ChemWiki - User contributions [en]

Rep:Mod:Peebo

2015-12-18T11:38:14Z

Oi513: /* The Cope rearrangement: Computational Investigations */

== Introduction ==

=== Overview ===
Fundamental to organic chemistry are pericyclic reactions that involve concerted movement of electrons through a cyclic transition state. Cycloadditions, a subset of pericyclic reactions, serve as a essential synthetic tool for organic chemists as a basis for accessing more complex structures in, for example, total synthesis of natural products [1]. In addition, sigmatropic rearrangements, and electrocyclic reactions are also a set of important pericyclic reactions that see Δσ 0 or ±1 respectively. For Diels alder and ene reactions, the initial arrangement of the fragments is brought into question when trying to understand the stereochemical outcome of the reaction. Other than these geometric factors, the frontier orbitals of the two fragments contain valuable information into predicting whether the two reactants may proceed to reach a product[2].

Robert Burns Woodward and Roald Hoffman established rules to explain whether a given pericyclic reaction may be thermally or photochemically allowed to give the said product. Naturally incorporated in their approach is considerations of the molecular orbitals involved in the reaction, the number of electrons, and the symmetry with respect to the connectivity between the two fragments. First applied to electrocyclic reactions [3], the two would then go on to publish more papers to fully develop their rules setting a universal foundation for understanding these class of reactions

Given the wealth factors that contribute towards going from reactants --> products, it is of the best interests to synthetic chemists to understand the mechanistic basis behind the reaction and therefore ,for example, the observed stereochemistry as opposed to whether a given reaction may be allowed or forbidden (in conjunction with Woodward-Hoffman rules). As such, computational methods into investigating diels alder reaction pathways have come to light[4][5] and have shown to provide insight into the optimal positioning of fragments and the structure and energy of Transition states. Studying transition states in particular are a huge advantage in computational studies; through this medium, calculations on energies of these states can be probes that would otherwise be immeasurable due to the fleeting nature of the transition state.

=== Experimental Aims ===
In this exercise, we first investigate the energies of varying 1-5 hexadiene conformers and investigate the possible cyclic transition states whilst it undergoes the cope rearrangement using the Hartree-Fock/3-21G and B3LYP/6-31G(d) levels of theory in addition to exploring Transition state optimization methods QTS2 and TS(Berny). Using similar methods, we then go on to develop our discussion of transition states by through investigating the regioselectivity of the Diels Alder reaction between maelic anhydride and 1-3 cyclohexadiene including molecular orbital interactions.

=== Brief note: Computational Methods ===

In this investigation, we explore different levels of theory to apply alongside our calculations as each have both advantageous features, and their respective drawbacks. Hatree fock method is used to determine both energies and quantum mechanical wavefunction of a multi-body system in state that has its probability density (position of the body in question) independent of time (i.e a stationary state). Amongst the appreciable number of approximations made by this method, the assumption that many electron wavefunction of the body in question will take the form of a just an isolated determinant (slater determinant) derived from a single electron wavefunction. Whist in theory this is entirely possible through linear combination of atomic orbitals, this naturally causes this approach to overlook the replusive interactions between the electrons in the system thus producing energies that are overestimated.

By virtue The Hohenberg-Kohn Theorems, the total energy of a ground state is exclusively dependent on electron density and distribution. Focusing in on this aspect and overlooking the electronic wavefunctions give rise to density functional theory. This method will aim to minimize energy via changes in electron density in a body. In addition to this, Electron correlations are taken into account and the mean field approximation is relaxed However, one key drawback in this theory is that it is not certain that using a more complicated basis set my necessarily produce a more accurate answer; the theory is not variational whereas the HF theory actively is.

== The Cope rearrangement: Computational Investigations ==

=== Overview ===

1-5 hexadiene provides a relatively simple system to observe a cope rearrangement. Through Woodward-Hoffmann analysis, we see that this [3,3] sigmatropic rearrangement is thermally allowed by virtue of the equation (4q + 2)s + (4r)a. Figure 2 provides one way in which the reaction can proceed via these rules with a single σ2s component and two π2a components. [[File:Computation_Coperearrangement.jpg|thumb|Figure 1: An overview of the cope rearrangement going through the cyclic 6M transition state.]]
During the concerted formation/dissociation of bonds, the transition state resembles that of a six membered ring which can exhibit a chair or boat topology (in line with the conformers of cyclohexane) These transition states represent energy maxima on the reaction pathway from reactants to products. On the other hand, 1-5 hexadiene exists in many conformers representing an energy minimum. In the following section, we obtain optimal structures for the diene on different levels of theory followed by locating the position of the TS on the potential energy surface. In doing this, we can appropriately deduce the activation energy involve in the cope rearrangement through the chair TS and boat TS pathways.

[[File:CompLab_Figure3_hexadieneconformers.jpg|thumb|Figure 3: Newman projections for hexadiene showing antiperiplanar and gauche arrangements of vinyl groups.150px]]
[[File:Complab_copeWoodwardHoffman.jpg|thumb|Figure 2: Woodward-Hoffmann analysis of the [3,3] sigmatropic rearrangement. the orbitals can "connect" through an suprafacial or antarafacial manner to make or break the bonds in the product.]]

=== Optimizing reactants and products ===

The substrate under investigation can adopt many different conformers with respect to the central C3-C4 bond as seen in figure 3. Within the conformers laid out in the diagram exists a subset of more isomers that differ in the exact positioning of the vinyl group relative to the rest of the molecule as opposed to just the other vinyl group. Initiative would serve to think the antiperiplanar set of isomers would be of lower energy than the gauche type isomers purely on the argument of steric repulsion between the two vinyl groups. Various conformers of Hexadiene the consist of gauche and antiperiplanr motifs were optimized and the results posted in the table below. The nomenclature of conformers are with respect to appendix 2

{| class="wikitable" border="1"
|+ Optimization of 1-5 hexadiene conformers
! placeholder !! Gauche3 !! Anti2 !! Anti1 !! Gauche(1)
|-
| Image || <jmol><jmolApplet>
<title></title>
<color>White</color>
<size>200</size>
<uploadedFileContents>Gauche3conformer.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet></jmol>|| <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet>react_anticonformer.mol2</jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_gaucheconformer.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy (Hartres) || -231.69266122 || -231.69253516 || -231.69260235 || -231.68771610
|-
| Point Group || C1 || Ci || C2 || C2
|-
| log || [https://wiki.ch.ic.ac.uk/wiki/images/c/c1/GAUCHE3CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/dd/REACT_ANTICONFORMER.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/6b/TRAILCONFORMER_TWO_ANTI1CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/REACT_GAUCHECONFORMER_oi513.LOG file]
|}

In comparison with literature reference values there is very good agreement. Interestingly, the lowest energy conformer reveals itself as a gauche type conformer which is contrary to initial predictions. Visualizing the molecular orbitals indicates favorable electronic interactions in the gauche3 setup; the two pi systems of the vinyl groups are in close enough proximity to yield a favourable in phase overlap which isn't possible in the anti conformation purely on the grounds of spacial arrangement. The gauche3 conformer serves as a balance between repulsive steric interactions and attractive molecular orbital-overlap interactions.

[[File:CompLab_Figure4_conformerorbitals.jpg|thumb|Figure 4: The orbitals HOMO of Gauche3 and Anti1 conformers on the left and right respectively of 1-5 hexadiene. As seen, there is a favourable in phase overlap between the the pi systems of the two vinyl groups]]

We can now approach the optimization of hexadiene on a different level of theory. The HF_3-21G optimized anti2 conformer of the alkene was then re-optimized under DFT_6-31G(d) level of theory. The geometrical differences arising form these two different methods of computation are summarized below.

{| class="wikitable" border="1"
|+anti conformer
|-
!colspan="4" style="text-align: left;"|[[File:anti2conformer_forrepresentingtheHF_321Glevel.png|600px]]
|-
|   ||   || HF/3-21G || B3LYP/6-31G*
|-
| rowspan="3" | Bond Lengths (Angstrom) || C1-C2 || 1.32 || 1.33
|-
| C2-C3 || 1.51 || 1.50
|-
| C3-C4 || 1.55 || 1.55
|-
| rowspan="3" | Bond Angles (Degrees) || C1-C2-C3 || 124.80 || 125.29
|-
| C2-C3-C4 || 111.34 || 112.65
|-
| C1-C2-C3-C4 || 114.63 || 118.58
|}

Being immediately observable is the increase in bond length with the B3LYP/6-31G* level of theory in comparison to HF/3-21G. Within the same level of theory however, the HF/3-21G method describes less of a distinction between bond lengths of C-C single bonds and C-C double bonds. This may also be detectable by running frequency calculations and visualizing the vibrations involving the C=C bonds in both conformers.

=== frequency investigations ===

Frequency analysis of the B3LYP/6-31G* optimised structure was carried out. Gaussian carries out this procedure by applying the equation for force constants [[File:Force_constant_equation_oi513.png]] (where C = 1/2π) and preforming calculations to see a convergence in the force constant. The absence of imaginary frequencies would indicate that we have indeed reached a true minimum on the potential energy surface. A summary of the optimisation is given below

{| class="wikitable" border="1"
|+ Frequency calculations
! Frequency summary !! Spectrum
|-
| [[File:CompLab_SpectraofFrequencies_oi513.png]]|| [[File:CompLab SummaryofFrequencies oi513.png]]
|}

The thermodynamic properties were noted post-optimisation and printed as follows (units in Hartrees)

Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461864
Sum of electronic and thermal Enthalpies= -234.460920

=== Transition state investigations ===

==== Overview ====

Having processed information about the reaction reactants/products, we can now try to approach mining information about a different area on the potential energy surface; the transition states.

As eluded to earlier, the reaction proceeds via a 6 membered ring transition state that can exhibit a boat or chair toplogy. In this section, we aim to find these states on the potential energy surface, assess their energies and consequently determine the activation energy involved in both pathways. We will start by building and optimising the fragments of the transition states, and running further frequency/optimisation calculations.

Defining a transition state requires a degree of appreciation for the reaction mechanism being explored. In this case, the two allyl fragements that will be used need to exhibit sensible geometry to allow for a completed freq + opt calculation to be run to completion. Two different methods of computing the transition state are explored in this section. In the first method, the frozen coordinates approach is taken. This involves locking the reaction coordinate whilst minimisation of the rest of the molecule is performed (through any method of choice including Hf/3-21G, B3LYP/6-31G* levels of theory). Another optimsation can then be run which will optimize the rest of the molecule.

The second approach involves calculating the force constant along the reaction coordinate with both the number of steps along the coordinate and the direction to run the calculation both being defined by the user. In this approach however, It is important that the guess structure of the transition state is quite close to the actual case.

To start this investigation, the frozen coordinate methods were applied.

==== The Chair ====

After optimising an single allyl (CH2CHCH2) through the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/0/05/ALLYLFRAG_HF_321G_oi513.LOG here]), two of the said fragments were arranged in a chair conformation, with terminal C-C bond distance (between two fragements) set to 2.2 Å

<jmol><jmolApplet>
<title>HF/3-21G allyl fragment</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Allylfrag_HF_321g_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

This "guess" transition state was then run through an Frequency + Optimisation job (the log file of which can be located [https://wiki.ch.ic.ac.uk/wiki/images/0/0e/TSHYPOTHESIS_TRAILTWO_oi513.LOG here]) introducing the TS(Berny) optimisation method. This method works by employing the Berny algorithm. An approximate Hessian matrix (constituted by calculating second derivatives of energy) is developed using parameters of the initial structure including the valence force field. this approximation is then updated by calculating energies along the reaction pathway until a convergence is observed. Thus, the approximate matrix is a key factor in determining the success of the calculation. For most cases, using the approximate hessian serves well for the rest of the optimisation of the molecule, but in the cases where the the hessian changes dramatically, the force constant can be computed along every point of the reaction pathway. At the expense of time and computational power, the opitmisation will be able to find the local minimum.

<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

Inspection of the vibrations shows a single imaginary frequency (negative cm-1) at -817.94 cm-1 This "guess structure" method provides a reference/basis to which the frozen method can be compared with.

Imaginary frequencies are given such names due to the complex nature of their absolute values. Eigenvalues of hessian matrices correspond to squared harmonic oscillations of the normal vibration modes. thus a the square root of a negative eigenvalue gives rise a complex number with an imaginary component. Taking a simple plot of the harmonic oscillator (potential energy vs bond displacement), a negative second derivative would indicate that the geometry to which the reaction coordinate is abiding by is hitting a maximum (i.e. achieving transition state status). Thus if a transition state has been calculated, only one imaginary frequency should be as a result of the optimisation.

The frozen coordinate approach was then used to compute the transition. The (to be formed) bond between the terminal C's on both allyl fragments were strictly fixed/frozen to 2.2 Å followed by an optimisation. The log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/b/bb/TSBONDMODIFY_TCSET_COPY_TRAILONE_oi513.LOG here]. Having optimised the rest of the molecule with the mentioned bonds of interest fixed, the bonds will be accounted for in a second optimisation to which the log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/TSBONDMODIFY_TCSET_UNIDENTIFIEDDESTINATION_oi513.LOG here]

To summarize, the chair transition state has be investigated through a reference setup and an frozen coordinate setup. The table of results below give an account of the results of the two setups.

{| class="wikitable" border="1"
|+ Chair Transition State analysis
|-
| colspan="3" align="center"|[[File:CompLab_ChairTS_oi513.png]]
|-
! !! Guess TS !! Frozen TS
|-
| Terminal C-C Bond Length (Angstrom) || 2.02 || 2.02
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.39
|-
| C-C-C angle || 120.50 || 120.49
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSBondmodify_TCset_Unidentifieddestination_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==== The Boat ====

Having exhausted the chair TS, computations in the Boat conformer will be brought under investigation. In this section, more computational methods that investigate transition states will be explored. The QTS2 methods works by using user defined reactants and products and attempts to conceive new data points via interpolation such to find the transition state between them. The substrate was setup and labelled to depict reactants and product and was subsequently processed with the QTS2 method. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/c/c5/BOATTS_TWOMOLECULESETUP_SECONDTRAIL_oi513.LOG here]

Having run this initial calculation, the geometries of the reactants and products were edited to resemble that of a boat transition state. The same calculation was run again ( log file [https://wiki.ch.ic.ac.uk/wiki/images/5/53/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_oi513.LOG here]) The results of the two runs are summarized in the table below.

{| class="wikitable" border="1"
|+ Boat Transition state: QTS2 method
|-
! !! Arbitrary !! Boat-Like
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_secondtrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_properconformer_firsttrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Terminal C-C bond length (Angstrom)|| 2.02 || 2.14
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.38
|}

==== Endpiece: Comparing the Boat & Chair ====

To conclude this section of the study, the transition states will be optimised using the Intrinsic reaction coordinate (IRC) method. Arguably the defining feature of this approach is the ability to track the reaction coordinate from the transition state to a local minimum by taking minute steps along negative,steep gradients of the potential energy surface. This bears many favourable features for users to define at will namely defining how many steps to be taken in the calculation and the direction of the gradient should run from the transition state.

The IRC method was applied to the optimised chair conformer. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/a/a3/TSHYPOTHESIS_TRAILTWO_ForIRCcalculation_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_ForIRC_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

The same molecule was then further optimised to find a minimum under the HF/3-21G level of theory. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/d/d5/TSHYPOTHESIS_TRAILTWO_ForIRC_oi513.LOG here] 

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_PostIRC_Reopt.mol2</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC graphs oi513.png|thumb| figure 5: The Intrinsic Reaction Coordinates for the calculation. The convergence to a zero gradient indicates the structure optmisation has converged.]]

