www.ch.ic.ac.uk/local/organic/conf/ lecture course] on the topic to be given in the spring term.

=== Enantiomers vs Diastereomers Part 1: Butanes and Helicenes. ===

This problem illustrates, using models, the difference between an enantiomer and a diastereomer.

#[[Image:diastereo.gif|thumb|right|2-bromo-3-chlorobutane]][[Image:pentahelicene.gif|thumb|right|Pentahelicene]]The compound 2-bromo-3-chlorobutane has two [[chiral]] centres, and four isomers (22) are therefore possible. Calculate all four isomers, and for each be careful to label each of the two stereo centres '''R''' or '''S''' as you go. For each of the four isomers '''R,R''', '''S,S''', '''R,S''', '''S,R''' you will have to think about whether you have obtained the lowest energy [[conformer]].
#Can your four energies be grouped in any way? You should think about the expected difference between '''enantiomers''', '''diastereomers''' and '''conformers'''.
{|
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#Construct some helicenes (pentahelicene or [5]helicene is shown on the right), using '''conjugated''' bonds for all the ring bonds. Benzene, naphthalene, phenanthrene and benzophenanthrene are in fact the first four members of this series. At what point in this series can you detect helicity cropping up? This is manifested by a non-planar helical wind of the molecule. If you do detect it, note how the wind is either left or right handed, ie the two forms are '''enantiomers''' of each other. Try displaying the molecule in '''spacefill mode''' (see above) to see if you can identify the source of the helicity. (Note: the smallest helicene which can be resolved experimentally into enantiomers is in fact [5]helicene]).
#The higher helicenes are well known (up to about [14]helicene) and amongst the ''most chiral'' molecules known (in terms of how much they rotate the plane of polarised light).
#[7]circulene is a known molecule, with a unique saddle-shaped structure, shown on the left (there is no real need for you to build this model, but do please do so if you are curious). [http://en.wikipedia.org/wiki/Graphene Graphene] is a related polymeric molecule, of much topical interest in the semi-conducting and other industries (Nobel Prize 2010).
|}
==== References ====

#[http://en.wikipedia.org/wiki/Diastereomer Wikipedia article on Diastereomers]
#[http://en.wikipedia.org/wiki/Helicene Wikipedia article on Helicenes and related molecules]
#R. H. Janke, G. Haufe, E.-U. Würthwein, and J. H. Borkent, ''Racemization Barriers of Helicenes: A Computational Study'', ''J. Am. Chem. Soc.'', '''1996''', ''118'' 6031 - 6035 {{DOI|10.1021/ja950774t}}

=== Conformational analysis II: ''cis'' and ''trans''-decalins, Steroids and Podcasts! ===
{|
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<jmol><jmolApplet><title>Woodward</title><color>white</color>
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# [[Image:cis-decalin.gif|thumb|right|cis Decalin]]This is the famous molecule that started the whole molecular mechanics modelling ball rolling. [http://www.ch.ic.ac.uk/video/barton/barton1.pdf Barton] in 1948 sought to find out which [[conformation]] of ''cis''-decalin was the most stable (see [http://www.ch.ic.ac.uk/video/barton/index_qt.html here] for video). You should be able to find at least three conformations of this molecule. Try locating these, and conclude which is the most stable. Identify any [[chair]] rings and any [[boat]].
#Measure some dihedral angles to see if the [[staggered]] relationships hold (i.e. for such a relationship, the dihedral angle should be close to 60 degrees).
#A key step in Woodward's famous synthesis of [http://en.wikipedia.org/wiki/Cortisone cortisone] is a quinone+butadiene [[Diels-Alder]] reaction to give a cis-decalin (left), with an assumption that [[epimerisation]] to a trans-decalin is thermodynamically favourable. [[Image:Cortisone.gif|thumb|left|cis Cortisone]]Can you verify whether the trans-isomer is indeed more stable? Its not so obvious, since this compound has two extra double bonds in the rings and six sp2 centres which might perturb things.
#[[Image:App.gif|thumb|right|trans Decalin]]The two diastereomeric ''trans''-decalin tosylates react quite differently with NaBH4. Construct models for both isomers (use methoxy as a model for the Tosyl group) and from the [[antiperiplanar]] alignments of bonds that you can find in each isomer, can you make a connection to the reactivity of each form? Consider very carefully where you would put a lone pair located on the nitrogen (i.e. include the N-Lp "bond" in your antiperiplanar alignments) asuming the this atom is tetrahedral rather than planar. Does this lone pair play any part in either reaction in this position?. Note that the relative energy of the axial/equatorial N-Methyl group will not be an accurate reflection of any [[antiperiplanar]] alignments, since these are predominantly electronic in origin, and this mechanics method does not take these into account.
##'''Optional:''' The second (elimination) reaction is very slow compared to the first. Discuss with tutors why this might be so (for Hints, see [[organic:entropy|here]] or [[organic:ngp|here]]).
##'''Optional''': These reactions do not appear to occur for the corresponding ''cis''-decalins6. Why not?

|}

==== References and Footnotes ====
# D. H. R. Barton, ''Interactions between non-bonded atoms, and the structure of cis-decalin'', ''J. Chem. Soc.'', '''1948''', 340-342. {{DOI|10.1039/JR9480000340}}
#[http://en.wikipedia.org/wiki/Decalin Wikipedia article]
# For a modern application of mechanics to this molecule, see J. M. A. Baas, B. Van de Graaf, D. Tavernier, and P. Vanhee, ''Empirical force field calculations. 10. Conformational analysis of cis-decalin'', ''J. Am. Chem. Soc.'', '''1981''', ''103'', 5014 - 5021; {{DOI|10.1021/ja00407a007}}.
# For a video-Podcast of Barton and Woodward (and other Nobel prize winners), subscribe [http://www.ch.ic.ac.uk/video/index.rss here]
# R. B. Woodward, F. Sondheimer, and D. Taub, ''The total Synthesis of Cortisone'', ''J. Am. Chem. Soc.'', '''1951''', ''73'', 4057 - 4057. {{DOI|10.1021/ja01152a551}}.
# P.-W. Phuan and M. C. Kozlowski, ''Control of the Conformational Equilibria in Aza-cis-Decalins: Structural Modification, Solvation, and Metal Chelation'', ''J. Org. Chem.'', '''2002''', ''67'', 6339 - 6346; {{DOI|10.1021/jo025544t}}

=== Menthone/''iso''menthone and Bridgehead enols: Thermodynamic vs Kinetic Control Part 1.===

{|
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#[[Image:Menthone.gif|thumb|right|Menthone]] Beckmann (of rearrangement fame) in 1889 dissolved optically active levorotatory (-) (S,R)-menthone ([α]D -28°) in conc. sulfuric acid, followed by quenching on ice to give what Beckmann assumed was pure (and what we would nowadays call [[diastereomeric]]) (+) (R,R)-isomenthone, [α]D +28°. He suggested for the first time that such an isomerisation, involving epimerisation at the asymmetric centre next to the keto group, proceeded via an intermediate enol in which the tetrahedral asymmetric carbon becomes planar. But this famous (perhaps even notorious2) early example of a [[reaction mechanism]] makes an interesting assumption, which can be tested by molecular modelling.
# Two possible enols can be formed, only one of which allows the [S] asymmetric carbon to become planar and then protonate to the [R] epimer. This is the so called [[thermodynamic enol]]. The other, which leaves the [S]-centre untouched is the [[kinetic enol]]. Find out if simple molecular modelling correctly predicts that the thermodynamic enol is indeed the more stable of the two. '''Hint:''' Model the enol and '''not''' the ketone. Consider carefully any conformational isomers possible.
# Given that the optical rotation3 of pure (+)-isomenthone is now known to be [α]D +101° rather than +28°, we can infer that Beckmann's product contains only 43% isomenthone and hence still contains 57% of original menthone, corresponding to an equilibrium constant of K= 0.75. This can be related to a (free energy) difference using the equation ΔG = -RT ln K, or ΔG = 0.7 kJ/mol (menthone being lower in energy by this amount compared to isomenthone). Can this energy difference be verified using molecular mechanics modelling? Can you explain why menthone is the more stable? (For another hint, or possibly a fright, visit [http://chemistry.gsu.edu/glactone/modeling/Luise/organic/cychexon.html this page]).
|}

==== References and footnotes ====
# E. Beckmann, ''Annalen'', '''1889''', ''250'', 322. {{DOI|10.1002/jlac.18892500306}}.
# Many of Beckmann's misconceptions were corrected by O. Wallach, ''Annalen'', '''1893''', ''276'', 296. {{DOI|10.1002/jlac.18932760306}}. The notoriety is because the coincidence of equal but opposite optical rotations obtained in this experiment led Beckmann to believe that he had obtained the [[enantiomer]] of menthone, and not as we now know, the impure (R,R) [[diastereomer]]. It should be borne in mind that the concept of tetrahedral and asymmetric carbon was only 15 years old at this time (see [http://en.wikipedia.org/wiki/Jacobus_van_%27t_Hoff Jacobus Henricus van't Hoff] and [http://en.wikipedia.org/wiki/Achille_Le_Bel Joseph Achille Le Bel]). Nevertheless confusion over this aspect persisted for some time after, and was often evident in the writings of even very famous chemists of the time (and Beckmann was very famous)!.
#[http://en.wikipedia.org/wiki/Menthone Wikipedia article]
# From about 1890-1935, mechanistic organic chemistry was born. In the absence of UV, IR, NMR, MS and X-Ray techniques, the [http://en.wikipedia.org/wiki/Polarimeter polarimeter] occupied a pivotal role. Many of the great discoveries in reaction mechanisms (keto-enol tautomerism as seen here, [[Organic:tutorial:meerwein| carbocations]], the Walden inversion, etc) relied on polarimetric measurements.
# A notorious modern example of (unwanted) epimerisation of a ketone is [http://en.wikipedia.org/wiki/Thalidomide Thalidomide], where one epimer inhibits morning sickness in pregnant women, and the other epimer is teratogenic, causing fetal abnormalities. The equilibrium in this case does not require conc. sulfuric acid, but can occur at physiological pH.

== Additional Molecular modelling Coursework ==

Please feel free to try these problems in your own time, and to discuss these with your organic tutors and lecturers. Note also that the relevant lectures may occur in the spring as well as autumn terms.
=== Axial/Equatorial preferences in cyclohexane and cyclohexanone and Hydrogen Bonding ===
{|
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#Construct a chair cyclohexane and replace firstly one of the [[axial]] hydrogens with the following groups: '''methyl''', '''t-butyl''', '''OH'''. Calculate the energy of the axial isomer.
# Then repeat (either by deleting/redrawing or by moving) for the equatorial forms. Compare the energies of the two isomers. Does any energy difference increase with the size of the group? Does OH fit into this in terms of size?
# [[Image:Thiomethylcyclohexanone.gif|right|thumb|thiomethyl cyclohexanone]]The dissolving metal reduction of cyclohexanones in a protic solvent (i.e. one capable of hydrogen bonding) is thermodynamically controlled and gives the more stable, equatorial alcohol. In fact, its probably the alkoxide that is the product, not the free alcohol. It is thought the alkoxide is actually a lot larger than the alcohol, accounting for the substantial equatorial preference. Can you think why its larger? [Ghemical cannot in fact model this, since the force field does not include parameters for the alkoxide anion].
# Determine the axial/equatorial preference of 2-methylthio-cyclohexanone (Hint: there are many conformations possible, and you should try a few to see if you can get the lowest).
|}
==== References and Footnotes ====

# A. H. Lewin and S. Winstein, ''NMR. Spectra and Conformational Analysis of 4-Alkylcyclohexanols'' ''J. Am. Chem. Soc.''; '''1962''', ''84'', 2464 - 2465; {{DOI|10.1021/ja00871a049}}
#F. R. Jensen and L. H. Gale, ''The Conformational Preference of the Bromo and Methyl Groups in Cyclohexane by IR Spectral Analysis'', ''J. Org. Chem.'', '''1960''', ''25'', 2075 - 2078. {{DOI|10.1021/jo01082a001}}
# K. B. Wiberg, J. D. Hammer, H. Castejon, W. F. Bailey, E. L. DeLeon, and R. M. Jarret, ''Conformational Studies in the Cyclohexane Series. 1. Experimental and Computational Investigation of Methyl, Ethyl, Isopropyl, and tert-Butylcyclohexanes'', ''J. Org. Chem.'', '''1999''', ''64'', 2085 - 2095; {{DOI|10.1021/jo990056f}}. The salient point here is that the [[enthalpy]] and [[entropy]] of this series differ in their trends.
# Just when you are starting to think that things are quite simple, along comes the observation: S. E. Biali, ''Axial monoalkyl cyclohexanes'', ''J. Org. Chem.'', '''1992''', ''57'', 2979 - 2980; {{DOI|10.1021/jo00037a001}}
# And this one with knobs on: ''In all-trans-1,2,3,4,5,6-hexaisopropylcyclohexane, all the alkyl groups are located at axial rather than equatorial positions: O. Golan, Z. Goren, and S. E. Biali, ''Axial-equatorial stability reversal in all-trans-polyalkylcyclohexanes'', ''J. Am. Chem. Soc.'', '''1990''', ''112'', 9300 - 9307. {{DOI|10.1021/ja00181a036}}.
#J. A. Anderson, K. Crager, Kelly, L.Fedoroff, G. S. Tschumper, Gregory S. ''Anchoring the potential energy surface of the cyclic water trimer.'' ''J. Chem. Physics'', '''2004''', ''121'', 11023-11029. {{DOI|10.1063/1.1799931}}.
#R. R. Fraser, N. C. Faibish, ''On the purported axial preference in 2-methylthio- and 2-methoxycyclohexanones: steric effects versus orbital interactions'', ''Can. J. Chem.'', '''1995''', ''73'', 88-94.
=== How to induce room temperature hydrolysis of a peptide ===
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<uploadedFileContents>peptide-13.3.mol</uploadedFileContents>
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[[Image:amide-cleavage.png|thumb|right|Peptide hydrolysis]] This introduces a further example of how simple conformational analysis can quickly rationalize kinetic behaviour. At neutral pH and 25° the half life for hydrolysis of a peptide bond is around 500 years (and thank goodness, or we would ourselves all rapidly hydrolise to a mush!). Some enzymes however can achieve this in less than 1 second, an acceleration of 1013! Organic chemists are not quite so clever, but they can achieve room temperature hydrolysis of a peptide in 21 minutes by careful conformational design. The two isomers shown on the right differ only in their stereochemistry, one hydrolysing quickly, the other slowly. Build a model of each compound, and calculate two isomers for each, varying in whether the ring N-substituent is oriented axial or equatorial with respect to the decalin ring. On the basis of your two pairs of energies, can you rationalise the observed kinetic behaviour? Do you know why both of these compounds take very much less than 500 years to hydrolise the peptide bond?

