Rep:Mod:JONS007

2012-11-02T15:00:38Z

Js4310: /* Optimising Chair and Boat Transitions */

='''''THE COPE REARRANGEMENT=
'''Jonathan Shute'''

==Introduction / Background Theory==

This report aims to investigate the thermochemistry of the following reaction:

[[Image:Pic1.jpg|Thumb|250x90px]]

It is understood that the reaction occurs in a concerted fashion via either chair or boat like transition state:

[[File:Pic2b.jpg]] [[File:Pic2b.jpg]]

In the tutorial section, the enthalpy of the reactant has been found when it is in its most energetically stable conformer. In the second part, the chair and boat transition geometries have been located and their energies calcualted. These data were then used to calculate the activation energy of the reaction.

Several methods were employed to obtain the transition states. Every transition state has with it associated one imaginary frequency. This is because bonds can be modelled as vibrational springs obeying Hooke's law, F= -kx. The frequencies are computed using the following equation:

<math> {1\over {2 \pi}} \sqrt{k \over \mu}. \!</math>

The force constants are negative at the transition state so the frequency is imaginary.

In the project, Diels-Alder reactions were investigated. In the diels alder reaction, the endo product is formed preferentially despite being the less thermodynamically stable product. (It suffers more from sterics). The reaction is consequently under kinetic control and the stereoselectivity can be explained by invoking the secondary orbital effect which stabilises the transition state and so lowers the activation energy for formation of the exo product which forms faster. In the project, the orbitals involved with this effect were computed and studied.

==Optimising the Reactants and Products==

'''1,5-hexadiene'''

(a)The energy of the anti conformer is -231.6926(0235) a.u and the symmetry is C1
[[File:Hexatriene_anti_optimised_321Gjs.log]]

(b)The energy of the gauche conformer is -231.6915(30325) [[File:HEXATRIENEGAUGEjs_321G.LOG]]

The gauche conformer is slightly higher in energy due to the carbons 1 and 4 of the central carbons eclipsing each other a little and causing steric repulsion whist in the staggered conformation, there is less interaction between them. In the antiperiplaner conformation, there is overlap between the sigma C-C bonding orbital for carbons C1 and C2 and the C-C antibonding orbital between C3 and C4. This lowers the energy slightly.

In both structures, A1,3 eclipsed conformation <ref name = "Rzep" /> is evident with the H atoms on the carbon adjacent to C=C at
roughly 120o to the pi system, although not exactly and in both structures one of the H's is at a slightly larger angle than this. The A1,3 conformation is a compromise between having two hydrogen's sigma orbitals aligned fairly well with the pi star orbitals and also there is an attractive vdw force between the H atom on the C=C and on the H atom on the neighbouring carbon. The distance is slightly larger in the gauche.

[[Image:Banana2js.png|Thumb|300x300px|]]

These orbitals show interaction of the sigma H orbital with the pi star orbitals is effective for both conformers.

(c) The lowest energy conformers of 1,5-hexadiene in the table are anti1 and gauche3

(d)By comparison with the appendix table, my optimised conformers were anti1 and gauche4. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summaryhexatriene_631G.PNG My Optimisation Summary Table]]

(e)The optimised molecule had point group Ci and an energy matching the value given in appendix of -231.69253528 a.u precisely. [[File:TRIAL2VER2_321G.LOG]]

<pre>
Low frequencies --- -5.6849 -2.3517 -2.0910 -0.0008 -0.0004 -0.0002
Low frequencies --- 71.1980 85.6851 116.1458

</pre>
<pre>
Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916
</pre>

This gives an electronic energy of 231.692535 (by subtracting the zero point correction to the sum of electronic and zero point energies).

All is in close agreement with the appendix table (only variation in the sixth decimal place)

(f)The conformation of the molecule appears the same when both basis sets are used though the C=C bond length is a little longer with the better basis set at 1.333 A compared to 1.316 A. The energy is very significantly different at -234.611706. This is why the energy of different molecules can only be compared if it was computed with the same basis set.
[[File:HEXATRIENEANIT2CI_631GD.LOG]]
[[File:HEXATRIENEANIT2CI_631GD_FREQCHECKjs.LOG]]

[[Image:IRspecjs.PNG|Thumb|400x600px|]]

<pre>
''' Low frequencies --- -9.1026 0.0005 0.0005 0.0008 4.2776 13.4006
Low frequencies --- 74.2705 80.9525 121.5200 </pre>'''

<pre>
Zero-point correction= 0.142504 (Hartree/Particle)
Thermal correction to Energy= 0.149851
Thermal correction to Enthalpy= 0.150795
Thermal correction to Gibbs Free Energy= 0.110929

Sum of electronic and zero-point Energies= -234.469207
Sum of electronic and thermal Energies= -234.461859
Sum of electronic and thermal Enthalpies= -234.460915
Sum of electronic and thermal Free Energies= -234.500782
</pre>

(It is a little surprising that the low frequencies are higher for the optimisation with the better basis set)

==Optimising Chair and Boat Transitions==

(b)
<pre>
Low frequencies --- -817.9271 -7.0897 -5.4674 -4.3204 -0.0004 0.0004
Low frequencies --- 0.0005 209.4156 396.0571
****** 1 imaginary frequencies (negative Signs) ******
</pre>

{{DOI|10042/21119}} (optimised log file of chair guessed transition state) 

<pre> Zero-point correction= 0.152627 (Hartree/Particle)
Thermal correction to Energy= 0.157986
Thermal correction to Enthalpy= 0.158930
Thermal correction to Gibbs Free Energy= 0.124120
Sum of electronic and zero-point Energies= -231.466696
Sum of electronic and thermal Energies= -231.461336
Sum of electronic and thermal Enthalpies= -231.460392
Sum of electronic and thermal Free Energies= -231.495202 </pre>

These results agree with those given in the appendix with variation in fifth d.p only.

(c)

[[File:INCORRRECTjs.LOG]]


(d)[[FILE:CORRRECTED_OPTIMISE_TOA_TRANSITION_STATE.LOG‎ ]]Optimisation to a transition state was successful but initially failed until write connectivity was unchecked under the general tab. The bond lengths were 2.01995 A. This is corroborated by the results for the optimised chair in part (b) which gave a bond length of 2.0205 remarkably similar considering the differences in the models used.

<pre>Zero-point correction= 0.151377 (Hartree/Particle)
Thermal correction to Energy= 0.157016
Thermal correction to Enthalpy= 0.157960
Thermal correction to Gibbs Free Energy= 0.122592
Sum of electronic and zero-point Energies= -231.463821
Sum of electronic and thermal Energies= -231.458181
Sum of electronic and thermal Enthalpies= -231.457237
Sum of electronic and thermal Free Energies= -231.492605</pre>

-231.619322
-231.466705
-231.461346

(e) File:gauge_TS(QST2)_ERRDEFAULTSPIN successful optimisation with 2.140 bond length. Only one imaginary frequency (which is vibration of the two bonds which are forming):

<jmolFile text="Animation supposed to show vibrations at ts">TS-Vibrationjs.mol</jmolFile>

<pre>

Low frequencies --- -840.1011 -4.0811 -0.0011 -0.0010 -0.0009 3.5285
Low frequencies --- 5.2099 155.3480 382.0830
****** 1 imaginary frequencies (negative Signs) ******

</pre>

<pre>
Zero-point correction= 0.151874 (Hartree/Particle)
Thermal correction to Energy= 0.157502
Thermal correction to Enthalpy= 0.158447
Thermal correction to Gibbs Free Energy= 0.123029
Sum of electronic and zero-point Energies= -231.450929
Sum of electronic and thermal Energies= -231.445300
Sum of electronic and thermal Enthalpies= -231.444356
Sum of electronic and thermal Free Energies= -231.479774
</pre>

This results are very close to those in the appendix table for 321G HF basis set and method.
(f) {{DOI|10042/21197}} file shows the IRC on the chair transition state calculated using redundant method.
(Need to reach a minimum.... - maybe check for graph also)

(g) (Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way under the extra working section) The calculation below is with the correct method.

i) Correct method
{{DOI|10042/21294}}

<pre>
Zero-point correction= 0.140741 (Hartree/Particle)
Thermal correction to Energy= 0.147079
Thermal correction to Enthalpy= 0.148023
Thermal correction to Gibbs Free Energy= 0.111326
Sum of electronic and zero-point Energies= -234.402355
Sum of electronic and thermal Energies= -234.396016
Sum of electronic and thermal Enthalpies= -234.395072
Sum of electronic and thermal Free Energies= -234.431769
</pre>

There is a small variation when compared to appendix values in the fifth d.p.

ii) {{DOI|10042/21304}} {{DOI|10042/21305}}
Reoptimised the chair calculated in part b to B3YLP/6-31G* level:

<pre>
Zero-point correction= 0.142054 (Hartree/Particle)
Thermal correction to Energy= 0.147975
Thermal correction to Enthalpy= 0.148919
Thermal correction to Gibbs Free Energy= 0.113168
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443815 </pre>

Again, these results are in close agreement with those in the appendix table to the fifth d.p

'''Conclusion'''

The energy of the chair minus the thermal correction is -234.557 a.u. The energy of the reactant is -234.612 a.u
Need to subtract energy of starting materials and reactants to give the extra energy of the transition state which must be overcome for reaction to occur.
1 Hartree = 627.509 kcal/mol

Hence, the difference in energy is -5.471*10^-2. This is '''34.3 kcal mol-1.'''

The energy of the boat is -234.543 a.u. This gives Ea = 0.0689 a.u or '''43.2 kcal mol-1'''

These values compare to the literature values of 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure. This is surprisingly good agreement as the basis set used B3LYP/6-31G* is quite an inexact basis set.

==Extra Working==

Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way below as an extension to the tutorial!

(g) {{DOI|10042/21218}} this is the optimised boat HF/3-21G reoptimised
file is IRC_chair_redundant. The results are given below:

<pre>
Low frequencies --- -852.3991 -6.1132 -4.0906 -1.4954 -0.0005 0.0006
Low frequencies --- 0.0007 145.9558 320.2847
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.150402 (Hartree/Particle)
Thermal correction to Energy= 0.156295
Thermal correction to Enthalpy= 0.157239
Thermal correction to Gibbs Free Energy= 0.121318
Sum of electronic and zero-point Energies= -232.727993
Sum of electronic and thermal Energies= -232.722099
Sum of electronic and thermal Enthalpies= -232.721155
Sum of electronic and thermal Free Energies= -232.757076
</pre>

The optimisation at the HF/6-31G* level reached a minimum with the energy derivatives very close to zero after the eighth step (smaller than 10^-4) however due to an error in the program (unstable algorithm) it continued beyond this point and the final structure was incorrect. The eighth intermediate geometry has a bond length of 2.203 A. The following link is to screenshots of the optimisation graphs and the energy derivatives:
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Graphs_of_optimisationjs.png Optimisation_Graphs]]

='''''DA PROJECT=

==Results==

i) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

ii)Optimisation using method in part b) (HF/321G) file = partA_RETRY in folder ii)

The animation clearly shows the correct transition state has been attained.

<jmol> <jmolApplet> <title>Vibration</title><color>white</color><size>200</size> <script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10; </script><uploadedFileContents>Ts_vib.mol</uploadedFileContents> </jmolApplet> </jmol>

The animation is supposed to show concerted bond formation.

<pre> Low frequencies --- -818.4961 -0.0007 -0.0006 -0.0003 1.4348 1.8772
Low frequencies --- 2.7185 166.5539 284.3675
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157558
Thermal correction to Enthalpy= 0.158502
Thermal correction to Gibbs Free Energy= 0.122930
Sum of electronic and zero-point Energies= -231.451338
Sum of electronic and thermal Energies= -231.445650
Sum of electronic and thermal Enthalpies= -231.444706
Sum of electronic and thermal Free Energies= -231.480279
</pre>

iii)
'''Exo Transition States'''
{{DOI|10042/21391}} This is the file for my optimised exo transition state calculated using the derivatise bond method. I also calculated the transition state using the first method in the tutorial section

Modredundant method: 99_frozengif is the input file, output log is 99_99_99
{{DOI|10042/21447}}
<pre>
Low frequencies --- -643.0720 -10.8719 -0.0008 -0.0008 -0.0004 11.9743
Low frequencies --- 15.1280 49.8386 133.6533
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195473 (Hartree/Particle)
Thermal correction to Energy= 0.204891
Thermal correction to Enthalpy= 0.205835
Thermal correction to Gibbs Free Energy= 0.160107
Sum of electronic and zero-point Energies= -605.408011
Sum of electronic and thermal Energies= -605.398593
Sum of electronic and thermal Enthalpies= -605.397649
Sum of electronic and thermal Free Energies= -605.443378 </pre>

Opt=NoEigen method:
{{DOI|10042/21449}}
<pre>

Low frequencies --- -647.3174 -2.2007 -0.0010 -0.0009 -0.0008 1.7640
Low frequencies --- 3.1286 42.6020 131.4691
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195451 (Hartree/Particle)
Thermal correction to Energy= 0.204911
Thermal correction to Enthalpy= 0.205855
Thermal correction to Gibbs Free Energy= 0.159905
Sum of electronic and zero-point Energies= -605.408140
Sum of electronic and thermal Energies= -605.398681
Sum of electronic and thermal Enthalpies= -605.397736
Sum of electronic and thermal Free Energies= -605.443686
</pre>

methodA = 9999log.... file ? Note some disagreement in the transition state optimal distance!
Could also include guess file?

'''The endo transition state:'''
DSPACE LINK TO include. Fies are endo_optimise_ts_A_take2 and log_65019

I optimised this using the opt=noeigen method and the modredundant method to check. First I drew a guess transition state by drawing the product, optimising it to a minimum and then increasing the bond forming lengths to 2.2A The energies are given below and are in good agreement for the different methods. The transition state geometries are very similar for both, with C-C bond forming distances of 2.231 with both methods which agree to the third decimal place.

Calculation using opt=noeigen key word:
{{DOI|10042/21451}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_A_tsjs.PNG Optimisation Summary Table ]

<pre> Low frequencies --- -643.5783 -0.0005 -0.0002 0.0006 0.6895 1.1675
Low frequencies --- 1.7996 65.0129 142.0450
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre> Zero-point correction= 0.195464 (Hartree/Particle)
Thermal correction to Energy= 0.204889
Thermal correction to Enthalpy= 0.205834
Thermal correction to Gibbs Free Energy= 0.160235
Sum of electronic and zero-point Energies= -605.414905
Sum of electronic and thermal Energies= -605.405479
Sum of electronic and thermal Enthalpies= -605.404535
Sum of electronic and thermal Free Energies= -605.450133 </pre>

Calculation using modredundant keyword: {{DOI|10042/21452}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_C_tsjs.PNG Optimisation Summary Table]

<pre>Low frequencies --- -644.2611 -0.0007 -0.0003 0.0006 1.8423 3.3886
Low frequencies --- 6.6938 65.0647 142.3913
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>Zero-point correction= 0.195454 (Hartree/Particle)
Thermal correction to Energy= 0.204879
Thermal correction to Enthalpy= 0.205823
Thermal correction to Gibbs Free Energy= 0.160231
Sum of electronic and zero-point Energies= -605.414912
Sum of electronic and thermal Energies= -605.405487
Sum of electronic and thermal Enthalpies= -605.404543
Sum of electronic and thermal Free Energies= -605.450135
</pre>

Bond formation is concerted

[[File:MethodCmodredundantjs_ts_animation.gif]]

==Discussion Questions==

1) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

2)
Below is illustrated the HOMO left and LUMO right for the unsubsituted Diels Alder transitions state. Both orbitals are symmetric with respect to the plane.