As seen by the the results of re-optimisation post-IRC, the conformer best represent that of the gauche2 state supported by the point group being C2. To allow activation energies to be calculated, a gauche 2 conformer was constructed and optimised under the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/5/51/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_HF312G_oi513.LOG here]) followed by the B3LYP/631G* level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/b/b8/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_REOPT_631GD_oi513.LOG here]) The thermochemical data can then be retrieved and be used as the reactants on the reaction coordinate pathway. Thus the difference in energy between the gauche2 conformer and the boat and chair transition states can be calculated

Lastly, optmised chair and boat structures were re-optimised under the a higher level of theory (B3LYP/6-31G*) with the resultant log files presented [https://wiki.ch.ic.ac.uk/wiki/images/3/34/TSHYPOTHESIS_TRAILTWO_ChairTS_631GdOpt_oi513.LOG here] and [https://wiki.ch.ic.ac.uk/wiki/images/5/5e/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_631Gd_reopt.LOG there] respectively

== The Diels Alder Cycloaddition: Computational Investigations ==

=== Overview ===

=== Simple Systems: S-cis butadiene and ethene ===

As an introduction to a cycloaddition, the reaction between ethene and butadiene was investigated.
setting the two vinyl protons in the same plane (i.e C1C2C3C4 dihedral angle = 0), the molecule was optmised under the Semi empirical am 1 method. Similarly, a molecule of cis-butadiene was optimised. The table below shows the results of optimisation

{| class="wikitable" border="1"
! !! Ethene !! S-cis butadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ethene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cisbutadiene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Point Group || C2v || d2h
|-
| HOMO || [[File:HOMO_ethene_oi513.png]] || [[File:HOMO_butadiene.png]]
|-
| LUMO || [[File:LUMO_Ethene_oi513.png]] || [[File:LUMO_butadiene_oi513.png]]
|-
| LOG files || [https://wiki.ch.ic.ac.uk/wiki/images/f/fa/ETHENE_OPT_SEMIEM_AM1_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/64/CISBUTADIENE_OPT_SEMIEM_AM1_T1_oi513.LOG file]
|}

following reactant optimisation,the fragments were arranged into a guess transition state (using the same concepts explored in the cope rearrangement investigations. The terminal Carbons on each fragment was fixed to be 2.2 angstrom apart. The resultant TS structure had a single imaginary frequency confirming formation of a transition state. The log file for optmisation can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/UNDOCUMETEDTS_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents></uploadedFileContents>
</jmolApplet>UndocumetedTS_oi513.mol2</jmol>

[[File:HOMO_firstDA_oi513.png|thumb| figure 6: HOMO of the Diels Alder between the two subtrates.]]
[[File:LUMO_firstDA_oi513.png|thumb| figure 7: LUMO of Diels Alder between the two subtrates.]]

=== Complex systems: Maelic anydride and Cyclohexadiene ===

Using the same concepts explored in the cycloaddition investigations with the two unfunctionalised alkenes, the properties of the Diels Alder reaction between Maleic anhydride and cyclohexa-1,3-diene was investigated. As we will see, the regiochemistry of the reaction comes into play as the arrangement of the two subtrates prior to bond making/breaking gives rise to two different trasnition states (an exo and an endo state). Obtaining Molecular orbital data for of the two states will account for differences in the observed energies of the transition states.

the two reactants were optimised under the Semi empirical am1 method. The results of the calculations are presented in the table below

{| class="wikitable" border="1"
Optmising the reactants
! !! Maelic anhydride !! Cyclohexadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>MAnydride_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cyclobutadiene_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|Point group || C2 || C1
|-
|HOMO || [[File:HOMO_MAnhydride_oi513.png]] || [[File:HOMO_Cylodiene_oi513.png]]
|-
|LUMO || [[File:LUMO_MAnhydride_oi513.png]] || [[File:LUMO_Cyclodiene_oi513.png]]
|-
|LOG || [https://wiki.ch.ic.ac.uk/wiki/images/3/31/MANYDRIDE_OPT_SEMEM_AM1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/7/7a/CYCLOBUTADIENE_OPT_SEMEM_AM1_oi513.LOG file]
|}

As per routine, a guess transition structure had to be constructed using the optimised fragments. In this case, we have stereo-distinction between two possible transition states, and exo form and an endo form.

For both endo and exo forms, terminal C-C bond distances were set and fixed to 2.2 Angstrom and the molecule adapted to represent a postulated transition state fro the respective forms. an optimisation + frequency calculation was carried out an the results given below

{| class="wikitable" border="1"
! !! Exo transition state !! Endo Transition state
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess3_Exo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess_Endo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|HOMO || [[File:HOMO_secondDA_Exo_oi513.png]] || [[File:HOMO_secondDA_Endo_oi513.png]]
|-
|LUMO || [[File:LUMO_SecondDA_Exo_oi513.png]] || [[File:LUMO_secondDA_Endo_oi513.png]]
|-
Log files || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/TSGUESS3_EXO_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/9/90/TSGUESS_ENDO_T1_oi513.LOG file]
|}

Geometry data for the two states was also collected. The results are presented below

{| class="wikitable" border="1"
! colspan="2"|Exo transition State !! ! colspan="3"|Endo Transition state
|-
| colspan="2"|[[File:NumberingforExotransitionstate_oi513.png]] || colspan="2"|[[File:NumberingofEndoTransitionstate_oi513.png]]
|-
|bond || values (Angstrom)|| bond || values (Angstrom)
|-
| C1-C2 || 1.41 || C1-C2 || 1.49
|-
| C2-C3 || 1.49 || C4-C5 || 1.49
|-
| C5-C1 || 1.49 || C5-C1 || 1.41
|-
| C2-C9 || 2.17 || C1-C9 || 2.16
|-
| C1-C6 || 2.17 || C5-C6 || 2.16
|-
| C6-C7 || 1.34 || C6-C7 || 1.49
|-
| C7-C8 || 1.40 || C7-C8 || 1.52
|-
| C8-C9 || 1.39 || C8-C9 || 1.49
|-
| C9-C10 || 1.49 || C9-C10 || 1.39
|-
| C10-C11 || 1.52 || C10-C11 || 1.40
|-
| C11-C6 || 1.49 || C11-C6 || 1.49
|}
Lastly, thermochemical data was collated and the results given below

Exo

Sum of electronic and zero-point Energies= 0.134882
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.0991180.099118

Endo

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

To end this section on the more complex systems, the overall energy of the Endo transition state is lower than that of the exo (refer to the log file for the energies). This is due to the so called secondary orbital overlap effect. Looking at the image of the HOMO in the endo state there is possible overlap between orbitals on the Oxygen including the lone pairs and the pi system on the cyclodiene

== References ==

[1] K. Takao, R. Munakata, K. Tadano, Chem. Rev. 2005, 105, 4779−4807
[2] K. N. Houk, J. Am. Chem. Soc., 1973, 95, 4092–4094
[3] R. B. Woodward, R. Hoffman, J. Am. Chem. Soc., 1965, 87, 395–397
[4] M. Manoharan, F. De Proft, P. Geerlings, J. Org. Chem., 2000, 65, 7971–7976
[5] M. Svensson, S. Humbel, R. D. J. Froese, T. Matsubara, S. Seiber, K. Morokuma, J. Phys. Chem., 1996, 100, pp 19357–19363

Rep:Mod:Peebo

2015-12-18T11:33:08Z

Oi513: /* Simple Systems: S-cis butadiene and ethene */

== Introduction ==

=== Overview ===
Fundamental to organic chemistry are pericyclic reactions that involve concerted movement of electrons through a cyclic transition state. Cycloadditions, a subset of pericyclic reactions, serve as a essential synthetic tool for organic chemists as a basis for accessing more complex structures in, for example, total synthesis of natural products [1]. In addition, sigmatropic rearrangements, and electrocyclic reactions are also a set of important pericyclic reactions that see Δσ 0 or ±1 respectively. For Diels alder and ene reactions, the initial arrangement of the fragments is brought into question when trying to understand the stereochemical outcome of the reaction. Other than these geometric factors, the frontier orbitals of the two fragments contain valuable information into predicting whether the two reactants may proceed to reach a product[2].

Robert Burns Woodward and Roald Hoffman established rules to explain whether a given pericyclic reaction may be thermally or photochemically allowed to give the said product. Naturally incorporated in their approach is considerations of the molecular orbitals involved in the reaction, the number of electrons, and the symmetry with respect to the connectivity between the two fragments. First applied to electrocyclic reactions [3], the two would then go on to publish more papers to fully develop their rules setting a universal foundation for understanding these class of reactions

Given the wealth factors that contribute towards going from reactants --> products, it is of the best interests to synthetic chemists to understand the mechanistic basis behind the reaction and therefore ,for example, the observed stereochemistry as opposed to whether a given reaction may be allowed or forbidden (in conjunction with Woodward-Hoffman rules). As such, computational methods into investigating diels alder reaction pathways have come to light[4][5] and have shown to provide insight into the optimal positioning of fragments and the structure and energy of Transition states. Studying transition states in particular are a huge advantage in computational studies; through this medium, calculations on energies of these states can be probes that would otherwise be immeasurable due to the fleeting nature of the transition state.

=== Experimental Aims ===
In this exercise, we first investigate the energies of varying 1-5 hexadiene conformers and investigate the possible cyclic transition states whilst it undergoes the cope rearrangement using the Hartree-Fock/3-21G and B3LYP/6-31G(d) levels of theory in addition to exploring Transition state optimization methods QTS2 and TS(Berny). Using similar methods, we then go on to develop our discussion of transition states by through investigating the regioselectivity of the Diels Alder reaction between maelic anhydride and 1-3 cyclohexadiene including molecular orbital interactions.

=== Brief note: Computational Methods ===

In this investigation, we explore different levels of theory to apply alongside our calculations as each have both advantageous features, and their respective drawbacks. Hatree fock method is used to determine both energies and quantum mechanical wavefunction of a multi-body system in state that has its probability density (position of the body in question) independent of time (i.e a stationary state). Amongst the appreciable number of approximations made by this method, the assumption that many electron wavefunction of the body in question will take the form of a just an isolated determinant (slater determinant) derived from a single electron wavefunction. Whist in theory this is entirely possible through linear combination of atomic orbitals, this naturally causes this approach to overlook the replusive interactions between the electrons in the system thus producing energies that are overestimated.

By virtue The Hohenberg-Kohn Theorems, the total energy of a ground state is exclusively dependent on electron density and distribution. Focusing in on this aspect and overlooking the electronic wavefunctions give rise to density functional theory. This method will aim to minimize energy via changes in electron density in a body. In addition to this, Electron correlations are taken into account and the mean field approximation is relaxed However, one key drawback in this theory is that it is not certain that using a more complicated basis set my necessarily produce a more accurate answer; the theory is not variational whereas the HF theory actively is.

== The Cope rearrangement: Computational Investigations ==

=== Overview ===

1-5 hexadiene provides a relatively simple system to observe a cope rearrangement. Through Woodward-Hoffmann analysis, we see that this [3,3] sigmatropic rearrangement is thermally allowed by virtue of the equation (4q + 2)s + (4r)a. Figure 2 provides one way in which the reaction can proceed via these rules with a single σ2s component and two π2a components. [[File:Computation_Coperearrangement.jpg|thumb|Figure 1: An overview of the cope rearrangement going through the cyclic 6M transition state.]]
During the concerted formation/dissociation of bonds, the transition state resembles that of a six membered ring which can exhibit a chair or boat topology (in line with the conformers of cyclohexane) These transition states represent energy maxima on the reaction pathway from reactants to products. On the other hand, 1-5 hexadiene exists in many conformers representing an energy minimum. In the following section, we obtain optimal structures for the diene on different levels of theory followed by locating the position of the TS on the potential energy surface. In doing this, we can appropriately deduce the activation energy involve in the cope rearrangement through the chair TS and boat TS pathways.

[[File:CompLab_Figure3_hexadieneconformers.jpg|thumb|Figure 3: Newman projections for hexadiene showing antiperiplanar and gauche arrangements of vinyl groups.150px]]
[[File:Complab_copeWoodwardHoffman.jpg|thumb|Figure 2: Woodward-Hoffmann analysis of the [3,3] sigmatropic rearrangement. the orbitals can "connect" through an suprafacial or antarafacial manner to make or break the bonds in the product.]]

=== Optimizing reactants and products ===

The substrate under investigation can adopt many different conformers with respect to the central C3-C4 bond as seen in figure 3. Within the conformers laid out in the diagram exists a subset of more isomers that differ in the exact positioning of the vinyl group relative to the rest of the molecule as opposed to just the other vinyl group. Initiative would serve to think the antiperiplanar set of isomers would be of lower energy than the gauche type isomers purely on the argument of steric repulsion between the two vinyl groups. Various conformers of Hexadiene the consist of gauche and antiperiplanr motifs were optimized and the results posted in the table below. The nomenclature of conformers are with respect to appendix 2

{| class="wikitable" border="1"
|+ Optimization of 1-5 hexadiene conformers
! placeholder !! Gauche3 !! Anti2 !! Anti1 !! Gauche(1)
|-
| Image || <jmol><jmolApplet>
<title></title>
<color>White</color>
<size>200</size>
<uploadedFileContents>Gauche3conformer.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet></jmol>|| <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet>react_anticonformer.mol2</jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_gaucheconformer.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy (Hartres) || -231.69266122 || -231.69253516 || -231.69260235 || -231.68771610
|-
| Point Group || C1 || Ci || C2 || C2
|-
| log || [https://wiki.ch.ic.ac.uk/wiki/images/c/c1/GAUCHE3CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/dd/REACT_ANTICONFORMER.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/6b/TRAILCONFORMER_TWO_ANTI1CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/REACT_GAUCHECONFORMER_oi513.LOG file]
|}

In comparison with literature reference values there is very good agreement. Interestingly, the lowest energy conformer reveals itself as a gauche type conformer which is contrary to initial predictions. Visualizing the molecular orbitals indicates favorable electronic interactions in the gauche3 setup; the two pi systems of the vinyl groups are in close enough proximity to yield a favourable in phase overlap which isn't possible in the anti conformation purely on the grounds of spacial arrangement. The gauche3 conformer serves as a balance between repulsive steric interactions and attractive molecular orbital-overlap interactions.

[[File:CompLab_Figure4_conformerorbitals.jpg|thumb|Figure 4: The orbitals HOMO of Gauche3 and Anti1 conformers on the left and right respectively of 1-5 hexadiene. As seen, there is a favourable in phase overlap between the the pi systems of the two vinyl groups]]

We can now approach the optimization of hexadiene on a different level of theory. The HF_3-21G optimized anti2 conformer of the alkene was then re-optimized under DFT_6-31G(d) level of theory. The geometrical differences arising form these two different methods of computation are summarized below.

{| class="wikitable" border="1"
|+anti conformer
|-
!colspan="4" style="text-align: left;"|[[File:anti2conformer_forrepresentingtheHF_321Glevel.png|600px]]
|-
|   ||   || HF/3-21G || B3LYP/6-31G*
|-
| rowspan="3" | Bond Lengths (Angstrom) || C1-C2 || 1.32 || 1.33
|-
| C2-C3 || 1.51 || 1.50
|-
| C3-C4 || 1.55 || 1.55
|-
| rowspan="3" | Bond Angles (Degrees) || C1-C2-C3 || 124.80 || 125.29
|-
| C2-C3-C4 || 111.34 || 112.65
|-
| C1-C2-C3-C4 || 114.63 || 118.58
|}

Being immediately observable is the increase in bond length with the B3LYP/6-31G* level of theory in comparison to HF/3-21G. Within the same level of theory however, the HF/3-21G method describes less of a distinction between bond lengths of C-C single bonds and C-C double bonds. This may also be detectable by running frequency calculations and visualizing the vibrations involving the C=C bonds in both conformers.