'''Hint1:''' Use the chair-chair conformation for cis-decalin as your template for constructing this system.

'''Hint2:''' When constructing your models, think if there are any hydrogen bonds that might stabilize the structure!

'''Hint3:''' Hydrolysis can only occur when the OH group can approach the carbonyl of the peptide bond close enough to react, and at the right angle of approach.
|}

==== Reference ====

# M. Fernandes, F. Fache, M. Rosen, P.-L. Nguyen, and D. E. Hansen, 'Rapid Cleavage of Unactivated, Unstrained Amide Bonds at Neutral pH', ''J. Org. Chem.,'' '''2008''', ASAP: {{DOI|10.1021/jo800706y}}

=== Caryophyllene: The phenomenon of Atropisomerism ===

# [[Image:caryophyllene-ketone.gif|thumb|right|Caryophyllene ketone]] [http://en.wikipedia.org/wiki/Caryophyllene Caryophyllene], a constituent of many essential oils, include clove oil, has a [[trans]] alkene contained in a 9-membered ring. One interesting property is that it has 4 [[diastereoisomers]] possible, originating from a total of three asymmetric centres present in the molecule. Two of these are conventional chiral centres, one is present in the form of a disymmetric trans double bond. To understand why such a bond can result in two configurations, one must appreciate that (concurrent) rotation about the two C-C single bonds adjacent to the alkene is in fact restricted, because to the hydrogen labelled Ha cannot easily pass by the edge of the 4-membered ring. Construct this molecule (in fact the ketone rather than the alkene) and optimize its geometry. Note in particular that the ring junction is ''trans'' and not ''cis''.
# You will find you may well have obtained one of two forms. In the first, the Ha hydrogen will be opposite the C=O group, in the other it will be adjacent to it. Record the energy of whatever form you got. At the end of the course, we will try to find the ''winner'' with the lowest energy (this is not as trivial as it sounds!).
# Next, take your structure, and try to ''flip'' the [[trans]] alkene bond around so that eg if the methyl were previously pointing up, now it will point down. You may find a combination of erasing/redrawing or of moving, will accomplish this. You may also find another trick useful, of deleting all hydrogens, and then re-sprouting them back on again. Re-optimise your structure and compare the energy with your first isomer.
# Another feature of this model is that you can judge which group is in the so-called shielded region of the carbonyl group magnetic anisotropy. Using this information, you can see if there are any anomalous 1H chemical shifts that might need explaining!

==== References ====
# M. Clericuzio, G. Alagona, C. Ghio, and L. Toma, ''Ab Initio and Density Functional Evaluations of the Molecular Conformations of -Caryophyllene and 6-Hydroxycaryophyllene'', ''J. Org. Chem.'' '''2000''', ''65'', 6910 - 6916. {{DOI|10.1021/jo000404+}}.
#[http://en.wikipedia.org/wiki/Caryophyllene Wikipedia article]
# For a recent application of this phenomenon, see P. C. Bulman Page, B. R. Buckley, S. D.R. Christie, M. Edgar, A. M. Poulton, M. R.J. Elsegood and V. McKee, ''A new paradigm in N-heterocyclic carbenoid ligands'', ''J. Organometallic Chem.'', '''2005''', ''690'', 6210-6216. D {{DOI|10.1016/j.jorganchem.2005.09.015}}.

=== Germacrene: Conformational analysis of medium sized rings ===

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# [[Image:Germacrene.gif|thumb|right|Germacrene and the thermal reaction product]]Germacrene is a natural product with a ten-membered ring; it has the triene structure shown. Assuming that it adopts a crown conformation, build a three-dimensional model.
# On heating, germacrene is converted into one of the stereoisomers of the divinylcyclohexane, via a [3,3] sigmatropic pericyclic reaction. Predict from your model for Germacrene whether the product will have the two vinyl groups [[cis]] or [[trans]] to one another.
|}

==== References ====

# K. Shimazaki, M. Mori, K. Okada, T. Chuman, H. Goto, K. Sakakibara and M. Hirota, ''Conformational analyses of periplanone analogs by molecular mechanics calculations'', '' J. Chem. Ecology'', '''1991''', ''17'', 779-88. {{DOI|10.1007/BF00994200}}.
# H. Shirahama, E. Sawa and T. Matsumoto, ''Conformational aspects of germacrene B. Are the germacrenes resolvable ?'', ''Tetrahedron Lett.'', '''1979''', ''20'', 2245-2246. {{DOI|10.1016/S0040-4039(01)93687-1}}. See also {{DOI|10.1039/P19750002332}} for an explanation of the selective epoxidation of germacrene.

=== Xestoquinone: Regio and Stereoselectivity in the Diels Alder reaction===

# [[Image:xestoquinone.gif|thumb|right|Xestoquinone precursor]] This compound is a precursor to a natural product called Xestoquinone. It has four alkene groups, which can individually be considered as the alkene component in a π2s + π4s [[Diels Alder]] [[cycloaddition]]. The pair of alkenes ''a+b'' or ''c+d'' can also act as the diene component in the π2s + π4s [[Diels Alder]] [[cycloaddition]]. Construct a model of the product of e.g. forming a bond between alkene ''a'' or alkene ''b'' and diene ''c+d'', and then reverse the addition by using either ''c'' or ''d'' adding to the diene ''a+b''. The stereochemistry of addition should always be [[suprafacial]], i.e. preserving the stereochemical relationships of the alkenes. You should very carefully check that this is so in your final model.
# Whilst you should stop at '''two''' models, it is possible to construct many more. For example, one might be able to add to either the ''top'' face of alkene ''b'' or to its ''bottom'' face. Identify the model with the lower energy, and save it for the end of the workshop. We will identify the isomer of lowest energy from everyone's results, this being a communal [[Monte Carlo]] experiment to find the [[global minimum]].

==== References ====

#[http://en.wikipedia.org/wiki/Diels-Alder_reaction Wikipedia article]
#For the original literature on this synthesis, see R. Carlini, K. Higgs, C. Older, S. Randhawa, and R. Rodrigo, ''Intramolecular Diels-Alder and Cope Reactions of o-Quinonoid Monoketals and Their Adducts: Efficient Syntheses of (±)-Xestoquinone and Heterocycles Related to Viridin'', ''J. Org. Chem.'', '''1997''', ''62'', 2330 - 2331. {{DOI|10.1021/jo970394l}} where you can check to see which isomers actually do form!

=== Aldol Reaction and anti-Bredt Rings ===

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# [[Image:Aldol.gif|thumb|right|Aldol Reaction]]When the diketone shown is treated with base, it undergoes an aldol condensation. Two obvious possibililties are elimination of the combination Ha and Oa, or of the alternative combination Hb and Ob. In fact, only a single product is formed. On the basis of energies for both products, can you predict which one is actually formed?
# Measure a few dihedral angles, ie to find out how planar the alkene present is. Does this suggest a reason why one isomer is less stable than the other?
# There is a third very remote structural possibility. If you have time, verify that this third product truly is unlikely.
|}

==== References ====
#[http://en.wikipedia.org/wiki/Bredt's_Rule Bredt's Rule]
# I. Novak, ''Molecular Modeling of Anti-Bredt Compounds'', ''J. Chem. Inf. Model.'', '''2005''', ''45'', 334 - 338. {{DOI|10.1021/ci0497354}}
# See also this article A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, ''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins'', ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}} in conjunction with Project 9.

=== Conformational Preference for asymmetric hydride reduction of a ketone ===

# [[Image:Felkin.gif|thumb|right|Asymmetric hydride reduction]]The hydride ([http://en.wikipedia.org/wiki/Lithium_aluminium_hydride BH4, AlH4, etc]) reduction of the ketone shown here is stereospecific, resulting in an alcohol with the stereochemistry shown (known as the [http://en.wikipedia.org/wiki/Chiral_induction Cram or the Felkin-Anh] rule). Construct a model of the ketone and establish which of at least two conformations is the lowest in energy.
# If the hydride anion is delivered from the least hindered position, is the conformation you have consistent with the stereochemistry shown for the product?
# You can see from Ref 4 that the situation can be far more complex, depending on many other factors.

====References ====
# [http://en.wikipedia.org/wiki/Chiral_induction Wikipedia article]
# D. J. Cram and D. R. Wilson, ''Studies in Stereochemistry. XXXII. Models for 1,2-Asymmetric Induction'', ''J. Am. Chem. Soc.'', '''1963''', ''85'', 1245 - 1249. {{DOI|10.1021/ja00892a008}}.
# Y. Yamamoto, K. Matsuoka, and H. Nemoto, ''Anti-Cram selective reduction of acyclic ketones via electron transfer initiated processes'', ''J. Am. Chem. Soc.'', '''1988''', ''110'', 4475 - 4476; {{DOI|10.1021/ja00221a093}}.
# A. Mengel and O. Reiser, ''Around and beyond Cram's Rule'', ''Chem. Rev.'', '''1999''', ''99'', 1191 - 1224. {{DOI|10.1021/cr980379w}}.

=== Enantiomers vs Diastereomers Part 2: NMR Coupling constants ===

#[[Image:karplus.gif|thumb|Axial-equatorial interconversion|right]]In Project 2.2 above, we saw how the energies of diastereomeric compounds could be compared with the corresponding enantiomers. In this extension, we show how molecular modelling can cast light on the conformation adopted by 2-ethyl-4-methyl-1-oxa-cyclopentane-3-carboxylic acid estimated using measured 1H NMR coupling constants. The (2S,3S,4S) diastereomer has couplings of 3JH2,H3 8.3 Hz and 3JH3,H4 9.8 Hz. Two possible conformations of this diastereomer are shown on the right. They differ in that one has Et axial, and Me/COOH equatorial, and the other Et equatorial and Me/COOH axial.
#[[Image:karplus.jpg|Karplus plot|thumb|left]]By calculating the geometries of both conformations, and measuring the dihedral angle H2-C-C-H3 and H3-C-C-H4, one can assess by using the Karplus equation (left, taken from Ref 2 and relevant for a cyclopentane, but the values for which might be modified by the presence of electronegative substituents), which conformation leads to the best agreement between the calculated angle and the measured coupling constants (Hint: on the basis of the predicted couplings, you should be able to eliminate one of the two conformations shown for this molecule).
#[[Image:5-circulene.gif|thumb|5-circulene|right]]In Project 2.2 we also introduced molecules such as helicenes and circulenes. The 1H NMR of the [5]-circulene shown to the right revealed a complex spectrum at δ 2.98 ppm and again at 3.75 ppm. On the face of it, the four protons labeled Ha and Hb should all be equivalent, and the spectrum should be a single peak, not two complex multiplets. Indeed, if the NMR is recorded at high temperatures, this is exactly what is observed. By constructing a model of the [5]-circulene shown, can you explain why at normal temperatures, the NMR spectrum is so complex? 
#[[Image:Lab_expt.jpg|thumb|Synthesis lab experiment|right]]A practical application of this technique is to determine the stereochemistry of the product of the reaction between E,E-2,4-hexadien-1-ol and maleic anhydride. You will have the 1H NMR spectrum of your sample recorded, and evident from that will be peak multiplicities of the various proton resonances. You should endeavour from your analysis to come up with a suggestion for the structure of compound '''Y''', and from this, estimates of the numerical values (but not the signs) of the 2J and 3J couplings visible. Now using the techniques described above, construct a model of your proposed structure for '''Y'''. Measure the dihedral angles for all the 3J couplings, and very approximately estimate what the corresponding 3J might be from the diagram above. Does this help you assign the stereochemistry of the product?
#'''Advanced topic''': Part of the spectroscopic analysis of the compound '''Y''' involves interpreting the IR spectrum. Theory can be used in fact to simulate the full IR spectrum. In section 5.3 below, you will find instructions on how to use the model you have calculated here to initiate a so called '''density functional''' calculation. This will provide you with the required IR simulation. Follow these instructions, and open the resulting .log file in Gaussview. Go to the '''Results''' menu and select '''vibrations'''. The IR spectrum will be displayed. Does it match the one you have recorded for yourself?

==== References ====

#M. Karplus, ''Vicinal Proton Coupling in Nuclear Magnetic Resonance'', '' J. Am. Chem. Soc.'', '''1963''', ''85'', 2870 - 2871; {{DOI|10.1021/ja00901a059}}
#A. Wu, D. Cremer, A. A. Auer, and J. Gauss, ''Extension of the Karplus Relationship for NMR Spin-Spin Coupling Constants to Nonplanar Ring Systems: Pseudorotation of Cyclopentane'', ''J. Phys. Chem. A,'', '''2002''', ''106'', 657 -667; {{DOI|10.1021/jp013160l}}
#C. A. Stortz and M. S. Maier, ''Configurational assignments of diastereomeric γ-lactones using vicinal H–H NMR coupling constants and molecular modelling'', ''J. Chem. Soc., Perkin Trans. 2'', '''2000''', 1832 - 1836. {{DOI|10.1039/b003862h}}
# A. H. Abdourazak, A. Sygula, and P. W. Rabideau ''Locking the bowl-shaped geometry of corannulene: cyclopentacorannulene'', ''J. Am. Chem. Soc.'', '''1993''', ''115'', 3010 - 3011. {{DOI|10.1021/ja00060a073}}

=== Bridgehead enols: Thermodynamic vs Kinetic Control Part 2.===
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#[[Image:Bredt.gif|thumb|right|Brendanone]] The ketone Brendan-2-one shown right exhibits unusual behaviour.6 When treated with NaOD/MeOD, deuterium substitution occurs easily and rapidly only in position Hb. Enolisation must of necessity form a bridgehead double bond (''anti-Bredt''), but clearly one isomer is more stable than the other possible form. Does molecular modelling predict this correctly?
#The unusually facile enolisation of this ketone (given that it forms an anti-Bredt enol) can also be investigated by molecular modelling. '''Measure''' the dihedral angle between the C-Ha or C-Hb vector and the carbonyl group. Assuming that the ''ideal'' angle for proton removal is around 90°, which proton is better set up for abstraction? Might this be kinetic rather than thermodynamic control?
#[[Image:Cortisone.gif|thumb|right|Cortisone]]One could also revisit Problem 2.3.3 above. Here, proton abstraction forms an enol which eventually epimerises the bridgehead position to form a ''trans'' ring junction. Why should this proton be particularly easy to remove? From what you have learnt above, would this be for kinetic or for thermodynamic reasons (or both?). Are all the relevant effects modelled using the mechanics approach or is consideration of the electrons also necessary?
|}
==== References and Footnotes====

# A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, {{doi-inline|10.1021/ja00837a043|''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins''}}, ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}}.