[[Image:HOMOandLUMO(r)js.png|Thumb|300x150px]] [[Image:MOHOMO-1js.PNG|Thumb|300x150px|HOMO-1]]

[[Image:MO4js.PNG|Thumb|300x150px|HOMO]][[Image:MO3js.PNG|Thumb|300x150px|LUMO]] [[Image:MO1js.PNG|Thumb|300x150px|HOMO-1]]

These diagrams show the orbital contributions of the MOs above them.

The HOMO has a node in between the diene and the dienophile.

Allowed reactions:
The reaction is allowed by Woodward-Hoffmann rules as there are six electrons, it is suprafacial and a thermal process.
Frontier orbital theory predicts the stereochemistry. As two new bonds are being formed simultaneously, there are symmetry constraints on the reaction. If '''both''' p orbitals on the alkene form constructive overlap with the p orbitals on the terminal carbons of the diene, then the reaction is allowed.

In the HOMO the alkene and diene both have the same symmetry and interact to strengthen the bonds which are forming. (Both components have no nodes)and both components are '''symmetric'''

In the HOMO-1, both components have the same symmetry for overlap and this strengthens the two bonds which are forming both components are '''antisymmetric'''

The LUMO is interesting because the two components are symmetric and they have to correct symmetry to interact however they do so destructively and so weaken the 2 bonds which are forming. However, the orbitals deform and the p orbitals on the alkene balloon out to interact with the p orbitals on the central two carbons of the diene so this would cause a little weak bonding between these atoms.

A further point to make is that the HOMO-1 is the key MO as it has strong positive overlap inbetween the diene and dienophile and so is the major bonding attraction which causes the transition state to roll onto the products. This is because electrons inhabiting this low energy orbital attract the two fragments together.

A "real" Diels Alder reaction requires an electron deficient dienophile and this lowers the energy of its LUMO whilst the diene has a high energy HOMO so the interactions of this orbital (the far right one)are strengthened even more. In reverse demand reactions the following interaction is preferred: [[Image:MO2js.PNG|Thumb|150x75px]]

3) [[File:Ts_moviejs.gif]]

Bond forming distance: 2.209 A. According to a table on wikipedia <ref name = "wikibondlength"/>, the average bond lengths are as follows:
sp2-sp2 C-C = 1.47 A (BUT the alkene double bond length according to the same table is 1.34A Gaussview gives the bond length in ethene of 1.325)
sp3-sp3 C-C = 1.54 A (gaussview has 1.5 for ethane)
sp3-sp2 C-C = 1.50 A
longest C-C = 1.74 A
Additionally, the Van der Waals radius for carbon is 1.7 A <ref name = "wikivdw"/>

The reason that bond lengths are less than the corrosponding average of the radii of the two atoms is that their electron clouds overlap when forming the bond so the nuclei are draw in towards each other somewhat. Two carbon atoms can't form a normal covalent bond in their distance exceeds the van der waals radius. There may be some intermolecular attraction but there isn't a bond. There will be some overlap between the sigma orbitals but it must be weak at this distance. It might have been expected that the length would be upwards from the average of the vdw radius distance and that of a normal sp3 C bond which would be 1.6A but the distance is much more than this.

This, along with the other bond lengths implies that the transition state is "reactant like" i.e. an early transition state. The dienophile has a C=C bond length of 1.375 which is far closer to the double bond length than the single bond length. The dienophile has two bond lengths of 1.39 and two of 1.37 whilst these are all quite short, this also implies that the transition state is at least somewhat more reactant like than product like.

This synchronous vibration compares to the asynchronous one below (however this vibration has sideways motion as well as asynchronous in and out motion).

[[File:Ts_movie2js.gif]]
(This is actually the second lowest positive frequency but the lowest one doesn't show the two molecules moving closer or further apart, only moving sideways relative to each other)

'''Substitution'''

4) The exo transition state is a slighlty more strained as the maleic anhydride componant points towards the bridging carbons. The Oxygen atoms are a little closer to the hydrogens which are on sp3 carbons and so jut out more than the nearest hydrogens on sp2 like carbon to the maleic anhydride component in the endo. This is in part due to the fact that the transition state appears more product like in the endo and more reactant like in the exo. In the actual products, this affect may be extenuated as in the endo transition state, the maleic anhydride oxygen atoms are pulled closer to the C=C to increase secondary orbital overlap.

[[Image:Tsjs.png|Thumb|300x150px]]

5) The endo transition state has energy = -605.610 a.u. The exo transition structure has energy -605.603 a.u this gives a difference of 4.4 kcal mol-1.

[[Image:HOMO-1js.PNG|Thumb|300x150px]]

This is the HOMO-1 in the endo transition state showing positive overlap between the orbitals on the oxygen atoms and the C=C

[[Image:HOMOjs.PNG|Thumb|300x150px]]

This shows the HOMO. (There is a node between the p on the oxygen atoms and the diene showing that in the HOMO, the endo could be slightly destabilised by this interaction. In the HOMO-1 shown above, there is constructive overlap between the oxygen atoms and the rest of the molecule - though any interaction atall is very weak)

According to the theory <ref name = "wikifrontier" /> ,the secondary orbital overlap is caused by the interation between the pi star C=O and the C=C. However, it is the p on C which interacts, not the p on oxygen which is too far out:

[[File:Mofrontiersjs.PNG]]

However, in my HOMO, it appears that the p on C doesn't contribute unless its been "swallowed up" into the nearby p orbitals on the other C atoms.

the overlap is strong enough to dictate the favoured stereochemsitry, it isn't strong enough to form a new bond.

==References==

<References>

<ref name = "wikibondlength"> http://en.wikipedia.org/wiki/Bond_length </ref>

<ref name = "wikivdw" > http://en.wikipedia.org/wiki/Van_der_Waals_radius </ref>

<ref name = "Rzep" > Second year lecture course, "conformational analysis" by Dr Rzepa http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct </ref>

<ref name = "wikifrontier" > http://en.wikipedia.org/wiki/Frontier_molecular_orbital_theory </ref>

</references>

Rep:Mod:JONS007

2012-11-02T14:54:50Z

2012-11-02T14:05:28Z

Js4310:

Rep:Mod:JONS007

2012-11-02T13:38:54Z

Js4310: /* Conclusion */

='''''THE COPE REARRANGEMENT=
'''Jonathan Shute'''

==Introduction==

This report aims to investigate the thermochemistry of the following reaction:

[[Image:Pic1.jpg|Thumb|250x90px]]

It is understood that the reaction occurs in a concerted fashion via either chair or boat like transition state:

[[File:Pic2b.jpg]] [[File:Pic2b.jpg]]

In the tutorial section, the enthalpy of the reactant has been found when it is in its most energetically stable conformer. In the second part, the chair and boat transition geometries have been located and their energies calcualted. These data were then used to calculate the activation energy of the reaction.

Several methods were employed to obtain the transition states. Every transition state has with it associated one imaginary frequency. This is because bonds can be modelled as vibrational springs obeying Hooke's law, F= -kx. The frequencies are computed using the following equation:

<math> {1\over {2 \pi}} \sqrt{k \over \mu}. \!</math>

The force constants are negative at the transition state so the frequency is imaginary.

==Optimising the Reactants and Products==

'''1,5-hexadiene'''

(a)The energy of the anti conformer is -231.6926(0235) a.u and the symmetry is C1
[[File:Hexatriene_anti_optimised_321Gjs.log]]

(b)The energy of the gauche conformer is -231.6915(30325) [[File:HEXATRIENEGAUGEjs_321G.LOG]]

The gauche conformer is slightly higher in energy due to the carbons 1 and 4 of the central carbons eclipsing each other a little and causing steric repulsion whist in the staggered conformation, there is less interaction between them. In the antiperiplaner conformation, there is overlap between the sigma C-C bonding orbital for carbons C1 and C2 and the C-C antibonding orbital between C3 and C4. This lowers the energy slightly.

In both structures, A1,3 eclipsed conformation <ref name = "Rzep" /> is evident with the H atoms on the carbon adjacent to C=C at
roughly 120o to the pi system, although not exactly and in both structures one of the H's is at a slightly larger angle than this. The A1,3 conformation is a compromise between having two hydrogen's sigma orbitals aligned fairly well with the pi star orbitals and also there is an attractive vdw force between the H atom on the C=C and on the H atom on the neighbouring carbon. The distance is slightly larger in the gauche.

[[Image:Banana2js.png|Thumb|300x300px|]]

These orbitals show interaction of the sigma H orbital with the pi star orbitals is effective for both conformers.

(c) The lowest energy conformers of 1,5-hexadiene in the table are anti1 and gauche3

(d)By comparison with the appendix table, my optimised conformers were anti1 and gauche4. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summaryhexatriene_631G.PNG My Optimisation Summary Table]]

(e)The optimised molecule had point group Ci and an energy matching the value given in appendix of -231.69253528 a.u precisely. [[File:TRIAL2VER2_321G.LOG]]

<pre>
Low frequencies --- -5.6849 -2.3517 -2.0910 -0.0008 -0.0004 -0.0002
Low frequencies --- 71.1980 85.6851 116.1458

</pre>
<pre>
Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916
</pre>

This gives an electronic energy of 231.692535 (by subtracting the zero point correction to the sum of electronic and zero point energies).

All is in close agreement with the appendix table (only variation in the sixth decimal place)

(f)The conformation of the molecule appears the same when both basis sets are used though the C=C bond length is a little longer with the better basis set at 1.333 A compared to 1.316 A. The energy is very significantly different at -234.611706. This is why the energy of different molecules can only be compared if it was computed with the same basis set.
[[File:HEXATRIENEANIT2CI_631GD.LOG]]
[[File:HEXATRIENEANIT2CI_631GD_FREQCHECKjs.LOG]]

[[Image:IRspecjs.PNG|Thumb|400x600px|]]

<pre>
''' Low frequencies --- -9.1026 0.0005 0.0005 0.0008 4.2776 13.4006
Low frequencies --- 74.2705 80.9525 121.5200 </pre>'''

<pre>
Zero-point correction= 0.142504 (Hartree/Particle)
Thermal correction to Energy= 0.149851
Thermal correction to Enthalpy= 0.150795
Thermal correction to Gibbs Free Energy= 0.110929

Sum of electronic and zero-point Energies= -234.469207
Sum of electronic and thermal Energies= -234.461859
Sum of electronic and thermal Enthalpies= -234.460915
Sum of electronic and thermal Free Energies= -234.500782
</pre>

(It is a little surprising that the low frequencies are higher for the optimisation with the better basis set)

==Optimising Chair and Boat Transitions==

(b)
<pre>
Low frequencies --- -817.9271 -7.0897 -5.4674 -4.3204 -0.0004 0.0004
Low frequencies --- 0.0005 209.4156 396.0571
****** 1 imaginary frequencies (negative Signs) ******
</pre>

{{DOI|10042/21119}} (optimised log file of chair guessed transition state)chair_guesstransition_optimis_freq on my computer this is: log_64342

<pre> Zero-point correction= 0.152627 (Hartree/Particle)
Thermal correction to Energy= 0.157986
Thermal correction to Enthalpy= 0.158930
Thermal correction to Gibbs Free Energy= 0.124120
Sum of electronic and zero-point Energies= -231.466696
Sum of electronic and thermal Energies= -231.461336
Sum of electronic and thermal Enthalpies= -231.460392
Sum of electronic and thermal Free Energies= -231.495202 </pre>

These results agree with those given in the appendix with variation in fifth d.p only.

(c)
-can't optimise exactly! TBC
THE FILE IS CALLED INCORRECT. It works!(This part took a very long time due to the incompleteness of the instructions which mislead me!)

(d)Optimisation to a transition state was successful but initially failed until write connectivity was unchecked under the general tab. The bond lengths were 2.01995 A. This is corroborated by the results for the optimised chair in part (b) which gave a bond length of 2.0205 remarkably similar considering the differences in the models used.

File name: incorrect_optimise_toa_transition_state

<pre>Zero-point correction= 0.151377 (Hartree/Particle)
Thermal correction to Energy= 0.157016
Thermal correction to Enthalpy= 0.157960
Thermal correction to Gibbs Free Energy= 0.122592
Sum of electronic and zero-point Energies= -231.463821
Sum of electronic and thermal Energies= -231.458181
Sum of electronic and thermal Enthalpies= -231.457237
Sum of electronic and thermal Free Energies= -231.492605</pre>

-231.619322
-231.466705
-231.461346

(e) File:gauge_TS(QST2)_ERRDEFAULTSPIN successful optimisation with 2.140 bond length. Only one imaginary frequency (which is vibration of the two bonds which are forming):

<jmolFile text="Explanatory text for link">TS-Vibrationjs.mol</jmolFile>

<pre>

Low frequencies --- -840.1011 -4.0811 -0.0011 -0.0010 -0.0009 3.5285
Low frequencies --- 5.2099 155.3480 382.0830
****** 1 imaginary frequencies (negative Signs) ******

</pre>

<pre>
Zero-point correction= 0.151874 (Hartree/Particle)
Thermal correction to Energy= 0.157502
Thermal correction to Enthalpy= 0.158447
Thermal correction to Gibbs Free Energy= 0.123029
Sum of electronic and zero-point Energies= -231.450929
Sum of electronic and thermal Energies= -231.445300
Sum of electronic and thermal Enthalpies= -231.444356
Sum of electronic and thermal Free Energies= -231.479774
</pre>

This results are very close to those in the appendix table for 321G HF basis set and method.
(f) {{DOI|10042/21197}} file shows the IRC on the chair transition state calculated using redundant method.
(Need to reach a minimum.... - maybe check for graph also)

(g) (Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way under the extra working section) The calculation below is with the correct method.

i) Correct method
{{DOI|10042/21294}}

<pre>
Zero-point correction= 0.140741 (Hartree/Particle)
Thermal correction to Energy= 0.147079
Thermal correction to Enthalpy= 0.148023
Thermal correction to Gibbs Free Energy= 0.111326
Sum of electronic and zero-point Energies= -234.402355
Sum of electronic and thermal Energies= -234.396016
Sum of electronic and thermal Enthalpies= -234.395072
Sum of electronic and thermal Free Energies= -234.431769
</pre>

There is a small variation when compared to appendix values in the fifth d.p.

ii) {{DOI|10042/21304}} {{DOI|10042/21305}}
Reoptimised the chair calculated in part b to B3YLP/6-31G* level:

<pre>
Zero-point correction= 0.142054 (Hartree/Particle)
Thermal correction to Energy= 0.147975
Thermal correction to Enthalpy= 0.148919
Thermal correction to Gibbs Free Energy= 0.113168
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443815 </pre>

Again, these results are in close agreement with those in the appendix table to the fifth d.p

'''Conclusion'''

The energy of the chair minus the thermal correction is -234.557 a.u. The energy of the reactant is -234.612 a.u
Need to subtract energy of starting materials and reactants to give the extra energy of the transition state which must be overcome for reaction to occur.
1 Hartree = 627.509 kcal/mol

Hence, the difference in energy is -5.471*10^-2. This is '''34.3 kcal mol-1.'''

The energy of the boat is -234.543 a.u. This gives Ea = 0.0689 a.u or '''43.2 kcal mol-1'''

These values compare to the literature values of 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure. This is surprisingly good agreement as the basis set used B3LYP/6-31G* is quite an inexact basis set.

==Extra Working==

Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way below as an extension to the tutorial!