Frequency analysis of the B3LYP/6-31G* optimised structure was carried out. Gaussian carries out this procedure by applying the equation for force constants [[File:Force_constant_equation_oi513.png]] (where C = 1/2π) and preforming calculations to see a convergence in the force constant. The absence of imaginary frequencies would indicate that we have indeed reached a true minimum on the potential energy surface. A summary of the optimisation is given below

{| class="wikitable" border="1"
|+ Frequency calculations
! Frequency summary !! Spectrum
|-
| [[File:CompLab_SpectraofFrequencies_oi513.png]]|| [[File:CompLab SummaryofFrequencies oi513.png]]
|}

The thermodynamic properties were noted post-optimisation and printed as follows (units in Hartrees)

Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461864
Sum of electronic and thermal Enthalpies= -234.460920

=== Transition state investigations ===

==== Overview ====

Having processed information about the reaction reactants/products, we can now try to approach mining information about a different area on the potential energy surface; the transition states.

As eluded to earlier, the reaction proceeds via a 6 membered ring transition state that can exhibit a boat or chair toplogy. In this section, we aim to find these states on the potential energy surface, assess their energies and consequently determine the activation energy involved in both pathways. We will start by building and optimising the fragments of the transition states, and running further frequency/optimisation calculations.

Defining a transition state requires a degree of appreciation for the reaction mechanism being explored. In this case, the two allyl fragements that will be used need to exhibit sensible geometry to allow for a completed freq + opt calculation to be run to completion. Two different methods of computing the transition state are explored in this section. In the first method, the frozen coordinates approach is taken. This involves locking the reaction coordinate whilst minimisation of the rest of the molecule is performed (through any method of choice including Hf/3-21G, B3LYP/6-31G* levels of theory). Another optimsation can then be run which will optimize the rest of the molecule.

The second approach involves calculating the force constant along the reaction coordinate with both the number of steps along the coordinate and the direction to run the calculation both being defined by the user. In this approach however, It is important that the guess structure of the transition state is quite close to the actual case.

To start this investigation, the frozen coordinate methods were applied.

==== The Chair ====

After optimising an single allyl (CH2CHCH2) through the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/0/05/ALLYLFRAG_HF_321G_oi513.LOG here]), two of the said fragments were arranged in a chair conformation, with terminal C-C bond distance (between two fragements) set to 2.2 Å

<jmol><jmolApplet>
<title>HF/3-21G allyl fragment</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Allylfrag_HF_321g_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

This "guess" transition state was then run through an Frequency + Optimisation job (the log file of which can be located [https://wiki.ch.ic.ac.uk/wiki/images/0/0e/TSHYPOTHESIS_TRAILTWO_oi513.LOG here]) introducing the TS(Berny) optimisation method. This method works by employing the Berny algorithm. An approximate Hessian matrix (constituted by calculating second derivatives of energy) is developed using parameters of the initial structure including the valence force field. this approximation is then updated by calculating energies along the reaction pathway until a convergence is observed. Thus, the approximate matrix is a key factor in determining the success of the calculation. For most cases, using the approximate hessian serves well for the rest of the optimisation of the molecule, but in the cases where the the hessian changes dramatically, the force constant can be computed along every point of the reaction pathway. At the expense of time and computational power, the opitmisation will be able to find the local minimum.

<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

Inspection of the vibrations shows a single imaginary frequency (negative cm-1) at -817.94 cm-1 This "guess structure" method provides a reference/basis to which the frozen method can be compared with.

Imaginary frequencies are given such names due to the complex nature of their absolute values. Eigenvalues of hessian matrices correspond to squared harmonic oscillations of the normal vibration modes. thus a the square root of a negative eigenvalue gives rise a complex number with an imaginary component. Taking a simple plot of the harmonic oscillator (potential energy vs bond displacement), a negative second derivative would indicate that the geometry to which the reaction coordinate is abiding by is hitting a maximum (i.e. achieving transition state status). Thus if a transition state has been calculated, only one imaginary frequency should be as a result of the optimisation.

The frozen coordinate approach was then used to compute the transition. The (to be formed) bond between the terminal C's on both allyl fragments were strictly fixed/frozen to 2.2 Å followed by an optimisation. The log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/b/bb/TSBONDMODIFY_TCSET_COPY_TRAILONE_oi513.LOG here]. Having optimised the rest of the molecule with the mentioned bonds of interest fixed, the bonds will be accounted for in a second optimisation to which the log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/TSBONDMODIFY_TCSET_UNIDENTIFIEDDESTINATION_oi513.LOG here]

To summarize, the chair transition state has be investigated through a reference setup and an frozen coordinate setup. The table of results below give an account of the results of the two setups.

{| class="wikitable" border="1"
|+ Chair Transition State analysis
|-
| colspan="3" align="center"|[[File:CompLab_ChairTS_oi513.png]]
|-
! !! Guess TS !! Frozen TS
|-
| Terminal C-C Bond Length (Angstrom) || 2.02 || 2.02
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.39
|-
| C-C-C angle || 120.50 || 120.49
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSBondmodify_TCset_Unidentifieddestination_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==== The Boat ====

Having exhausted the chair TS, computations in the Boat conformer will be brought under investigation. In this section, more computational methods that investigate transition states will be explored. The QTS2 methods works by using user defined reactants and products and attempts to conceive new data points via interpolation such to find the transition state between them. The substrate was setup and labelled to depict reactants and product and was subsequently processed with the QTS2 method. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/c/c5/BOATTS_TWOMOLECULESETUP_SECONDTRAIL_oi513.LOG here]

Having run this initial calculation, the geometries of the reactants and products were edited to resemble that of a boat transition state. The same calculation was run again ( log file [https://wiki.ch.ic.ac.uk/wiki/images/5/53/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_oi513.LOG here]) The results of the two runs are summarized in the table below.

{| class="wikitable" border="1"
|+ Boat Transition state: QTS2 method
|-
! !! Arbitrary !! Boat-Like
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_secondtrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_properconformer_firsttrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Terminal C-C bond length (Angstrom)|| 2.02 || 2.14
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.38
|}

==== Endpiece: Comparing the Boat & Chair ====

To conclude this section of the study, the transition states will be optimised using the Intrinsic reaction coordinate (IRC) method. Arguably the defining feature of this approach is the ability to track the reaction coordinate from the transition state to a local minimum by taking minute steps along negative,steep gradients of the potential energy surface. This bears many favourable features for users to define at will namely defining how many steps to be taken in the calculation and the direction of the gradient should run from the transition state.

The IRC method was applied to the optimised chair conformer. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/a/a3/TSHYPOTHESIS_TRAILTWO_ForIRCcalculation_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_ForIRC_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

The same molecule was then further optimised to find a minimum under the HF/3-21G level of theory. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/d/d5/TSHYPOTHESIS_TRAILTWO_ForIRC_oi513.LOG here] 

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_PostIRC_Reopt.mol2</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC graphs oi513.png|thumb| figure 5: The Intrinsic Reaction Coordinates for the calculation. The convergence to a zero gradient indicates the structure optmisation has converged.]]

As seen by the the results of re-optimisation post-IRC, the conformer best represent that of the gauche2 state supported by the point group being C2. To allow activation energies to be calculated, a gauche 2 conformer was constructed and optimised under the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/5/51/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_HF312G_oi513.LOG here]) followed by the B3LYP/631G* level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/b/b8/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_REOPT_631GD_oi513.LOG here]) The thermochemical data can then be retrieved and be used as the reactants on the reaction coordinate pathway. Thus the difference in energy between the gauche2 conformer and the boat and chair transition states can be calculated

Lastly, optmised chair and boat structures were re-optimised under the a higher level of theory (B3LYP/6-31G*) with the resultant log files presented [https://wiki.ch.ic.ac.uk/wiki/images/3/34/TSHYPOTHESIS_TRAILTWO_ChairTS_631GdOpt_oi513.LOG here] and [https://wiki.ch.ic.ac.uk/wiki/images/5/5e/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_631Gd_reopt.LOG there] respectively

== The Diels Alder Cycloaddition: Computational Investigations ==

=== Overview ===

=== Simple Systems: S-cis butadiene and ethene ===

As an introduction to a cycloaddition, the reaction between ethene and butadiene was investigated.
setting the two vinyl protons in the same plane (i.e C1C2C3C4 dihedral angle = 0), the molecule was optmised under the Semi empirical am 1 method. Similarly, a molecule of cis-butadiene was optimised. The table below shows the results of optimisation

{| class="wikitable" border="1"
! !! Ethene !! S-cis butadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ethene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cisbutadiene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Point Group || C2v || d2h
|-
| HOMO || [[File:HOMO_ethene_oi513.png]] || [[File:HOMO_butadiene.png]]
|-
| LUMO || [[File:LUMO_Ethene_oi513.png]] || [[File:LUMO_butadiene_oi513.png]]
|-
| LOG files || [https://wiki.ch.ic.ac.uk/wiki/images/f/fa/ETHENE_OPT_SEMIEM_AM1_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/64/CISBUTADIENE_OPT_SEMIEM_AM1_T1_oi513.LOG file]
|}

following reactant optimisation,the fragments were arranged into a guess transition state (using the same concepts explored in the cope rearrangement investigations. The terminal Carbons on each fragment was fixed to be 2.2 angstrom apart. The resultant TS structure had a single imaginary frequency confirming formation of a transition state. The log file for optmisation can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/UNDOCUMETEDTS_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents></uploadedFileContents>
</jmolApplet>UndocumetedTS_oi513.mol2</jmol>

[[File:HOMO_firstDA_oi513.png|thumb| figure 6: HOMO of the Diels Alder between the two subtrates.]]
[[File:LUMO_firstDA_oi513.png|thumb| figure 7: LUMO of Diels Alder between the two subtrates.]]

=== Complex systems: Maelic anydride and Cyclohexadiene ===

Using the same concepts explored in the cycloaddition investigations with the two unfunctionalised alkenes, the properties of the Diels Alder reaction between Maleic anhydride and cyclohexa-1,3-diene was investigated. As we will see, the regiochemistry of the reaction comes into play as the arrangement of the two subtrates prior to bond making/breaking gives rise to two different trasnition states (an exo and an endo state). Obtaining Molecular orbital data for of the two states will account for differences in the observed energies of the transition states.

the two reactants were optimised under the Semi empirical am1 method. The results of the calculations are presented in the table below

{| class="wikitable" border="1"
Optmising the reactants
! !! Maelic anhydride !! Cyclohexadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>MAnydride_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cyclobutadiene_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|Point group || C2 || C1
|-
|HOMO || [[File:HOMO_MAnhydride_oi513.png]] || [[File:HOMO_Cylodiene_oi513.png]]
|-
|LUMO || [[File:LUMO_MAnhydride_oi513.png]] || [[File:LUMO_Cyclodiene_oi513.png]]
|-
|LOG || [https://wiki.ch.ic.ac.uk/wiki/images/3/31/MANYDRIDE_OPT_SEMEM_AM1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/7/7a/CYCLOBUTADIENE_OPT_SEMEM_AM1_oi513.LOG file]
|}

As per routine, a guess transition structure had to be constructed using the optimised fragments. In this case, we have stereo-distinction between two possible transition states, and exo form and an endo form.

For both endo and exo forms, terminal C-C bond distances were set and fixed to 2.2 Angstrom and the molecule adapted to represent a postulated transition state fro the respective forms. an optimisation + frequency calculation was carried out an the results given below

{| class="wikitable" border="1"
! !! Exo transition state !! Endo Transition state
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess3_Exo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess_Endo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|HOMO || [[File:HOMO_secondDA_Exo_oi513.png]] || [[File:HOMO_secondDA_Endo_oi513.png]]
|-
|LUMO || [[File:LUMO_SecondDA_Exo_oi513.png]] || [[File:LUMO_secondDA_Endo_oi513.png]]
|-
Log files || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/TSGUESS3_EXO_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/9/90/TSGUESS_ENDO_T1_oi513.LOG file]
|}

Geometry data for the two states was also collected. The results are presented below

{| class="wikitable" border="1"
! colspan="2"|Exo transition State !! ! colspan="3"|Endo Transition state
|-
| colspan="2"|[[File:NumberingforExotransitionstate_oi513.png]] || colspan="2"|[[File:NumberingofEndoTransitionstate_oi513.png]]
|-
|bond || values (Angstrom)|| bond || values (Angstrom)
|-
| C1-C2 || 1.41 || C1-C2 || 1.49
|-
| C2-C3 || 1.49 || C4-C5 || 1.49
|-
| C5-C1 || 1.49 || C5-C1 || 1.41
|-
| C2-C9 || 2.17 || C1-C9 || 2.16
|-
| C1-C6 || 2.17 || C5-C6 || 2.16
|-
| C6-C7 || 1.34 || C6-C7 || 1.49
|-
| C7-C8 || 1.40 || C7-C8 || 1.52
|-
| C8-C9 || 1.39 || C8-C9 || 1.49
|-
| C9-C10 || 1.49 || C9-C10 || 1.39
|-
| C10-C11 || 1.52 || C10-C11 || 1.40
|-
| C11-C6 || 1.49 || C11-C6 || 1.49
|}
Lastly, thermochemical data was collated and the results given below

Exo

Sum of electronic and zero-point Energies= 0.134882
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.0991180.099118

Endo

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

To end this section on the more complex systems, the overall energy of the Endo transition state is lower than that of the exo (refer to the log file for the energies). This is due to the so called secondary orbital overlap effect. Looking at the image of the HOMO in the endo state there is possible overlap between orbitals on the Oxygen including the lone pairs and the pi system on the cyclodiene

== References ==

[1] K. Takao, R. Munakata, K. Tadano, Chem. Rev. 2005, 105, 4779−4807
[2] K. N. Houk, J. Am. Chem. Soc., 1973, 95, 4092–4094
[3] R. B. Woodward, R. Hoffman, J. Am. Chem. Soc., 1965, 87, 395–397
[4] M. Manoharan, F. De Proft, P. Geerlings, J. Org. Chem., 2000, 65, 7971–7976
[5] M. Svensson, S. Humbel, R. D. J. Froese, T. Matsubara, S. Seiber, K. Morokuma, J. Phys. Chem., 1996, 100, pp 19357–19363

Rep:Mod:Peebo

2015-12-18T11:28:53Z

Oi513: /* Complex systems: Maelic anydride and Cyclohexadiene */

== Introduction ==

=== Overview ===
Fundamental to organic chemistry are pericyclic reactions that involve concerted movement of electrons through a cyclic transition state. Cycloadditions, a subset of pericyclic reactions, serve as a essential synthetic tool for organic chemists as a basis for accessing more complex structures in, for example, total synthesis of natural products [1]. In addition, sigmatropic rearrangements, and electrocyclic reactions are also a set of important pericyclic reactions that see Δσ 0 or ±1 respectively. For Diels alder and ene reactions, the initial arrangement of the fragments is brought into question when trying to understand the stereochemical outcome of the reaction. Other than these geometric factors, the frontier orbitals of the two fragments contain valuable information into predicting whether the two reactants may proceed to reach a product[2].

Robert Burns Woodward and Roald Hoffman established rules to explain whether a given pericyclic reaction may be thermally or photochemically allowed to give the said product. Naturally incorporated in their approach is considerations of the molecular orbitals involved in the reaction, the number of electrons, and the symmetry with respect to the connectivity between the two fragments. First applied to electrocyclic reactions [3], the two would then go on to publish more papers to fully develop their rules setting a universal foundation for understanding these class of reactions

Given the wealth factors that contribute towards going from reactants --> products, it is of the best interests to synthetic chemists to understand the mechanistic basis behind the reaction and therefore ,for example, the observed stereochemistry as opposed to whether a given reaction may be allowed or forbidden (in conjunction with Woodward-Hoffman rules). As such, computational methods into investigating diels alder reaction pathways have come to light[4][5] and have shown to provide insight into the optimal positioning of fragments and the structure and energy of Transition states. Studying transition states in particular are a huge advantage in computational studies; through this medium, calculations on energies of these states can be probes that would otherwise be immeasurable due to the fleeting nature of the transition state.