===Sulfonylation of Naphthalene: Thermodynamic vs Kinetic Control Part 3.===

[[Image:Sulfonylation.gif|right|thumb|Sulfonylation of naphthalene]]The sulfonylation of naphthalene using sulfuric acid is a good example of a mechanism combining both steric and electronic influences. The Molecular mechanics method intrinsic to the Ghemical program can only model the former, and not the latter. It is a worthwhile exercise to establish whether this anticipated deficiency does indeed lead to a model which only partially explains experiment.

It has been known for some time that treating naphthalene with sulfuric acids at low temperatures produces mostly substitution at the 1-position of the naphthalene. Heating the reaction mixture, or conducting the reaction at elevated temperatures produces mostly the 2-isomer. This is indeed a classic example of [[kinetic]] vs [[thermodynamic]] control, the 1-isomer being the kinetic one and the 2-isomer the thermodynamic one. To model the kinetic reaction, we have to inspect the [[transition state]] for the reaction, and here we can approximate this by the [[Wheland Intermediate]]. To model the thermodynamic reaction, we have to inspect the product (rather than the transition state) for the reaction.

#Build models for all four species shown in the diagram on the right. For the two products, define ''conjugated'' bond types for all the ring bonds, and define the sulfonyl group with two S=O double bonds and one S-O single bond. Take care to optimise the conformation of the sulfonyl group with respect to the aromatic ring. For the two Wheland intermediates, the limitations of Ghemical will force us to ''cheat''. Ghemical does not have parameters for a carbocation. So define the C2-C3 bond as conjugated (for the 1-Wheland intermediate). When you '''add hydrogens''' it will in fact add a second hydrogen to C2. Delete this one hydrogen. Ghemical will calculated the energy regardless of not knowing C2 is actually a carbonium ion! For the 2-Wheland intermediate, ensure that you use '''exactly''' the same number of ''conjugated'' bond types as you did for the 1-isomer (the two models in a mechanics sense are only comparable if you have the same total number of bond types in each model). You will have to decide whether these (undoubted) approximations have produced reasonable models or not (is the naphthalene framework planar for example, as it should be?).
#Record the pairs of energies (two for the 1- and 2-products, and two for each preceeding transition (Wheland) state.
#By turning the spacefilling representation on, which of the two products has the least unfavourable steric interactions between the sulfonic acid group and any adjacent hydrogens? Does this match with their relative energies?
#Do any unfavourable steric interactions observed in the product(s) also exist in the Wheland intermediates (as models for the transition states)?
#The relative stability of the Wheland intermediates is always assumed to be an '''electronic''' phenomenon. The conventional explanation is that the 1-Wheland isomer is stablized by both one aromatic ring '''and''' an allyl cation conjugated to it. The 2-Wheland isomer is stabilised by one aromatic ring conjugated to a secondary carbocation and an alkene. This type of ''cross conjugation'' is conventionally assumed to be less favourable. Does a purely mechanical approach to this problem reproduce this expectation? Or is this ''mechanical'' approximation to an ''electronic'' model too severe? It seems a good point to stop this course, since the next time you will build models, it will indeed be using methods which properly approximate the electronic components.
====References====

#R. Lantz, ''Mechanism of the monosulfonation of naphthalene'', ''Compt. Rend''. '''1935''', ''201'', 149-52.
#G. W. Wheland, ''A Quantum Mechanical Investigation of the Orientation of Substituents in Aromatic Molecules'', ''J. Am. Chem. Soc.'' '''1942''', ''64'', 900 - 908; {{DOI|10.1021/ja01256a047}}
#C. A. Reed, N. L. P. Fackler, K-C. Kim, D. Stasko, D. R. Evans, P. D. W. Boyd, and C. E. F. Rickard, ''Isolation of Protonated Arenes (Wheland Intermediates) with BArF and Carborane Anions. A Novel Crystalline Superacid'', ''J. Am. Chem. Soc.'' '''1999''', ''121'', 6314 - 6315 {{DOI|10.1021/ja981861z}}

== Coursework not to be attempted at any time: Antimodelling Molecules ==

The following represent molecules that should '''not''' be modelled under any circumstances! You should instead attempt to '''NAME''' them.

[[Image:Contraceptive.gif|Contraceptive (NO in every conceivable position)]] [[Image:Paradise.gif|Paradise lost]] [[Image:Synoptic.gif|Synoptic]] [[Image:Cisters.gif|Cisters]] [[Image:Transisters.gif|Transisters]] [[Image:Metaphor.gif|Metaphor]] [[Image:Metastasis.gif|Metastasis]] [[Image:Cyclone.gif|Cyclone]] [[Image:Anticyclone.gif|Anticyclone]] [[Image:Arsole.gif|Arsole]] [[Image:Orthodox.gif|Orthodox]] [[Image:Synthesis.gif|Synthesis and Antithesis]] [[Image:Aphrodisiac.gif|Name this yourself. Does Meg Ryan spring to mind?]] [[Image:Cyclops.gif|Cyclops]] [[Image:Paradox.gif|Paradox]] [[Image:Transparent.gif|Transparent]] [[Image:Encyclopedia.gif|Encyclopedia]] [[Image:Maths.jpg|Find X]] [[Image:VanderMaxforce.jpg|150px|Max Whitby stuck to a strangely attractive Lamp Post]] [[Image:nanoballet.jpg|200px|Nanoballet dancer]] [[Image:NanoCossacks.jpg|200px|NanoCossacks]]
[[Image:Paralysis.png|200px|Paralysis]]

If you know of any other antimodelling molecules, please add them here!

====Acknowledgements ====

Some of these cartoons are from [http://www.nearingzero.net/sci_chemistry.html here], and six are original. A superb collection of '''''silly names''''' is maintained
by [http://www.chm.bris.ac.uk/sillymolecules/sillymols.htm Paul May] [[Organic:Model_answers|.]] See {{DOI|10.1021/jo0349227}} for the nanoputians.

----
[[Second_Year_Modelling_Workshop|Back to introduction]]
----

Coursework

2010-10-15T14:32:41Z

Nm607: /* Coursework not to be attempted at any time: Antimodelling Molecules */

[[Second_Year_Modelling_Workshop|Back to introduction]]
----
== Molecular modelling Coursework to be attempted during Scheduled Sessions ==

These projects are arranged in increasing order of difficulty, and time taken to complete. You should do as many as you can in the 2 hour session allocated to you, and return to finish the rest if you wish at your convenience. At the end of the session, we will conduct a ''number auction''. For each project, the bidding will start with the first volunteer offering an energy for the system (or one of the isomers). If anyone has a lower energy for that molecule, they will then bid that energy. The winner will be the one with the lowest energy.

=== Conformational analysis I: Chair and Boat-like conformations of Cyclohexane ===
{|
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#Construct '''[[chair]]''' and '''[[boat]]'''-like '''[[conformation]]s''' of [[cyclohexane]]. Compare the energies of both forms.
#Check carefully if your boat really is a boat, or whether it has any apparent distorsion.
#Try changing one or more of the CH2 groups into an oxygen and see if that affects things.
#For the record, the point group symmetries of the various species which may be involved are D3d for the chair conformation, C2v for a boat geometry, and D2 for any twisted boat form. Is any of these forms '''chiral'''?
#The molecule on the left is called '''chiralane'''. Are its rings boats or chairs?
|}
====References ====
# The first suggestion of two forms for cyclohexane goes as far back as H. Sachse, ''Chem. Ber'', 1890, '''23''', 1363 and ''Z. Physik. Chem.'', 1892, 10, 203. This is nicely explained [http://www.chem.yale.edu/~chem125/125/history/Baeyer/Sachse.html here]. E. Mohr, ''J. Prakt. Chem.'', 1918, '''98''', 315 and ''Chem. Ber.'', 1922, '''55''', 230, translated Sachse's argument into a pictorial one.
# The article that put [[conformational analysis]] on the map: D. H. R. Barton and R. C. Cookson, ''The principles of conformational analysis'', ''Q. Rev. Chem. Soc.'', '''1956''', ''10'', 44. {{DOI|10.1039/QR9561000044}}
#[http://en.wikipedia.org/wiki/Chair_conformation Wikipedia article]
#D. A. Dixon and A. Komornicki, ''Ab initio conformational analysis of cyclohexane'', ''J. Phys. Chem.'', '''1990''', ''94'', 5630 - 5636; {{DOI|10.1021/j100377a041}}.
#A nice exploration of the potential energy surfaces for cyclohexane can be viewed [http://www.springer.com/carey-sundberg/cyclohex/cyclohex.php here].
# For a more modern application of this technique, see I. Columbus, R. E. Hoffman, and S. E. Biali, ''Stereochemistry and Conformational Anomalies of 1,2,3- and 1,2,3,4-Polycyclohexylcyclohexanes''. ''J. Am. Chem. Soc.'', '''1996''', ''118'', 6890 - 6896; {{DOI|10.1021/ja960380h}}.
# The second molecule shown in this section is called [6.6]chiralane. It is peculiar for having many six-membered saturated rings, all of them as twist-boats rather than chairs! (a chair has a plane of symmetry, a twist boat only axes, which of course allows it to be chiral). See [http://petitjeanmichel.free.fr/itoweb.petitjean.graphs.html#CHIR here] for more details.
# More detail on the conformation of rings (and acyclic systems) will be found in the [http://www.ch.ic.ac.uk/local/organic/conf/ lecture course] on the topic to be given in the spring term.

=== Enantiomers vs Diastereomers Part 1: Butanes and Helicenes. ===

This problem illustrates, using models, the difference between an enantiomer and a diastereomer.

#[[Image:diastereo.gif|thumb|right|2-bromo-3-chlorobutane]][[Image:pentahelicene.gif|thumb|right|Pentahelicene]]The compound 2-bromo-3-chlorobutane has two [[chiral]] centres, and four isomers (22) are therefore possible. Calculate all four isomers, and for each be careful to label each of the two stereo centres '''R''' or '''S''' as you go. For each of the four isomers '''R,R''', '''S,S''', '''R,S''', '''S,R''' you will have to think about whether you have obtained the lowest energy [[conformer]].
#Can your four energies be grouped in any way? You should think about the expected difference between '''enantiomers''', '''diastereomers''' and '''conformers'''.
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#Construct some helicenes (pentahelicene or [5]helicene is shown on the right), using '''conjugated''' bonds for all the ring bonds. Benzene, naphthalene, phenanthrene and benzophenanthrene are in fact the first four members of this series. At what point in this series can you detect helicity cropping up? This is manifested by a non-planar helical wind of the molecule. If you do detect it, note how the wind is either left or right handed, ie the two forms are '''enantiomers''' of each other. Try displaying the molecule in '''spacefill mode''' (see above) to see if you can identify the source of the helicity. (Note: the smallest helicene which can be resolved experimentally into enantiomers is in fact [5]helicene]).
#The higher helicenes are well known (up to about [14]helicene) and amongst the ''most chiral'' molecules known (in terms of how much they rotate the plane of polarised light).
#[7]circulene is a known molecule, with a unique saddle-shaped structure, shown on the left (there is no real need for you to build this model, but do please do so if you are curious). [http://en.wikipedia.org/wiki/Graphene Graphene] is a related polymeric molecule, of much topical interest in the semi-conducting and other industries (Nobel Prize 2010).
|}
==== References ====

#[http://en.wikipedia.org/wiki/Diastereomer Wikipedia article on Diastereomers]
#[http://en.wikipedia.org/wiki/Helicene Wikipedia article on Helicenes and related molecules]
#R. H. Janke, G. Haufe, E.-U. Würthwein, and J. H. Borkent, ''Racemization Barriers of Helicenes: A Computational Study'', ''J. Am. Chem. Soc.'', '''1996''', ''118'' 6031 - 6035 {{DOI|10.1021/ja950774t}}

=== Conformational analysis II: ''cis'' and ''trans''-decalins, Steroids and Podcasts! ===
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# [[Image:cis-decalin.gif|thumb|right|cis Decalin]]This is the famous molecule that started the whole molecular mechanics modelling ball rolling. [http://www.ch.ic.ac.uk/video/barton/barton1.pdf Barton] in 1948 sought to find out which [[conformation]] of ''cis''-decalin was the most stable (see [http://www.ch.ic.ac.uk/video/barton/index_qt.html here] for video). You should be able to find at least three conformations of this molecule. Try locating these, and conclude which is the most stable. Identify any [[chair]] rings and any [[boat]].
#Measure some dihedral angles to see if the [[staggered]] relationships hold (i.e. for such a relationship, the dihedral angle should be close to 60 degrees).
#A key step in Woodward's famous synthesis of [http://en.wikipedia.org/wiki/Cortisone cortisone] is a quinone+butadiene [[Diels-Alder]] reaction to give a cis-decalin (left), with an assumption that [[epimerisation]] to a trans-decalin is thermodynamically favourable. [[Image:Cortisone.gif|thumb|left|cis Cortisone]]Can you verify whether the trans-isomer is indeed more stable? Its not so obvious, since this compound has two extra double bonds in the rings and six sp2 centres which might perturb things.
#[[Image:App.gif|thumb|right|trans Decalin]]The two diastereomeric ''trans''-decalin tosylates react quite differently with NaBH4. Construct models for both isomers (use methoxy as a model for the Tosyl group) and from the [[antiperiplanar]] alignments of bonds that you can find in each isomer, can you make a connection to the reactivity of each form? Consider very carefully where you would put a lone pair located on the nitrogen (i.e. include the N-Lp "bond" in your antiperiplanar alignments) asuming the this atom is tetrahedral rather than planar. Does this lone pair play any part in either reaction in this position?. Note that the relative energy of the axial/equatorial N-Methyl group will not be an accurate reflection of any [[antiperiplanar]] alignments, since these are predominantly electronic in origin, and this mechanics method does not take these into account.
##'''Optional:''' The second (elimination) reaction is very slow compared to the first. Discuss with tutors why this might be so (for Hints, see [[organic:entropy|here]] or [[organic:ngp|here]]).
##'''Optional''': These reactions do not appear to occur for the corresponding ''cis''-decalins6. Why not?