(g) {{DOI|10042/21218}} this is the optimised boat HF/3-21G reoptimised
file is IRC_chair_redundant. The results are given below:

<pre>
Low frequencies --- -852.3991 -6.1132 -4.0906 -1.4954 -0.0005 0.0006
Low frequencies --- 0.0007 145.9558 320.2847
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.150402 (Hartree/Particle)
Thermal correction to Energy= 0.156295
Thermal correction to Enthalpy= 0.157239
Thermal correction to Gibbs Free Energy= 0.121318
Sum of electronic and zero-point Energies= -232.727993
Sum of electronic and thermal Energies= -232.722099
Sum of electronic and thermal Enthalpies= -232.721155
Sum of electronic and thermal Free Energies= -232.757076
</pre>

The optimisation at the HF/6-31G* level reached a minimum with the energy derivatives very close to zero after the eighth step (smaller than 10^-4) however due to an error in the program (unstable algorithm) it continued beyond this point and the final structure was incorrect. The eighth intermediate geometry has a bond length of 2.203 A. The following link is to screenshots of the optimisation graphs and the energy derivatives:
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Graphs_of_optimisationjs.png Optimisation_Graphs]]

='''''DA PROJECT=

==Results==

i) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

ii)Optimisation using method in part b) (HF/321G) file = partA_RETRY in folder ii)

The animation clearly shows the correct transition state has been attained.

<jmol> <jmolApplet> <title>Vibration</title><color>white</color><size>200</size> <script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10; </script><uploadedFileContents>Ts_vib.mol</uploadedFileContents> </jmolApplet> </jmol>

The animation is supposed to show concerted bond formation.

<pre> Low frequencies --- -818.4961 -0.0007 -0.0006 -0.0003 1.4348 1.8772
Low frequencies --- 2.7185 166.5539 284.3675
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157558
Thermal correction to Enthalpy= 0.158502
Thermal correction to Gibbs Free Energy= 0.122930
Sum of electronic and zero-point Energies= -231.451338
Sum of electronic and thermal Energies= -231.445650
Sum of electronic and thermal Enthalpies= -231.444706
Sum of electronic and thermal Free Energies= -231.480279
</pre>

iii)
'''Exo Transition States'''
{{DOI|10042/21391}} This is the file for my optimised exo transition state calculated using the derivatise bond method. I also calculated the transition state using the first method in the tutorial section

Modredundant method: 99_frozengif is the input file, output log is 99_99_99
{{DOI|10042/21447}}
<pre>
Low frequencies --- -643.0720 -10.8719 -0.0008 -0.0008 -0.0004 11.9743
Low frequencies --- 15.1280 49.8386 133.6533
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195473 (Hartree/Particle)
Thermal correction to Energy= 0.204891
Thermal correction to Enthalpy= 0.205835
Thermal correction to Gibbs Free Energy= 0.160107
Sum of electronic and zero-point Energies= -605.408011
Sum of electronic and thermal Energies= -605.398593
Sum of electronic and thermal Enthalpies= -605.397649
Sum of electronic and thermal Free Energies= -605.443378 </pre>

Opt=NoEigen method:
{{DOI|10042/21449}}
<pre>

Low frequencies --- -647.3174 -2.2007 -0.0010 -0.0009 -0.0008 1.7640
Low frequencies --- 3.1286 42.6020 131.4691
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195451 (Hartree/Particle)
Thermal correction to Energy= 0.204911
Thermal correction to Enthalpy= 0.205855
Thermal correction to Gibbs Free Energy= 0.159905
Sum of electronic and zero-point Energies= -605.408140
Sum of electronic and thermal Energies= -605.398681
Sum of electronic and thermal Enthalpies= -605.397736
Sum of electronic and thermal Free Energies= -605.443686
</pre>

methodA = 9999log.... file ? Note some disagreement in the transition state optimal distance!
Could also include guess file?

'''The endo transition state:'''
DSPACE LINK TO include. Fies are endo_optimise_ts_A_take2 and log_65019

I optimised this using the opt=noeigen method and the modredundant method to check. First I drew a guess transition state by drawing the product, optimising it to a minimum and then increasing the bond forming lengths to 2.2A The energies are given below and are in good agreement for the different methods. The transition state geometries are very similar for both, with C-C bond forming distances of 2.231 with both methods which agree to the third decimal place.

Calculation using opt=noeigen key word:
{{DOI|10042/21451}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_A_tsjs.PNG Optimisation Summary Table ]

<pre> Low frequencies --- -643.5783 -0.0005 -0.0002 0.0006 0.6895 1.1675
Low frequencies --- 1.7996 65.0129 142.0450
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre> Zero-point correction= 0.195464 (Hartree/Particle)
Thermal correction to Energy= 0.204889
Thermal correction to Enthalpy= 0.205834
Thermal correction to Gibbs Free Energy= 0.160235
Sum of electronic and zero-point Energies= -605.414905
Sum of electronic and thermal Energies= -605.405479
Sum of electronic and thermal Enthalpies= -605.404535
Sum of electronic and thermal Free Energies= -605.450133 </pre>

Calculation using modredundant keyword: {{DOI|10042/21452}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_C_tsjs.PNG Optimisation Summary Table]

<pre>Low frequencies --- -644.2611 -0.0007 -0.0003 0.0006 1.8423 3.3886
Low frequencies --- 6.6938 65.0647 142.3913
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>Zero-point correction= 0.195454 (Hartree/Particle)
Thermal correction to Energy= 0.204879
Thermal correction to Enthalpy= 0.205823
Thermal correction to Gibbs Free Energy= 0.160231
Sum of electronic and zero-point Energies= -605.414912
Sum of electronic and thermal Energies= -605.405487
Sum of electronic and thermal Enthalpies= -605.404543
Sum of electronic and thermal Free Energies= -605.450135
</pre>

Bond formation is concerted

[[File:MethodCmodredundantjs_ts_animation.gif]]

==Discussion Questions==

1) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

2)
Below is illustrated the HOMO left and LUMO right for the unsubsituted Diels Alder transitions state. Both orbitals are symmetric with respect to the plane.

[[Image:HOMOandLUMO(r)js.png|Thumb|300x150px]] [[Image:MOHOMO-1js.PNG|Thumb|300x150px|HOMO-1]]

[[Image:MO4js.PNG|Thumb|300x150px|HOMO]][[Image:MO3js.PNG|Thumb|300x150px|LUMO]] [[Image:MO1js.PNG|Thumb|300x150px|HOMO-1]]

These diagrams show the orbital contributions of the MOs above them.

The HOMO has a node in between the diene and the dienophile.

Allowed reactions: as two new bonds are being formed simultaneously, there are symmetry constraints on the reaction. If both p orbitals on the alkene form constructive overlap with the p orbitals on the terminal carbons of the diene, then the reaction is allowed.

In the HOMO the alkene and diene both have the same symmetry and interact to strengthen the bonds which are forming. (Both components have no nodes)

In the HOMO-1, both components have the same symmetry for overlap and this strengthens the two bonds which are forming

The LUMO is interesting because the two components have different symmetries so weaken the 2 bonds which are forming. However, the orbitals deform and the p orbitals on the alkene balloon out to interact with the p orbitals on the central two carbons of the diene so this would cause a little weak bonding between these atoms.

A further point to make is that the HOMO-1 is the key MO as it has strong positive overlap inbetween the diene and dienophile and so is the major bonding attraction which causes the transition state to roll onto the products. This is because electrons inhabiting this low energy orbital attract the two fragments together.

A "real" Diels Alder reaction requires an electron deficient dienophile and this lowers the energy of its LUMO whilst the diene has a high energy HOMO so the interactions of this orbital (the far right one)are strengthened even more. In reverse demand reactions the following interaction is preferred: [[Image:MO2js.PNG|Thumb|150x75px]]

3) [[File:Ts_moviejs.gif]]

Bond forming distance: 2.209 A. According to a table on wikipedia <ref name = "wikibondlength"/>, the average bond lengths are as follows:
sp2-sp2 C-C = 1.47 A (BUT the alkene double bond length according to the same table is 1.34A Gaussview gives the bond length in ethene of 1.325)
sp3-sp3 C-C = 1.54 A (gaussview has 1.5 for ethane)
sp3-sp2 C-C = 1.50 A
longest C-C = 1.74 A
Additionally, the Van der Waals radius for carbon is 1.7 A <ref name = "wikivdw"/>

The reason that bond lengths are less than the corrosponding average of the radii of the two atoms is that their electron clouds overlap when forming the bond so the nuclei are draw in towards each other somewhat. Two carbon atoms can't form a normal covalent bond in their distance exceeds the van der waals radius. There may be some intermolecular attraction but there isn't a bond. There will be some overlap between the sigma orbitals but it must be weak at this distance. It might have been expected that the length would be upwards from the average of the vdw radius distance and that of a normal sp3 C bond which would be 1.6A but the distance is much more than this.

This, along with the other bond lengths implies that the transition state is "reactant like" i.e. an early transition state. The dienophile has a C=C bond length of 1.375 which is far closer to the double bond length than the single bond length. The dienophile has two bond lengths of 1.39 and two of 1.37 whilst these are all quite short, this also implies that the transition state is at least somewhat more reactant like than product like.

This synchronous vibration compares to the asynchronous one below (however this vibration has sideways motion as well as asynchronous in and out motion).

[[File:Ts_movie2js.gif]]
(This is actually the second lowest positive frequency but the lowest one doesn't show the two molecules moving closer or further apart, only moving sideways relative to each other)

'''Substitution'''

4) The exo transition state is a slighlty more strained as the maleic anhydride componant points towards the bridging carbons. The Oxygen atoms are a little closer to the hydrogens which are on sp3 carbons and so jut out more than the nearest hydrogens on sp2 like carbon to the maleic anhydride component in the endo. This is in part due to the fact that the transition state appears more product like in the endo and more reactant like in the exo. In the actual products, this affect may be extenuated as in the endo transition state, the maleic anhydride oxygen atoms are pulled closer to the C=C to increase secondary orbital overlap.

[[Image:Tsjs.png|Thumb|300x150px]]

5) The endo transition state has energy = -605.610 a.u. The exo transition structure has energy -605.603 a.u this gives a difference of 4.4 kcal mol-1.

[[Image:HOMO-1js.PNG|Thumb|300x150px]]

This is the HOMO-1 in the endo transition state showing positive overlap between the orbitals on the oxygen atoms and the C=C

[[Image:HOMOjs.PNG|Thumb|300x150px]]

This shows the HOMO. There is a node between the oxygen atoms and the diene showing that in the HOMO, the endo is in fact destabilised by secondary orbital interactions relative to the exo. However, in the HOMO-1 shown above, there is constructive overlap between the oxygen atoms and the rest of the molecule. Overall, there is a greater lowering in energy from these overlaps than raising of energy.

However, for both HOMO and HOMO-1, the secondary orbital overlap isn't that strong. The oxygen atoms are far enough away from the pi system such that the orbital surfaces don't combine at the probability densities represented by the orbitals. Hence the electrons don't spend all that much time in between the oxygen atoms and the pi system so although the overlap is strong enough to dictate the favoured stereochemsitry, it isn't strong enough to form a new bond.

==References==

<References>

<ref name = "wikibondlength"> http://en.wikipedia.org/wiki/Bond_length </ref>

<ref name = "wikivdw" > http://en.wikipedia.org/wiki/Van_der_Waals_radius </ref>

<ref name = "Rzep" > Second year lecture course, "conformational analysis" by Dr Rzepa http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct </ref>

</references>

Rep:Mod:JONS007

2012-11-02T13:30:48Z

Js4310: /* Introduction */

='''''THE COPE REARRANGEMENT=
'''Jonathan Shute'''

==Introduction==

This report aims to investigate the thermochemistry of the following reaction:

[[Image:Pic1.jpg|Thumb|250x90px]]

It is understood that the reaction occurs in a concerted fashion via either chair or boat like transition state:

[[File:Pic2b.jpg]] [[File:Pic2b.jpg]]

In the tutorial section, the enthalpy of the reactant has been found when it is in its most energetically stable conformer. In the second part, the chair and boat transition geometries have been located and their energies calcualted. These data were then used to calculate the activation energy of the reaction.

Several methods were employed to obtain the transition states. Every transition state has with it associated one imaginary frequency. This is because bonds can be modelled as vibrational springs obeying Hooke's law, F= -kx. The frequencies are computed using the following equation:

<math> {1\over {2 \pi}} \sqrt{k \over \mu}. \!</math>

The force constants are negative at the transition state so the frequency is imaginary.

==Optimising the Reactants and Products==

'''1,5-hexadiene'''

(a)The energy of the anti conformer is -231.6926(0235) a.u and the symmetry is C1
[[File:Hexatriene_anti_optimised_321Gjs.log]]

(b)The energy of the gauche conformer is -231.6915(30325) [[File:HEXATRIENEGAUGEjs_321G.LOG]]

The gauche conformer is slightly higher in energy due to the carbons 1 and 4 of the central carbons eclipsing each other a little and causing steric repulsion whist in the staggered conformation, there is less interaction between them. In the antiperiplaner conformation, there is overlap between the sigma C-C bonding orbital for carbons C1 and C2 and the C-C antibonding orbital between C3 and C4. This lowers the energy slightly.

In both structures, A1,3 eclipsed conformation <ref name = "Rzep" /> is evident with the H atoms on the carbon adjacent to C=C at
roughly 120o to the pi system, although not exactly and in both structures one of the H's is at a slightly larger angle than this. The A1,3 conformation is a compromise between having two hydrogen's sigma orbitals aligned fairly well with the pi star orbitals and also there is an attractive vdw force between the H atom on the C=C and on the H atom on the neighbouring carbon. The distance is slightly larger in the gauche.

[[Image:Banana2js.png|Thumb|300x300px|]]

These orbitals show interaction of the sigma H orbital with the pi star orbitals is effective for both conformers.

(c) The lowest energy conformers of 1,5-hexadiene in the table are anti1 and gauche3

(d)By comparison with the appendix table, my optimised conformers were anti1 and gauche4. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summaryhexatriene_631G.PNG My Optimisation Summary Table]]

(e)The optimised molecule had point group Ci and an energy matching the value given in appendix of -231.69253528 a.u precisely. [[File:TRIAL2VER2_321G.LOG]]

<pre>
Low frequencies --- -5.6849 -2.3517 -2.0910 -0.0008 -0.0004 -0.0002
Low frequencies --- 71.1980 85.6851 116.1458

</pre>
<pre>
Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916
</pre>

This gives an electronic energy of 231.692535 (by subtracting the zero point correction to the sum of electronic and zero point energies).

All is in close agreement with the appendix table (only variation in the sixth decimal place)

(f)The conformation of the molecule appears the same when both basis sets are used though the C=C bond length is a little longer with the better basis set at 1.333 A compared to 1.316 A. The energy is very significantly different at -234.611706. This is why the energy of different molecules can only be compared if it was computed with the same basis set.
[[File:HEXATRIENEANIT2CI_631GD.LOG]]
[[File:HEXATRIENEANIT2CI_631GD_FREQCHECKjs.LOG]]

[[Image:IRspecjs.PNG|Thumb|400x600px|]]

<pre>
''' Low frequencies --- -9.1026 0.0005 0.0005 0.0008 4.2776 13.4006
Low frequencies --- 74.2705 80.9525 121.5200 </pre>'''

<pre>
Zero-point correction= 0.142504 (Hartree/Particle)
Thermal correction to Energy= 0.149851
Thermal correction to Enthalpy= 0.150795
Thermal correction to Gibbs Free Energy= 0.110929

Sum of electronic and zero-point Energies= -234.469207
Sum of electronic and thermal Energies= -234.461859
Sum of electronic and thermal Enthalpies= -234.460915
Sum of electronic and thermal Free Energies= -234.500782
</pre>

(It is a little surprising that the low frequencies are higher for the optimisation with the better basis set)

==Optimising Chair and Boat Transitions==

(b)
<pre>
Low frequencies --- -817.9271 -7.0897 -5.4674 -4.3204 -0.0004 0.0004
Low frequencies --- 0.0005 209.4156 396.0571
****** 1 imaginary frequencies (negative Signs) ******
</pre>

{{DOI|10042/21119}} (optimised log file of chair guessed transition state)chair_guesstransition_optimis_freq on my computer this is: log_64342

<pre> Zero-point correction= 0.152627 (Hartree/Particle)
Thermal correction to Energy= 0.157986
Thermal correction to Enthalpy= 0.158930
Thermal correction to Gibbs Free Energy= 0.124120
Sum of electronic and zero-point Energies= -231.466696
Sum of electronic and thermal Energies= -231.461336
Sum of electronic and thermal Enthalpies= -231.460392
Sum of electronic and thermal Free Energies= -231.495202 </pre>

These results agree with those given in the appendix with variation in fifth d.p only.