=== Experimental Aims ===
In this exercise, we first investigate the energies of varying 1-5 hexadiene conformers and investigate the possible cyclic transition states whilst it undergoes the cope rearrangement using the Hartree-Fock/3-21G and B3LYP/6-31G(d) levels of theory in addition to exploring Transition state optimization methods QTS2 and TS(Berny). Using similar methods, we then go on to develop our discussion of transition states by through investigating the regioselectivity of the Diels Alder reaction between maelic anhydride and 1-3 cyclohexadiene including molecular orbital interactions.

=== Brief note: Computational Methods ===

In this investigation, we explore different levels of theory to apply alongside our calculations as each have both advantageous features, and their respective drawbacks. Hatree fock method is used to determine both energies and quantum mechanical wavefunction of a multi-body system in state that has its probability density (position of the body in question) independent of time (i.e a stationary state). Amongst the appreciable number of approximations made by this method, the assumption that many electron wavefunction of the body in question will take the form of a just an isolated determinant (slater determinant) derived from a single electron wavefunction. Whist in theory this is entirely possible through linear combination of atomic orbitals, this naturally causes this approach to overlook the replusive interactions between the electrons in the system thus producing energies that are overestimated.

By virtue The Hohenberg-Kohn Theorems, the total energy of a ground state is exclusively dependent on electron density and distribution. Focusing in on this aspect and overlooking the electronic wavefunctions give rise to density functional theory. This method will aim to minimize energy via changes in electron density in a body. In addition to this, Electron correlations are taken into account and the mean field approximation is relaxed However, one key drawback in this theory is that it is not certain that using a more complicated basis set my necessarily produce a more accurate answer; the theory is not variational whereas the HF theory actively is.

== The Cope rearrangement: Computational Investigations ==

=== Overview ===

1-5 hexadiene provides a relatively simple system to observe a cope rearrangement. Through Woodward-Hoffmann analysis, we see that this [3,3] sigmatropic rearrangement is thermally allowed by virtue of the equation (4q + 2)s + (4r)a. Figure 2 provides one way in which the reaction can proceed via these rules with a single σ2s component and two π2a components. [[File:Computation_Coperearrangement.jpg|thumb|Figure 1: An overview of the cope rearrangement going through the cyclic 6M transition state.]]
During the concerted formation/dissociation of bonds, the transition state resembles that of a six membered ring which can exhibit a chair or boat topology (in line with the conformers of cyclohexane) These transition states represent energy maxima on the reaction pathway from reactants to products. On the other hand, 1-5 hexadiene exists in many conformers representing an energy minimum. In the following section, we obtain optimal structures for the diene on different levels of theory followed by locating the position of the TS on the potential energy surface. In doing this, we can appropriately deduce the activation energy involve in the cope rearrangement through the chair TS and boat TS pathways.

[[File:CompLab_Figure3_hexadieneconformers.jpg|thumb|Figure 3: Newman projections for hexadiene showing antiperiplanar and gauche arrangements of vinyl groups.150px]]
[[File:Complab_copeWoodwardHoffman.jpg|thumb|Figure 2: Woodward-Hoffmann analysis of the [3,3] sigmatropic rearrangement. the orbitals can "connect" through an suprafacial or antarafacial manner to make or break the bonds in the product.]]

=== Optimizing reactants and products ===

The substrate under investigation can adopt many different conformers with respect to the central C3-C4 bond as seen in figure 3. Within the conformers laid out in the diagram exists a subset of more isomers that differ in the exact positioning of the vinyl group relative to the rest of the molecule as opposed to just the other vinyl group. Initiative would serve to think the antiperiplanar set of isomers would be of lower energy than the gauche type isomers purely on the argument of steric repulsion between the two vinyl groups. Various conformers of Hexadiene the consist of gauche and antiperiplanr motifs were optimized and the results posted in the table below. The nomenclature of conformers are with respect to appendix 2

{| class="wikitable" border="1"
|+ Optimization of 1-5 hexadiene conformers
! placeholder !! Gauche3 !! Anti2 !! Anti1 !! Gauche(1)
|-
| Image || <jmol><jmolApplet>
<title></title>
<color>White</color>
<size>200</size>
<uploadedFileContents>Gauche3conformer.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet></jmol>|| <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet>react_anticonformer.mol2</jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_gaucheconformer.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy (Hartres) || -231.69266122 || -231.69253516 || -231.69260235 || -231.68771610
|-
| Point Group || C1 || Ci || C2 || C2
|-
| log || [https://wiki.ch.ic.ac.uk/wiki/images/c/c1/GAUCHE3CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/dd/REACT_ANTICONFORMER.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/6b/TRAILCONFORMER_TWO_ANTI1CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/REACT_GAUCHECONFORMER_oi513.LOG file]
|}

In comparison with literature reference values there is very good agreement. Interestingly, the lowest energy conformer reveals itself as a gauche type conformer which is contrary to initial predictions. Visualizing the molecular orbitals indicates favorable electronic interactions in the gauche3 setup; the two pi systems of the vinyl groups are in close enough proximity to yield a favourable in phase overlap which isn't possible in the anti conformation purely on the grounds of spacial arrangement. The gauche3 conformer serves as a balance between repulsive steric interactions and attractive molecular orbital-overlap interactions.

[[File:CompLab_Figure4_conformerorbitals.jpg|thumb|Figure 4: The orbitals HOMO of Gauche3 and Anti1 conformers on the left and right respectively of 1-5 hexadiene. As seen, there is a favourable in phase overlap between the the pi systems of the two vinyl groups]]

We can now approach the optimization of hexadiene on a different level of theory. The HF_3-21G optimized anti2 conformer of the alkene was then re-optimized under DFT_6-31G(d) level of theory. The geometrical differences arising form these two different methods of computation are summarized below.

{| class="wikitable" border="1"
|+anti conformer
|-
!colspan="4" style="text-align: left;"|[[File:anti2conformer_forrepresentingtheHF_321Glevel.png|600px]]
|-
|   ||   || HF/3-21G || B3LYP/6-31G*
|-
| rowspan="3" | Bond Lengths (Angstrom) || C1-C2 || 1.32 || 1.33
|-
| C2-C3 || 1.51 || 1.50
|-
| C3-C4 || 1.55 || 1.55
|-
| rowspan="3" | Bond Angles (Degrees) || C1-C2-C3 || 124.80 || 125.29
|-
| C2-C3-C4 || 111.34 || 112.65
|-
| C1-C2-C3-C4 || 114.63 || 118.58
|}

Being immediately observable is the increase in bond length with the B3LYP/6-31G* level of theory in comparison to HF/3-21G. Within the same level of theory however, the HF/3-21G method describes less of a distinction between bond lengths of C-C single bonds and C-C double bonds. This may also be detectable by running frequency calculations and visualizing the vibrations involving the C=C bonds in both conformers.

Frequency analysis of the B3LYP/6-31G* optimised structure was carried out. Gaussian carries out this procedure by applying the equation for force constants [[File:Force_constant_equation_oi513.png]] (where C = 1/2π) and preforming calculations to see a convergence in the force constant. The absence of imaginary frequencies would indicate that we have indeed reached a true minimum on the potential energy surface. A summary of the optimisation is given below

{| class="wikitable" border="1"
|+ Frequency calculations
! Frequency summary !! Spectrum
|-
| [[File:CompLab_SpectraofFrequencies_oi513.png]]|| [[File:CompLab SummaryofFrequencies oi513.png]]
|}

The thermodynamic properties were noted post-optimisation and printed as follows (units in Hartrees)

Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461864
Sum of electronic and thermal Enthalpies= -234.460920

=== Transition state investigations ===

==== Overview ====

Having processed information about the reaction reactants/products, we can now try to approach mining information about a different area on the potential energy surface; the transition states.

As eluded to earlier, the reaction proceeds via a 6 membered ring transition state that can exhibit a boat or chair toplogy. In this section, we aim to find these states on the potential energy surface, assess their energies and consequently determine the activation energy involved in both pathways. We will start by building and optimising the fragments of the transition states, and running further frequency/optimisation calculations.

Defining a transition state requires a degree of appreciation for the reaction mechanism being explored. In this case, the two allyl fragements that will be used need to exhibit sensible geometry to allow for a completed freq + opt calculation to be run to completion. Two different methods of computing the transition state are explored in this section. In the first method, the frozen coordinates approach is taken. This involves locking the reaction coordinate whilst minimisation of the rest of the molecule is performed (through any method of choice including Hf/3-21G, B3LYP/6-31G* levels of theory). Another optimsation can then be run which will optimize the rest of the molecule.

The second approach involves calculating the force constant along the reaction coordinate with both the number of steps along the coordinate and the direction to run the calculation both being defined by the user. In this approach however, It is important that the guess structure of the transition state is quite close to the actual case.

To start this investigation, the frozen coordinate methods were applied.

==== The Chair ====

After optimising an single allyl (CH2CHCH2) through the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/0/05/ALLYLFRAG_HF_321G_oi513.LOG here]), two of the said fragments were arranged in a chair conformation, with terminal C-C bond distance (between two fragements) set to 2.2 Å

<jmol><jmolApplet>
<title>HF/3-21G allyl fragment</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Allylfrag_HF_321g_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

This "guess" transition state was then run through an Frequency + Optimisation job (the log file of which can be located [https://wiki.ch.ic.ac.uk/wiki/images/0/0e/TSHYPOTHESIS_TRAILTWO_oi513.LOG here]) introducing the TS(Berny) optimisation method. This method works by employing the Berny algorithm. An approximate Hessian matrix (constituted by calculating second derivatives of energy) is developed using parameters of the initial structure including the valence force field. this approximation is then updated by calculating energies along the reaction pathway until a convergence is observed. Thus, the approximate matrix is a key factor in determining the success of the calculation. For most cases, using the approximate hessian serves well for the rest of the optimisation of the molecule, but in the cases where the the hessian changes dramatically, the force constant can be computed along every point of the reaction pathway. At the expense of time and computational power, the opitmisation will be able to find the local minimum.

<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

Inspection of the vibrations shows a single imaginary frequency (negative cm-1) at -817.94 cm-1 This "guess structure" method provides a reference/basis to which the frozen method can be compared with.

Imaginary frequencies are given such names due to the complex nature of their absolute values. Eigenvalues of hessian matrices correspond to squared harmonic oscillations of the normal vibration modes. thus a the square root of a negative eigenvalue gives rise a complex number with an imaginary component. Taking a simple plot of the harmonic oscillator (potential energy vs bond displacement), a negative second derivative would indicate that the geometry to which the reaction coordinate is abiding by is hitting a maximum (i.e. achieving transition state status). Thus if a transition state has been calculated, only one imaginary frequency should be as a result of the optimisation.

The frozen coordinate approach was then used to compute the transition. The (to be formed) bond between the terminal C's on both allyl fragments were strictly fixed/frozen to 2.2 Å followed by an optimisation. The log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/b/bb/TSBONDMODIFY_TCSET_COPY_TRAILONE_oi513.LOG here]. Having optimised the rest of the molecule with the mentioned bonds of interest fixed, the bonds will be accounted for in a second optimisation to which the log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/TSBONDMODIFY_TCSET_UNIDENTIFIEDDESTINATION_oi513.LOG here]

To summarize, the chair transition state has be investigated through a reference setup and an frozen coordinate setup. The table of results below give an account of the results of the two setups.

{| class="wikitable" border="1"
|+ Chair Transition State analysis
|-
| colspan="3" align="center"|[[File:CompLab_ChairTS_oi513.png]]
|-
! !! Guess TS !! Frozen TS
|-
| Terminal C-C Bond Length (Angstrom) || 2.02 || 2.02
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.39
|-
| C-C-C angle || 120.50 || 120.49
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSBondmodify_TCset_Unidentifieddestination_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==== The Boat ====

Having exhausted the chair TS, computations in the Boat conformer will be brought under investigation. In this section, more computational methods that investigate transition states will be explored. The QTS2 methods works by using user defined reactants and products and attempts to conceive new data points via interpolation such to find the transition state between them. The substrate was setup and labelled to depict reactants and product and was subsequently processed with the QTS2 method. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/c/c5/BOATTS_TWOMOLECULESETUP_SECONDTRAIL_oi513.LOG here]

Having run this initial calculation, the geometries of the reactants and products were edited to resemble that of a boat transition state. The same calculation was run again ( log file [https://wiki.ch.ic.ac.uk/wiki/images/5/53/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_oi513.LOG here]) The results of the two runs are summarized in the table below.

{| class="wikitable" border="1"
|+ Boat Transition state: QTS2 method
|-
! !! Arbitrary !! Boat-Like
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_secondtrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_properconformer_firsttrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Terminal C-C bond length (Angstrom)|| 2.02 || 2.14
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.38
|}

==== Endpiece: Comparing the Boat & Chair ====

To conclude this section of the study, the transition states will be optimised using the Intrinsic reaction coordinate (IRC) method. Arguably the defining feature of this approach is the ability to track the reaction coordinate from the transition state to a local minimum by taking minute steps along negative,steep gradients of the potential energy surface. This bears many favourable features for users to define at will namely defining how many steps to be taken in the calculation and the direction of the gradient should run from the transition state.

The IRC method was applied to the optimised chair conformer. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/a/a3/TSHYPOTHESIS_TRAILTWO_ForIRCcalculation_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_ForIRC_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

The same molecule was then further optimised to find a minimum under the HF/3-21G level of theory. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/d/d5/TSHYPOTHESIS_TRAILTWO_ForIRC_oi513.LOG here] 

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_PostIRC_Reopt.mol2</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC graphs oi513.png|thumb| figure 5: The Intrinsic Reaction Coordinates for the calculation. The convergence to a zero gradient indicates the structure optmisation has converged.]]

As seen by the the results of re-optimisation post-IRC, the conformer best represent that of the gauche2 state supported by the point group being C2. To allow activation energies to be calculated, a gauche 2 conformer was constructed and optimised under the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/5/51/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_HF312G_oi513.LOG here]) followed by the B3LYP/631G* level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/b/b8/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_REOPT_631GD_oi513.LOG here]) The thermochemical data can then be retrieved and be used as the reactants on the reaction coordinate pathway. Thus the difference in energy between the gauche2 conformer and the boat and chair transition states can be calculated

Lastly, optmised chair and boat structures were re-optimised under the a higher level of theory (B3LYP/6-31G*) with the resultant log files presented [https://wiki.ch.ic.ac.uk/wiki/images/3/34/TSHYPOTHESIS_TRAILTWO_ChairTS_631GdOpt_oi513.LOG here] and [https://wiki.ch.ic.ac.uk/wiki/images/5/5e/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_631Gd_reopt.LOG there] respectively

== The Diels Alder Cycloaddition: Computational Investigations ==

=== Overview ===

=== Simple Systems: S-cis butadiene and ethene ===

As an introduction to a cycloaddition, the reaction between ethene and butadiene was investigated.
setting the two vinyl protons in the same plane (i.e C1C2C3C4 dihedral angle = 0), the molecule was optmised under the Semi empirical am 1 method. Similarly, a molecule of cis-butadiene was optimised. The table below shows the results of optimisation

{| class="wikitable" border="1"
! !! Ethene !! S-cis butadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ethene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cisbutadiene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Point Group || C2v || d2h
|-
| HOMO || [[File:HOMO_ethene_oi513.png]] || [[File:HOMO_butadiene.png]]
|-
| LUMO || [[File:LUMO_Ethene_oi513.png]] || [[File:LUMO_butadiene_oi513.png]]
|-
| LOG files || [https://wiki.ch.ic.ac.uk/wiki/images/f/fa/ETHENE_OPT_SEMIEM_AM1_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/64/CISBUTADIENE_OPT_SEMIEM_AM1_T1_oi513.LOG file]
|}

following reactant optimisation,the fragments were arranged into a guess transition state (using the same concepts explored in the cope rearrangement investigations. The terminal Carbons on each fragment was fixed to be 2.2 angstrom apart. The resultant TS structure had a single imaginary frequency confirming formation of a transition state. The log file for optmisation can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/UNDOCUMETEDTS_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents></uploadedFileContents>
</jmolApplet>UndocumetedTS_oi513.mol2</jmol>

[[File:HOMO_firstDA_oi513.png]|thumb| figure 6: HOMO of the Diels Alder between the two subtrates.]
[[File:LUMO_firstDA_oi513.png]|thumb| figure 7: LUMO of Diels Alder between the two subtrates]

=== Complex systems: Maelic anydride and Cyclohexadiene ===

Using the same concepts explored in the cycloaddition investigations with the two unfunctionalised alkenes, the properties of the Diels Alder reaction between Maleic anhydride and cyclohexa-1,3-diene was investigated. As we will see, the regiochemistry of the reaction comes into play as the arrangement of the two subtrates prior to bond making/breaking gives rise to two different trasnition states (an exo and an endo state). Obtaining Molecular orbital data for of the two states will account for differences in the observed energies of the transition states.

the two reactants were optimised under the Semi empirical am1 method. The results of the calculations are presented in the table below

{| class="wikitable" border="1"
Optmising the reactants
! !! Maelic anhydride !! Cyclohexadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>MAnydride_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cyclobutadiene_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|Point group || C2 || C1
|-
|HOMO || [[File:HOMO_MAnhydride_oi513.png]] || [[File:HOMO_Cylodiene_oi513.png]]
|-
|LUMO || [[File:LUMO_MAnhydride_oi513.png]] || [[File:LUMO_Cyclodiene_oi513.png]]
|-
|LOG || [https://wiki.ch.ic.ac.uk/wiki/images/3/31/MANYDRIDE_OPT_SEMEM_AM1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/7/7a/CYCLOBUTADIENE_OPT_SEMEM_AM1_oi513.LOG file]
|}

As per routine, a guess transition structure had to be constructed using the optimised fragments. In this case, we have stereo-distinction between two possible transition states, and exo form and an endo form.