|}

==== References and Footnotes ====
# D. H. R. Barton, ''Interactions between non-bonded atoms, and the structure of cis-decalin'', ''J. Chem. Soc.'', '''1948''', 340-342. {{DOI|10.1039/JR9480000340}}
#[http://en.wikipedia.org/wiki/Decalin Wikipedia article]
# For a modern application of mechanics to this molecule, see J. M. A. Baas, B. Van de Graaf, D. Tavernier, and P. Vanhee, ''Empirical force field calculations. 10. Conformational analysis of cis-decalin'', ''J. Am. Chem. Soc.'', '''1981''', ''103'', 5014 - 5021; {{DOI|10.1021/ja00407a007}}.
# For a video-Podcast of Barton and Woodward (and other Nobel prize winners), subscribe [http://www.ch.ic.ac.uk/video/index.rss here]
# R. B. Woodward, F. Sondheimer, and D. Taub, ''The total Synthesis of Cortisone'', ''J. Am. Chem. Soc.'', '''1951''', ''73'', 4057 - 4057. {{DOI|10.1021/ja01152a551}}.
# P.-W. Phuan and M. C. Kozlowski, ''Control of the Conformational Equilibria in Aza-cis-Decalins: Structural Modification, Solvation, and Metal Chelation'', ''J. Org. Chem.'', '''2002''', ''67'', 6339 - 6346; {{DOI|10.1021/jo025544t}}

=== Menthone/''iso''menthone and Bridgehead enols: Thermodynamic vs Kinetic Control Part 1.===

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#[[Image:Menthone.gif|thumb|right|Menthone]] Beckmann (of rearrangement fame) in 1889 dissolved optically active levorotatory (-) (S,R)-menthone ([α]D -28°) in conc. sulfuric acid, followed by quenching on ice to give what Beckmann assumed was pure (and what we would nowadays call [[diastereomeric]]) (+) (R,R)-isomenthone, [α]D +28°. He suggested for the first time that such an isomerisation, involving epimerisation at the asymmetric centre next to the keto group, proceeded via an intermediate enol in which the tetrahedral asymmetric carbon becomes planar. But this famous (perhaps even notorious2) early example of a [[reaction mechanism]] makes an interesting assumption, which can be tested by molecular modelling.
# Two possible enols can be formed, only one of which allows the [S] asymmetric carbon to become planar and then protonate to the [R] epimer. This is the so called [[thermodynamic enol]]. The other, which leaves the [S]-centre untouched is the [[kinetic enol]]. Find out if simple molecular modelling correctly predicts that the thermodynamic enol is indeed the more stable of the two. '''Hint:''' Model the enol and '''not''' the ketone. Consider carefully any conformational isomers possible.
# Given that the optical rotation3 of pure (+)-isomenthone is now known to be [α]D +101° rather than +28°, we can infer that Beckmann's product contains only 43% isomenthone and hence still contains 57% of original menthone, corresponding to an equilibrium constant of K= 0.75. This can be related to a (free energy) difference using the equation ΔG = -RT ln K, or ΔG = 0.7 kJ/mol (menthone being lower in energy by this amount compared to isomenthone). Can this energy difference be verified using molecular mechanics modelling? Can you explain why menthone is the more stable? (For another hint, or possibly a fright, visit [http://chemistry.gsu.edu/glactone/modeling/Luise/organic/cychexon.html this page]).
|}

==== References and footnotes ====
# E. Beckmann, ''Annalen'', '''1889''', ''250'', 322. {{DOI|10.1002/jlac.18892500306}}.
# Many of Beckmann's misconceptions were corrected by O. Wallach, ''Annalen'', '''1893''', ''276'', 296. {{DOI|10.1002/jlac.18932760306}}. The notoriety is because the coincidence of equal but opposite optical rotations obtained in this experiment led Beckmann to believe that he had obtained the [[enantiomer]] of menthone, and not as we now know, the impure (R,R) [[diastereomer]]. It should be borne in mind that the concept of tetrahedral and asymmetric carbon was only 15 years old at this time (see [http://en.wikipedia.org/wiki/Jacobus_van_%27t_Hoff Jacobus Henricus van't Hoff] and [http://en.wikipedia.org/wiki/Achille_Le_Bel Joseph Achille Le Bel]). Nevertheless confusion over this aspect persisted for some time after, and was often evident in the writings of even very famous chemists of the time (and Beckmann was very famous)!.
#[http://en.wikipedia.org/wiki/Menthone Wikipedia article]
# From about 1890-1935, mechanistic organic chemistry was born. In the absence of UV, IR, NMR, MS and X-Ray techniques, the [http://en.wikipedia.org/wiki/Polarimeter polarimeter] occupied a pivotal role. Many of the great discoveries in reaction mechanisms (keto-enol tautomerism as seen here, [[Organic:tutorial:meerwein| carbocations]], the Walden inversion, etc) relied on polarimetric measurements.
# A notorious modern example of (unwanted) epimerisation of a ketone is [http://en.wikipedia.org/wiki/Thalidomide Thalidomide], where one epimer inhibits morning sickness in pregnant women, and the other epimer is teratogenic, causing fetal abnormalities. The equilibrium in this case does not require conc. sulfuric acid, but can occur at physiological pH.

== Additional Molecular modelling Coursework ==

Please feel free to try these problems in your own time, and to discuss these with your organic tutors and lecturers. Note also that the relevant lectures may occur in the spring as well as autumn terms.
=== Axial/Equatorial preferences in cyclohexane and cyclohexanone and Hydrogen Bonding ===
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#Construct a chair cyclohexane and replace firstly one of the [[axial]] hydrogens with the following groups: '''methyl''', '''t-butyl''', '''OH'''. Calculate the energy of the axial isomer.
# Then repeat (either by deleting/redrawing or by moving) for the equatorial forms. Compare the energies of the two isomers. Does any energy difference increase with the size of the group? Does OH fit into this in terms of size?
# [[Image:Thiomethylcyclohexanone.gif|right|thumb|thiomethyl cyclohexanone]]The dissolving metal reduction of cyclohexanones in a protic solvent (i.e. one capable of hydrogen bonding) is thermodynamically controlled and gives the more stable, equatorial alcohol. In fact, its probably the alkoxide that is the product, not the free alcohol. It is thought the alkoxide is actually a lot larger than the alcohol, accounting for the substantial equatorial preference. Can you think why its larger? [Ghemical cannot in fact model this, since the force field does not include parameters for the alkoxide anion].
# Determine the axial/equatorial preference of 2-methylthio-cyclohexanone (Hint: there are many conformations possible, and you should try a few to see if you can get the lowest).
|}
==== References and Footnotes ====

# A. H. Lewin and S. Winstein, ''NMR. Spectra and Conformational Analysis of 4-Alkylcyclohexanols'' ''J. Am. Chem. Soc.''; '''1962''', ''84'', 2464 - 2465; {{DOI|10.1021/ja00871a049}}
#F. R. Jensen and L. H. Gale, ''The Conformational Preference of the Bromo and Methyl Groups in Cyclohexane by IR Spectral Analysis'', ''J. Org. Chem.'', '''1960''', ''25'', 2075 - 2078. {{DOI|10.1021/jo01082a001}}
# K. B. Wiberg, J. D. Hammer, H. Castejon, W. F. Bailey, E. L. DeLeon, and R. M. Jarret, ''Conformational Studies in the Cyclohexane Series. 1. Experimental and Computational Investigation of Methyl, Ethyl, Isopropyl, and tert-Butylcyclohexanes'', ''J. Org. Chem.'', '''1999''', ''64'', 2085 - 2095; {{DOI|10.1021/jo990056f}}. The salient point here is that the [[enthalpy]] and [[entropy]] of this series differ in their trends.
# Just when you are starting to think that things are quite simple, along comes the observation: S. E. Biali, ''Axial monoalkyl cyclohexanes'', ''J. Org. Chem.'', '''1992''', ''57'', 2979 - 2980; {{DOI|10.1021/jo00037a001}}
# And this one with knobs on: ''In all-trans-1,2,3,4,5,6-hexaisopropylcyclohexane, all the alkyl groups are located at axial rather than equatorial positions: O. Golan, Z. Goren, and S. E. Biali, ''Axial-equatorial stability reversal in all-trans-polyalkylcyclohexanes'', ''J. Am. Chem. Soc.'', '''1990''', ''112'', 9300 - 9307. {{DOI|10.1021/ja00181a036}}.
#J. A. Anderson, K. Crager, Kelly, L.Fedoroff, G. S. Tschumper, Gregory S. ''Anchoring the potential energy surface of the cyclic water trimer.'' ''J. Chem. Physics'', '''2004''', ''121'', 11023-11029. {{DOI|10.1063/1.1799931}}.
#R. R. Fraser, N. C. Faibish, ''On the purported axial preference in 2-methylthio- and 2-methoxycyclohexanones: steric effects versus orbital interactions'', ''Can. J. Chem.'', '''1995''', ''73'', 88-94.
=== How to induce room temperature hydrolysis of a peptide ===
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[[Image:amide-cleavage.png|thumb|right|Peptide hydrolysis]] This introduces a further example of how simple conformational analysis can quickly rationalize kinetic behaviour. At neutral pH and 25° the half life for hydrolysis of a peptide bond is around 500 years (and thank goodness, or we would ourselves all rapidly hydrolise to a mush!). Some enzymes however can achieve this in less than 1 second, an acceleration of 1013! Organic chemists are not quite so clever, but they can achieve room temperature hydrolysis of a peptide in 21 minutes by careful conformational design. The two isomers shown on the right differ only in their stereochemistry, one hydrolysing quickly, the other slowly. Build a model of each compound, and calculate two isomers for each, varying in whether the ring N-substituent is oriented axial or equatorial with respect to the decalin ring. On the basis of your two pairs of energies, can you rationalise the observed kinetic behaviour? Do you know why both of these compounds take very much less than 500 years to hydrolise the peptide bond?

'''Hint1:''' Use the chair-chair conformation for cis-decalin as your template for constructing this system.

'''Hint2:''' When constructing your models, think if there are any hydrogen bonds that might stabilize the structure!

'''Hint3:''' Hydrolysis can only occur when the OH group can approach the carbonyl of the peptide bond close enough to react, and at the right angle of approach.
|}

==== Reference ====

# M. Fernandes, F. Fache, M. Rosen, P.-L. Nguyen, and D. E. Hansen, 'Rapid Cleavage of Unactivated, Unstrained Amide Bonds at Neutral pH', ''J. Org. Chem.,'' '''2008''', ASAP: {{DOI|10.1021/jo800706y}}

=== Caryophyllene: The phenomenon of Atropisomerism ===

# [[Image:caryophyllene-ketone.gif|thumb|right|Caryophyllene ketone]] [http://en.wikipedia.org/wiki/Caryophyllene Caryophyllene], a constituent of many essential oils, include clove oil, has a [[trans]] alkene contained in a 9-membered ring. One interesting property is that it has 4 [[diastereoisomers]] possible, originating from a total of three asymmetric centres present in the molecule. Two of these are conventional chiral centres, one is present in the form of a disymmetric trans double bond. To understand why such a bond can result in two configurations, one must appreciate that (concurrent) rotation about the two C-C single bonds adjacent to the alkene is in fact restricted, because to the hydrogen labelled Ha cannot easily pass by the edge of the 4-membered ring. Construct this molecule (in fact the ketone rather than the alkene) and optimize its geometry. Note in particular that the ring junction is ''trans'' and not ''cis''.
# You will find you may well have obtained one of two forms. In the first, the Ha hydrogen will be opposite the C=O group, in the other it will be adjacent to it. Record the energy of whatever form you got. At the end of the course, we will try to find the ''winner'' with the lowest energy (this is not as trivial as it sounds!).
# Next, take your structure, and try to ''flip'' the [[trans]] alkene bond around so that eg if the methyl were previously pointing up, now it will point down. You may find a combination of erasing/redrawing or of moving, will accomplish this. You may also find another trick useful, of deleting all hydrogens, and then re-sprouting them back on again. Re-optimise your structure and compare the energy with your first isomer.
# Another feature of this model is that you can judge which group is in the so-called shielded region of the carbonyl group magnetic anisotropy. Using this information, you can see if there are any anomalous 1H chemical shifts that might need explaining!

==== References ====
# M. Clericuzio, G. Alagona, C. Ghio, and L. Toma, ''Ab Initio and Density Functional Evaluations of the Molecular Conformations of -Caryophyllene and 6-Hydroxycaryophyllene'', ''J. Org. Chem.'' '''2000''', ''65'', 6910 - 6916. {{DOI|10.1021/jo000404+}}.
#[http://en.wikipedia.org/wiki/Caryophyllene Wikipedia article]
# For a recent application of this phenomenon, see P. C. Bulman Page, B. R. Buckley, S. D.R. Christie, M. Edgar, A. M. Poulton, M. R.J. Elsegood and V. McKee, ''A new paradigm in N-heterocyclic carbenoid ligands'', ''J. Organometallic Chem.'', '''2005''', ''690'', 6210-6216. D {{DOI|10.1016/j.jorganchem.2005.09.015}}.

=== Germacrene: Conformational analysis of medium sized rings ===

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# [[Image:Germacrene.gif|thumb|right|Germacrene and the thermal reaction product]]Germacrene is a natural product with a ten-membered ring; it has the triene structure shown. Assuming that it adopts a crown conformation, build a three-dimensional model.
# On heating, germacrene is converted into one of the stereoisomers of the divinylcyclohexane, via a [3,3] sigmatropic pericyclic reaction. Predict from your model for Germacrene whether the product will have the two vinyl groups [[cis]] or [[trans]] to one another.
|}

==== References ====

# K. Shimazaki, M. Mori, K. Okada, T. Chuman, H. Goto, K. Sakakibara and M. Hirota, ''Conformational analyses of periplanone analogs by molecular mechanics calculations'', '' J. Chem. Ecology'', '''1991''', ''17'', 779-88. {{DOI|10.1007/BF00994200}}.
# H. Shirahama, E. Sawa and T. Matsumoto, ''Conformational aspects of germacrene B. Are the germacrenes resolvable ?'', ''Tetrahedron Lett.'', '''1979''', ''20'', 2245-2246. {{DOI|10.1016/S0040-4039(01)93687-1}}. See also {{DOI|10.1039/P19750002332}} for an explanation of the selective epoxidation of germacrene.

=== Xestoquinone: Regio and Stereoselectivity in the Diels Alder reaction===

# [[Image:xestoquinone.gif|thumb|right|Xestoquinone precursor]] This compound is a precursor to a natural product called Xestoquinone. It has four alkene groups, which can individually be considered as the alkene component in a π2s + π4s [[Diels Alder]] [[cycloaddition]]. The pair of alkenes ''a+b'' or ''c+d'' can also act as the diene component in the π2s + π4s [[Diels Alder]] [[cycloaddition]]. Construct a model of the product of e.g. forming a bond between alkene ''a'' or alkene ''b'' and diene ''c+d'', and then reverse the addition by using either ''c'' or ''d'' adding to the diene ''a+b''. The stereochemistry of addition should always be [[suprafacial]], i.e. preserving the stereochemical relationships of the alkenes. You should very carefully check that this is so in your final model.
# Whilst you should stop at '''two''' models, it is possible to construct many more. For example, one might be able to add to either the ''top'' face of alkene ''b'' or to its ''bottom'' face. Identify the model with the lower energy, and save it for the end of the workshop. We will identify the isomer of lowest energy from everyone's results, this being a communal [[Monte Carlo]] experiment to find the [[global minimum]].