(c)
-can't optimise exactly! TBC
THE FILE IS CALLED INCORRECT. It works!(This part took a very long time due to the incompleteness of the instructions which mislead me!)

(d)Optimisation to a transition state was successful but initially failed until write connectivity was unchecked under the general tab. The bond lengths were 2.01995 A. This is corroborated by the results for the optimised chair in part (b) which gave a bond length of 2.0205 remarkably similar considering the differences in the models used.

File name: incorrect_optimise_toa_transition_state

<pre>Zero-point correction= 0.151377 (Hartree/Particle)
Thermal correction to Energy= 0.157016
Thermal correction to Enthalpy= 0.157960
Thermal correction to Gibbs Free Energy= 0.122592
Sum of electronic and zero-point Energies= -231.463821
Sum of electronic and thermal Energies= -231.458181
Sum of electronic and thermal Enthalpies= -231.457237
Sum of electronic and thermal Free Energies= -231.492605</pre>

-231.619322
-231.466705
-231.461346

(e) File:gauge_TS(QST2)_ERRDEFAULTSPIN successful optimisation with 2.140 bond length. Only one imaginary frequency (which is vibration of the two bonds which are forming):

<jmolFile text="Explanatory text for link">TS-Vibrationjs.mol</jmolFile>

<pre>

Low frequencies --- -840.1011 -4.0811 -0.0011 -0.0010 -0.0009 3.5285
Low frequencies --- 5.2099 155.3480 382.0830
****** 1 imaginary frequencies (negative Signs) ******

</pre>

<pre>
Zero-point correction= 0.151874 (Hartree/Particle)
Thermal correction to Energy= 0.157502
Thermal correction to Enthalpy= 0.158447
Thermal correction to Gibbs Free Energy= 0.123029
Sum of electronic and zero-point Energies= -231.450929
Sum of electronic and thermal Energies= -231.445300
Sum of electronic and thermal Enthalpies= -231.444356
Sum of electronic and thermal Free Energies= -231.479774
</pre>

This results are very close to those in the appendix table for 321G HF basis set and method.
(f) {{DOI|10042/21197}} file shows the IRC on the chair transition state calculated using redundant method.
(Need to reach a minimum.... - maybe check for graph also)

(g) (Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way under the extra working section) The calculation below is with the correct method.

i) Correct method
{{DOI|10042/21294}}

<pre>
Zero-point correction= 0.140741 (Hartree/Particle)
Thermal correction to Energy= 0.147079
Thermal correction to Enthalpy= 0.148023
Thermal correction to Gibbs Free Energy= 0.111326
Sum of electronic and zero-point Energies= -234.402355
Sum of electronic and thermal Energies= -234.396016
Sum of electronic and thermal Enthalpies= -234.395072
Sum of electronic and thermal Free Energies= -234.431769
</pre>

There is a small variation when compared to appendix values in the fifth d.p.

ii) {{DOI|10042/21304}} {{DOI|10042/21305}}
Reoptimised the chair calculated in part b to B3YLP/6-31G* level:

<pre>
Zero-point correction= 0.142054 (Hartree/Particle)
Thermal correction to Energy= 0.147975
Thermal correction to Enthalpy= 0.148919
Thermal correction to Gibbs Free Energy= 0.113168
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443815 </pre>

Again, these results are in close agreement with those in the appendix table to the fifth d.p

'''Conclusion'''

The energy of the chair minus the thermal correction is -234.557 a.u. The energy of the reactant is -234.612 a.u
Need to subtract energy of starting materials and reactants to give the extra energy of the transition state which must be overcome for reaction to occur.
1 Hartree = 627.509 kcal/mol

Hence, the difference in energy is -5.471*10^-2. This is '''34.3 kcal mol-1.'''

The energy of the boat is -234.543 a.u. This gives Ea = 0.0689 a.u or '''43.2 kcal mol-1'''

These values compare to the literature values of 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure. This is surprisingly good agreement as the basis set used B3LYP/6-31G* is quite an inexact basis set.

==Extra Working==

Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way below as an extension to the tutorial!

(g) {{DOI|10042/21218}} this is the optimised boat HF/3-21G reoptimised
file is IRC_chair_redundant. The results are given below:

<pre>
Low frequencies --- -852.3991 -6.1132 -4.0906 -1.4954 -0.0005 0.0006
Low frequencies --- 0.0007 145.9558 320.2847
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.150402 (Hartree/Particle)
Thermal correction to Energy= 0.156295
Thermal correction to Enthalpy= 0.157239
Thermal correction to Gibbs Free Energy= 0.121318
Sum of electronic and zero-point Energies= -232.727993
Sum of electronic and thermal Energies= -232.722099
Sum of electronic and thermal Enthalpies= -232.721155
Sum of electronic and thermal Free Energies= -232.757076
</pre>

The optimisation at the HF/6-31G* level reached a minimum with the energy derivatives very close to zero after the eighth step (smaller than 10^-4) however due to an error in the program (unstable algorithm) it continued beyond this point and the final structure was incorrect. The eighth intermediate geometry has a bond length of 2.203 A. The following link is to screenshots of the optimisation graphs and the energy derivatives:
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Graphs_of_optimisationjs.png Optimisation_Graphs]]

== Conclusion ==

<br />

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| '''Boat TS'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| '''Reactant (''anti2'')'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|}

='''''DA PROJECT=

==Results==

i) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

ii)Optimisation using method in part b) (HF/321G) file = partA_RETRY in folder ii)

The animation clearly shows the correct transition state has been attained.

<jmol> <jmolApplet> <title>Vibration</title><color>white</color><size>200</size> <script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10; </script><uploadedFileContents>Ts_vib.mol</uploadedFileContents> </jmolApplet> </jmol>

The animation is supposed to show concerted bond formation.

<pre> Low frequencies --- -818.4961 -0.0007 -0.0006 -0.0003 1.4348 1.8772
Low frequencies --- 2.7185 166.5539 284.3675
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157558
Thermal correction to Enthalpy= 0.158502
Thermal correction to Gibbs Free Energy= 0.122930
Sum of electronic and zero-point Energies= -231.451338
Sum of electronic and thermal Energies= -231.445650
Sum of electronic and thermal Enthalpies= -231.444706
Sum of electronic and thermal Free Energies= -231.480279
</pre>

iii)
'''Exo Transition States'''
{{DOI|10042/21391}} This is the file for my optimised exo transition state calculated using the derivatise bond method. I also calculated the transition state using the first method in the tutorial section

Modredundant method: 99_frozengif is the input file, output log is 99_99_99
{{DOI|10042/21447}}
<pre>
Low frequencies --- -643.0720 -10.8719 -0.0008 -0.0008 -0.0004 11.9743
Low frequencies --- 15.1280 49.8386 133.6533
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195473 (Hartree/Particle)
Thermal correction to Energy= 0.204891
Thermal correction to Enthalpy= 0.205835
Thermal correction to Gibbs Free Energy= 0.160107
Sum of electronic and zero-point Energies= -605.408011
Sum of electronic and thermal Energies= -605.398593
Sum of electronic and thermal Enthalpies= -605.397649
Sum of electronic and thermal Free Energies= -605.443378 </pre>

Opt=NoEigen method:
{{DOI|10042/21449}}
<pre>

Low frequencies --- -647.3174 -2.2007 -0.0010 -0.0009 -0.0008 1.7640
Low frequencies --- 3.1286 42.6020 131.4691
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195451 (Hartree/Particle)
Thermal correction to Energy= 0.204911
Thermal correction to Enthalpy= 0.205855
Thermal correction to Gibbs Free Energy= 0.159905
Sum of electronic and zero-point Energies= -605.408140
Sum of electronic and thermal Energies= -605.398681
Sum of electronic and thermal Enthalpies= -605.397736
Sum of electronic and thermal Free Energies= -605.443686
</pre>

methodA = 9999log.... file ? Note some disagreement in the transition state optimal distance!
Could also include guess file?

'''The endo transition state:'''
DSPACE LINK TO include. Fies are endo_optimise_ts_A_take2 and log_65019

I optimised this using the opt=noeigen method and the modredundant method to check. First I drew a guess transition state by drawing the product, optimising it to a minimum and then increasing the bond forming lengths to 2.2A The energies are given below and are in good agreement for the different methods. The transition state geometries are very similar for both, with C-C bond forming distances of 2.231 with both methods which agree to the third decimal place.

Calculation using opt=noeigen key word:
{{DOI|10042/21451}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_A_tsjs.PNG Optimisation Summary Table ]

<pre> Low frequencies --- -643.5783 -0.0005 -0.0002 0.0006 0.6895 1.1675
Low frequencies --- 1.7996 65.0129 142.0450
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre> Zero-point correction= 0.195464 (Hartree/Particle)
Thermal correction to Energy= 0.204889
Thermal correction to Enthalpy= 0.205834
Thermal correction to Gibbs Free Energy= 0.160235
Sum of electronic and zero-point Energies= -605.414905
Sum of electronic and thermal Energies= -605.405479
Sum of electronic and thermal Enthalpies= -605.404535
Sum of electronic and thermal Free Energies= -605.450133 </pre>

Calculation using modredundant keyword: {{DOI|10042/21452}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_C_tsjs.PNG Optimisation Summary Table]

<pre>Low frequencies --- -644.2611 -0.0007 -0.0003 0.0006 1.8423 3.3886
Low frequencies --- 6.6938 65.0647 142.3913
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>Zero-point correction= 0.195454 (Hartree/Particle)
Thermal correction to Energy= 0.204879
Thermal correction to Enthalpy= 0.205823
Thermal correction to Gibbs Free Energy= 0.160231
Sum of electronic and zero-point Energies= -605.414912
Sum of electronic and thermal Energies= -605.405487
Sum of electronic and thermal Enthalpies= -605.404543
Sum of electronic and thermal Free Energies= -605.450135
</pre>

Bond formation is concerted

[[File:MethodCmodredundantjs_ts_animation.gif]]

==Discussion Questions==

1) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

2)
Below is illustrated the HOMO left and LUMO right for the unsubsituted Diels Alder transitions state. Both orbitals are symmetric with respect to the plane.

[[Image:HOMOandLUMO(r)js.png|Thumb|300x150px]] [[Image:MOHOMO-1js.PNG|Thumb|300x150px|HOMO-1]]

[[Image:MO4js.PNG|Thumb|300x150px|HOMO]][[Image:MO3js.PNG|Thumb|300x150px|LUMO]] [[Image:MO1js.PNG|Thumb|300x150px|HOMO-1]]

These diagrams show the orbital contributions of the MOs above them.

The HOMO has a node in between the diene and the dienophile.

Allowed reactions: as two new bonds are being formed simultaneously, there are symmetry constraints on the reaction. If both p orbitals on the alkene form constructive overlap with the p orbitals on the terminal carbons of the diene, then the reaction is allowed.

In the HOMO the alkene and diene both have the same symmetry and interact to strengthen the bonds which are forming. (Both components have no nodes)

In the HOMO-1, both components have the same symmetry for overlap and this strengthens the two bonds which are forming

The LUMO is interesting because the two components have different symmetries so weaken the 2 bonds which are forming. However, the orbitals deform and the p orbitals on the alkene balloon out to interact with the p orbitals on the central two carbons of the diene so this would cause a little weak bonding between these atoms.

A further point to make is that the HOMO-1 is the key MO as it has strong positive overlap inbetween the diene and dienophile and so is the major bonding attraction which causes the transition state to roll onto the products. This is because electrons inhabiting this low energy orbital attract the two fragments together.

A "real" Diels Alder reaction requires an electron deficient dienophile and this lowers the energy of its LUMO whilst the diene has a high energy HOMO so the interactions of this orbital (the far right one)are strengthened even more. In reverse demand reactions the following interaction is preferred: [[Image:MO2js.PNG|Thumb|150x75px]]

3) [[File:Ts_moviejs.gif]]

Bond forming distance: 2.209 A. According to a table on wikipedia <ref name = "wikibondlength"/>, the average bond lengths are as follows:
sp2-sp2 C-C = 1.47 A (BUT the alkene double bond length according to the same table is 1.34A Gaussview gives the bond length in ethene of 1.325)
sp3-sp3 C-C = 1.54 A (gaussview has 1.5 for ethane)
sp3-sp2 C-C = 1.50 A
longest C-C = 1.74 A
Additionally, the Van der Waals radius for carbon is 1.7 A <ref name = "wikivdw"/>

The reason that bond lengths are less than the corrosponding average of the radii of the two atoms is that their electron clouds overlap when forming the bond so the nuclei are draw in towards each other somewhat. Two carbon atoms can't form a normal covalent bond in their distance exceeds the van der waals radius. There may be some intermolecular attraction but there isn't a bond. There will be some overlap between the sigma orbitals but it must be weak at this distance. It might have been expected that the length would be upwards from the average of the vdw radius distance and that of a normal sp3 C bond which would be 1.6A but the distance is much more than this.

This, along with the other bond lengths implies that the transition state is "reactant like" i.e. an early transition state. The dienophile has a C=C bond length of 1.375 which is far closer to the double bond length than the single bond length. The dienophile has two bond lengths of 1.39 and two of 1.37 whilst these are all quite short, this also implies that the transition state is at least somewhat more reactant like than product like.

This synchronous vibration compares to the asynchronous one below (however this vibration has sideways motion as well as asynchronous in and out motion).

[[File:Ts_movie2js.gif]]
(This is actually the second lowest positive frequency but the lowest one doesn't show the two molecules moving closer or further apart, only moving sideways relative to each other)

'''Substitution'''

4) The exo transition state is a slighlty more strained as the maleic anhydride componant points towards the bridging carbons. The Oxygen atoms are a little closer to the hydrogens which are on sp3 carbons and so jut out more than the nearest hydrogens on sp2 like carbon to the maleic anhydride component in the endo. This is in part due to the fact that the transition state appears more product like in the endo and more reactant like in the exo. In the actual products, this affect may be extenuated as in the endo transition state, the maleic anhydride oxygen atoms are pulled closer to the C=C to increase secondary orbital overlap.

[[Image:Tsjs.png|Thumb|300x150px]]

5) The endo transition state has energy = -605.610 a.u. The exo transition structure has energy -605.603 a.u this gives a difference of 4.4 kcal mol-1.

[[Image:HOMO-1js.PNG|Thumb|300x150px]]

This is the HOMO-1 in the endo transition state showing positive overlap between the orbitals on the oxygen atoms and the C=C

[[Image:HOMOjs.PNG|Thumb|300x150px]]

This shows the HOMO. There is a node between the oxygen atoms and the diene showing that in the HOMO, the endo is in fact destabilised by secondary orbital interactions relative to the exo. However, in the HOMO-1 shown above, there is constructive overlap between the oxygen atoms and the rest of the molecule. Overall, there is a greater lowering in energy from these overlaps than raising of energy.

However, for both HOMO and HOMO-1, the secondary orbital overlap isn't that strong. The oxygen atoms are far enough away from the pi system such that the orbital surfaces don't combine at the probability densities represented by the orbitals. Hence the electrons don't spend all that much time in between the oxygen atoms and the pi system so although the overlap is strong enough to dictate the favoured stereochemsitry, it isn't strong enough to form a new bond.