For both endo and exo forms, terminal C-C bond distances were set and fixed to 2.2 Angstrom and the molecule adapted to represent a postulated transition state fro the respective forms. an optimisation + frequency calculation was carried out an the results given below

{| class="wikitable" border="1"
! !! Exo transition state !! Endo Transition state
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess3_Exo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess_Endo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|HOMO || [[File:HOMO_secondDA_Exo_oi513.png]] || [[File:HOMO_secondDA_Endo_oi513.png]]
|-
|LUMO || [[File:LUMO_SecondDA_Exo_oi513.png]] || [[File:LUMO_secondDA_Endo_oi513.png]]
|-
Log files || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/TSGUESS3_EXO_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/9/90/TSGUESS_ENDO_T1_oi513.LOG file]
|}

Geometry data for the two states was also collected. The results are presented below

{| class="wikitable" border="1"
! colspan="2"|Exo transition State !! ! colspan="3"|Endo Transition state
|-
| colspan="2"|[[File:NumberingforExotransitionstate_oi513.png]] || colspan="2"|[[File:NumberingofEndoTransitionstate_oi513.png]]
|-
|bond || values (Angstrom)|| bond || values (Angstrom)
|-
| C1-C2 || 1.41 || C1-C2 || 1.49
|-
| C2-C3 || 1.49 || C4-C5 || 1.49
|-
| C5-C1 || 1.49 || C5-C1 || 1.41
|-
| C2-C9 || 2.17 || C1-C9 || 2.16
|-
| C1-C6 || 2.17 || C5-C6 || 2.16
|-
| C6-C7 || 1.34 || C6-C7 || 1.49
|-
| C7-C8 || 1.40 || C7-C8 || 1.52
|-
| C8-C9 || 1.39 || C8-C9 || 1.49
|-
| C9-C10 || 1.49 || C9-C10 || 1.39
|-
| C10-C11 || 1.52 || C10-C11 || 1.40
|-
| C11-C6 || 1.49 || C11-C6 || 1.49
|}
Lastly, thermochemical data was collated and the results given below

Exo

Sum of electronic and zero-point Energies= 0.134882
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.0991180.099118

Endo

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

To end this section on the more complex systems, the overall energy of the Endo transition state is lower than that of the exo (refer to the log file for the energies). This is due to the so called secondary orbital overlap effect. Looking at the image of the HOMO in the endo state there is possible overlap between orbitals on the Oxygen including the lone pairs and the pi system on the cyclodiene

== References ==

[1] K. Takao, R. Munakata, K. Tadano, Chem. Rev. 2005, 105, 4779−4807
[2] K. N. Houk, J. Am. Chem. Soc., 1973, 95, 4092–4094
[3] R. B. Woodward, R. Hoffman, J. Am. Chem. Soc., 1965, 87, 395–397
[4] M. Manoharan, F. De Proft, P. Geerlings, J. Org. Chem., 2000, 65, 7971–7976
[5] M. Svensson, S. Humbel, R. D. J. Froese, T. Matsubara, S. Seiber, K. Morokuma, J. Phys. Chem., 1996, 100, pp 19357–19363

Rep:Mod:Peebo

2015-12-18T11:20:23Z

Oi513: /* The Diels Alder Cycloaddition: Computational Investigations */

== Introduction ==

=== Overview ===
Fundamental to organic chemistry are pericyclic reactions that involve concerted movement of electrons through a cyclic transition state. Cycloadditions, a subset of pericyclic reactions, serve as a essential synthetic tool for organic chemists as a basis for accessing more complex structures in, for example, total synthesis of natural products [1]. In addition, sigmatropic rearrangements, and electrocyclic reactions are also a set of important pericyclic reactions that see Δσ 0 or ±1 respectively. For Diels alder and ene reactions, the initial arrangement of the fragments is brought into question when trying to understand the stereochemical outcome of the reaction. Other than these geometric factors, the frontier orbitals of the two fragments contain valuable information into predicting whether the two reactants may proceed to reach a product[2].

Robert Burns Woodward and Roald Hoffman established rules to explain whether a given pericyclic reaction may be thermally or photochemically allowed to give the said product. Naturally incorporated in their approach is considerations of the molecular orbitals involved in the reaction, the number of electrons, and the symmetry with respect to the connectivity between the two fragments. First applied to electrocyclic reactions [3], the two would then go on to publish more papers to fully develop their rules setting a universal foundation for understanding these class of reactions

Given the wealth factors that contribute towards going from reactants --> products, it is of the best interests to synthetic chemists to understand the mechanistic basis behind the reaction and therefore ,for example, the observed stereochemistry as opposed to whether a given reaction may be allowed or forbidden (in conjunction with Woodward-Hoffman rules). As such, computational methods into investigating diels alder reaction pathways have come to light[4][5] and have shown to provide insight into the optimal positioning of fragments and the structure and energy of Transition states. Studying transition states in particular are a huge advantage in computational studies; through this medium, calculations on energies of these states can be probes that would otherwise be immeasurable due to the fleeting nature of the transition state.

=== Experimental Aims ===
In this exercise, we first investigate the energies of varying 1-5 hexadiene conformers and investigate the possible cyclic transition states whilst it undergoes the cope rearrangement using the Hartree-Fock/3-21G and B3LYP/6-31G(d) levels of theory in addition to exploring Transition state optimization methods QTS2 and TS(Berny). Using similar methods, we then go on to develop our discussion of transition states by through investigating the regioselectivity of the Diels Alder reaction between maelic anhydride and 1-3 cyclohexadiene including molecular orbital interactions.

=== Brief note: Computational Methods ===

In this investigation, we explore different levels of theory to apply alongside our calculations as each have both advantageous features, and their respective drawbacks. Hatree fock method is used to determine both energies and quantum mechanical wavefunction of a multi-body system in state that has its probability density (position of the body in question) independent of time (i.e a stationary state). Amongst the appreciable number of approximations made by this method, the assumption that many electron wavefunction of the body in question will take the form of a just an isolated determinant (slater determinant) derived from a single electron wavefunction. Whist in theory this is entirely possible through linear combination of atomic orbitals, this naturally causes this approach to overlook the replusive interactions between the electrons in the system thus producing energies that are overestimated.

By virtue The Hohenberg-Kohn Theorems, the total energy of a ground state is exclusively dependent on electron density and distribution. Focusing in on this aspect and overlooking the electronic wavefunctions give rise to density functional theory. This method will aim to minimize energy via changes in electron density in a body. In addition to this, Electron correlations are taken into account and the mean field approximation is relaxed However, one key drawback in this theory is that it is not certain that using a more complicated basis set my necessarily produce a more accurate answer; the theory is not variational whereas the HF theory actively is.

== The Cope rearrangement: Computational Investigations ==

=== Overview ===

1-5 hexadiene provides a relatively simple system to observe a cope rearrangement. Through Woodward-Hoffmann analysis, we see that this [3,3] sigmatropic rearrangement is thermally allowed by virtue of the equation (4q + 2)s + (4r)a. Figure 2 provides one way in which the reaction can proceed via these rules with a single σ2s component and two π2a components. [[File:Computation_Coperearrangement.jpg|thumb|Figure 1: An overview of the cope rearrangement going through the cyclic 6M transition state.]]
During the concerted formation/dissociation of bonds, the transition state resembles that of a six membered ring which can exhibit a chair or boat topology (in line with the conformers of cyclohexane) These transition states represent energy maxima on the reaction pathway from reactants to products. On the other hand, 1-5 hexadiene exists in many conformers representing an energy minimum. In the following section, we obtain optimal structures for the diene on different levels of theory followed by locating the position of the TS on the potential energy surface. In doing this, we can appropriately deduce the activation energy involve in the cope rearrangement through the chair TS and boat TS pathways.

[[File:CompLab_Figure3_hexadieneconformers.jpg|thumb|Figure 3: Newman projections for hexadiene showing antiperiplanar and gauche arrangements of vinyl groups.150px]]
[[File:Complab_copeWoodwardHoffman.jpg|thumb|Figure 2: Woodward-Hoffmann analysis of the [3,3] sigmatropic rearrangement. the orbitals can "connect" through an suprafacial or antarafacial manner to make or break the bonds in the product.]]

=== Optimizing reactants and products ===

The substrate under investigation can adopt many different conformers with respect to the central C3-C4 bond as seen in figure 3. Within the conformers laid out in the diagram exists a subset of more isomers that differ in the exact positioning of the vinyl group relative to the rest of the molecule as opposed to just the other vinyl group. Initiative would serve to think the antiperiplanar set of isomers would be of lower energy than the gauche type isomers purely on the argument of steric repulsion between the two vinyl groups. Various conformers of Hexadiene the consist of gauche and antiperiplanr motifs were optimized and the results posted in the table below. The nomenclature of conformers are with respect to appendix 2

{| class="wikitable" border="1"
|+ Optimization of 1-5 hexadiene conformers
! placeholder !! Gauche3 !! Anti2 !! Anti1 !! Gauche(1)
|-
| Image || <jmol><jmolApplet>
<title></title>
<color>White</color>
<size>200</size>
<uploadedFileContents>Gauche3conformer.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet></jmol>|| <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet>react_anticonformer.mol2</jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_gaucheconformer.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy (Hartres) || -231.69266122 || -231.69253516 || -231.69260235 || -231.68771610
|-
| Point Group || C1 || Ci || C2 || C2
|-
| log || [https://wiki.ch.ic.ac.uk/wiki/images/c/c1/GAUCHE3CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/dd/REACT_ANTICONFORMER.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/6b/TRAILCONFORMER_TWO_ANTI1CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/REACT_GAUCHECONFORMER_oi513.LOG file]
|}

In comparison with literature reference values there is very good agreement. Interestingly, the lowest energy conformer reveals itself as a gauche type conformer which is contrary to initial predictions. Visualizing the molecular orbitals indicates favorable electronic interactions in the gauche3 setup; the two pi systems of the vinyl groups are in close enough proximity to yield a favourable in phase overlap which isn't possible in the anti conformation purely on the grounds of spacial arrangement. The gauche3 conformer serves as a balance between repulsive steric interactions and attractive molecular orbital-overlap interactions.

[[File:CompLab_Figure4_conformerorbitals.jpg|thumb|Figure 4: The orbitals HOMO of Gauche3 and Anti1 conformers on the left and right respectively of 1-5 hexadiene. As seen, there is a favourable in phase overlap between the the pi systems of the two vinyl groups]]

We can now approach the optimization of hexadiene on a different level of theory. The HF_3-21G optimized anti2 conformer of the alkene was then re-optimized under DFT_6-31G(d) level of theory. The geometrical differences arising form these two different methods of computation are summarized below.

{| class="wikitable" border="1"
|+anti conformer
|-
!colspan="4" style="text-align: left;"|[[File:anti2conformer_forrepresentingtheHF_321Glevel.png|600px]]
|-
|   ||   || HF/3-21G || B3LYP/6-31G*
|-
| rowspan="3" | Bond Lengths (Angstrom) || C1-C2 || 1.32 || 1.33
|-
| C2-C3 || 1.51 || 1.50
|-
| C3-C4 || 1.55 || 1.55
|-
| rowspan="3" | Bond Angles (Degrees) || C1-C2-C3 || 124.80 || 125.29
|-
| C2-C3-C4 || 111.34 || 112.65
|-
| C1-C2-C3-C4 || 114.63 || 118.58
|}

Being immediately observable is the increase in bond length with the B3LYP/6-31G* level of theory in comparison to HF/3-21G. Within the same level of theory however, the HF/3-21G method describes less of a distinction between bond lengths of C-C single bonds and C-C double bonds. This may also be detectable by running frequency calculations and visualizing the vibrations involving the C=C bonds in both conformers.

Frequency analysis of the B3LYP/6-31G* optimised structure was carried out. Gaussian carries out this procedure by applying the equation for force constants [[File:Force_constant_equation_oi513.png]] (where C = 1/2π) and preforming calculations to see a convergence in the force constant. The absence of imaginary frequencies would indicate that we have indeed reached a true minimum on the potential energy surface. A summary of the optimisation is given below

{| class="wikitable" border="1"
|+ Frequency calculations
! Frequency summary !! Spectrum
|-
| [[File:CompLab_SpectraofFrequencies_oi513.png]]|| [[File:CompLab SummaryofFrequencies oi513.png]]
|}

The thermodynamic properties were noted post-optimisation and printed as follows (units in Hartrees)

Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461864
Sum of electronic and thermal Enthalpies= -234.460920

=== Transition state investigations ===

==== Overview ====

Having processed information about the reaction reactants/products, we can now try to approach mining information about a different area on the potential energy surface; the transition states.

As eluded to earlier, the reaction proceeds via a 6 membered ring transition state that can exhibit a boat or chair toplogy. In this section, we aim to find these states on the potential energy surface, assess their energies and consequently determine the activation energy involved in both pathways. We will start by building and optimising the fragments of the transition states, and running further frequency/optimisation calculations.

Defining a transition state requires a degree of appreciation for the reaction mechanism being explored. In this case, the two allyl fragements that will be used need to exhibit sensible geometry to allow for a completed freq + opt calculation to be run to completion. Two different methods of computing the transition state are explored in this section. In the first method, the frozen coordinates approach is taken. This involves locking the reaction coordinate whilst minimisation of the rest of the molecule is performed (through any method of choice including Hf/3-21G, B3LYP/6-31G* levels of theory). Another optimsation can then be run which will optimize the rest of the molecule.

The second approach involves calculating the force constant along the reaction coordinate with both the number of steps along the coordinate and the direction to run the calculation both being defined by the user. In this approach however, It is important that the guess structure of the transition state is quite close to the actual case.

To start this investigation, the frozen coordinate methods were applied.