==== References ====

#[http://en.wikipedia.org/wiki/Diels-Alder_reaction Wikipedia article]
#For the original literature on this synthesis, see R. Carlini, K. Higgs, C. Older, S. Randhawa, and R. Rodrigo, ''Intramolecular Diels-Alder and Cope Reactions of o-Quinonoid Monoketals and Their Adducts: Efficient Syntheses of (±)-Xestoquinone and Heterocycles Related to Viridin'', ''J. Org. Chem.'', '''1997''', ''62'', 2330 - 2331. {{DOI|10.1021/jo970394l}} where you can check to see which isomers actually do form!

=== Aldol Reaction and anti-Bredt Rings ===

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# [[Image:Aldol.gif|thumb|right|Aldol Reaction]]When the diketone shown is treated with base, it undergoes an aldol condensation. Two obvious possibililties are elimination of the combination Ha and Oa, or of the alternative combination Hb and Ob. In fact, only a single product is formed. On the basis of energies for both products, can you predict which one is actually formed?
# Measure a few dihedral angles, ie to find out how planar the alkene present is. Does this suggest a reason why one isomer is less stable than the other?
# There is a third very remote structural possibility. If you have time, verify that this third product truly is unlikely.
|}

==== References ====
#[http://en.wikipedia.org/wiki/Bredt's_Rule Bredt's Rule]
# I. Novak, ''Molecular Modeling of Anti-Bredt Compounds'', ''J. Chem. Inf. Model.'', '''2005''', ''45'', 334 - 338. {{DOI|10.1021/ci0497354}}
# See also this article A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, ''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins'', ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}} in conjunction with Project 9.

=== Conformational Preference for asymmetric hydride reduction of a ketone ===

# [[Image:Felkin.gif|thumb|right|Asymmetric hydride reduction]]The hydride ([http://en.wikipedia.org/wiki/Lithium_aluminium_hydride BH4, AlH4, etc]) reduction of the ketone shown here is stereospecific, resulting in an alcohol with the stereochemistry shown (known as the [http://en.wikipedia.org/wiki/Chiral_induction Cram or the Felkin-Anh] rule). Construct a model of the ketone and establish which of at least two conformations is the lowest in energy.
# If the hydride anion is delivered from the least hindered position, is the conformation you have consistent with the stereochemistry shown for the product?
# You can see from Ref 4 that the situation can be far more complex, depending on many other factors.

====References ====
# [http://en.wikipedia.org/wiki/Chiral_induction Wikipedia article]
# D. J. Cram and D. R. Wilson, ''Studies in Stereochemistry. XXXII. Models for 1,2-Asymmetric Induction'', ''J. Am. Chem. Soc.'', '''1963''', ''85'', 1245 - 1249. {{DOI|10.1021/ja00892a008}}.
# Y. Yamamoto, K. Matsuoka, and H. Nemoto, ''Anti-Cram selective reduction of acyclic ketones via electron transfer initiated processes'', ''J. Am. Chem. Soc.'', '''1988''', ''110'', 4475 - 4476; {{DOI|10.1021/ja00221a093}}.
# A. Mengel and O. Reiser, ''Around and beyond Cram's Rule'', ''Chem. Rev.'', '''1999''', ''99'', 1191 - 1224. {{DOI|10.1021/cr980379w}}.

=== Enantiomers vs Diastereomers Part 2: NMR Coupling constants ===

#[[Image:karplus.gif|thumb|Axial-equatorial interconversion|right]]In Project 2.2 above, we saw how the energies of diastereomeric compounds could be compared with the corresponding enantiomers. In this extension, we show how molecular modelling can cast light on the conformation adopted by 2-ethyl-4-methyl-1-oxa-cyclopentane-3-carboxylic acid estimated using measured 1H NMR coupling constants. The (2S,3S,4S) diastereomer has couplings of 3JH2,H3 8.3 Hz and 3JH3,H4 9.8 Hz. Two possible conformations of this diastereomer are shown on the right. They differ in that one has Et axial, and Me/COOH equatorial, and the other Et equatorial and Me/COOH axial.
#[[Image:karplus.jpg|Karplus plot|thumb|left]]By calculating the geometries of both conformations, and measuring the dihedral angle H2-C-C-H3 and H3-C-C-H4, one can assess by using the Karplus equation (left, taken from Ref 2 and relevant for a cyclopentane, but the values for which might be modified by the presence of electronegative substituents), which conformation leads to the best agreement between the calculated angle and the measured coupling constants (Hint: on the basis of the predicted couplings, you should be able to eliminate one of the two conformations shown for this molecule).
#[[Image:5-circulene.gif|thumb|5-circulene|right]]In Project 2.2 we also introduced molecules such as helicenes and circulenes. The 1H NMR of the [5]-circulene shown to the right revealed a complex spectrum at δ 2.98 ppm and again at 3.75 ppm. On the face of it, the four protons labeled Ha and Hb should all be equivalent, and the spectrum should be a single peak, not two complex multiplets. Indeed, if the NMR is recorded at high temperatures, this is exactly what is observed. By constructing a model of the [5]-circulene shown, can you explain why at normal temperatures, the NMR spectrum is so complex? 
#[[Image:Lab_expt.jpg|thumb|Synthesis lab experiment|right]]A practical application of this technique is to determine the stereochemistry of the product of the reaction between E,E-2,4-hexadien-1-ol and maleic anhydride. You will have the 1H NMR spectrum of your sample recorded, and evident from that will be peak multiplicities of the various proton resonances. You should endeavour from your analysis to come up with a suggestion for the structure of compound '''Y''', and from this, estimates of the numerical values (but not the signs) of the 2J and 3J couplings visible. Now using the techniques described above, construct a model of your proposed structure for '''Y'''. Measure the dihedral angles for all the 3J couplings, and very approximately estimate what the corresponding 3J might be from the diagram above. Does this help you assign the stereochemistry of the product?
#'''Advanced topic''': Part of the spectroscopic analysis of the compound '''Y''' involves interpreting the IR spectrum. Theory can be used in fact to simulate the full IR spectrum. In section 5.3 below, you will find instructions on how to use the model you have calculated here to initiate a so called '''density functional''' calculation. This will provide you with the required IR simulation. Follow these instructions, and open the resulting .log file in Gaussview. Go to the '''Results''' menu and select '''vibrations'''. The IR spectrum will be displayed. Does it match the one you have recorded for yourself?

==== References ====

#M. Karplus, ''Vicinal Proton Coupling in Nuclear Magnetic Resonance'', '' J. Am. Chem. Soc.'', '''1963''', ''85'', 2870 - 2871; {{DOI|10.1021/ja00901a059}}
#A. Wu, D. Cremer, A. A. Auer, and J. Gauss, ''Extension of the Karplus Relationship for NMR Spin-Spin Coupling Constants to Nonplanar Ring Systems: Pseudorotation of Cyclopentane'', ''J. Phys. Chem. A,'', '''2002''', ''106'', 657 -667; {{DOI|10.1021/jp013160l}}
#C. A. Stortz and M. S. Maier, ''Configurational assignments of diastereomeric γ-lactones using vicinal H–H NMR coupling constants and molecular modelling'', ''J. Chem. Soc., Perkin Trans. 2'', '''2000''', 1832 - 1836. {{DOI|10.1039/b003862h}}
# A. H. Abdourazak, A. Sygula, and P. W. Rabideau ''Locking the bowl-shaped geometry of corannulene: cyclopentacorannulene'', ''J. Am. Chem. Soc.'', '''1993''', ''115'', 3010 - 3011. {{DOI|10.1021/ja00060a073}}

=== Bridgehead enols: Thermodynamic vs Kinetic Control Part 2.===
{|
| <jmol><jmolApplet><title>Bridgehead</title><color>white</color>
<size>150</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Bridgehead2.xyz</uploadedFileContents>
</jmolApplet></jmol>
|
#[[Image:Bredt.gif|thumb|right|Brendanone]] The ketone Brendan-2-one shown right exhibits unusual behaviour.6 When treated with NaOD/MeOD, deuterium substitution occurs easily and rapidly only in position Hb. Enolisation must of necessity form a bridgehead double bond (''anti-Bredt''), but clearly one isomer is more stable than the other possible form. Does molecular modelling predict this correctly?
#The unusually facile enolisation of this ketone (given that it forms an anti-Bredt enol) can also be investigated by molecular modelling. '''Measure''' the dihedral angle between the C-Ha or C-Hb vector and the carbonyl group. Assuming that the ''ideal'' angle for proton removal is around 90°, which proton is better set up for abstraction? Might this be kinetic rather than thermodynamic control?
#[[Image:Cortisone.gif|thumb|right|Cortisone]]One could also revisit Problem 2.3.3 above. Here, proton abstraction forms an enol which eventually epimerises the bridgehead position to form a ''trans'' ring junction. Why should this proton be particularly easy to remove? From what you have learnt above, would this be for kinetic or for thermodynamic reasons (or both?). Are all the relevant effects modelled using the mechanics approach or is consideration of the electrons also necessary?
|}
==== References and Footnotes====

# A. Nickon, D. F. Covey, F.-C. Huang, and Y.-N. Kuo, {{doi-inline|10.1021/ja00837a043|''Unusually facile bridgehead enolization. Locked boat forms in anti-Bredt olefins''}}, ''J. Am. Chem. Soc.'', '''1975''', ''97'', 904 - 905; {{DOI|10.1021/ja00837a043}}.

===Sulfonylation of Naphthalene: Thermodynamic vs Kinetic Control Part 3.===

[[Image:Sulfonylation.gif|right|thumb|Sulfonylation of naphthalene]]The sulfonylation of naphthalene using sulfuric acid is a good example of a mechanism combining both steric and electronic influences. The Molecular mechanics method intrinsic to the Ghemical program can only model the former, and not the latter. It is a worthwhile exercise to establish whether this anticipated deficiency does indeed lead to a model which only partially explains experiment.

It has been known for some time that treating naphthalene with sulfuric acids at low temperatures produces mostly substitution at the 1-position of the naphthalene. Heating the reaction mixture, or conducting the reaction at elevated temperatures produces mostly the 2-isomer. This is indeed a classic example of [[kinetic]] vs [[thermodynamic]] control, the 1-isomer being the kinetic one and the 2-isomer the thermodynamic one. To model the kinetic reaction, we have to inspect the [[transition state]] for the reaction, and here we can approximate this by the [[Wheland Intermediate]]. To model the thermodynamic reaction, we have to inspect the product (rather than the transition state) for the reaction.

#Build models for all four species shown in the diagram on the right. For the two products, define ''conjugated'' bond types for all the ring bonds, and define the sulfonyl group with two S=O double bonds and one S-O single bond. Take care to optimise the conformation of the sulfonyl group with respect to the aromatic ring. For the two Wheland intermediates, the limitations of Ghemical will force us to ''cheat''. Ghemical does not have parameters for a carbocation. So define the C2-C3 bond as conjugated (for the 1-Wheland intermediate). When you '''add hydrogens''' it will in fact add a second hydrogen to C2. Delete this one hydrogen. Ghemical will calculated the energy regardless of not knowing C2 is actually a carbonium ion! For the 2-Wheland intermediate, ensure that you use '''exactly''' the same number of ''conjugated'' bond types as you did for the 1-isomer (the two models in a mechanics sense are only comparable if you have the same total number of bond types in each model). You will have to decide whether these (undoubted) approximations have produced reasonable models or not (is the naphthalene framework planar for example, as it should be?).
#Record the pairs of energies (two for the 1- and 2-products, and two for each preceeding transition (Wheland) state.
#By turning the spacefilling representation on, which of the two products has the least unfavourable steric interactions between the sulfonic acid group and any adjacent hydrogens? Does this match with their relative energies?
#Do any unfavourable steric interactions observed in the product(s) also exist in the Wheland intermediates (as models for the transition states)?
#The relative stability of the Wheland intermediates is always assumed to be an '''electronic''' phenomenon. The conventional explanation is that the 1-Wheland isomer is stablized by both one aromatic ring '''and''' an allyl cation conjugated to it. The 2-Wheland isomer is stabilised by one aromatic ring conjugated to a secondary carbocation and an alkene. This type of ''cross conjugation'' is conventionally assumed to be less favourable. Does a purely mechanical approach to this problem reproduce this expectation? Or is this ''mechanical'' approximation to an ''electronic'' model too severe? It seems a good point to stop this course, since the next time you will build models, it will indeed be using methods which properly approximate the electronic components.
====References====

#R. Lantz, ''Mechanism of the monosulfonation of naphthalene'', ''Compt. Rend''. '''1935''', ''201'', 149-52.
#G. W. Wheland, ''A Quantum Mechanical Investigation of the Orientation of Substituents in Aromatic Molecules'', ''J. Am. Chem. Soc.'' '''1942''', ''64'', 900 - 908; {{DOI|10.1021/ja01256a047}}
#C. A. Reed, N. L. P. Fackler, K-C. Kim, D. Stasko, D. R. Evans, P. D. W. Boyd, and C. E. F. Rickard, ''Isolation of Protonated Arenes (Wheland Intermediates) with BArF and Carborane Anions. A Novel Crystalline Superacid'', ''J. Am. Chem. Soc.'' '''1999''', ''121'', 6314 - 6315 {{DOI|10.1021/ja981861z}}

== Coursework not to be attempted at any time: Antimodelling Molecules ==

The following represent molecules that should '''not''' be modelled under any circumstances! You should instead attempt to '''NAME''' them.

[[Image:Contraceptive.gif|Contraceptive (NO in every conceivable position)]] [[Image:Paradise.gif|Paradise lost]] [[Image:Synoptic.gif|Synoptic]] [[Image:Cisters.gif|Cisters]] [[Image:Transisters.gif|Transisters]] [[Image:Metaphor.gif|Metaphor]] [[Image:Metastasis.gif|Metastasis]] [[Image:Cyclone.gif|Cyclone]] [[Image:Anticyclone.gif|Anticyclone]] [[Image:Arsole.gif|Arsole]] [[Image:Orthodox.gif|Orthodox]] [[Image:Synthesis.gif|Synthesis and Antithesis]] [[Image:Aphrodisiac.gif|Name this yourself. Does Meg Ryan spring to mind?]] [[Image:Cyclops.gif|Cyclops]] [[Image:Paradox.gif|Paradox]] [[Image:Transparent.gif|Transparent]] [[Image:Encyclopedia.gif|Encyclopedia]] [[Image:Maths.jpg|Find X]] [[Image:VanderMaxforce.jpg|150px|Max Whitby stuck to a strangely attractive Lamp Post]] [[Image:nanoballet.jpg|200px|Nanoballet dancer]] [[Image:NanoCossacks.jpg|200px|NanoCossacks]]
[[Image:Paralysis.png|Paralysis]]

If you know of any other antimodelling molecules, please add them here!