==References==

<References>

<ref name = "wikibondlength"> http://en.wikipedia.org/wiki/Bond_length </ref>

<ref name = "wikivdw" > http://en.wikipedia.org/wiki/Van_der_Waals_radius </ref>

<ref name = "Rzep" > Second year lecture course, "conformational analysis" by Dr Rzepa http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct </ref>

</references>

Rep:Mod:JONS007

2012-11-02T13:27:19Z

Js4310: /* Introduction */

='''''THE COPE REARRANGEMENT=
'''Jonathan Shute'''

==Introduction==

This report aims to investigate the thermochemistry of the following reaction:

[[Image:Pic1.jpg|Thumb|250x90px]]

It is understood that the reaction occurs in a concerted fashion via either chair or boat like transition state:

[[File:Pic2b.jpg]] [[File:Pic2b.jpg]]

In the tutorial section, the enthalpy of the reactant has been found when it is in its most energetically stable conformer. In the second part, the chair and boat transition geometries have been located and their energies calcualted. These data were then used to calculate the activation energy of the reaction.

Several methods were employed to obtain the transition states. Every transition state has with it associated one imaginary frequency. This is because bonds can be modelled as vibrational springs obeying Hooke's law, F= -kx. The frequencies are computed using the following equation:

<math> {1\over {2 \pi}} \sqrt{k \over \mu}. \!</math>

==Optimising the Reactants and Products==

'''1,5-hexadiene'''

(a)The energy of the anti conformer is -231.6926(0235) a.u and the symmetry is C1
[[File:Hexatriene_anti_optimised_321Gjs.log]]

(b)The energy of the gauche conformer is -231.6915(30325) [[File:HEXATRIENEGAUGEjs_321G.LOG]]

The gauche conformer is slightly higher in energy due to the carbons 1 and 4 of the central carbons eclipsing each other a little and causing steric repulsion whist in the staggered conformation, there is less interaction between them. In the antiperiplaner conformation, there is overlap between the sigma C-C bonding orbital for carbons C1 and C2 and the C-C antibonding orbital between C3 and C4. This lowers the energy slightly.

In both structures, A1,3 eclipsed conformation <ref name = "Rzep" /> is evident with the H atoms on the carbon adjacent to C=C at
roughly 120o to the pi system, although not exactly and in both structures one of the H's is at a slightly larger angle than this. The A1,3 conformation is a compromise between having two hydrogen's sigma orbitals aligned fairly well with the pi star orbitals and also there is an attractive vdw force between the H atom on the C=C and on the H atom on the neighbouring carbon. The distance is slightly larger in the gauche.

[[Image:Banana2js.png|Thumb|300x300px|]]

These orbitals show interaction of the sigma H orbital with the pi star orbitals is effective for both conformers.

(c) The lowest energy conformers of 1,5-hexadiene in the table are anti1 and gauche3

(d)By comparison with the appendix table, my optimised conformers were anti1 and gauche4. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summaryhexatriene_631G.PNG My Optimisation Summary Table]]

(e)The optimised molecule had point group Ci and an energy matching the value given in appendix of -231.69253528 a.u precisely. [[File:TRIAL2VER2_321G.LOG]]

<pre>
Low frequencies --- -5.6849 -2.3517 -2.0910 -0.0008 -0.0004 -0.0002
Low frequencies --- 71.1980 85.6851 116.1458

</pre>
<pre>
Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916
</pre>

This gives an electronic energy of 231.692535 (by subtracting the zero point correction to the sum of electronic and zero point energies).

All is in close agreement with the appendix table (only variation in the sixth decimal place)

(f)The conformation of the molecule appears the same when both basis sets are used though the C=C bond length is a little longer with the better basis set at 1.333 A compared to 1.316 A. The energy is very significantly different at -234.611706. This is why the energy of different molecules can only be compared if it was computed with the same basis set.
[[File:HEXATRIENEANIT2CI_631GD.LOG]]
[[File:HEXATRIENEANIT2CI_631GD_FREQCHECKjs.LOG]]

[[Image:IRspecjs.PNG|Thumb|400x600px|]]

<pre>
''' Low frequencies --- -9.1026 0.0005 0.0005 0.0008 4.2776 13.4006
Low frequencies --- 74.2705 80.9525 121.5200 </pre>'''

<pre>
Zero-point correction= 0.142504 (Hartree/Particle)
Thermal correction to Energy= 0.149851
Thermal correction to Enthalpy= 0.150795
Thermal correction to Gibbs Free Energy= 0.110929

Sum of electronic and zero-point Energies= -234.469207
Sum of electronic and thermal Energies= -234.461859
Sum of electronic and thermal Enthalpies= -234.460915
Sum of electronic and thermal Free Energies= -234.500782
</pre>

(It is a little surprising that the low frequencies are higher for the optimisation with the better basis set)

==Optimising Chair and Boat Transitions==

(b)
<pre>
Low frequencies --- -817.9271 -7.0897 -5.4674 -4.3204 -0.0004 0.0004
Low frequencies --- 0.0005 209.4156 396.0571
****** 1 imaginary frequencies (negative Signs) ******
</pre>

{{DOI|10042/21119}} (optimised log file of chair guessed transition state)chair_guesstransition_optimis_freq on my computer this is: log_64342

<pre> Zero-point correction= 0.152627 (Hartree/Particle)
Thermal correction to Energy= 0.157986
Thermal correction to Enthalpy= 0.158930
Thermal correction to Gibbs Free Energy= 0.124120
Sum of electronic and zero-point Energies= -231.466696
Sum of electronic and thermal Energies= -231.461336
Sum of electronic and thermal Enthalpies= -231.460392
Sum of electronic and thermal Free Energies= -231.495202 </pre>

These results agree with those given in the appendix with variation in fifth d.p only.

(c)
-can't optimise exactly! TBC
THE FILE IS CALLED INCORRECT. It works!(This part took a very long time due to the incompleteness of the instructions which mislead me!)

(d)Optimisation to a transition state was successful but initially failed until write connectivity was unchecked under the general tab. The bond lengths were 2.01995 A. This is corroborated by the results for the optimised chair in part (b) which gave a bond length of 2.0205 remarkably similar considering the differences in the models used.

File name: incorrect_optimise_toa_transition_state

<pre>Zero-point correction= 0.151377 (Hartree/Particle)
Thermal correction to Energy= 0.157016
Thermal correction to Enthalpy= 0.157960
Thermal correction to Gibbs Free Energy= 0.122592
Sum of electronic and zero-point Energies= -231.463821
Sum of electronic and thermal Energies= -231.458181
Sum of electronic and thermal Enthalpies= -231.457237
Sum of electronic and thermal Free Energies= -231.492605</pre>

-231.619322
-231.466705
-231.461346

(e) File:gauge_TS(QST2)_ERRDEFAULTSPIN successful optimisation with 2.140 bond length. Only one imaginary frequency (which is vibration of the two bonds which are forming):

<jmolFile text="Explanatory text for link">TS-Vibrationjs.mol</jmolFile>

<pre>

Low frequencies --- -840.1011 -4.0811 -0.0011 -0.0010 -0.0009 3.5285
Low frequencies --- 5.2099 155.3480 382.0830
****** 1 imaginary frequencies (negative Signs) ******

</pre>

<pre>
Zero-point correction= 0.151874 (Hartree/Particle)
Thermal correction to Energy= 0.157502
Thermal correction to Enthalpy= 0.158447
Thermal correction to Gibbs Free Energy= 0.123029
Sum of electronic and zero-point Energies= -231.450929
Sum of electronic and thermal Energies= -231.445300
Sum of electronic and thermal Enthalpies= -231.444356
Sum of electronic and thermal Free Energies= -231.479774
</pre>

This results are very close to those in the appendix table for 321G HF basis set and method.
(f) {{DOI|10042/21197}} file shows the IRC on the chair transition state calculated using redundant method.
(Need to reach a minimum.... - maybe check for graph also)

(g) (Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way under the extra working section) The calculation below is with the correct method.

i) Correct method
{{DOI|10042/21294}}

<pre>
Zero-point correction= 0.140741 (Hartree/Particle)
Thermal correction to Energy= 0.147079
Thermal correction to Enthalpy= 0.148023
Thermal correction to Gibbs Free Energy= 0.111326
Sum of electronic and zero-point Energies= -234.402355
Sum of electronic and thermal Energies= -234.396016
Sum of electronic and thermal Enthalpies= -234.395072
Sum of electronic and thermal Free Energies= -234.431769
</pre>

There is a small variation when compared to appendix values in the fifth d.p.

ii) {{DOI|10042/21304}} {{DOI|10042/21305}}
Reoptimised the chair calculated in part b to B3YLP/6-31G* level:

<pre>
Zero-point correction= 0.142054 (Hartree/Particle)
Thermal correction to Energy= 0.147975
Thermal correction to Enthalpy= 0.148919
Thermal correction to Gibbs Free Energy= 0.113168
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443815 </pre>

Again, these results are in close agreement with those in the appendix table to the fifth d.p

'''Conclusion'''

The energy of the chair minus the thermal correction is -234.557 a.u. The energy of the reactant is -234.612 a.u
Need to subtract energy of starting materials and reactants to give the extra energy of the transition state which must be overcome for reaction to occur.
1 Hartree = 627.509 kcal/mol

Hence, the difference in energy is -5.471*10^-2. This is '''34.3 kcal mol-1.'''

The energy of the boat is -234.543 a.u. This gives Ea = 0.0689 a.u or '''43.2 kcal mol-1'''

These values compare to the literature values of 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure. This is surprisingly good agreement as the basis set used B3LYP/6-31G* is quite an inexact basis set.

==Extra Working==

Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way below as an extension to the tutorial!

(g) {{DOI|10042/21218}} this is the optimised boat HF/3-21G reoptimised
file is IRC_chair_redundant. The results are given below:

<pre>
Low frequencies --- -852.3991 -6.1132 -4.0906 -1.4954 -0.0005 0.0006
Low frequencies --- 0.0007 145.9558 320.2847
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.150402 (Hartree/Particle)
Thermal correction to Energy= 0.156295
Thermal correction to Enthalpy= 0.157239
Thermal correction to Gibbs Free Energy= 0.121318
Sum of electronic and zero-point Energies= -232.727993
Sum of electronic and thermal Energies= -232.722099
Sum of electronic and thermal Enthalpies= -232.721155
Sum of electronic and thermal Free Energies= -232.757076
</pre>

The optimisation at the HF/6-31G* level reached a minimum with the energy derivatives very close to zero after the eighth step (smaller than 10^-4) however due to an error in the program (unstable algorithm) it continued beyond this point and the final structure was incorrect. The eighth intermediate geometry has a bond length of 2.203 A. The following link is to screenshots of the optimisation graphs and the energy derivatives:
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Graphs_of_optimisationjs.png Optimisation_Graphs]]

== Conclusion ==

<br />

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| '''Boat TS'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| '''Reactant (''anti2'')'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|}

='''''DA PROJECT=

==Results==

i) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

ii)Optimisation using method in part b) (HF/321G) file = partA_RETRY in folder ii)

The animation clearly shows the correct transition state has been attained.

<jmol> <jmolApplet> <title>Vibration</title><color>white</color><size>200</size> <script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10; </script><uploadedFileContents>Ts_vib.mol</uploadedFileContents> </jmolApplet> </jmol>

The animation is supposed to show concerted bond formation.

<pre> Low frequencies --- -818.4961 -0.0007 -0.0006 -0.0003 1.4348 1.8772
Low frequencies --- 2.7185 166.5539 284.3675
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157558
Thermal correction to Enthalpy= 0.158502
Thermal correction to Gibbs Free Energy= 0.122930
Sum of electronic and zero-point Energies= -231.451338
Sum of electronic and thermal Energies= -231.445650
Sum of electronic and thermal Enthalpies= -231.444706
Sum of electronic and thermal Free Energies= -231.480279
</pre>

iii)
'''Exo Transition States'''
{{DOI|10042/21391}} This is the file for my optimised exo transition state calculated using the derivatise bond method. I also calculated the transition state using the first method in the tutorial section

Modredundant method: 99_frozengif is the input file, output log is 99_99_99
{{DOI|10042/21447}}
<pre>
Low frequencies --- -643.0720 -10.8719 -0.0008 -0.0008 -0.0004 11.9743
Low frequencies --- 15.1280 49.8386 133.6533
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195473 (Hartree/Particle)
Thermal correction to Energy= 0.204891
Thermal correction to Enthalpy= 0.205835
Thermal correction to Gibbs Free Energy= 0.160107
Sum of electronic and zero-point Energies= -605.408011
Sum of electronic and thermal Energies= -605.398593
Sum of electronic and thermal Enthalpies= -605.397649
Sum of electronic and thermal Free Energies= -605.443378 </pre>

Opt=NoEigen method:
{{DOI|10042/21449}}
<pre>

Low frequencies --- -647.3174 -2.2007 -0.0010 -0.0009 -0.0008 1.7640
Low frequencies --- 3.1286 42.6020 131.4691
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195451 (Hartree/Particle)
Thermal correction to Energy= 0.204911
Thermal correction to Enthalpy= 0.205855
Thermal correction to Gibbs Free Energy= 0.159905
Sum of electronic and zero-point Energies= -605.408140
Sum of electronic and thermal Energies= -605.398681
Sum of electronic and thermal Enthalpies= -605.397736
Sum of electronic and thermal Free Energies= -605.443686
</pre>

methodA = 9999log.... file ? Note some disagreement in the transition state optimal distance!
Could also include guess file?

'''The endo transition state:'''
DSPACE LINK TO include. Fies are endo_optimise_ts_A_take2 and log_65019

I optimised this using the opt=noeigen method and the modredundant method to check. First I drew a guess transition state by drawing the product, optimising it to a minimum and then increasing the bond forming lengths to 2.2A The energies are given below and are in good agreement for the different methods. The transition state geometries are very similar for both, with C-C bond forming distances of 2.231 with both methods which agree to the third decimal place.

Calculation using opt=noeigen key word:
{{DOI|10042/21451}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_A_tsjs.PNG Optimisation Summary Table ]

<pre> Low frequencies --- -643.5783 -0.0005 -0.0002 0.0006 0.6895 1.1675
Low frequencies --- 1.7996 65.0129 142.0450
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre> Zero-point correction= 0.195464 (Hartree/Particle)
Thermal correction to Energy= 0.204889
Thermal correction to Enthalpy= 0.205834
Thermal correction to Gibbs Free Energy= 0.160235
Sum of electronic and zero-point Energies= -605.414905
Sum of electronic and thermal Energies= -605.405479
Sum of electronic and thermal Enthalpies= -605.404535
Sum of electronic and thermal Free Energies= -605.450133 </pre>

Calculation using modredundant keyword: {{DOI|10042/21452}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_C_tsjs.PNG Optimisation Summary Table]

<pre>Low frequencies --- -644.2611 -0.0007 -0.0003 0.0006 1.8423 3.3886
Low frequencies --- 6.6938 65.0647 142.3913
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>Zero-point correction= 0.195454 (Hartree/Particle)
Thermal correction to Energy= 0.204879
Thermal correction to Enthalpy= 0.205823
Thermal correction to Gibbs Free Energy= 0.160231
Sum of electronic and zero-point Energies= -605.414912
Sum of electronic and thermal Energies= -605.405487
Sum of electronic and thermal Enthalpies= -605.404543
Sum of electronic and thermal Free Energies= -605.450135
</pre>

Bond formation is concerted

[[File:MethodCmodredundantjs_ts_animation.gif]]

==Discussion Questions==

1) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

2)
Below is illustrated the HOMO left and LUMO right for the unsubsituted Diels Alder transitions state. Both orbitals are symmetric with respect to the plane.