==== The Chair ====

After optimising an single allyl (CH2CHCH2) through the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/0/05/ALLYLFRAG_HF_321G_oi513.LOG here]), two of the said fragments were arranged in a chair conformation, with terminal C-C bond distance (between two fragements) set to 2.2 Å

<jmol><jmolApplet>
<title>HF/3-21G allyl fragment</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Allylfrag_HF_321g_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

This "guess" transition state was then run through an Frequency + Optimisation job (the log file of which can be located [https://wiki.ch.ic.ac.uk/wiki/images/0/0e/TSHYPOTHESIS_TRAILTWO_oi513.LOG here]) introducing the TS(Berny) optimisation method. This method works by employing the Berny algorithm. An approximate Hessian matrix (constituted by calculating second derivatives of energy) is developed using parameters of the initial structure including the valence force field. this approximation is then updated by calculating energies along the reaction pathway until a convergence is observed. Thus, the approximate matrix is a key factor in determining the success of the calculation. For most cases, using the approximate hessian serves well for the rest of the optimisation of the molecule, but in the cases where the the hessian changes dramatically, the force constant can be computed along every point of the reaction pathway. At the expense of time and computational power, the opitmisation will be able to find the local minimum.

<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

Inspection of the vibrations shows a single imaginary frequency (negative cm-1) at -817.94 cm-1 This "guess structure" method provides a reference/basis to which the frozen method can be compared with.

Imaginary frequencies are given such names due to the complex nature of their absolute values. Eigenvalues of hessian matrices correspond to squared harmonic oscillations of the normal vibration modes. thus a the square root of a negative eigenvalue gives rise a complex number with an imaginary component. Taking a simple plot of the harmonic oscillator (potential energy vs bond displacement), a negative second derivative would indicate that the geometry to which the reaction coordinate is abiding by is hitting a maximum (i.e. achieving transition state status). Thus if a transition state has been calculated, only one imaginary frequency should be as a result of the optimisation.

The frozen coordinate approach was then used to compute the transition. The (to be formed) bond between the terminal C's on both allyl fragments were strictly fixed/frozen to 2.2 Å followed by an optimisation. The log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/b/bb/TSBONDMODIFY_TCSET_COPY_TRAILONE_oi513.LOG here]. Having optimised the rest of the molecule with the mentioned bonds of interest fixed, the bonds will be accounted for in a second optimisation to which the log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/TSBONDMODIFY_TCSET_UNIDENTIFIEDDESTINATION_oi513.LOG here]

To summarize, the chair transition state has be investigated through a reference setup and an frozen coordinate setup. The table of results below give an account of the results of the two setups.

{| class="wikitable" border="1"
|+ Chair Transition State analysis
|-
| colspan="3" align="center"|[[File:CompLab_ChairTS_oi513.png]]
|-
! !! Guess TS !! Frozen TS
|-
| Terminal C-C Bond Length (Angstrom) || 2.02 || 2.02
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.39
|-
| C-C-C angle || 120.50 || 120.49
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSBondmodify_TCset_Unidentifieddestination_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==== The Boat ====

Having exhausted the chair TS, computations in the Boat conformer will be brought under investigation. In this section, more computational methods that investigate transition states will be explored. The QTS2 methods works by using user defined reactants and products and attempts to conceive new data points via interpolation such to find the transition state between them. The substrate was setup and labelled to depict reactants and product and was subsequently processed with the QTS2 method. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/c/c5/BOATTS_TWOMOLECULESETUP_SECONDTRAIL_oi513.LOG here]

Having run this initial calculation, the geometries of the reactants and products were edited to resemble that of a boat transition state. The same calculation was run again ( log file [https://wiki.ch.ic.ac.uk/wiki/images/5/53/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_oi513.LOG here]) The results of the two runs are summarized in the table below.

{| class="wikitable" border="1"
|+ Boat Transition state: QTS2 method
|-
! !! Arbitrary !! Boat-Like
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_secondtrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_properconformer_firsttrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Terminal C-C bond length (Angstrom)|| 2.02 || 2.14
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.38
|}

==== Endpiece: Comparing the Boat & Chair ====

To conclude this section of the study, the transition states will be optimised using the Intrinsic reaction coordinate (IRC) method. Arguably the defining feature of this approach is the ability to track the reaction coordinate from the transition state to a local minimum by taking minute steps along negative,steep gradients of the potential energy surface. This bears many favourable features for users to define at will namely defining how many steps to be taken in the calculation and the direction of the gradient should run from the transition state.

The IRC method was applied to the optimised chair conformer. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/a/a3/TSHYPOTHESIS_TRAILTWO_ForIRCcalculation_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_ForIRC_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

The same molecule was then further optimised to find a minimum under the HF/3-21G level of theory. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/d/d5/TSHYPOTHESIS_TRAILTWO_ForIRC_oi513.LOG here] 

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_PostIRC_Reopt.mol2</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC graphs oi513.png|thumb| figure 5: The Intrinsic Reaction Coordinates for the calculation. The convergence to a zero gradient indicates the structure optmisation has converged.]]

As seen by the the results of re-optimisation post-IRC, the conformer best represent that of the gauche2 state supported by the point group being C2. To allow activation energies to be calculated, a gauche 2 conformer was constructed and optimised under the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/5/51/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_HF312G_oi513.LOG here]) followed by the B3LYP/631G* level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/b/b8/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_REOPT_631GD_oi513.LOG here]) The thermochemical data can then be retrieved and be used as the reactants on the reaction coordinate pathway. Thus the difference in energy between the gauche2 conformer and the boat and chair transition states can be calculated

Lastly, optmised chair and boat structures were re-optimised under the a higher level of theory (B3LYP/6-31G*) with the resultant log files presented [https://wiki.ch.ic.ac.uk/wiki/images/3/34/TSHYPOTHESIS_TRAILTWO_ChairTS_631GdOpt_oi513.LOG here] and [https://wiki.ch.ic.ac.uk/wiki/images/5/5e/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_631Gd_reopt.LOG there] respectively

== The Diels Alder Cycloaddition: Computational Investigations ==

=== Overview ===

=== Simple Systems: S-cis butadiene and ethene ===

As an introduction to a cycloaddition, the reaction between ethene and butadiene was investigated.
setting the two vinyl protons in the same plane (i.e C1C2C3C4 dihedral angle = 0), the molecule was optmised under the Semi empirical am 1 method. Similarly, a molecule of cis-butadiene was optimised. The table below shows the results of optimisation

{| class="wikitable" border="1"
! !! Ethene !! S-cis butadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ethene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cisbutadiene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Point Group || C2v || d2h
|-
| HOMO || [[File:HOMO_ethene_oi513.png]] || [[File:HOMO_butadiene.png]]
|-
| LUMO || [[File:LUMO_Ethene_oi513.png]] || [[File:LUMO_butadiene_oi513.png]]
|-
| LOG files || [https://wiki.ch.ic.ac.uk/wiki/images/f/fa/ETHENE_OPT_SEMIEM_AM1_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/64/CISBUTADIENE_OPT_SEMIEM_AM1_T1_oi513.LOG file]
|}

following reactant optimisation,the fragments were arranged into a guess transition state (using the same concepts explored in the cope rearrangement investigations. The terminal Carbons on each fragment was fixed to be 2.2 angstrom apart. The resultant TS structure had a single imaginary frequency confirming formation of a transition state. The log file for optmisation can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/UNDOCUMETEDTS_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents></uploadedFileContents>
</jmolApplet>UndocumetedTS_oi513.mol2</jmol>

[[File:HOMO_firstDA_oi513.png]|thumb| figure 6: HOMO of the Diels Alder between the two subtrates.]
[[File:LUMO_firstDA_oi513.png]|thumb| figure 7: LUMO of Diels Alder between the two subtrates]

=== Complex systems: Maelic anydride and Cyclohexadiene ===

Using the same concepts explored in the cycloaddition investigations with the two unfunctionalised alkenes, the properties of the Diels Alder reaction between Maleic anhydride and cyclohexa-1,3-diene was investigated. As we will see, the regiochemistry of the reaction comes into play as the arrangement of the two subtrates prior to bond making/breaking gives rise to two different trasnition states (an exo and an endo state). Obtaining Molecular orbital data for of the two states will account for differences in the observed energies of the transition states.

the two reactants were optimised under the Semi empirical am1 method. The results of the calculations are presented in the table below

{| class="wikitable" border="1"
Optmising the reactants
! !! Maelic anhydride !! Cyclohexadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>MAnydride_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cyclobutadiene_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|Point group || C2 || C1
|-
|HOMO || [[File:HOMO_MAnhydride_oi513.png]] || [[File:HOMO_Cylodiene_oi513.png]]
|-
|LUMO || [[File:LUMO_MAnhydride_oi513.png]] || [[File:LUMO_Cyclodiene_oi513.png]]
|-
|LOG || [https://wiki.ch.ic.ac.uk/wiki/images/3/31/MANYDRIDE_OPT_SEMEM_AM1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/7/7a/CYCLOBUTADIENE_OPT_SEMEM_AM1_oi513.LOG file]
|}

As per routine, a guess transition structure had to be constructed using the optimised fragments. In this case, we have stereo-distinction between two possible transition states, and exo form and an endo form.

For both endo and exo forms, terminal C-C bond distances were set and fixed to 2.2 Angstrom and the molecule adapted to represent a postulated transition state fro the respective forms. an optimisation + frequency calculation was carried out an the results given below

{| class="wikitable" border="1"
! !! Exo transition state !! Endo Transition state
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess3_Exo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess_Endo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|HOMO || [[File:HOMO_secondDA_Exo_oi513.png]] || [[File:HOMO_secondDA_Endo_oi513.png]]
|-
|LUMO || [[File:LUMO_SecondDA_Exo_oi513.png]] || [[File:LUMO_secondDA_Endo_oi513.png]]
|-
|Imaginary frequency || cell || cell
|-
Log files || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/TSGUESS3_EXO_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/9/90/TSGUESS_ENDO_T1_oi513.LOG file]
|}

Geometry data for the two states was also collected. The results are presented below

{| class="wikitable" border="1"
! colspan="2"|Exo transition State !! ! colspan="3"|Endo Transition state
|-
| colspan="2"|[[File:NumberingforExotransitionstate_oi513.png]] || colspan="2"|[[File:NumberingofEndoTransitionstate_oi513.png]]
|-
|bond || values || bond || values
|-
| C1-C2 || 1.41 || C1-C2 || 1.49
|-
| C2-C3 || 1.49 || C4-C5 || 1.49
|-
| C5-C1 || 1.49 || C5-C1 || 1.41
|-
| C2-C9 || 2.17 || C1-C9 || 2.16
|-
| C1-C6 || 2.17 || C5-C6 || 2.16
|-
| C6-C7 || 1.34 || C6-C7 || 1.49
|-
| C7-C8 || 1.40 || C7-C8 || 1.52
|-
| C8-C9 || 1.39 || C8-C9 || 1.49
|-
| C9-C10 || 1.49 || C9-C10 || 1.39
|-
| C10-C11 || 1.52 || C10-C11 || 1.40
|-
| C11-C6 || 1.49 || C11-C6 || 1.49
|}
Lastly, thermochemical data was collated and the results given below

Exo

Sum of electronic and zero-point Energies= 0.134882
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.0991180.099118

Endo

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

Rep:Mod:Peebo

2015-12-18T11:18:53Z

Oi513: /* The Diels Alder Cycloaddition: Computational Investigations */

== Introduction ==

=== Overview ===
Fundamental to organic chemistry are pericyclic reactions that involve concerted movement of electrons through a cyclic transition state. Cycloadditions, a subset of pericyclic reactions, serve as a essential synthetic tool for organic chemists as a basis for accessing more complex structures in, for example, total synthesis of natural products [1]. In addition, sigmatropic rearrangements, and electrocyclic reactions are also a set of important pericyclic reactions that see Δσ 0 or ±1 respectively. For Diels alder and ene reactions, the initial arrangement of the fragments is brought into question when trying to understand the stereochemical outcome of the reaction. Other than these geometric factors, the frontier orbitals of the two fragments contain valuable information into predicting whether the two reactants may proceed to reach a product[2].

Robert Burns Woodward and Roald Hoffman established rules to explain whether a given pericyclic reaction may be thermally or photochemically allowed to give the said product. Naturally incorporated in their approach is considerations of the molecular orbitals involved in the reaction, the number of electrons, and the symmetry with respect to the connectivity between the two fragments. First applied to electrocyclic reactions [3], the two would then go on to publish more papers to fully develop their rules setting a universal foundation for understanding these class of reactions

Given the wealth factors that contribute towards going from reactants --> products, it is of the best interests to synthetic chemists to understand the mechanistic basis behind the reaction and therefore ,for example, the observed stereochemistry as opposed to whether a given reaction may be allowed or forbidden (in conjunction with Woodward-Hoffman rules). As such, computational methods into investigating diels alder reaction pathways have come to light[4][5] and have shown to provide insight into the optimal positioning of fragments and the structure and energy of Transition states. Studying transition states in particular are a huge advantage in computational studies; through this medium, calculations on energies of these states can be probes that would otherwise be immeasurable due to the fleeting nature of the transition state.

=== Experimental Aims ===
In this exercise, we first investigate the energies of varying 1-5 hexadiene conformers and investigate the possible cyclic transition states whilst it undergoes the cope rearrangement using the Hartree-Fock/3-21G and B3LYP/6-31G(d) levels of theory in addition to exploring Transition state optimization methods QTS2 and TS(Berny). Using similar methods, we then go on to develop our discussion of transition states by through investigating the regioselectivity of the Diels Alder reaction between maelic anhydride and 1-3 cyclohexadiene including molecular orbital interactions.

=== Brief note: Computational Methods ===

In this investigation, we explore different levels of theory to apply alongside our calculations as each have both advantageous features, and their respective drawbacks. Hatree fock method is used to determine both energies and quantum mechanical wavefunction of a multi-body system in state that has its probability density (position of the body in question) independent of time (i.e a stationary state). Amongst the appreciable number of approximations made by this method, the assumption that many electron wavefunction of the body in question will take the form of a just an isolated determinant (slater determinant) derived from a single electron wavefunction. Whist in theory this is entirely possible through linear combination of atomic orbitals, this naturally causes this approach to overlook the replusive interactions between the electrons in the system thus producing energies that are overestimated.

By virtue The Hohenberg-Kohn Theorems, the total energy of a ground state is exclusively dependent on electron density and distribution. Focusing in on this aspect and overlooking the electronic wavefunctions give rise to density functional theory. This method will aim to minimize energy via changes in electron density in a body. In addition to this, Electron correlations are taken into account and the mean field approximation is relaxed However, one key drawback in this theory is that it is not certain that using a more complicated basis set my necessarily produce a more accurate answer; the theory is not variational whereas the HF theory actively is.

== The Cope rearrangement: Computational Investigations ==

=== Overview ===

1-5 hexadiene provides a relatively simple system to observe a cope rearrangement. Through Woodward-Hoffmann analysis, we see that this [3,3] sigmatropic rearrangement is thermally allowed by virtue of the equation (4q + 2)s + (4r)a. Figure 2 provides one way in which the reaction can proceed via these rules with a single σ2s component and two π2a components. [[File:Computation_Coperearrangement.jpg|thumb|Figure 1: An overview of the cope rearrangement going through the cyclic 6M transition state.]]
During the concerted formation/dissociation of bonds, the transition state resembles that of a six membered ring which can exhibit a chair or boat topology (in line with the conformers of cyclohexane) These transition states represent energy maxima on the reaction pathway from reactants to products. On the other hand, 1-5 hexadiene exists in many conformers representing an energy minimum. In the following section, we obtain optimal structures for the diene on different levels of theory followed by locating the position of the TS on the potential energy surface. In doing this, we can appropriately deduce the activation energy involve in the cope rearrangement through the chair TS and boat TS pathways.