====Acknowledgements ====

Some of these cartoons are from [http://www.nearingzero.net/sci_chemistry.html here], and six are original. A superb collection of '''''silly names''''' is maintained
by [http://www.chm.bris.ac.uk/sillymolecules/sillymols.htm Paul May] [[Organic:Model_answers|.]] See {{DOI|10.1021/jo0349227}} for the nanoputians.

----
[[Second_Year_Modelling_Workshop|Back to introduction]]
----

File:Paralysis.png

2010-10-15T14:32:15Z

Nm607:

Rep:Mod3:nathanmarch

2009-12-17T10:53:57Z

Nm607: /* iii) */

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations were not calculated, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 

=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.

=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
Once a sensible minimum has been reached at a low optimization level it is advisable to reoptimize using a better basis set; this may not alter the geometry significantly, however a proper estimate of the energy of a conformer can be essential for making good predictions about a reaction.

'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.

=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 

=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to an energy minimum; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
Thus the method used for reaching the transition state is inconsequential, only reaching the transition state matters.

=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced did not finalize (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (originally 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 

=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 

The vibrations of each transition state were of the right character to suggest that the transitionstate had in fact been reached and both calculations converged. The endo transition state had a calculated imaginary frequency of -806(.39) cm-1:
 
[[Image:Nm607_endo_transition_state_vibration-806.jpg|frame|left|Fig. 23 - Endo imaginary vibration]]
 
Likewise the exo transition state had an imaginary vibration that displayed symultaneous formation of both σ-bonds:
 
[[Image:Nm607_exo_transition_state_vibration-812.jpg|frame|left|Fig. 24 - Exo imaginary vibration]]
 
Diels Alder chemistry is sensitive to molecular orbital overlap, prior to bonding so analysing the molecular orbitals of the trasition states is vital for an understanding of the reaction kinetics. To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-17T10:39:30Z

Nm607: /* d) */

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations were not calculated, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 

=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.

=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
Once a sensible minimum has been reached at a low optimization level it is advisable to reoptimize using a better basis set; this may not alter the geometry significantly, however a proper estimate of the energy of a conformer can be essential for making good predictions about a reaction.

'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.

=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 

=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to an energy minimum; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
Thus the method used for reaching the transition state is inconsequential, only reaching the transition state matters.

=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced did not finalize (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (originally 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 

=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 

The vibrations of each transition state were of the right character to suggest that the transitionstate had in fact been reached and both calculations converged. The endo transition state had a calculated imaginary frequency of -806(.39) cm-1:
 
[[Image:Nm607_endo_transition_state_vibration-806.jpg.jpg|frame|left|Fig. 23 - Endo imaginary vibration]]
 
Likewise the exo transition state had an imaginary vibration that displayed symultaneous formation of both σ-bonds:
 
[[Image:Nm607_exo_transition_state_vibration-812.jpg|frame|left|Fig. 24 - Exo imaginary vibration]]
 
Diels Alder chemistry is sensitive to molecular orbital overlap, prior to bonding so analysing the molecular orbitals of the trasition states is vital for an understanding of the reaction kinetics. To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-17T10:35:54Z

Nm607: /* c) */

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations were not calculated, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 

=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.

=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
Once a sensible minimum has been reached at a low optimization level it is advisable to reoptimize using a better basis set; this may not alter the geometry significantly, however a proper estimate of the energy of a conformer can be essential for making good predictions about a reaction.

'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.

=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 

=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to an energy minimum; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced did not finalize (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (originally 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 

=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 

The vibrations of each transition state were of the right character to suggest that the transitionstate had in fact been reached and both calculations converged. The endo transition state had a calculated imaginary frequency of -806(.39) cm-1:
 
[[Image:Nm607_endo_transition_state_vibration-806.jpg.jpg|frame|left|Fig. 23 - Endo imaginary vibration]]
 
Likewise the exo transition state had an imaginary vibration that displayed symultaneous formation of both σ-bonds:
 
[[Image:Nm607_exo_transition_state_vibration-812.jpg|frame|left|Fig. 24 - Exo imaginary vibration]]
 
Diels Alder chemistry is sensitive to molecular orbital overlap, prior to bonding so analysing the molecular orbitals of the trasition states is vital for an understanding of the reaction kinetics. To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-17T10:27:41Z

Nm607: /* e) */

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations were not calculated, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 

=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.

=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
Once a sensible minimum has been reached at a low optimization level it is advisable to reoptimize using a better basis set; this may not alter the geometry significantly, however a proper estimate of the energy of a conformer can be essential for making good predictions about a reaction.

'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.

=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 

=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced did not finalize (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (originally 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 

=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 

The vibrations of each transition state were of the right character to suggest that the transitionstate had in fact been reached and both calculations converged. The endo transition state had a calculated imaginary frequency of -806(.39) cm-1:
 
[[Image:Nm607_endo_transition_state_vibration-806.jpg.jpg|frame|left|Fig. 23 - Endo imaginary vibration]]
 
Likewise the exo transition state had an imaginary vibration that displayed symultaneous formation of both σ-bonds:
 
[[Image:Nm607_exo_transition_state_vibration-812.jpg|frame|left|Fig. 24 - Exo imaginary vibration]]
 
Diels Alder chemistry is sensitive to molecular orbital overlap, prior to bonding so analysing the molecular orbitals of the trasition states is vital for an understanding of the reaction kinetics. To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-17T10:27:04Z

Nm607: /* e) */

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations were not calculated, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 

=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.

=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
Once a sensible minimum has been reached at a low optimization level it is advisable to reoptimize using a better basis set; this may not alter the geometry significantly, however a proper estimate of the energy of a conformer can be essential for making good predictions about a reaction.

'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.

=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 

=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced did not finalize (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 

=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 

The vibrations of each transition state were of the right character to suggest that the transitionstate had in fact been reached and both calculations converged. The endo transition state had a calculated imaginary frequency of -806(.39) cm-1:
 
[[Image:Nm607_endo_transition_state_vibration-806.jpg.jpg|frame|left|Fig. 23 - Endo imaginary vibration]]
 
Likewise the exo transition state had an imaginary vibration that displayed symultaneous formation of both σ-bonds:
 
[[Image:Nm607_exo_transition_state_vibration-812.jpg|frame|left|Fig. 24 - Exo imaginary vibration]]
 
Diels Alder chemistry is sensitive to molecular orbital overlap, prior to bonding so analysing the molecular orbitals of the trasition states is vital for an understanding of the reaction kinetics. To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-17T10:25:56Z

Nm607: /* b) */

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations were not calculated, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 

=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.

=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
Once a sensible minimum has been reached at a low optimization level it is advisable to reoptimize using a better basis set; this may not alter the geometry significantly, however a proper estimate of the energy of a conformer can be essential for making good predictions about a reaction.

'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.

=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 

=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 

The vibrations of each transition state were of the right character to suggest that the transitionstate had in fact been reached and both calculations converged. The endo transition state had a calculated imaginary frequency of -806(.39) cm-1:
 
[[Image:Nm607_endo_transition_state_vibration-806.jpg.jpg|frame|left|Fig. 23 - Endo imaginary vibration]]
 
Likewise the exo transition state had an imaginary vibration that displayed symultaneous formation of both σ-bonds:
 
[[Image:Nm607_exo_transition_state_vibration-812.jpg|frame|left|Fig. 24 - Exo imaginary vibration]]
 
Diels Alder chemistry is sensitive to molecular orbital overlap, prior to bonding so analysing the molecular orbitals of the trasition states is vital for an understanding of the reaction kinetics. To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-17T10:19:57Z

Nm607: /* f) */

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations were not calculated, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 

=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.

=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
Once a sensible minimum has been reached at a low optimization level it is advisable to reoptimize using a better basis set; this may not alter the geometry significantly, however a proper estimate of the energy of a conformer can be essential for making good predictions about a reaction.

'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.

=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 

The vibrations of each transition state were of the right character to suggest that the transitionstate had in fact been reached and both calculations converged. The endo transition state had a calculated imaginary frequency of -806(.39) cm-1:
 
[[Image:Nm607_endo_transition_state_vibration-806.jpg.jpg|frame|left|Fig. 23 - Endo imaginary vibration]]
 
Likewise the exo transition state had an imaginary vibration that displayed symultaneous formation of both σ-bonds:
 
[[Image:Nm607_exo_transition_state_vibration-812.jpg|frame|left|Fig. 24 - Exo imaginary vibration]]
 
Diels Alder chemistry is sensitive to molecular orbital overlap, prior to bonding so analysing the molecular orbitals of the trasition states is vital for an understanding of the reaction kinetics. To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-17T10:12:19Z

Nm607: /* c) */

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations were not calculated, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 

=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.

=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 

The vibrations of each transition state were of the right character to suggest that the transitionstate had in fact been reached and both calculations converged. The endo transition state had a calculated imaginary frequency of -806(.39) cm-1:
 
[[Image:Nm607_endo_transition_state_vibration-806.jpg.jpg|frame|left|Fig. 23 - Endo imaginary vibration]]
 
Likewise the exo transition state had an imaginary vibration that displayed symultaneous formation of both σ-bonds:
 
[[Image:Nm607_exo_transition_state_vibration-812.jpg|frame|left|Fig. 24 - Exo imaginary vibration]]
 
Diels Alder chemistry is sensitive to molecular orbital overlap, prior to bonding so analysing the molecular orbitals of the trasition states is vital for an understanding of the reaction kinetics. To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-17T10:11:14Z

Nm607: /* b) */

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations were not calculated, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 

=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 

The vibrations of each transition state were of the right character to suggest that the transitionstate had in fact been reached and both calculations converged. The endo transition state had a calculated imaginary frequency of -806(.39) cm-1:
 
[[Image:Nm607_endo_transition_state_vibration-806.jpg.jpg|frame|left|Fig. 23 - Endo imaginary vibration]]
 
Likewise the exo transition state had an imaginary vibration that displayed symultaneous formation of both σ-bonds:
 
[[Image:Nm607_exo_transition_state_vibration-812.jpg|frame|left|Fig. 24 - Exo imaginary vibration]]
 
Diels Alder chemistry is sensitive to molecular orbital overlap, prior to bonding so analysing the molecular orbitals of the trasition states is vital for an understanding of the reaction kinetics. To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-15T09:44:55Z

Nm607:

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations are not available, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 
=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 

The vibrations of each transition state were of the right character to suggest that the transitionstate had in fact been reached and both calculations converged. The endo transition state had a calculated imaginary frequency of -806(.39) cm-1:
 
[[Image:Nm607_endo_transition_state_vibration-806.jpg.jpg|frame|left|Fig. 23 - Endo imaginary vibration]]
 
Likewise the exo transition state had an imaginary vibration that displayed symultaneous formation of both σ-bonds:
 
[[Image:Nm607_exo_transition_state_vibration-812.jpg|frame|left|Fig. 24 - Exo imaginary vibration]]
 
Diels Alder chemistry is sensitive to molecular orbital overlap, prior to bonding so analysing the molecular orbitals of the trasition states is vital for an understanding of the reaction kinetics. To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

===References===
<references />

File:Nm607 endo transition state vibration-806.jpg

2009-12-15T09:42:40Z

Nm607:

File:Nm607 exo transition state vibration-812.jpg

2009-12-15T09:39:47Z

Nm607:

Rep:Mod3:nathanmarch

2009-12-14T21:15:37Z

Nm607:

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations are not available, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 
=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 
To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-14T21:14:58Z

Nm607:

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations are not available, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 
=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 
To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more
----

===References===
<references />

File:Nm607 exo opt results summary.txt

2009-12-14T21:10:04Z

Nm607:

File:Nm607 endo opt results summary.txt

2009-12-14T21:09:25Z

Nm607:

Rep:Mod3:nathanmarch

2009-12-14T21:07:21Z

Nm607:

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations are not available, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 
=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 
To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>.
----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-14T21:02:47Z

Nm607:

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations are not available, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 
=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 
To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 

----

===References===
<references />

File:Nm607 destabilization.gif

2009-12-14T21:01:44Z

Nm607:

File:Nm607 seconary orbital interactions.gif

2009-12-14T20:53:06Z

Nm607:

Rep:Mod3:nathanmarch

2009-12-14T20:35:06Z

Nm607:

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations are not available, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 
=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 
To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

Looking at the energies of the two isomers one is lead to the conclusion that

----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-14T20:24:58Z

Nm607: /* ii) */

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations are not available, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 
=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
[[Image:Nm607_be_transition_series.JPG|thumb|left|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 
To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-14T20:24:28Z

Nm607:

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations are not available, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 
=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. [[Image:Nm607_be_transition_series.JPG|thumb|right|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.
=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 
To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

----

===References===
<references />

File:Nm607 exo transition state LUMO.jpg

2009-12-14T20:23:39Z

Nm607:

File:Nm607 exo transition state LUMO(side).jpg

2009-12-14T20:23:33Z

Nm607:

File:Nm607 exo transition state HOMO(side).jpg

2009-12-14T20:23:27Z

Nm607:

File:Nm607 exo transition state HOMO.jpg

2009-12-14T20:23:19Z

Nm607:

File:Nm607 exo transition state.jpg

2009-12-14T20:21:00Z

Nm607:

File:Nm607 endo transition state.jpg

2009-12-14T20:19:12Z

Nm607:

File:Nm607 exo transition state results summary.txt

2009-12-14T20:15:54Z

Nm607:

File:NM607 EXO TRANSITION STATE.LOG

2009-12-14T20:15:29Z

Nm607:

Rep:Mod3:nathanmarch

2009-12-14T20:09:52Z

Nm607:

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations are not available, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 
=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. [[Image:Nm607_be_transition_series.JPG|thumb|right|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.
=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the

{|border="1"
|-
!colspan="2"|Table 10 - Molecular orbitals of the endo transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

----

===References===
<references />

File:Nm607 endo transition state LUMO(side).jpg

2009-12-14T20:08:41Z

Nm607:

File:Nm607 endo transition state HOMO(side).jpg

2009-12-14T20:08:33Z

Nm607:

Rep:Mod3:nathanmarch

2009-12-14T19:49:08Z

Nm607:

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations are not available, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 
=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. [[Image:Nm607_be_transition_series.JPG|thumb|right|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.
=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

To properly analyse the molecular orbitals of the transition states it is first necessary to examine the

{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}

{|border="1"
|-
!colspan="2"|Table 10 - Molecular orbitals of the endo transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}

----

===References===
<references />

Rep:Mod3:nathanmarch

2009-12-14T19:48:37Z

Nm607:

The following is a summary of work carried out using ChemBio3D 12.0 Ultra, Gaussian 09W and GaussView 5.0.8c, Imperial College Chemistry Department - 3rd Year Computational Labs.