[[Image:HOMOandLUMO(r)js.png|Thumb|300x150px]] [[Image:MOHOMO-1js.PNG|Thumb|300x150px|HOMO-1]]

[[Image:MO4js.PNG|Thumb|300x150px|HOMO]][[Image:MO3js.PNG|Thumb|300x150px|LUMO]] [[Image:MO1js.PNG|Thumb|300x150px|HOMO-1]]

These diagrams show the orbital contributions of the MOs above them.

The HOMO has a node in between the diene and the dienophile.

Allowed reactions: as two new bonds are being formed simultaneously, there are symmetry constraints on the reaction. If both p orbitals on the alkene form constructive overlap with the p orbitals on the terminal carbons of the diene, then the reaction is allowed.

In the HOMO the alkene and diene both have the same symmetry and interact to strengthen the bonds which are forming. (Both components have no nodes)

In the HOMO-1, both components have the same symmetry for overlap and this strengthens the two bonds which are forming

The LUMO is interesting because the two components have different symmetries so weaken the 2 bonds which are forming. However, the orbitals deform and the p orbitals on the alkene balloon out to interact with the p orbitals on the central two carbons of the diene so this would cause a little weak bonding between these atoms.

A further point to make is that the HOMO-1 is the key MO as it has strong positive overlap inbetween the diene and dienophile and so is the major bonding attraction which causes the transition state to roll onto the products. This is because electrons inhabiting this low energy orbital attract the two fragments together.

A "real" Diels Alder reaction requires an electron deficient dienophile and this lowers the energy of its LUMO whilst the diene has a high energy HOMO so the interactions of this orbital (the far right one)are strengthened even more. In reverse demand reactions the following interaction is preferred: [[Image:MO2js.PNG|Thumb|150x75px]]

3) [[File:Ts_moviejs.gif]]

Bond forming distance: 2.209 A. According to a table on wikipedia <ref name = "wikibondlength"/>, the average bond lengths are as follows:
sp2-sp2 C-C = 1.47 A (BUT the alkene double bond length according to the same table is 1.34A Gaussview gives the bond length in ethene of 1.325)
sp3-sp3 C-C = 1.54 A (gaussview has 1.5 for ethane)
sp3-sp2 C-C = 1.50 A
longest C-C = 1.74 A
Additionally, the Van der Waals radius for carbon is 1.7 A <ref name = "wikivdw"/>

The reason that bond lengths are less than the corrosponding average of the radii of the two atoms is that their electron clouds overlap when forming the bond so the nuclei are draw in towards each other somewhat. Two carbon atoms can't form a normal covalent bond in their distance exceeds the van der waals radius. There may be some intermolecular attraction but there isn't a bond. There will be some overlap between the sigma orbitals but it must be weak at this distance. It might have been expected that the length would be upwards from the average of the vdw radius distance and that of a normal sp3 C bond which would be 1.6A but the distance is much more than this.

This, along with the other bond lengths implies that the transition state is "reactant like" i.e. an early transition state. The dienophile has a C=C bond length of 1.375 which is far closer to the double bond length than the single bond length. The dienophile has two bond lengths of 1.39 and two of 1.37 whilst these are all quite short, this also implies that the transition state is at least somewhat more reactant like than product like.

This synchronous vibration compares to the asynchronous one below (however this vibration has sideways motion as well as asynchronous in and out motion).

[[File:Ts_movie2js.gif]]
(This is actually the second lowest positive frequency but the lowest one doesn't show the two molecules moving closer or further apart, only moving sideways relative to each other)

'''Substitution'''

4) The exo transition state is a slighlty more strained as the maleic anhydride componant points towards the bridging carbons. The Oxygen atoms are a little closer to the hydrogens which are on sp3 carbons and so jut out more than the nearest hydrogens on sp2 like carbon to the maleic anhydride component in the endo. This is in part due to the fact that the transition state appears more product like in the endo and more reactant like in the exo. In the actual products, this affect may be extenuated as in the endo transition state, the maleic anhydride oxygen atoms are pulled closer to the C=C to increase secondary orbital overlap.

[[Image:Tsjs.png|Thumb|300x150px]]

5) The endo transition state has energy = -605.610 a.u. The exo transition structure has energy -605.603 a.u this gives a difference of 4.4 kcal mol-1.

[[Image:HOMO-1js.PNG|Thumb|300x150px]]

This is the HOMO-1 in the endo transition state showing positive overlap between the orbitals on the oxygen atoms and the C=C

[[Image:HOMOjs.PNG|Thumb|300x150px]]

This shows the HOMO. There is a node between the oxygen atoms and the diene showing that in the HOMO, the endo is in fact destabilised by secondary orbital interactions relative to the exo. However, in the HOMO-1 shown above, there is constructive overlap between the oxygen atoms and the rest of the molecule. Overall, there is a greater lowering in energy from these overlaps than raising of energy.

However, for both HOMO and HOMO-1, the secondary orbital overlap isn't that strong. The oxygen atoms are far enough away from the pi system such that the orbital surfaces don't combine at the probability densities represented by the orbitals. Hence the electrons don't spend all that much time in between the oxygen atoms and the pi system so although the overlap is strong enough to dictate the favoured stereochemsitry, it isn't strong enough to form a new bond.

==References==

<References>

<ref name = "wikibondlength"> http://en.wikipedia.org/wiki/Bond_length </ref>

<ref name = "wikivdw" > http://en.wikipedia.org/wiki/Van_der_Waals_radius </ref>

<ref name = "Rzep" > Second year lecture course, "conformational analysis" by Dr Rzepa http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct </ref>

</references>

Rep:Mod:JONS007

2012-11-02T13:26:46Z

Js4310: /* Introduction */

='''''THE COPE REARRANGEMENT=
'''Jonathan Shute'''

==Introduction==

This report aims to investigate the thermochemistry of the following reaction:

[[Image:Pic1.jpg|Thumb|250x90px]]

It is understood that the reaction occurs in a concerted fashion via either chair or boat like transition state:

[[File:Pic2b.jpg]] [[File:Pic2b.jpg]]

In the tutorial section, the enthalpy of the reactant has been found when it is in its most energetically stable conformer. In the second part, the chair and boat transition geometries have been located and their energies calcualted. These data were then used to calculate the activation energy of the reaction.

Several methods were employed to obtain the transition states. Every transition state has with it associated one imaginary frequency. This is because bonds can be modelled as vibrational springs obeying Hooke's law, F= -kx. The frequencies are computed using the following equation:

{1\over {2 \pi}} \sqrt{k \over \mu}. \!</math>

==Optimising the Reactants and Products==

'''1,5-hexadiene'''

(a)The energy of the anti conformer is -231.6926(0235) a.u and the symmetry is C1
[[File:Hexatriene_anti_optimised_321Gjs.log]]

(b)The energy of the gauche conformer is -231.6915(30325) [[File:HEXATRIENEGAUGEjs_321G.LOG]]

The gauche conformer is slightly higher in energy due to the carbons 1 and 4 of the central carbons eclipsing each other a little and causing steric repulsion whist in the staggered conformation, there is less interaction between them. In the antiperiplaner conformation, there is overlap between the sigma C-C bonding orbital for carbons C1 and C2 and the C-C antibonding orbital between C3 and C4. This lowers the energy slightly.

In both structures, A1,3 eclipsed conformation <ref name = "Rzep" /> is evident with the H atoms on the carbon adjacent to C=C at
roughly 120o to the pi system, although not exactly and in both structures one of the H's is at a slightly larger angle than this. The A1,3 conformation is a compromise between having two hydrogen's sigma orbitals aligned fairly well with the pi star orbitals and also there is an attractive vdw force between the H atom on the C=C and on the H atom on the neighbouring carbon. The distance is slightly larger in the gauche.

[[Image:Banana2js.png|Thumb|300x300px|]]

These orbitals show interaction of the sigma H orbital with the pi star orbitals is effective for both conformers.

(c) The lowest energy conformers of 1,5-hexadiene in the table are anti1 and gauche3

(d)By comparison with the appendix table, my optimised conformers were anti1 and gauche4. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summaryhexatriene_631G.PNG My Optimisation Summary Table]]

(e)The optimised molecule had point group Ci and an energy matching the value given in appendix of -231.69253528 a.u precisely. [[File:TRIAL2VER2_321G.LOG]]

<pre>
Low frequencies --- -5.6849 -2.3517 -2.0910 -0.0008 -0.0004 -0.0002
Low frequencies --- 71.1980 85.6851 116.1458

</pre>
<pre>
Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916
</pre>

This gives an electronic energy of 231.692535 (by subtracting the zero point correction to the sum of electronic and zero point energies).

All is in close agreement with the appendix table (only variation in the sixth decimal place)

(f)The conformation of the molecule appears the same when both basis sets are used though the C=C bond length is a little longer with the better basis set at 1.333 A compared to 1.316 A. The energy is very significantly different at -234.611706. This is why the energy of different molecules can only be compared if it was computed with the same basis set.
[[File:HEXATRIENEANIT2CI_631GD.LOG]]
[[File:HEXATRIENEANIT2CI_631GD_FREQCHECKjs.LOG]]

[[Image:IRspecjs.PNG|Thumb|400x600px|]]

<pre>
''' Low frequencies --- -9.1026 0.0005 0.0005 0.0008 4.2776 13.4006
Low frequencies --- 74.2705 80.9525 121.5200 </pre>'''

<pre>
Zero-point correction= 0.142504 (Hartree/Particle)
Thermal correction to Energy= 0.149851
Thermal correction to Enthalpy= 0.150795
Thermal correction to Gibbs Free Energy= 0.110929

Sum of electronic and zero-point Energies= -234.469207
Sum of electronic and thermal Energies= -234.461859
Sum of electronic and thermal Enthalpies= -234.460915
Sum of electronic and thermal Free Energies= -234.500782
</pre>

(It is a little surprising that the low frequencies are higher for the optimisation with the better basis set)

==Optimising Chair and Boat Transitions==

(b)
<pre>
Low frequencies --- -817.9271 -7.0897 -5.4674 -4.3204 -0.0004 0.0004
Low frequencies --- 0.0005 209.4156 396.0571
****** 1 imaginary frequencies (negative Signs) ******
</pre>

{{DOI|10042/21119}} (optimised log file of chair guessed transition state)chair_guesstransition_optimis_freq on my computer this is: log_64342

<pre> Zero-point correction= 0.152627 (Hartree/Particle)
Thermal correction to Energy= 0.157986
Thermal correction to Enthalpy= 0.158930
Thermal correction to Gibbs Free Energy= 0.124120
Sum of electronic and zero-point Energies= -231.466696
Sum of electronic and thermal Energies= -231.461336
Sum of electronic and thermal Enthalpies= -231.460392
Sum of electronic and thermal Free Energies= -231.495202 </pre>

These results agree with those given in the appendix with variation in fifth d.p only.

(c)
-can't optimise exactly! TBC
THE FILE IS CALLED INCORRECT. It works!(This part took a very long time due to the incompleteness of the instructions which mislead me!)

(d)Optimisation to a transition state was successful but initially failed until write connectivity was unchecked under the general tab. The bond lengths were 2.01995 A. This is corroborated by the results for the optimised chair in part (b) which gave a bond length of 2.0205 remarkably similar considering the differences in the models used.

File name: incorrect_optimise_toa_transition_state

<pre>Zero-point correction= 0.151377 (Hartree/Particle)
Thermal correction to Energy= 0.157016
Thermal correction to Enthalpy= 0.157960
Thermal correction to Gibbs Free Energy= 0.122592
Sum of electronic and zero-point Energies= -231.463821
Sum of electronic and thermal Energies= -231.458181
Sum of electronic and thermal Enthalpies= -231.457237
Sum of electronic and thermal Free Energies= -231.492605</pre>

-231.619322
-231.466705
-231.461346

(e) File:gauge_TS(QST2)_ERRDEFAULTSPIN successful optimisation with 2.140 bond length. Only one imaginary frequency (which is vibration of the two bonds which are forming):

<jmolFile text="Explanatory text for link">TS-Vibrationjs.mol</jmolFile>

<pre>

Low frequencies --- -840.1011 -4.0811 -0.0011 -0.0010 -0.0009 3.5285
Low frequencies --- 5.2099 155.3480 382.0830
****** 1 imaginary frequencies (negative Signs) ******

</pre>

<pre>
Zero-point correction= 0.151874 (Hartree/Particle)
Thermal correction to Energy= 0.157502
Thermal correction to Enthalpy= 0.158447
Thermal correction to Gibbs Free Energy= 0.123029
Sum of electronic and zero-point Energies= -231.450929
Sum of electronic and thermal Energies= -231.445300
Sum of electronic and thermal Enthalpies= -231.444356
Sum of electronic and thermal Free Energies= -231.479774
</pre>

This results are very close to those in the appendix table for 321G HF basis set and method.
(f) {{DOI|10042/21197}} file shows the IRC on the chair transition state calculated using redundant method.
(Need to reach a minimum.... - maybe check for graph also)

(g) (Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way under the extra working section) The calculation below is with the correct method.

i) Correct method
{{DOI|10042/21294}}

<pre>
Zero-point correction= 0.140741 (Hartree/Particle)
Thermal correction to Energy= 0.147079
Thermal correction to Enthalpy= 0.148023
Thermal correction to Gibbs Free Energy= 0.111326
Sum of electronic and zero-point Energies= -234.402355
Sum of electronic and thermal Energies= -234.396016
Sum of electronic and thermal Enthalpies= -234.395072
Sum of electronic and thermal Free Energies= -234.431769
</pre>

There is a small variation when compared to appendix values in the fifth d.p.

ii) {{DOI|10042/21304}} {{DOI|10042/21305}}
Reoptimised the chair calculated in part b to B3YLP/6-31G* level:

<pre>
Zero-point correction= 0.142054 (Hartree/Particle)
Thermal correction to Energy= 0.147975
Thermal correction to Enthalpy= 0.148919
Thermal correction to Gibbs Free Energy= 0.113168
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443815 </pre>

Again, these results are in close agreement with those in the appendix table to the fifth d.p

'''Conclusion'''

The energy of the chair minus the thermal correction is -234.557 a.u. The energy of the reactant is -234.612 a.u
Need to subtract energy of starting materials and reactants to give the extra energy of the transition state which must be overcome for reaction to occur.
1 Hartree = 627.509 kcal/mol

Hence, the difference in energy is -5.471*10^-2. This is '''34.3 kcal mol-1.'''

The energy of the boat is -234.543 a.u. This gives Ea = 0.0689 a.u or '''43.2 kcal mol-1'''

These values compare to the literature values of 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure. This is surprisingly good agreement as the basis set used B3LYP/6-31G* is quite an inexact basis set.

==Extra Working==

Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way below as an extension to the tutorial!

(g) {{DOI|10042/21218}} this is the optimised boat HF/3-21G reoptimised
file is IRC_chair_redundant. The results are given below:

<pre>
Low frequencies --- -852.3991 -6.1132 -4.0906 -1.4954 -0.0005 0.0006
Low frequencies --- 0.0007 145.9558 320.2847
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.150402 (Hartree/Particle)
Thermal correction to Energy= 0.156295
Thermal correction to Enthalpy= 0.157239
Thermal correction to Gibbs Free Energy= 0.121318
Sum of electronic and zero-point Energies= -232.727993
Sum of electronic and thermal Energies= -232.722099
Sum of electronic and thermal Enthalpies= -232.721155
Sum of electronic and thermal Free Energies= -232.757076
</pre>

The optimisation at the HF/6-31G* level reached a minimum with the energy derivatives very close to zero after the eighth step (smaller than 10^-4) however due to an error in the program (unstable algorithm) it continued beyond this point and the final structure was incorrect. The eighth intermediate geometry has a bond length of 2.203 A. The following link is to screenshots of the optimisation graphs and the energy derivatives:
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Graphs_of_optimisationjs.png Optimisation_Graphs]]

== Conclusion ==

<br />

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| '''Boat TS'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| '''Reactant (''anti2'')'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|}

='''''DA PROJECT=

==Results==

i) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

ii)Optimisation using method in part b) (HF/321G) file = partA_RETRY in folder ii)

The animation clearly shows the correct transition state has been attained.