[[File:CompLab_Figure3_hexadieneconformers.jpg|thumb|Figure 3: Newman projections for hexadiene showing antiperiplanar and gauche arrangements of vinyl groups.150px]]
[[File:Complab_copeWoodwardHoffman.jpg|thumb|Figure 2: Woodward-Hoffmann analysis of the [3,3] sigmatropic rearrangement. the orbitals can "connect" through an suprafacial or antarafacial manner to make or break the bonds in the product.]]

=== Optimizing reactants and products ===

The substrate under investigation can adopt many different conformers with respect to the central C3-C4 bond as seen in figure 3. Within the conformers laid out in the diagram exists a subset of more isomers that differ in the exact positioning of the vinyl group relative to the rest of the molecule as opposed to just the other vinyl group. Initiative would serve to think the antiperiplanar set of isomers would be of lower energy than the gauche type isomers purely on the argument of steric repulsion between the two vinyl groups. Various conformers of Hexadiene the consist of gauche and antiperiplanr motifs were optimized and the results posted in the table below. The nomenclature of conformers are with respect to appendix 2

{| class="wikitable" border="1"
|+ Optimization of 1-5 hexadiene conformers
! placeholder !! Gauche3 !! Anti2 !! Anti1 !! Gauche(1)
|-
| Image || <jmol><jmolApplet>
<title></title>
<color>White</color>
<size>200</size>
<uploadedFileContents>Gauche3conformer.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet></jmol>|| <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet>react_anticonformer.mol2</jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_gaucheconformer.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy (Hartres) || -231.69266122 || -231.69253516 || -231.69260235 || -231.68771610
|-
| Point Group || C1 || Ci || C2 || C2
|-
| log || [https://wiki.ch.ic.ac.uk/wiki/images/c/c1/GAUCHE3CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/dd/REACT_ANTICONFORMER.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/6b/TRAILCONFORMER_TWO_ANTI1CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/REACT_GAUCHECONFORMER_oi513.LOG file]
|}

In comparison with literature reference values there is very good agreement. Interestingly, the lowest energy conformer reveals itself as a gauche type conformer which is contrary to initial predictions. Visualizing the molecular orbitals indicates favorable electronic interactions in the gauche3 setup; the two pi systems of the vinyl groups are in close enough proximity to yield a favourable in phase overlap which isn't possible in the anti conformation purely on the grounds of spacial arrangement. The gauche3 conformer serves as a balance between repulsive steric interactions and attractive molecular orbital-overlap interactions.

[[File:CompLab_Figure4_conformerorbitals.jpg|thumb|Figure 4: The orbitals HOMO of Gauche3 and Anti1 conformers on the left and right respectively of 1-5 hexadiene. As seen, there is a favourable in phase overlap between the the pi systems of the two vinyl groups]]

We can now approach the optimization of hexadiene on a different level of theory. The HF_3-21G optimized anti2 conformer of the alkene was then re-optimized under DFT_6-31G(d) level of theory. The geometrical differences arising form these two different methods of computation are summarized below.

{| class="wikitable" border="1"
|+anti conformer
|-
!colspan="4" style="text-align: left;"|[[File:anti2conformer_forrepresentingtheHF_321Glevel.png|600px]]
|-
|   ||   || HF/3-21G || B3LYP/6-31G*
|-
| rowspan="3" | Bond Lengths (Angstrom) || C1-C2 || 1.32 || 1.33
|-
| C2-C3 || 1.51 || 1.50
|-
| C3-C4 || 1.55 || 1.55
|-
| rowspan="3" | Bond Angles (Degrees) || C1-C2-C3 || 124.80 || 125.29
|-
| C2-C3-C4 || 111.34 || 112.65
|-
| C1-C2-C3-C4 || 114.63 || 118.58
|}

Being immediately observable is the increase in bond length with the B3LYP/6-31G* level of theory in comparison to HF/3-21G. Within the same level of theory however, the HF/3-21G method describes less of a distinction between bond lengths of C-C single bonds and C-C double bonds. This may also be detectable by running frequency calculations and visualizing the vibrations involving the C=C bonds in both conformers.

Frequency analysis of the B3LYP/6-31G* optimised structure was carried out. Gaussian carries out this procedure by applying the equation for force constants [[File:Force_constant_equation_oi513.png]] (where C = 1/2π) and preforming calculations to see a convergence in the force constant. The absence of imaginary frequencies would indicate that we have indeed reached a true minimum on the potential energy surface. A summary of the optimisation is given below

{| class="wikitable" border="1"
|+ Frequency calculations
! Frequency summary !! Spectrum
|-
| [[File:CompLab_SpectraofFrequencies_oi513.png]]|| [[File:CompLab SummaryofFrequencies oi513.png]]
|}

The thermodynamic properties were noted post-optimisation and printed as follows (units in Hartrees)

Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461864
Sum of electronic and thermal Enthalpies= -234.460920

=== Transition state investigations ===

==== Overview ====

Having processed information about the reaction reactants/products, we can now try to approach mining information about a different area on the potential energy surface; the transition states.

As eluded to earlier, the reaction proceeds via a 6 membered ring transition state that can exhibit a boat or chair toplogy. In this section, we aim to find these states on the potential energy surface, assess their energies and consequently determine the activation energy involved in both pathways. We will start by building and optimising the fragments of the transition states, and running further frequency/optimisation calculations.

Defining a transition state requires a degree of appreciation for the reaction mechanism being explored. In this case, the two allyl fragements that will be used need to exhibit sensible geometry to allow for a completed freq + opt calculation to be run to completion. Two different methods of computing the transition state are explored in this section. In the first method, the frozen coordinates approach is taken. This involves locking the reaction coordinate whilst minimisation of the rest of the molecule is performed (through any method of choice including Hf/3-21G, B3LYP/6-31G* levels of theory). Another optimsation can then be run which will optimize the rest of the molecule.

The second approach involves calculating the force constant along the reaction coordinate with both the number of steps along the coordinate and the direction to run the calculation both being defined by the user. In this approach however, It is important that the guess structure of the transition state is quite close to the actual case.

To start this investigation, the frozen coordinate methods were applied.

==== The Chair ====

After optimising an single allyl (CH2CHCH2) through the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/0/05/ALLYLFRAG_HF_321G_oi513.LOG here]), two of the said fragments were arranged in a chair conformation, with terminal C-C bond distance (between two fragements) set to 2.2 Å

<jmol><jmolApplet>
<title>HF/3-21G allyl fragment</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Allylfrag_HF_321g_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

This "guess" transition state was then run through an Frequency + Optimisation job (the log file of which can be located [https://wiki.ch.ic.ac.uk/wiki/images/0/0e/TSHYPOTHESIS_TRAILTWO_oi513.LOG here]) introducing the TS(Berny) optimisation method. This method works by employing the Berny algorithm. An approximate Hessian matrix (constituted by calculating second derivatives of energy) is developed using parameters of the initial structure including the valence force field. this approximation is then updated by calculating energies along the reaction pathway until a convergence is observed. Thus, the approximate matrix is a key factor in determining the success of the calculation. For most cases, using the approximate hessian serves well for the rest of the optimisation of the molecule, but in the cases where the the hessian changes dramatically, the force constant can be computed along every point of the reaction pathway. At the expense of time and computational power, the opitmisation will be able to find the local minimum.

<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

Inspection of the vibrations shows a single imaginary frequency (negative cm-1) at -817.94 cm-1 This "guess structure" method provides a reference/basis to which the frozen method can be compared with.

Imaginary frequencies are given such names due to the complex nature of their absolute values. Eigenvalues of hessian matrices correspond to squared harmonic oscillations of the normal vibration modes. thus a the square root of a negative eigenvalue gives rise a complex number with an imaginary component. Taking a simple plot of the harmonic oscillator (potential energy vs bond displacement), a negative second derivative would indicate that the geometry to which the reaction coordinate is abiding by is hitting a maximum (i.e. achieving transition state status). Thus if a transition state has been calculated, only one imaginary frequency should be as a result of the optimisation.

The frozen coordinate approach was then used to compute the transition. The (to be formed) bond between the terminal C's on both allyl fragments were strictly fixed/frozen to 2.2 Å followed by an optimisation. The log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/b/bb/TSBONDMODIFY_TCSET_COPY_TRAILONE_oi513.LOG here]. Having optimised the rest of the molecule with the mentioned bonds of interest fixed, the bonds will be accounted for in a second optimisation to which the log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/TSBONDMODIFY_TCSET_UNIDENTIFIEDDESTINATION_oi513.LOG here]

To summarize, the chair transition state has be investigated through a reference setup and an frozen coordinate setup. The table of results below give an account of the results of the two setups.

{| class="wikitable" border="1"
|+ Chair Transition State analysis
|-
| colspan="3" align="center"|[[File:CompLab_ChairTS_oi513.png]]
|-
! !! Guess TS !! Frozen TS
|-
| Terminal C-C Bond Length (Angstrom) || 2.02 || 2.02
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.39
|-
| C-C-C angle || 120.50 || 120.49
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSBondmodify_TCset_Unidentifieddestination_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==== The Boat ====

Having exhausted the chair TS, computations in the Boat conformer will be brought under investigation. In this section, more computational methods that investigate transition states will be explored. The QTS2 methods works by using user defined reactants and products and attempts to conceive new data points via interpolation such to find the transition state between them. The substrate was setup and labelled to depict reactants and product and was subsequently processed with the QTS2 method. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/c/c5/BOATTS_TWOMOLECULESETUP_SECONDTRAIL_oi513.LOG here]

Having run this initial calculation, the geometries of the reactants and products were edited to resemble that of a boat transition state. The same calculation was run again ( log file [https://wiki.ch.ic.ac.uk/wiki/images/5/53/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_oi513.LOG here]) The results of the two runs are summarized in the table below.

{| class="wikitable" border="1"
|+ Boat Transition state: QTS2 method
|-
! !! Arbitrary !! Boat-Like
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_secondtrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_properconformer_firsttrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Terminal C-C bond length (Angstrom)|| 2.02 || 2.14
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.38
|}

==== Endpiece: Comparing the Boat & Chair ====

To conclude this section of the study, the transition states will be optimised using the Intrinsic reaction coordinate (IRC) method. Arguably the defining feature of this approach is the ability to track the reaction coordinate from the transition state to a local minimum by taking minute steps along negative,steep gradients of the potential energy surface. This bears many favourable features for users to define at will namely defining how many steps to be taken in the calculation and the direction of the gradient should run from the transition state.

The IRC method was applied to the optimised chair conformer. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/a/a3/TSHYPOTHESIS_TRAILTWO_ForIRCcalculation_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_ForIRC_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

The same molecule was then further optimised to find a minimum under the HF/3-21G level of theory. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/d/d5/TSHYPOTHESIS_TRAILTWO_ForIRC_oi513.LOG here] 

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_PostIRC_Reopt.mol2</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC graphs oi513.png|thumb| figure 5: The Intrinsic Reaction Coordinates for the calculation. The convergence to a zero gradient indicates the structure optmisation has converged.]]

As seen by the the results of re-optimisation post-IRC, the conformer best represent that of the gauche2 state supported by the point group being C2. To allow activation energies to be calculated, a gauche 2 conformer was constructed and optimised under the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/5/51/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_HF312G_oi513.LOG here]) followed by the B3LYP/631G* level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/b/b8/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_REOPT_631GD_oi513.LOG here]) The thermochemical data can then be retrieved and be used as the reactants on the reaction coordinate pathway. Thus the difference in energy between the gauche2 conformer and the boat and chair transition states can be calculated

Lastly, optmised chair and boat structures were re-optimised under the a higher level of theory (B3LYP/6-31G*) with the resultant log files presented [https://wiki.ch.ic.ac.uk/wiki/images/3/34/TSHYPOTHESIS_TRAILTWO_ChairTS_631GdOpt_oi513.LOG here] and [https://wiki.ch.ic.ac.uk/wiki/images/5/5e/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_631Gd_reopt.LOG there] respectively

== The Diels Alder Cycloaddition: Computational Investigations ==

=== Overview ===

=== Simple Systems: S-cis butadiene and ethene ===

As an introduction to a cycloaddition, the reaction between ethene and butadiene was investigated.
setting the two vinyl protons in the same plane (i.e C1C2C3C4 dihedral angle = 0), the molecule was optmised under the Semi empirical am 1 method. Similarly, a molecule of cis-butadiene was optimised. The table below shows the results of optimisation

{| class="wikitable" border="1"
! !! Ethene !! S-cis butadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ethene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cisbutadiene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Point Group || C2v || d2h
|-
| HOMO || [[File:HOMO_ethene_oi513.png]] || [[File:HOMO_butadiene.png]]
|-
| LUMO || [[File:LUMO_Ethene_oi513.png]] || [[File:LUMO_butadiene_oi513.png]]
|-
| LOG files || [https://wiki.ch.ic.ac.uk/wiki/images/f/fa/ETHENE_OPT_SEMIEM_AM1_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/64/CISBUTADIENE_OPT_SEMIEM_AM1_T1_oi513.LOG file]
|}

following reactant optimisation,the fragments were arranged into a guess transition state (using the same concepts explored in the cope rearrangement investigations. The terminal Carbons on each fragment was fixed to be 2.2 angstrom apart. The resultant TS structure had a single imaginary frequency confirming formation of a transition state. The log file for optmisation can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/UNDOCUMETEDTS_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents></uploadedFileContents>
</jmolApplet>UndocumetedTS_oi513.mol2</jmol>

[[File:HOMO_firstDA_oi513.png]|thumb| figure 6: HOMO of the Diels Alder between the two subtrates.]
[[File:LUMO_firstDA_oi513.png]|thumb| figure 7: LUMO of Diels Alder between the two subtrates]

=== Complex systems: Maelic anydride and Cyclohexadiene ===

Using the same concepts explored in the cycloaddition investigations with the two unfunctionalised alkenes, the properties of the Diels Alder reaction between Maleic anhydride and cyclohexa-1,3-diene was investigated. As we will see, the regiochemistry of the reaction comes into play as the arrangement of the two subtrates prior to bond making/breaking gives rise to two different trasnition states (an exo and an endo state). Obtaining Molecular orbital data for of the two states will account for differences in the observed energies of the transition states.

the two reactants were optimised under the Semi empirical am1 method. The results of the calculations are presented in the table below

{| class="wikitable" border="1"
Optmising the reactants
! !! Maelic anhydride !! Cyclohexadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>MAnydride_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cyclobutadiene_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|Point group || C2 || C1
|-
|HOMO || [[File:HOMO_MAnhydride_oi513.png]] || [[File:HOMO_Cylodiene_oi513.png]]
|-
|LUMO || [[File:LUMO_MAnhydride_oi513.png]] || [[File:LUMO_Cyclodiene_oi513.png]]
|-
|LOG || [https://wiki.ch.ic.ac.uk/wiki/images/3/31/MANYDRIDE_OPT_SEMEM_AM1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/7/7a/CYCLOBUTADIENE_OPT_SEMEM_AM1_oi513.LOG file]
|}

As per routine, a guess transition structure had to be constructed using the optimised fragments. In this case, we have stereo-distinction between two possible transition states, and exo form and an endo form.