Conventions:
*Parentheses enclosing the final digits of a number indicate that the calculated figure has expressed digits that are beyond the accuracy of the method to ascertain i.e. an output bond length of 1.23456 Å will only be accurate to 0.01 Å and the figure will be written as 1.23(456)Å.
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
*Extracts from .gjf files have been edited such that they include only important information i.e. .chk directories are not shown
==Module 3==
===The Cope Rearrangement===
[[Image:Nm607_cope_rearrangement.gif|frame|right|Fig. 1 - The Cope Rearrangement]]The Cope Rearrangement is an example of a [3,3]-sigmatropic reaction, and is unusual in one main respect: the reactant, 1,5-hexadiene, is the product. While this may cause minor problems practically when trying to model the reaction i.e. with atoms labels and so forth, what this reaction does provide is a suitably simple introduction to the field of transition state modelling; the reaction profile is symmetric, so knowledge of just one molecule is necessary to understand the path to and from the transition state.
 
====Optimizing the Reactants and Products====
"Optimizing the Reactants and Products" boils down to "Optimizing 1,5-hexadiene". 1,5-hexdiene has five carbon-carbon bonds, with free rotation possible about three. Assuming that there are six possible dihedral angles (ignoring duplication via symmetry) there are 63 possible conformations. 729 is reduced to the 10 most stable conformations, shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Which conformation eventually leads to the transition state is of vital importance in understanding the kinetics of the Cope rearrangement; if the required conformation is a high energy conformation the reaction could be stifled. Thus characterization of the conformers of 1,5-hexadiene is necessary prior to examination of the transition state.
=====a)=====
Using the ethyl and vinyl fragments in GaussView the structure of 1,5-hexadiene was input. The dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar. Following a cleanup by GaussView the structure emerged as follows:
 
[[Image:Nm607_hexadiene_structure1_clean.jpg|frame|left|Structure 1]]
 
This structure was then subjected to the following:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 1 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/2/28/NM607_HEXADIENE_STRUCTURE1_OPT.LOG NM607_HEXADIENE_STRUCTURE1_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/9f/Nm607_hexadiene_structure1_opt_results_summary.txt Nm607_hexadiene_structure1_opt_results_summary.txt]

This first structure has C2{E,C2} symmetry:
 
[[Image:Nm607_hexadiene_structure1_postopt_C2.jpg|frame|left|Conformer 1]]
 
=====b)=====
A fresh structure was drawn, with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°, producing this structure:
 
[[Image:Nm607_hexadiene_structure2.jpg|frame|left|Structure 2]]
 
The energies of the two starting configurations are not available, but if they were it would be reasonable that the 'gauche' conformation would be of higher energy than the 'anti' conformation. This would be mainly due to methylene hydrogens being synperiplanar to vinyl hydrogens in the gauche form, creating steric strain. Without the energies of the starting conformations, the energies of their optimized structures will have to suffice: in this case there is not enough information to judge whether the outcome of one optimization with one structure will be lower in energy than the optimization of another structure.

This structure was optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 2 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/41/NM607_HEXADIENE_STRUCTURE2_OPT.LOG NM607_HEXADIENE_STRUCTURE2_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ce/Nm607_hexadiene_structure2_opt_results_summary.txt Nm607_hexadiene_structure2_opt_results_summary.txt]

This yielded a conformer with C2 symmetry:
 
[[Image:Nm607_hexadiene_structure2_opt_C2.jpg|frame|left|Conformer 2]]
 
=====c)=====
The two conformers differ in energy by about 3 kJ mol-1, with '''Conformer 1''' being the most stable. In an attempt yo yield an even more stable structure '''Conformer 1''' was adjusted such that the two vinyl groups were not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle was adjusted from ~60° to be 180°, and then the C3-C4-C5-C6 dihedral angle was changed from 109.38823 to -109.38823 so that the vinyl groups were further apart. This produced a molecule with a centre of inversion (Ci{E,i} symmetry):
 
[[Image:Nm607_hexadiene_structure3.jpg|frame|left|Structure 3]]
 
This was then optimized:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity

hexadiene structure 3 optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/c/c4/NM607_HEXADIENE_STRUCTURE3_OPT.LOG NM607_HEXADIENE_STRUCTURE3_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/7c/Nm607_hexadiene_structure3_opt_results_summary.txt Nm607_hexadiene_structure3_opt_results_summary.txt]
 
[[Image:Nm607_hexadiene_structure3_opt_Ci.jpg|frame|left|Conformer 3]]
 
The energy of '''Conformer 3''' is slightly higher than that of '''Conformer 1''', rather than being lower.
=====d)=====
The conformers produced above correspond to labelled equivalents [[Mod:phys3#Appendix 1|here]] (see Table 1).
{|border="1"
|-
!colspan="3"|Table 1 - Energies and labels for conformations
|-
!Conformer
!Energy / Eh
!Equivalent
|-
!1
|align="right"|-231.6926024
|''anti1''
|-
!2
|align="right"|-231.6915303
|''gauche4''
|-
!3
|align="right"|-231.6925353
|''anti2''
|}
 

=====e)=====
The energy of '''Conformer 3''' rounds down to that of the [[Mod:phys3#Appendix 1|''anti2'']] conformer.

=====f)=====
'''Conformer 3''' was optimized via a DFT-B3LYP/6-31G(d):
<pre>
# opt b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 2nd optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/1b/NM607_HEXADIENE_STRUCTURE3_OPT2.LOG NM607_HEXADIENE_STRUCTURE3_OPT2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0c/Nm607_hexadiene_structure3_opt2_results_summary.txt Nm607_hexadiene_structure3_opt2_results_summary.txt]

Overall the geometry changes very little after optimizing via the 6-31G(d) basis set, with no difference apparent when visually comparing the molecules.

{|border="1"
|-
!colspan="9"|Table 2 - Structural parameters of ''Conformer 3''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Bond Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
!C1-C2-C3 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
!C1-C2-C3-C4 / °
|align="right"|-114.6(84)
|align="right"|-118.5(88)
|-
!C2-C3 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C2-C3-C4 / °
|align="right"|111.3(46)
|align="right"|112.6(75)
!C2-C3-C4-C5 / °
|align="right"|-179.9(98)
|align="right"|180.0(00)
|-
!C3-C4 / Å
|align="right"|1.55(305)
|align="right"|1.54(808)
!C3-C4-C5 / °
|align="right"|111.3(45)
|align="right"|112.6(75)
!C3-C4-C5-C6 / °
|align="right"|114.6(94)
|align="right"|118.5(88)
|-
!C4-C5 / Å
|align="right"|1.50(886)
|align="right"|1.50(421)
!C4-C5-C6 / °
|align="right"|124.8(15)
|align="right"|125.2(86)
|-
!C5-C6 / Å
|align="right"|1.31(615)
|align="right"|1.33(352)
|}
 
The alteration in geometry after the 6-31G(d) optimization is apparent through direct measurements made with GaussView, as shown in Table 2. Bond angles change by portions of a degree and the dihedral angles differ by a few degrees at most - it is difficult to analyse exactly why however. What can be seen is that the HF/3-21G method overestimates the strength/underestimates the length of the C=C bonds relative to the DFT-B3LYP/6-31G(d), and is further from the literature value (Table 3). On the other hand the predicted angles from the DFT/3-21G method are closer to the experimental values than those of the DFT-B3LYP/6-31G(d) method.
 
{|border="1"
|-
!colspan="6"|Table 3 - Literature comparison of parameters of 1,5-hexadiene calculated with different basis sets
|-
|colspan="6"|''data for calculated values averaged from data given in Table 2''
|-
!Parameter
!Literature Value<ref name="0022-2860(94)09007-C">G. Schultz, I. Hargitta, ''J. Mol. Struc.'', '''1995''', ''346'', 63-69. {{DOI|10.1016/0022-2860(94)09007-C}}</ref>
!HF/3-21G
!Discrepancy
!DFT-B3LYP/6-31G(d)
!Discrepancy
|-
!align="right"|C=C / Å
|align="right"|1.340 ± 0.003
|align="right"|1.31(615)
|align="right"|-0.02(385)
|align="right"|1.33(352)
|align="right"|-0.00(648)
|-
!align="right"|C(H2)-C(H) / Å
|align="right"|1.508 ± 0.012
|align="right"|1.50(886)
|align="right"|0.00(086)
|align="right"|1.50(421)
|align="right"|-0.00(379)
|-
!align="right"|C(H2)-C(H2) / Å
|align="right"|1.538 ± 0.027
|align="right"|1.55(305)
|align="right"|0.01(505)
|align="right"|1.54(808)
|align="right"|0.01(008)
|-
!align="right"|C(H2)-C(H2)-C(H) / °
|align="right"|111.5 ± 0.9
|align="right"|111.3(46)
|align="right"|-0.1(55)
|align="right"|112.6(75)
|align="right"|1.1(75)
|-
!align="right"|C(H2)-C(H)=C(H2)/ °
|align="right"|124.6 ± 1.0
|align="right"|124.8(15)
|align="right"|0.2(15)
|align="right"|125.2(86)
|align="right"|0.6(86)
|}
 
Choosing one method over another should be informed by how closely the model yielded by the method matches reality. From the current evidence it is difficult to decide which method is preferable as both are realistic, and it is difficult to judge the relative importance of being more accurate in one prediction than in another.
=====g)=====
A frequency analysis of the 6-31G(d) optimized structure of '''Conformer 3''' was performed:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

hexadiene structure 3 postopt2 frequency analysis

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/f/f1/NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG NM607_HEXADIENE_STRUCTURE3_OPT2_FREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/9/97/Nm607_hexadiene_structure3_opt2_freq_results_summary.txt Nm607_hexadiene_structure3_opt2_freq_results_summary.txt]

The analysis converged, yielding all-positive frequencies.

{|border="1"
|-
!colspan="2"|Table 4 - Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
!align="left"|Sum of electronic and zero-point energies / Eh
|align="right"|-234.469204
|-
!align="left"|Sum of electronic and thermal energies / Eh
|align="right"|-234.461857
|-
!align="left"|Sum of electronic and thermal enthalpies / Eh
|align="right"|-234.460913
|-
!align="left"|Sum of electronic and free energies / Eh
|align="right"|-234.500777
|}
 
====Optimizing the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) was constructed in GaussView and optimized using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity

allyl fragment optimization

0 2
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_ALLYLFRAGMENT_OPT.LOG NM607_ALLYLFRAGMENT_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/85/Nm607_allylfragment_opt_results_summary.txt Nm607_allylfragment_opt_results_summary.txt]

[[Image:Nm607_chair1&2.JPG|thumb|300px|left|Fig. 2 - Chair arrangement of allylic fragments]]This allylic fragment was then duplicated and the two fragments were arranged to approximate the chair conformation of the transition state. The reactive carbon centre separation was set at 2.2 Å.
 

=====b)=====
The chair structure was then subjected to a frequency analysis and optimization to the transition state (additional keywords: opt=noeigen):
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

chair frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/7d/NM607_CHAIR_OPTFREQ.LOG NM607_CHAIR_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a6/Nm607_chair_optfreq_results_summary.txt Nm607_chair_optfreq_results_summary.txt]

[[Image:Nm607_chair_optfreq.jpg|thumb|300px|left|Fig. 3 - Optimized chair transition state<ref>Note bent-back hydrogens</ref>]]The above calculation yielded a vibration of -817(.98) cm<sup-1 (negative: imaginary), that corresponds exactly with the bond-making/bond-breaking required by the Cope rearrangement:
 
[[Image:Nm607_chair_vibration-818.jpg|thumb|300px|left|Fig. 4 - Chair transition state vibration (-817(.98) cm-1)]]A symmetric convergence of one carbon of each fragment is in antiphase to a symmetric divergence of the other pair, such that the vibration characterizes the change in bonding necessary to result in the [3,3]-sigmatropic shift.
 
=====c)=====
The method used in '''b)''' jumps straight from whatever estimate of the transition state has been input to the a better estimate of the transition state by ascending the potential surface. If a poor estimate is used the result may not actually represent the transition state, but might instead be a different local position on the potential surface that resembles a transition state. One way to minimise the chances of this is to do the optimization in two steps: in the first step the portions of the system that are undergoing bond-making/bond-breaking are 'frozen', and the remainder is optimized to a minimum energy; in the second step the bond-making/bond-breaking areas are 'unfrozen' and the system is optimized to the transition state. This method has advantages over that used in '''b)''' as one is more likely to find the transition state, and if for some reason the transition state is still not reached half the work has not been wasted as you have a partially optimized molecule to work with.