<jmol> <jmolApplet> <title>Vibration</title><color>white</color><size>200</size> <script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10; </script><uploadedFileContents>Ts_vib.mol</uploadedFileContents> </jmolApplet> </jmol>

The animation is supposed to show concerted bond formation.

<pre> Low frequencies --- -818.4961 -0.0007 -0.0006 -0.0003 1.4348 1.8772
Low frequencies --- 2.7185 166.5539 284.3675
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157558
Thermal correction to Enthalpy= 0.158502
Thermal correction to Gibbs Free Energy= 0.122930
Sum of electronic and zero-point Energies= -231.451338
Sum of electronic and thermal Energies= -231.445650
Sum of electronic and thermal Enthalpies= -231.444706
Sum of electronic and thermal Free Energies= -231.480279
</pre>

iii)
'''Exo Transition States'''
{{DOI|10042/21391}} This is the file for my optimised exo transition state calculated using the derivatise bond method. I also calculated the transition state using the first method in the tutorial section

Modredundant method: 99_frozengif is the input file, output log is 99_99_99
{{DOI|10042/21447}}
<pre>
Low frequencies --- -643.0720 -10.8719 -0.0008 -0.0008 -0.0004 11.9743
Low frequencies --- 15.1280 49.8386 133.6533
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195473 (Hartree/Particle)
Thermal correction to Energy= 0.204891
Thermal correction to Enthalpy= 0.205835
Thermal correction to Gibbs Free Energy= 0.160107
Sum of electronic and zero-point Energies= -605.408011
Sum of electronic and thermal Energies= -605.398593
Sum of electronic and thermal Enthalpies= -605.397649
Sum of electronic and thermal Free Energies= -605.443378 </pre>

Opt=NoEigen method:
{{DOI|10042/21449}}
<pre>

Low frequencies --- -647.3174 -2.2007 -0.0010 -0.0009 -0.0008 1.7640
Low frequencies --- 3.1286 42.6020 131.4691
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195451 (Hartree/Particle)
Thermal correction to Energy= 0.204911
Thermal correction to Enthalpy= 0.205855
Thermal correction to Gibbs Free Energy= 0.159905
Sum of electronic and zero-point Energies= -605.408140
Sum of electronic and thermal Energies= -605.398681
Sum of electronic and thermal Enthalpies= -605.397736
Sum of electronic and thermal Free Energies= -605.443686
</pre>

methodA = 9999log.... file ? Note some disagreement in the transition state optimal distance!
Could also include guess file?

'''The endo transition state:'''
DSPACE LINK TO include. Fies are endo_optimise_ts_A_take2 and log_65019

I optimised this using the opt=noeigen method and the modredundant method to check. First I drew a guess transition state by drawing the product, optimising it to a minimum and then increasing the bond forming lengths to 2.2A The energies are given below and are in good agreement for the different methods. The transition state geometries are very similar for both, with C-C bond forming distances of 2.231 with both methods which agree to the third decimal place.

Calculation using opt=noeigen key word:
{{DOI|10042/21451}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_A_tsjs.PNG Optimisation Summary Table ]

<pre> Low frequencies --- -643.5783 -0.0005 -0.0002 0.0006 0.6895 1.1675
Low frequencies --- 1.7996 65.0129 142.0450
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre> Zero-point correction= 0.195464 (Hartree/Particle)
Thermal correction to Energy= 0.204889
Thermal correction to Enthalpy= 0.205834
Thermal correction to Gibbs Free Energy= 0.160235
Sum of electronic and zero-point Energies= -605.414905
Sum of electronic and thermal Energies= -605.405479
Sum of electronic and thermal Enthalpies= -605.404535
Sum of electronic and thermal Free Energies= -605.450133 </pre>

Calculation using modredundant keyword: {{DOI|10042/21452}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_C_tsjs.PNG Optimisation Summary Table]

<pre>Low frequencies --- -644.2611 -0.0007 -0.0003 0.0006 1.8423 3.3886
Low frequencies --- 6.6938 65.0647 142.3913
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>Zero-point correction= 0.195454 (Hartree/Particle)
Thermal correction to Energy= 0.204879
Thermal correction to Enthalpy= 0.205823
Thermal correction to Gibbs Free Energy= 0.160231
Sum of electronic and zero-point Energies= -605.414912
Sum of electronic and thermal Energies= -605.405487
Sum of electronic and thermal Enthalpies= -605.404543
Sum of electronic and thermal Free Energies= -605.450135
</pre>

Bond formation is concerted

[[File:MethodCmodredundantjs_ts_animation.gif]]

==Discussion Questions==

1) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

2)
Below is illustrated the HOMO left and LUMO right for the unsubsituted Diels Alder transitions state. Both orbitals are symmetric with respect to the plane.

[[Image:HOMOandLUMO(r)js.png|Thumb|300x150px]] [[Image:MOHOMO-1js.PNG|Thumb|300x150px|HOMO-1]]

[[Image:MO4js.PNG|Thumb|300x150px|HOMO]][[Image:MO3js.PNG|Thumb|300x150px|LUMO]] [[Image:MO1js.PNG|Thumb|300x150px|HOMO-1]]

These diagrams show the orbital contributions of the MOs above them.

The HOMO has a node in between the diene and the dienophile.

Allowed reactions: as two new bonds are being formed simultaneously, there are symmetry constraints on the reaction. If both p orbitals on the alkene form constructive overlap with the p orbitals on the terminal carbons of the diene, then the reaction is allowed.

In the HOMO the alkene and diene both have the same symmetry and interact to strengthen the bonds which are forming. (Both components have no nodes)

In the HOMO-1, both components have the same symmetry for overlap and this strengthens the two bonds which are forming

The LUMO is interesting because the two components have different symmetries so weaken the 2 bonds which are forming. However, the orbitals deform and the p orbitals on the alkene balloon out to interact with the p orbitals on the central two carbons of the diene so this would cause a little weak bonding between these atoms.

A further point to make is that the HOMO-1 is the key MO as it has strong positive overlap inbetween the diene and dienophile and so is the major bonding attraction which causes the transition state to roll onto the products. This is because electrons inhabiting this low energy orbital attract the two fragments together.

A "real" Diels Alder reaction requires an electron deficient dienophile and this lowers the energy of its LUMO whilst the diene has a high energy HOMO so the interactions of this orbital (the far right one)are strengthened even more. In reverse demand reactions the following interaction is preferred: [[Image:MO2js.PNG|Thumb|150x75px]]

3) [[File:Ts_moviejs.gif]]

Bond forming distance: 2.209 A. According to a table on wikipedia <ref name = "wikibondlength"/>, the average bond lengths are as follows:
sp2-sp2 C-C = 1.47 A (BUT the alkene double bond length according to the same table is 1.34A Gaussview gives the bond length in ethene of 1.325)
sp3-sp3 C-C = 1.54 A (gaussview has 1.5 for ethane)
sp3-sp2 C-C = 1.50 A
longest C-C = 1.74 A
Additionally, the Van der Waals radius for carbon is 1.7 A <ref name = "wikivdw"/>

The reason that bond lengths are less than the corrosponding average of the radii of the two atoms is that their electron clouds overlap when forming the bond so the nuclei are draw in towards each other somewhat. Two carbon atoms can't form a normal covalent bond in their distance exceeds the van der waals radius. There may be some intermolecular attraction but there isn't a bond. There will be some overlap between the sigma orbitals but it must be weak at this distance. It might have been expected that the length would be upwards from the average of the vdw radius distance and that of a normal sp3 C bond which would be 1.6A but the distance is much more than this.

This, along with the other bond lengths implies that the transition state is "reactant like" i.e. an early transition state. The dienophile has a C=C bond length of 1.375 which is far closer to the double bond length than the single bond length. The dienophile has two bond lengths of 1.39 and two of 1.37 whilst these are all quite short, this also implies that the transition state is at least somewhat more reactant like than product like.

This synchronous vibration compares to the asynchronous one below (however this vibration has sideways motion as well as asynchronous in and out motion).

[[File:Ts_movie2js.gif]]
(This is actually the second lowest positive frequency but the lowest one doesn't show the two molecules moving closer or further apart, only moving sideways relative to each other)

'''Substitution'''

4) The exo transition state is a slighlty more strained as the maleic anhydride componant points towards the bridging carbons. The Oxygen atoms are a little closer to the hydrogens which are on sp3 carbons and so jut out more than the nearest hydrogens on sp2 like carbon to the maleic anhydride component in the endo. This is in part due to the fact that the transition state appears more product like in the endo and more reactant like in the exo. In the actual products, this affect may be extenuated as in the endo transition state, the maleic anhydride oxygen atoms are pulled closer to the C=C to increase secondary orbital overlap.

[[Image:Tsjs.png|Thumb|300x150px]]

5) The endo transition state has energy = -605.610 a.u. The exo transition structure has energy -605.603 a.u this gives a difference of 4.4 kcal mol-1.

[[Image:HOMO-1js.PNG|Thumb|300x150px]]

This is the HOMO-1 in the endo transition state showing positive overlap between the orbitals on the oxygen atoms and the C=C

[[Image:HOMOjs.PNG|Thumb|300x150px]]

This shows the HOMO. There is a node between the oxygen atoms and the diene showing that in the HOMO, the endo is in fact destabilised by secondary orbital interactions relative to the exo. However, in the HOMO-1 shown above, there is constructive overlap between the oxygen atoms and the rest of the molecule. Overall, there is a greater lowering in energy from these overlaps than raising of energy.

However, for both HOMO and HOMO-1, the secondary orbital overlap isn't that strong. The oxygen atoms are far enough away from the pi system such that the orbital surfaces don't combine at the probability densities represented by the orbitals. Hence the electrons don't spend all that much time in between the oxygen atoms and the pi system so although the overlap is strong enough to dictate the favoured stereochemsitry, it isn't strong enough to form a new bond.

==References==

<References>

<ref name = "wikibondlength"> http://en.wikipedia.org/wiki/Bond_length </ref>

<ref name = "wikivdw" > http://en.wikipedia.org/wiki/Van_der_Waals_radius </ref>

<ref name = "Rzep" > Second year lecture course, "conformational analysis" by Dr Rzepa http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct </ref>

</references>

Rep:Mod:JONS007

2012-11-02T13:20:02Z

Js4310: /* References */

='''''THE COPE REARRANGEMENT=
'''Jonathan Shute'''

==Introduction==

This report aims to investigate the thermochemistry of the following reaction:

[[Image:Pic1.jpg|Thumb|250x90px]]

It is understood that the reaction occurs in a concerted fashion via either chair or boat like transition state:

[[File:Pic2b.jpg]] [[File:Pic2b.jpg]]

In the tutorial section, the enthalpy of the reactant has been found when it is in its most energetically stable conformer. In the second part, the chair and boat transition geometries have been located and their energies calcualted. These data were then used to calculate the activation energy of the reaction.

DISCUSS TRANSITION STATE NEG

==Optimising the Reactants and Products==

'''1,5-hexadiene'''

(a)The energy of the anti conformer is -231.6926(0235) a.u and the symmetry is C1
[[File:Hexatriene_anti_optimised_321Gjs.log]]

(b)The energy of the gauche conformer is -231.6915(30325) [[File:HEXATRIENEGAUGEjs_321G.LOG]]

The gauche conformer is slightly higher in energy due to the carbons 1 and 4 of the central carbons eclipsing each other a little and causing steric repulsion whist in the staggered conformation, there is less interaction between them. In the antiperiplaner conformation, there is overlap between the sigma C-C bonding orbital for carbons C1 and C2 and the C-C antibonding orbital between C3 and C4. This lowers the energy slightly.

In both structures, A1,3 eclipsed conformation <ref name = "Rzep" /> is evident with the H atoms on the carbon adjacent to C=C at
roughly 120o to the pi system, although not exactly and in both structures one of the H's is at a slightly larger angle than this. The A1,3 conformation is a compromise between having two hydrogen's sigma orbitals aligned fairly well with the pi star orbitals and also there is an attractive vdw force between the H atom on the C=C and on the H atom on the neighbouring carbon. The distance is slightly larger in the gauche.

[[Image:Banana2js.png|Thumb|300x300px|]]

These orbitals show interaction of the sigma H orbital with the pi star orbitals is effective for both conformers.

(c) The lowest energy conformers of 1,5-hexadiene in the table are anti1 and gauche3

(d)By comparison with the appendix table, my optimised conformers were anti1 and gauche4. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summaryhexatriene_631G.PNG My Optimisation Summary Table]]

(e)The optimised molecule had point group Ci and an energy matching the value given in appendix of -231.69253528 a.u precisely. [[File:TRIAL2VER2_321G.LOG]]

<pre>
Low frequencies --- -5.6849 -2.3517 -2.0910 -0.0008 -0.0004 -0.0002
Low frequencies --- 71.1980 85.6851 116.1458

</pre>
<pre>
Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916
</pre>

This gives an electronic energy of 231.692535 (by subtracting the zero point correction to the sum of electronic and zero point energies).

All is in close agreement with the appendix table (only variation in the sixth decimal place)

(f)The conformation of the molecule appears the same when both basis sets are used though the C=C bond length is a little longer with the better basis set at 1.333 A compared to 1.316 A. The energy is very significantly different at -234.611706. This is why the energy of different molecules can only be compared if it was computed with the same basis set.
[[File:HEXATRIENEANIT2CI_631GD.LOG]]
[[File:HEXATRIENEANIT2CI_631GD_FREQCHECKjs.LOG]]

[[Image:IRspecjs.PNG|Thumb|400x600px|]]

<pre>
''' Low frequencies --- -9.1026 0.0005 0.0005 0.0008 4.2776 13.4006
Low frequencies --- 74.2705 80.9525 121.5200 </pre>'''

<pre>
Zero-point correction= 0.142504 (Hartree/Particle)
Thermal correction to Energy= 0.149851
Thermal correction to Enthalpy= 0.150795
Thermal correction to Gibbs Free Energy= 0.110929

Sum of electronic and zero-point Energies= -234.469207
Sum of electronic and thermal Energies= -234.461859
Sum of electronic and thermal Enthalpies= -234.460915
Sum of electronic and thermal Free Energies= -234.500782
</pre>

(It is a little surprising that the low frequencies are higher for the optimisation with the better basis set)

==Optimising Chair and Boat Transitions==

(b)
<pre>
Low frequencies --- -817.9271 -7.0897 -5.4674 -4.3204 -0.0004 0.0004
Low frequencies --- 0.0005 209.4156 396.0571
****** 1 imaginary frequencies (negative Signs) ******
</pre>

{{DOI|10042/21119}} (optimised log file of chair guessed transition state)chair_guesstransition_optimis_freq on my computer this is: log_64342

<pre> Zero-point correction= 0.152627 (Hartree/Particle)
Thermal correction to Energy= 0.157986
Thermal correction to Enthalpy= 0.158930
Thermal correction to Gibbs Free Energy= 0.124120
Sum of electronic and zero-point Energies= -231.466696
Sum of electronic and thermal Energies= -231.461336
Sum of electronic and thermal Enthalpies= -231.460392
Sum of electronic and thermal Free Energies= -231.495202 </pre>

These results agree with those given in the appendix with variation in fifth d.p only.

(c)
-can't optimise exactly! TBC
THE FILE IS CALLED INCORRECT. It works!(This part took a very long time due to the incompleteness of the instructions which mislead me!)