An optimization of the chair conformation made in '''a)''' was executed, with the reactive carbon separation frozen at 2.2 Å:
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_CHAIR_OPTRCE.LOG NM607_CHAIR_OPTRCE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/89/Nm607_chair_optRCE_results_summary.txt Nm607_chair_optRCE_results_summary.txt]

=====d)=====
[[Image:Nm607_chair_optRCE.jpg|thumb|300px|left|Fig. 5 - Optimized chair transition state (C-C fixed at 2.2 Å)]]The half-transition state produced in '''c)''' resembled the transition state produced in '''b)''', but with the reactive carbon centre separation at 2.2 Å. The next step required assigning Hessians to the bonds that were breaking or forming and optimizing the whole:
 
<pre>
# opt=modredundant hf/3-21g geom=connectivity

chair optimization RCE2

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e5/NM607_CHAIR_OPTRCE2.LOG NM607_CHAIR_OPTRCE2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/ca/Nm607_chair_optRCE2_results_summary.txt Nm607_chair_optRCE2_results_summary.txt]

This did not produce a transition state because it was mistakenly set to optimize to a minimum. The result was the product in a non-optimal conformation:
 
[[Image:Nm607_chair_optRCE2.jpg|thumb|300px|left|Fig. 6 - Minimum-optimized chair conformation ([[Mod:phys3#Appendix 1|''gauche2'')]])]]

The optimization was rerun, with the proper settings (the calculation failed without the additional keyword "opt=noeigen"):
 
<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity

chair optimization RCE3

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/66/NM607_CHAIR_OPTRCE3.LOG NM607_CHAIR_OPTRCE3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/e/e0/Nm607_chair_optRCE3_results_summary.txt Nm607_chair_optRCE3_results_summary.txt]

[[Image:Nm607_chair_optRCE3.jpg|thumb|300px|Fig. 7 - Optimized chair transition state (Method 2)]]The output transition state (Fig. 7) looks identical to that produced in '''b)''', and Table 5 shows that there a no significant numerical differences.
{|border="1"
|-
!colspan="3"|Table 5 - Parameter of chair transition state via Method 1 and 2
|-
!Parameter
!Method 1 Determination
!Method 2 Determination
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38(791)
|align="right"|1.38(922)
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01(992)
|align="right"|2.02(072)
|-
!align="right"|dihdral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9(64)
|align="right"|54.9(84)
|-
!align="right"|angle beteen allyl tip across trans-allyl bond (avg.) / °
|align="right"|101.8(65)
|align="right"|101.8(52)
|-
!align="right"|C(H)-H (avg.) / Å
|align="right"|1.07(586)
|align="right"|1.07(586)
|-
!align="right"|C(H2-H / Å
|align="right"|1.07(515)
|align="right"|1.07(514)
|-
!align="right"|Energy / Eh
|align="right"|-231.61932229
|align="right"|-231.61932239
|}
 
=====e)=====
To optimize to the boat transition state the QST2 method was used. The HF/3-21G optimized ''anti2'' structure was duplicated, maniputed and renumbered to produce the below:
 
[[Image:Nm607 boat reactant and product.JPG|thumb|300px|left|Fig. 8 - Reactant and product in ''anti2'' conformation]]
 
This method relies on translating portions of the reactant to yield the product, and stopping at the transition state.

The code for the calculation:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_OPTFREQ.LOG NM607_BOAT_OPTFREQ.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/74/Nm607_boat_optfreq_results_summary.txt Nm607_boat_optfreq_results_summary.txt]

[[Image:Nm607_boat_partial_migration.jpg|thumb|300px|left|Fig. 9 - Incomplete transition state from ''anti2'' conformer]][[Image:Nm607_boat_reactant_and_product2.JPG|thumb|300px|Fig. 10 - Modified pre-optimization structures]]The transition state produced has not finalized (the calculation failed) - see Fig. 9. What the QST2 method did not do was rotate about any of the bonds; this would have allowed a more effective movement of the allyl fragment, and maybe the discovery of a suitable transition state. The method was not abandoned, instead the conformation of the reactant and product were altered such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (original 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°). This yielded the structures shown in Fig. 10.
 
The calculation was rerun with the Fig. 10 structure:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity

boat frequency analysis and optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/0/0b/NM607_BOAT_OPTFREQ2.LOG NM607_BOAT_OPTFREQ2.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/8/86/Nm607_boat_optfreq2_results_summary.txt Nm607_boat_optfreq2_results_summary.txt]

[[Image:Nm607_boat_optfreq2.jpg|thumb|300px|left|Fig. 11 - Optimized boat transition state]]The first time this calculation was run it failed and produced an unsymmetric, non-optimal transition state. The input structure was then symmetritized and the calculation repeated to produce the files given above.
 
=====f)=====
The chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, while the boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformer. This is not, however, a sure sign of the conformer that would result from the completed reaction in either case. An Intricsic Reaction Coordinate calculation will find the geometric minimum starting from the transition state. Such a calculation was executed on the chair transition state, with a 50 step limit:
 
<pre>
# irc=(forward,maxpoints=50,calcfc) hf/3-21g geom=connectivity

chair IRC50

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/75/NM607_CHAIR_IRC50.LOG NM607_CHAIR_IRC50.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/7/71/Nm607_chair_IRC50_results_summary.txt Nm607_chair_IRC50_results_summary.txt]

[[Image:Nm607_chair_IRC50.jpg|left|thumb|300px|Fig. 12 - IRC output structure from chair transition state]]The structure produced was not one on the list of stable conformers, despite completing in only 26 steps. This can be rectified by calculating the force constants along with the IRC:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity

chair IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/6/62/NM607_CHAIR_IRC50FORCECONSTANTS.LOG NM607_CHAIR_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/df/Nm607_chair_IRCForceConstants_results_summary.txt Nm607_chair_IRCForceConstants_results_summary.txt]

[[Image:Nm607_chair_IRCForceConstants.jpg|thumb|300px|left|Fig. 13 - IRC output structure from chair transition state, using force constants]]Calculating the force constants resulted in a total of 47 steps, with the final product corresponding to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer (having the correct energy also).
 
This same process was also done for the boat transition state but with a maximum of 60 steps given how close the chair optimization came to its maximum:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity

boat IRC50 with force constants

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/index.php/Image:NM607_BOAT_IRC50FORCECONSTANTS.LOG NM607_BOAT_IRC50FORCECONSTANTS.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a5/Nm607_boat_IRCForceConstants_results_summary.txt Nm607_boat_IRCForceConstants_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants.jpg|thumb|300px|left|Fig. 14 - IRC output structure from boat transition state, using force constants]]As it happens, both transition states output the conformers predicted, with the boat transition state yielding a structure closest to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer(see Fig. 14). While it is close, it is not exact, therefore an HF/3-21G geometry optimization was executed:
 
<pre>
# opt hf/3-21g geom=connectivity

boat IRC50 with force constants optimization

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/7/73/NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG NM607_BOAT_IRC50FORCECONSTANTS_OPT.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/6/66/Nm607_boat_IRCForceConstants_opt_results_summary.txt Nm607_boat_IRCForceConstants_opt_results_summary.txt]

[[Image:Nm607_boat_IRC50ForceConstants_opt.jpg|thumb|300px|left|Fig. 15 - Optimized boat transition state post-IRC]]This did not yield the [[Mod:phys3#Appendix 1|''gauche3'']] conformer, but it seems that a novel conformer (Cs{E,σh}) has been identified, of noticably high energy (-231.68302525 Eh) but stable nonetheless. A check of the point group of the input configuration showed that the molecule had no enforced symmetry, so this conformer is valid.
 
=====g)=====
The activation energy for the Cope rearrangement can be determined by comparing the energies of the reactant with that the of the transition state. To achieve this it is best to use energies derived from high-level optimations; thus the chair and boat transition states were reoptimized (DFT-B3LYP/6-31G(d)):

The code for reoptimization of the chair transition state:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity

chair optimization 6-31G(d)

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3516]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/0/0b/Nm607_chair_opt6-31G%28d%29_results_summary.txt Nm607_chair_opt6-31G%28d%29_results_summary.txt]

The code for reoptimization of the boat transition state:
<pre>
# opt=(ts,modredundant,noeigen) b3lyp/6-31g(d) geom=connectivity

boat optimization 6-31G

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3515]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/d/dc/Nm607_boat_opt6-31G%28d%29_results_summary.txt Nm607_boat_opt6-31G%28d%29_results_summary.txt]

The 6-31G(d) optimization of the chair transition state did not converge, but was not repeated due to the long calculation period (>50 min); the energy value was in-range.

To determine the thermochemical data a frequency analysis of each structure was necessary:

The code for the frequency analysis of the chair transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

chair postopt6-31G(d) frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3518]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/2/2b/Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt Nm607_chair_opt6-31G%28d%29_freq_results_summary.txt]

The code for the frequency analysis of the boat transition state:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity

boat postopt6-31G frequency analysis

0 1
</pre>
:D-space reference: [http://hdl.handle.net/10042/to-3517]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/5/5b/Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt Nm607_boat_opt6-31G%28d%29_freq_results_summary.txt]

{|border="1"
|-
!colspan="4"|Table 6 - Energies of transition states and reactant
|-
!Quantity
!Chair Transition State
!Boat Transition State
!Reactant (''anti2'')
|-
!align="left"|Electronic Energy / Eh
|align="right"|-234.55493653
|align="right"|-234.54309292
|align="right"|-234.61171035
|-
!align="left"|Sum of Electronic and Zero-point Energies / Eh
|align="right"|-234.414005
|align="right"|-234.402336
|align="right"|-234.469204
|-
!align="left"|Sum of Electronic and Thermal Energies / Eh
|align="right"|-234.407802
|align="right"|-234.396003
|align="right"|-234.461857
|-
!align="left"|Sum of Electronic and Thermal Enthalpies / Eh
|align="right"|-234.406858
|align="right"|-234.395059
|align="right"|-234.460913
|-
!align="left"|Sum of Electronic and Free Energies / Eh
|align="right"|-234.443209
|align="right"|-234.431744
|align="right"|-234.500777
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kJ mol-1
|align="right"|141.92
|align="right"|172.90
|align="right"|0.00
|-
!align="left"|Relative Energy (from Sum of Electronic and Thermal Enthalpies) / kcal mol-1
|align="right"|33.92
|align="right"|41.32
|align="right"|0.00
|}

The relative stability of the reactant and the boat transition state is a little higher than that [[Mod:phys3#Appendix 2|given]], but that for the chair transition state is corrent to 2 d.p.. The discrepancy for the boat transition state is likely what lead to the novel product conformation; what precisely caused either is however unclear.

From the above data it is clear that the Cope rearrangement is markedly more favoured if proceding via the chair transition state; obviously this is a result of the minimisation in steric strain in the transition state.
===The Diels Alder Cycloaddition===
Diels Alder cycloadditions are commonly held to be concerted processes, where the formation of two σ-bonds between the termini of a diene and a dienophile happens symultaneously. A transition-state analysis should verify the truth of this. Another issue that can be understood via transition-state analysis is the selectivity of Diels Alder reactions towards the so-called 'endo' or 'exo' products - it is worth noting that an analysis of the kinetic of such a reaction was completed [[Mod:nathanmarch#The Hydrogenation of Cyclopentadiene Dimer|here]].

The first reaction that will studied could be considered the simplest Diels Alder reaction: butadiene + ethene.
=====i)=====
Cis-butadiene was built in GaussView and optimized via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity

cis-butadiene optimization AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/4/4d/NM607_CIS-BUTADIENE.LOG NM607_CIS-BUTADIENE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/b/be/Nm607_cis-butadiene_opt_results_summary.txt Nm607_cis-butadiene_opt_results_summary.txt]

The optimized cos-butadiene had a C=C bond length of 1.33(499) Å, a C-C bond length of 1.44(946) Å and a C-C-C bond angle of 125.6(62).

Examining the orbitals can provide information about the feasibility of a reaction; in the case of Diels Alder chemistry one expects the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. The plane of importance is the σv plane; orbitals can be classed as either symmetric or antisymmetric with respect to this plane, and only orbitals with the same symmetry will interact during bonding. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below. 'a' indicates that the orbital in question is antisymmetric with respect to the σv, while 's' indicates that the orbital is symmetric with respect to the same plane.
 
{|border="1"
|-
!colspan="4"|Table 7 - HOMOs and LUMOs of cis-butadiene and ethene
|-
!colspan="2"|cis-butadiene
!colspan="2"|ethene
|-
!Orbital
!Symmetry
!Orbital<ref>Calculated using same method as for cis-butadiene.</ref>
!Symmetry<ref>As if ethene were in the same plane as cis-butadiene, subject to the same symmetry element.</ref>
|-
|[[Image:Nm607_cis-butadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|[[Image:Nm607_ethene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cis-butadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_ethene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
Thus the HOMOs cannot interact with one another, nor the LUMOs together, but interaction between either HOMO/LUMO pair is perfectly possible.
=====ii)=====
To determine the transition state for the cis-butadiene/ethene reaction the QST3 method was used: the three structures necessary, cis-butadiene + ethene, the transition state and cyclohexene, were built using GaussView or built in ChemBio3D and exported into GaussView. [[Image:Nm607_be_transition_series.JPG|thumb|right|300px|Fig. 16 - Pre-QST3 configuration: reactants (left), product (middle) and guess at transition state (right)]]Next, the three structures were arranged to allow a QST3 calculation; the reactants were arranged to imply an angled trajectory (favoured by sterics); the transition state required only that the ethene be positioned close to the cis-butadiene (above the plane) and the product was left unaltered (in the conformation produced by ChemBio3D).
 
The code for QST3 optimization:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/1/17/NM607_TRANSITION_STATE.LOG NM607_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/4/4c/Nm607_be_transition_state_results_summary.txt Nm607_be_transition_state_results_summary.txt]

It is the LUMO of ethene that interacts with HOMO of cis-butadiene to yield the HOMO of the transition state, and it is the the HOMO of ethene interacts with the LUMO of cis-butadiene to produce the LUMO of the transition state. The reaction is a thermal π4s + π2s cycloaddition, it is a suprafacial addition of a four-electron π-system to a two-electron π-system; the reaction proceeds via a Hückel transition state, and is symmetry permitted.
 
{|border="1"
|-
!colspan="2"|Table 8 - Molecular orbitals of the cis-butadiene/ethene transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|}

[[Image:Nm607_transition_state.jpg|thumb|300px|left|Fig. 17 - Transition state]]As would be expected the C(H2)-C(H) bond lengths are longer than their equivalents in cis-butadiene, being 1.38(186) Å (avg.) and the C2-C3 bond demonstrates the imminent increase in bond order, being a more C=C-reminiscent 1.39(748) Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are 2.11(926) Å and 2.11(927) Å respectively, and thus the transition state can be considered symmetrical - both bonds form symultaneously. The Van der Waals radius of carbon is 1.70 Å<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>; the partially formed σ-bonds are less than double the Van der Waals radius.
 

[[Image:Nm607_transition_state_vibration-956.jpg|thumb|300px|left|Fig. 17 - Transition state vibration -956 cm-1 ''pictured with manual displacement at -1.0 and default vector magnitude'']][[Image:Nm607_transition_state_vibration147.jpg|thumb|300px|right|Fig. 18 - Transition state vibration 147 cm-1 ''pictured with manual displacement at -1.0 and increased vector magnitude'']]The bond vibration for the partial σ-bonds, that is evidence of a sound transition state, has a frequency of -956(.21) cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive-energy vibration (147(.24) cm-1) is, however, asymmetric and includes a torsional component about the ethene portion - this is indicative of the final structure that the product will adopt (Fig. 19).
 
[[Image:Nm607_cyclohexene.gif|frame|left|Fig. 19 - 'Ethene' twist in cyclohexene]]
 
This could indicate that in certain cases, where steric strain deters one end of the ethene approaching, there could be a delay in the formation of one σ-bond and asynchronous bond formation.
=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

To properly analyse the molecular orbitals of the transition states it is first necessary to examine the

{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}

{|border="1"
|-
!colspan="2"|Table 10 - Molecular orbitals of the endo transition state
|-
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}

----

===References===
<references />