(d)Optimisation to a transition state was successful but initially failed until write connectivity was unchecked under the general tab. The bond lengths were 2.01995 A. This is corroborated by the results for the optimised chair in part (b) which gave a bond length of 2.0205 remarkably similar considering the differences in the models used.

File name: incorrect_optimise_toa_transition_state

<pre>Zero-point correction= 0.151377 (Hartree/Particle)
Thermal correction to Energy= 0.157016
Thermal correction to Enthalpy= 0.157960
Thermal correction to Gibbs Free Energy= 0.122592
Sum of electronic and zero-point Energies= -231.463821
Sum of electronic and thermal Energies= -231.458181
Sum of electronic and thermal Enthalpies= -231.457237
Sum of electronic and thermal Free Energies= -231.492605</pre>

-231.619322
-231.466705
-231.461346

(e) File:gauge_TS(QST2)_ERRDEFAULTSPIN successful optimisation with 2.140 bond length. Only one imaginary frequency (which is vibration of the two bonds which are forming):

<jmolFile text="Explanatory text for link">TS-Vibrationjs.mol</jmolFile>

<pre>

Low frequencies --- -840.1011 -4.0811 -0.0011 -0.0010 -0.0009 3.5285
Low frequencies --- 5.2099 155.3480 382.0830
****** 1 imaginary frequencies (negative Signs) ******

</pre>

<pre>
Zero-point correction= 0.151874 (Hartree/Particle)
Thermal correction to Energy= 0.157502
Thermal correction to Enthalpy= 0.158447
Thermal correction to Gibbs Free Energy= 0.123029
Sum of electronic and zero-point Energies= -231.450929
Sum of electronic and thermal Energies= -231.445300
Sum of electronic and thermal Enthalpies= -231.444356
Sum of electronic and thermal Free Energies= -231.479774
</pre>

This results are very close to those in the appendix table for 321G HF basis set and method.
(f) {{DOI|10042/21197}} file shows the IRC on the chair transition state calculated using redundant method.
(Need to reach a minimum.... - maybe check for graph also)

(g) (Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way under the extra working section) The calculation below is with the correct method.

i) Correct method
{{DOI|10042/21294}}

<pre>
Zero-point correction= 0.140741 (Hartree/Particle)
Thermal correction to Energy= 0.147079
Thermal correction to Enthalpy= 0.148023
Thermal correction to Gibbs Free Energy= 0.111326
Sum of electronic and zero-point Energies= -234.402355
Sum of electronic and thermal Energies= -234.396016
Sum of electronic and thermal Enthalpies= -234.395072
Sum of electronic and thermal Free Energies= -234.431769
</pre>

There is a small variation when compared to appendix values in the fifth d.p.

ii) {{DOI|10042/21304}} {{DOI|10042/21305}}
Reoptimised the chair calculated in part b to B3YLP/6-31G* level:

<pre>
Zero-point correction= 0.142054 (Hartree/Particle)
Thermal correction to Energy= 0.147975
Thermal correction to Enthalpy= 0.148919
Thermal correction to Gibbs Free Energy= 0.113168
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443815 </pre>

Again, these results are in close agreement with those in the appendix table to the fifth d.p

'''Conclusion'''

The energy of the chair minus the thermal correction is -234.557 a.u. The energy of the reactant is -234.612 a.u
Need to subtract energy of starting materials and reactants to give the extra energy of the transition state which must be overcome for reaction to occur.
1 Hartree = 627.509 kcal/mol

Hence, the difference in energy is -5.471*10^-2. This is '''34.3 kcal mol-1.'''

The energy of the boat is -234.543 a.u. This gives Ea = 0.0689 a.u or '''43.2 kcal mol-1'''

These values compare to the literature values of 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure. This is surprisingly good agreement as the basis set used B3LYP/6-31G* is quite an inexact basis set.

==Extra Working==

Initially the boat was optimised to the HF/6-31G* level accidently. These results are included any way below as an extension to the tutorial!

(g) {{DOI|10042/21218}} this is the optimised boat HF/3-21G reoptimised
file is IRC_chair_redundant. The results are given below:

<pre>
Low frequencies --- -852.3991 -6.1132 -4.0906 -1.4954 -0.0005 0.0006
Low frequencies --- 0.0007 145.9558 320.2847
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.150402 (Hartree/Particle)
Thermal correction to Energy= 0.156295
Thermal correction to Enthalpy= 0.157239
Thermal correction to Gibbs Free Energy= 0.121318
Sum of electronic and zero-point Energies= -232.727993
Sum of electronic and thermal Energies= -232.722099
Sum of electronic and thermal Enthalpies= -232.721155
Sum of electronic and thermal Free Energies= -232.757076
</pre>

The optimisation at the HF/6-31G* level reached a minimum with the energy derivatives very close to zero after the eighth step (smaller than 10^-4) however due to an error in the program (unstable algorithm) it continued beyond this point and the final structure was incorrect. The eighth intermediate geometry has a bond length of 2.203 A. The following link is to screenshots of the optimisation graphs and the energy derivatives:
[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Graphs_of_optimisationjs.png Optimisation_Graphs]]

== Conclusion ==

<br />

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| '''Boat TS'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| '''Reactant (''anti2'')'''
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|}

='''''DA PROJECT=

==Results==

i) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

ii)Optimisation using method in part b) (HF/321G) file = partA_RETRY in folder ii)

The animation clearly shows the correct transition state has been attained.

<jmol> <jmolApplet> <title>Vibration</title><color>white</color><size>200</size> <script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10; </script><uploadedFileContents>Ts_vib.mol</uploadedFileContents> </jmolApplet> </jmol>

The animation is supposed to show concerted bond formation.

<pre> Low frequencies --- -818.4961 -0.0007 -0.0006 -0.0003 1.4348 1.8772
Low frequencies --- 2.7185 166.5539 284.3675
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157558
Thermal correction to Enthalpy= 0.158502
Thermal correction to Gibbs Free Energy= 0.122930
Sum of electronic and zero-point Energies= -231.451338
Sum of electronic and thermal Energies= -231.445650
Sum of electronic and thermal Enthalpies= -231.444706
Sum of electronic and thermal Free Energies= -231.480279
</pre>

iii)
'''Exo Transition States'''
{{DOI|10042/21391}} This is the file for my optimised exo transition state calculated using the derivatise bond method. I also calculated the transition state using the first method in the tutorial section

Modredundant method: 99_frozengif is the input file, output log is 99_99_99
{{DOI|10042/21447}}
<pre>
Low frequencies --- -643.0720 -10.8719 -0.0008 -0.0008 -0.0004 11.9743
Low frequencies --- 15.1280 49.8386 133.6533
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195473 (Hartree/Particle)
Thermal correction to Energy= 0.204891
Thermal correction to Enthalpy= 0.205835
Thermal correction to Gibbs Free Energy= 0.160107
Sum of electronic and zero-point Energies= -605.408011
Sum of electronic and thermal Energies= -605.398593
Sum of electronic and thermal Enthalpies= -605.397649
Sum of electronic and thermal Free Energies= -605.443378 </pre>

Opt=NoEigen method:
{{DOI|10042/21449}}
<pre>

Low frequencies --- -647.3174 -2.2007 -0.0010 -0.0009 -0.0008 1.7640
Low frequencies --- 3.1286 42.6020 131.4691
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.195451 (Hartree/Particle)
Thermal correction to Energy= 0.204911
Thermal correction to Enthalpy= 0.205855
Thermal correction to Gibbs Free Energy= 0.159905
Sum of electronic and zero-point Energies= -605.408140
Sum of electronic and thermal Energies= -605.398681
Sum of electronic and thermal Enthalpies= -605.397736
Sum of electronic and thermal Free Energies= -605.443686
</pre>

methodA = 9999log.... file ? Note some disagreement in the transition state optimal distance!
Could also include guess file?

'''The endo transition state:'''
DSPACE LINK TO include. Fies are endo_optimise_ts_A_take2 and log_65019

I optimised this using the opt=noeigen method and the modredundant method to check. First I drew a guess transition state by drawing the product, optimising it to a minimum and then increasing the bond forming lengths to 2.2A The energies are given below and are in good agreement for the different methods. The transition state geometries are very similar for both, with C-C bond forming distances of 2.231 with both methods which agree to the third decimal place.

Calculation using opt=noeigen key word:
{{DOI|10042/21451}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_A_tsjs.PNG Optimisation Summary Table ]

<pre> Low frequencies --- -643.5783 -0.0005 -0.0002 0.0006 0.6895 1.1675
Low frequencies --- 1.7996 65.0129 142.0450
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre> Zero-point correction= 0.195464 (Hartree/Particle)
Thermal correction to Energy= 0.204889
Thermal correction to Enthalpy= 0.205834
Thermal correction to Gibbs Free Energy= 0.160235
Sum of electronic and zero-point Energies= -605.414905
Sum of electronic and thermal Energies= -605.405479
Sum of electronic and thermal Enthalpies= -605.404535
Sum of electronic and thermal Free Energies= -605.450133 </pre>

Calculation using modredundant keyword: {{DOI|10042/21452}}
[https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Summary_endo_C_tsjs.PNG Optimisation Summary Table]

<pre>Low frequencies --- -644.2611 -0.0007 -0.0003 0.0006 1.8423 3.3886
Low frequencies --- 6.6938 65.0647 142.3913
****** 1 imaginary frequencies (negative Signs) ****** </pre>

<pre>Zero-point correction= 0.195454 (Hartree/Particle)
Thermal correction to Energy= 0.204879
Thermal correction to Enthalpy= 0.205823
Thermal correction to Gibbs Free Energy= 0.160231
Sum of electronic and zero-point Energies= -605.414912
Sum of electronic and thermal Energies= -605.405487
Sum of electronic and thermal Enthalpies= -605.404543
Sum of electronic and thermal Free Energies= -605.450135
</pre>

Bond formation is concerted

[[File:MethodCmodredundantjs_ts_animation.gif]]

==Discussion Questions==

1) This is my diagram of the LUMO left and the HOMO right. The LUMO is antisymmetric with respect to the plane and the HOMO is symmetric.

[[Image:CyclobutadieneMOjs.png|Thumb|300x150px]]

2)
Below is illustrated the HOMO left and LUMO right for the unsubsituted Diels Alder transitions state. Both orbitals are symmetric with respect to the plane.

[[Image:HOMOandLUMO(r)js.png|Thumb|300x150px]] [[Image:MOHOMO-1js.PNG|Thumb|300x150px|HOMO-1]]

[[Image:MO4js.PNG|Thumb|300x150px|HOMO]][[Image:MO3js.PNG|Thumb|300x150px|LUMO]] [[Image:MO1js.PNG|Thumb|300x150px|HOMO-1]]

These diagrams show the orbital contributions of the MOs above them.

The HOMO has a node in between the diene and the dienophile.

Allowed reactions: as two new bonds are being formed simultaneously, there are symmetry constraints on the reaction. If both p orbitals on the alkene form constructive overlap with the p orbitals on the terminal carbons of the diene, then the reaction is allowed.

In the HOMO the alkene and diene both have the same symmetry and interact to strengthen the bonds which are forming. (Both components have no nodes)

In the HOMO-1, both components have the same symmetry for overlap and this strengthens the two bonds which are forming

The LUMO is interesting because the two components have different symmetries so weaken the 2 bonds which are forming. However, the orbitals deform and the p orbitals on the alkene balloon out to interact with the p orbitals on the central two carbons of the diene so this would cause a little weak bonding between these atoms.

A further point to make is that the HOMO-1 is the key MO as it has strong positive overlap inbetween the diene and dienophile and so is the major bonding attraction which causes the transition state to roll onto the products. This is because electrons inhabiting this low energy orbital attract the two fragments together.

A "real" Diels Alder reaction requires an electron deficient dienophile and this lowers the energy of its LUMO whilst the diene has a high energy HOMO so the interactions of this orbital (the far right one)are strengthened even more. In reverse demand reactions the following interaction is preferred: [[Image:MO2js.PNG|Thumb|150x75px]]

3) [[File:Ts_moviejs.gif]]

Bond forming distance: 2.209 A. According to a table on wikipedia <ref name = "wikibondlength"/>, the average bond lengths are as follows:
sp2-sp2 C-C = 1.47 A (BUT the alkene double bond length according to the same table is 1.34A Gaussview gives the bond length in ethene of 1.325)
sp3-sp3 C-C = 1.54 A (gaussview has 1.5 for ethane)
sp3-sp2 C-C = 1.50 A
longest C-C = 1.74 A
Additionally, the Van der Waals radius for carbon is 1.7 A <ref name = "wikivdw"/>

The reason that bond lengths are less than the corrosponding average of the radii of the two atoms is that their electron clouds overlap when forming the bond so the nuclei are draw in towards each other somewhat. Two carbon atoms can't form a normal covalent bond in their distance exceeds the van der waals radius. There may be some intermolecular attraction but there isn't a bond. There will be some overlap between the sigma orbitals but it must be weak at this distance. It might have been expected that the length would be upwards from the average of the vdw radius distance and that of a normal sp3 C bond which would be 1.6A but the distance is much more than this.

This, along with the other bond lengths implies that the transition state is "reactant like" i.e. an early transition state. The dienophile has a C=C bond length of 1.375 which is far closer to the double bond length than the single bond length. The dienophile has two bond lengths of 1.39 and two of 1.37 whilst these are all quite short, this also implies that the transition state is at least somewhat more reactant like than product like.

This synchronous vibration compares to the asynchronous one below (however this vibration has sideways motion as well as asynchronous in and out motion).

[[File:Ts_movie2js.gif]]
(This is actually the second lowest positive frequency but the lowest one doesn't show the two molecules moving closer or further apart, only moving sideways relative to each other)

'''Substitution'''

4) The exo transition state is a slighlty more strained as the maleic anhydride componant points towards the bridging carbons. The Oxygen atoms are a little closer to the hydrogens which are on sp3 carbons and so jut out more than the nearest hydrogens on sp2 like carbon to the maleic anhydride component in the endo. This is in part due to the fact that the transition state appears more product like in the endo and more reactant like in the exo. In the actual products, this affect may be extenuated as in the endo transition state, the maleic anhydride oxygen atoms are pulled closer to the C=C to increase secondary orbital overlap.

[[Image:Tsjs.png|Thumb|300x150px]]

5) The endo transition state has energy = -605.610 a.u. The exo transition structure has energy -605.603 a.u this gives a difference of 4.4 kcal mol-1.

[[Image:HOMO-1js.PNG|Thumb|300x150px]]

This is the HOMO-1 in the endo transition state showing positive overlap between the orbitals on the oxygen atoms and the C=C

[[Image:HOMOjs.PNG|Thumb|300x150px]]

This shows the HOMO. There is a node between the oxygen atoms and the diene showing that in the HOMO, the endo is in fact destabilised by secondary orbital interactions relative to the exo. However, in the HOMO-1 shown above, there is constructive overlap between the oxygen atoms and the rest of the molecule. Overall, there is a greater lowering in energy from these overlaps than raising of energy.

However, for both HOMO and HOMO-1, the secondary orbital overlap isn't that strong. The oxygen atoms are far enough away from the pi system such that the orbital surfaces don't combine at the probability densities represented by the orbitals. Hence the electrons don't spend all that much time in between the oxygen atoms and the pi system so although the overlap is strong enough to dictate the favoured stereochemsitry, it isn't strong enough to form a new bond.

==References==

<References>

<ref name = "wikibondlength"> http://en.wikipedia.org/wiki/Bond_length </ref>

<ref name = "wikivdw" > http://en.wikipedia.org/wiki/Van_der_Waals_radius </ref>

<ref name = "Rzep" > Second year lecture course, "conformational analysis" by Dr Rzepa http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct </ref>

</references>