For both endo and exo forms, terminal C-C bond distances were set and fixed to 2.2 Angstrom and the molecule adapted to represent a postulated transition state fro the respective forms. an optimisation + frequency calculation was carried out an the results given below

{| class="wikitable" border="1"
! !! Exo transition state !! Endo Transition state
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess3_Exo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess_Endo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|HOMO || [[File:HOMO_secondDA_Exo_oi513.png]] || [[File:HOMO_secondDA_Endo_oi513]]
|-
|LUMO || [[File:LUMO_SecondDA_Exo_oi513.png]] || [[File:LUMO_secondDA_Endo_oi513]]
|-
|Imaginary frequency || cell || cell
|-
Log files || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/TSGUESS3_EXO_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/9/90/TSGUESS_ENDO_T1_oi513.LOG file]
|}

Geometry data for the two states was also collected. The results are presented below

{| class="wikitable" border="1"
! colspan="2"|Exo transition State !! ! colspan="3"|Endo Transition state
|-
| colspan="2"|[[File:NumberingforExotransitionstate_oi513.png]] || colspan="2"|[[File:NumberingofEndoTransitionstate_oi513.png]]
|-
|bond || values || bond || values
|-
| C1-C2 || 1.41 || C1-C2 || 1.49
|-
| C2-C3 || 1.49 || C4-C5 || 1.49
|-
| C5-C1 || 1.49 || C5-C1 || 1.41
|-
| C2-C9 || 2.17 || C1-C9 || 2.16
|-
| C1-C6 || 2.17 || C5-C6 || 2.16
|-
| C6-C7 || 1.34 || C6-C7 || 1.49
|-
| C7-C8 || 1.40 || C7-C8 || 1.52
|-
| C8-C9 || 1.39 || C8-C9 || 1.49
|-
| C9-C10 || 1.49 || C9-C10 || 1.39
|-
| C10-C11 || 1.52 || C10-C11 || 1.40
|-
| C11-C6 || 1.49 || C11-C6 || 1.49
|}
Lastly, thermochemical data was collated and the results given below

Exo

Sum of electronic and zero-point Energies= 0.134882
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.0991180.099118

Endo

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

File:HOMO secondDA Endo oi513.png

2015-12-18T11:16:31Z

Oi513: Oi513 uploaded a new version of File:HOMO secondDA Endo oi513.png

Rep:Mod:Peebo

2015-12-18T11:13:11Z

Oi513: /* Simple Systems: S-cis butadiene and ethene */

== Introduction ==

=== Overview ===
Fundamental to organic chemistry are pericyclic reactions that involve concerted movement of electrons through a cyclic transition state. Cycloadditions, a subset of pericyclic reactions, serve as a essential synthetic tool for organic chemists as a basis for accessing more complex structures in, for example, total synthesis of natural products [1]. In addition, sigmatropic rearrangements, and electrocyclic reactions are also a set of important pericyclic reactions that see Δσ 0 or ±1 respectively. For Diels alder and ene reactions, the initial arrangement of the fragments is brought into question when trying to understand the stereochemical outcome of the reaction. Other than these geometric factors, the frontier orbitals of the two fragments contain valuable information into predicting whether the two reactants may proceed to reach a product[2].

Robert Burns Woodward and Roald Hoffman established rules to explain whether a given pericyclic reaction may be thermally or photochemically allowed to give the said product. Naturally incorporated in their approach is considerations of the molecular orbitals involved in the reaction, the number of electrons, and the symmetry with respect to the connectivity between the two fragments. First applied to electrocyclic reactions [3], the two would then go on to publish more papers to fully develop their rules setting a universal foundation for understanding these class of reactions

Given the wealth factors that contribute towards going from reactants --> products, it is of the best interests to synthetic chemists to understand the mechanistic basis behind the reaction and therefore ,for example, the observed stereochemistry as opposed to whether a given reaction may be allowed or forbidden (in conjunction with Woodward-Hoffman rules). As such, computational methods into investigating diels alder reaction pathways have come to light[4][5] and have shown to provide insight into the optimal positioning of fragments and the structure and energy of Transition states. Studying transition states in particular are a huge advantage in computational studies; through this medium, calculations on energies of these states can be probes that would otherwise be immeasurable due to the fleeting nature of the transition state.

=== Experimental Aims ===
In this exercise, we first investigate the energies of varying 1-5 hexadiene conformers and investigate the possible cyclic transition states whilst it undergoes the cope rearrangement using the Hartree-Fock/3-21G and B3LYP/6-31G(d) levels of theory in addition to exploring Transition state optimization methods QTS2 and TS(Berny). Using similar methods, we then go on to develop our discussion of transition states by through investigating the regioselectivity of the Diels Alder reaction between maelic anhydride and 1-3 cyclohexadiene including molecular orbital interactions.

=== Brief note: Computational Methods ===

In this investigation, we explore different levels of theory to apply alongside our calculations as each have both advantageous features, and their respective drawbacks. Hatree fock method is used to determine both energies and quantum mechanical wavefunction of a multi-body system in state that has its probability density (position of the body in question) independent of time (i.e a stationary state). Amongst the appreciable number of approximations made by this method, the assumption that many electron wavefunction of the body in question will take the form of a just an isolated determinant (slater determinant) derived from a single electron wavefunction. Whist in theory this is entirely possible through linear combination of atomic orbitals, this naturally causes this approach to overlook the replusive interactions between the electrons in the system thus producing energies that are overestimated.

By virtue The Hohenberg-Kohn Theorems, the total energy of a ground state is exclusively dependent on electron density and distribution. Focusing in on this aspect and overlooking the electronic wavefunctions give rise to density functional theory. This method will aim to minimize energy via changes in electron density in a body. In addition to this, Electron correlations are taken into account and the mean field approximation is relaxed However, one key drawback in this theory is that it is not certain that using a more complicated basis set my necessarily produce a more accurate answer; the theory is not variational whereas the HF theory actively is.

== The Cope rearrangement: Computational Investigations ==

=== Overview ===

1-5 hexadiene provides a relatively simple system to observe a cope rearrangement. Through Woodward-Hoffmann analysis, we see that this [3,3] sigmatropic rearrangement is thermally allowed by virtue of the equation (4q + 2)s + (4r)a. Figure 2 provides one way in which the reaction can proceed via these rules with a single σ2s component and two π2a components. [[File:Computation_Coperearrangement.jpg|thumb|Figure 1: An overview of the cope rearrangement going through the cyclic 6M transition state.]]
During the concerted formation/dissociation of bonds, the transition state resembles that of a six membered ring which can exhibit a chair or boat topology (in line with the conformers of cyclohexane) These transition states represent energy maxima on the reaction pathway from reactants to products. On the other hand, 1-5 hexadiene exists in many conformers representing an energy minimum. In the following section, we obtain optimal structures for the diene on different levels of theory followed by locating the position of the TS on the potential energy surface. In doing this, we can appropriately deduce the activation energy involve in the cope rearrangement through the chair TS and boat TS pathways.

[[File:CompLab_Figure3_hexadieneconformers.jpg|thumb|Figure 3: Newman projections for hexadiene showing antiperiplanar and gauche arrangements of vinyl groups.150px]]
[[File:Complab_copeWoodwardHoffman.jpg|thumb|Figure 2: Woodward-Hoffmann analysis of the [3,3] sigmatropic rearrangement. the orbitals can "connect" through an suprafacial or antarafacial manner to make or break the bonds in the product.]]

=== Optimizing reactants and products ===

The substrate under investigation can adopt many different conformers with respect to the central C3-C4 bond as seen in figure 3. Within the conformers laid out in the diagram exists a subset of more isomers that differ in the exact positioning of the vinyl group relative to the rest of the molecule as opposed to just the other vinyl group. Initiative would serve to think the antiperiplanar set of isomers would be of lower energy than the gauche type isomers purely on the argument of steric repulsion between the two vinyl groups. Various conformers of Hexadiene the consist of gauche and antiperiplanr motifs were optimized and the results posted in the table below. The nomenclature of conformers are with respect to appendix 2

{| class="wikitable" border="1"
|+ Optimization of 1-5 hexadiene conformers
! placeholder !! Gauche3 !! Anti2 !! Anti1 !! Gauche(1)
|-
| Image || <jmol><jmolApplet>
<title></title>
<color>White</color>
<size>200</size>
<uploadedFileContents>Gauche3conformer.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet></jmol>|| <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet>react_anticonformer.mol2</jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_gaucheconformer.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy (Hartres) || -231.69266122 || -231.69253516 || -231.69260235 || -231.68771610
|-
| Point Group || C1 || Ci || C2 || C2
|-
| log || [https://wiki.ch.ic.ac.uk/wiki/images/c/c1/GAUCHE3CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/dd/REACT_ANTICONFORMER.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/6b/TRAILCONFORMER_TWO_ANTI1CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/REACT_GAUCHECONFORMER_oi513.LOG file]
|}

In comparison with literature reference values there is very good agreement. Interestingly, the lowest energy conformer reveals itself as a gauche type conformer which is contrary to initial predictions. Visualizing the molecular orbitals indicates favorable electronic interactions in the gauche3 setup; the two pi systems of the vinyl groups are in close enough proximity to yield a favourable in phase overlap which isn't possible in the anti conformation purely on the grounds of spacial arrangement. The gauche3 conformer serves as a balance between repulsive steric interactions and attractive molecular orbital-overlap interactions.

[[File:CompLab_Figure4_conformerorbitals.jpg|thumb|Figure 4: The orbitals HOMO of Gauche3 and Anti1 conformers on the left and right respectively of 1-5 hexadiene. As seen, there is a favourable in phase overlap between the the pi systems of the two vinyl groups]]

We can now approach the optimization of hexadiene on a different level of theory. The HF_3-21G optimized anti2 conformer of the alkene was then re-optimized under DFT_6-31G(d) level of theory. The geometrical differences arising form these two different methods of computation are summarized below.

{| class="wikitable" border="1"
|+anti conformer
|-
!colspan="4" style="text-align: left;"|[[File:anti2conformer_forrepresentingtheHF_321Glevel.png|600px]]
|-
|   ||   || HF/3-21G || B3LYP/6-31G*
|-
| rowspan="3" | Bond Lengths (Angstrom) || C1-C2 || 1.32 || 1.33
|-
| C2-C3 || 1.51 || 1.50
|-
| C3-C4 || 1.55 || 1.55
|-
| rowspan="3" | Bond Angles (Degrees) || C1-C2-C3 || 124.80 || 125.29
|-
| C2-C3-C4 || 111.34 || 112.65
|-
| C1-C2-C3-C4 || 114.63 || 118.58
|}

Being immediately observable is the increase in bond length with the B3LYP/6-31G* level of theory in comparison to HF/3-21G. Within the same level of theory however, the HF/3-21G method describes less of a distinction between bond lengths of C-C single bonds and C-C double bonds. This may also be detectable by running frequency calculations and visualizing the vibrations involving the C=C bonds in both conformers.

Frequency analysis of the B3LYP/6-31G* optimised structure was carried out. Gaussian carries out this procedure by applying the equation for force constants [[File:Force_constant_equation_oi513.png]] (where C = 1/2π) and preforming calculations to see a convergence in the force constant. The absence of imaginary frequencies would indicate that we have indeed reached a true minimum on the potential energy surface. A summary of the optimisation is given below

{| class="wikitable" border="1"
|+ Frequency calculations
! Frequency summary !! Spectrum
|-
| [[File:CompLab_SpectraofFrequencies_oi513.png]]|| [[File:CompLab SummaryofFrequencies oi513.png]]
|}

The thermodynamic properties were noted post-optimisation and printed as follows (units in Hartrees)

Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461864
Sum of electronic and thermal Enthalpies= -234.460920

=== Transition state investigations ===

==== Overview ====

Having processed information about the reaction reactants/products, we can now try to approach mining information about a different area on the potential energy surface; the transition states.

As eluded to earlier, the reaction proceeds via a 6 membered ring transition state that can exhibit a boat or chair toplogy. In this section, we aim to find these states on the potential energy surface, assess their energies and consequently determine the activation energy involved in both pathways. We will start by building and optimising the fragments of the transition states, and running further frequency/optimisation calculations.

Defining a transition state requires a degree of appreciation for the reaction mechanism being explored. In this case, the two allyl fragements that will be used need to exhibit sensible geometry to allow for a completed freq + opt calculation to be run to completion. Two different methods of computing the transition state are explored in this section. In the first method, the frozen coordinates approach is taken. This involves locking the reaction coordinate whilst minimisation of the rest of the molecule is performed (through any method of choice including Hf/3-21G, B3LYP/6-31G* levels of theory). Another optimsation can then be run which will optimize the rest of the molecule.

The second approach involves calculating the force constant along the reaction coordinate with both the number of steps along the coordinate and the direction to run the calculation both being defined by the user. In this approach however, It is important that the guess structure of the transition state is quite close to the actual case.

To start this investigation, the frozen coordinate methods were applied.

==== The Chair ====

After optimising an single allyl (CH2CHCH2) through the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/0/05/ALLYLFRAG_HF_321G_oi513.LOG here]), two of the said fragments were arranged in a chair conformation, with terminal C-C bond distance (between two fragements) set to 2.2 Å

<jmol><jmolApplet>
<title>HF/3-21G allyl fragment</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Allylfrag_HF_321g_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

This "guess" transition state was then run through an Frequency + Optimisation job (the log file of which can be located [https://wiki.ch.ic.ac.uk/wiki/images/0/0e/TSHYPOTHESIS_TRAILTWO_oi513.LOG here]) introducing the TS(Berny) optimisation method. This method works by employing the Berny algorithm. An approximate Hessian matrix (constituted by calculating second derivatives of energy) is developed using parameters of the initial structure including the valence force field. this approximation is then updated by calculating energies along the reaction pathway until a convergence is observed. Thus, the approximate matrix is a key factor in determining the success of the calculation. For most cases, using the approximate hessian serves well for the rest of the optimisation of the molecule, but in the cases where the the hessian changes dramatically, the force constant can be computed along every point of the reaction pathway. At the expense of time and computational power, the opitmisation will be able to find the local minimum.

<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

Inspection of the vibrations shows a single imaginary frequency (negative cm-1) at -817.94 cm-1 This "guess structure" method provides a reference/basis to which the frozen method can be compared with.

Imaginary frequencies are given such names due to the complex nature of their absolute values. Eigenvalues of hessian matrices correspond to squared harmonic oscillations of the normal vibration modes. thus a the square root of a negative eigenvalue gives rise a complex number with an imaginary component. Taking a simple plot of the harmonic oscillator (potential energy vs bond displacement), a negative second derivative would indicate that the geometry to which the reaction coordinate is abiding by is hitting a maximum (i.e. achieving transition state status). Thus if a transition state has been calculated, only one imaginary frequency should be as a result of the optimisation.

The frozen coordinate approach was then used to compute the transition. The (to be formed) bond between the terminal C's on both allyl fragments were strictly fixed/frozen to 2.2 Å followed by an optimisation. The log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/b/bb/TSBONDMODIFY_TCSET_COPY_TRAILONE_oi513.LOG here]. Having optimised the rest of the molecule with the mentioned bonds of interest fixed, the bonds will be accounted for in a second optimisation to which the log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/TSBONDMODIFY_TCSET_UNIDENTIFIEDDESTINATION_oi513.LOG here]

To summarize, the chair transition state has be investigated through a reference setup and an frozen coordinate setup. The table of results below give an account of the results of the two setups.

{| class="wikitable" border="1"
|+ Chair Transition State analysis
|-
| colspan="3" align="center"|[[File:CompLab_ChairTS_oi513.png]]
|-
! !! Guess TS !! Frozen TS
|-
| Terminal C-C Bond Length (Angstrom) || 2.02 || 2.02
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.39
|-
| C-C-C angle || 120.50 || 120.49
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSBondmodify_TCset_Unidentifieddestination_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==== The Boat ====

Having exhausted the chair TS, computations in the Boat conformer will be brought under investigation. In this section, more computational methods that investigate transition states will be explored. The QTS2 methods works by using user defined reactants and products and attempts to conceive new data points via interpolation such to find the transition state between them. The substrate was setup and labelled to depict reactants and product and was subsequently processed with the QTS2 method. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/c/c5/BOATTS_TWOMOLECULESETUP_SECONDTRAIL_oi513.LOG here]

Having run this initial calculation, the geometries of the reactants and products were edited to resemble that of a boat transition state. The same calculation was run again ( log file [https://wiki.ch.ic.ac.uk/wiki/images/5/53/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_oi513.LOG here]) The results of the two runs are summarized in the table below.

{| class="wikitable" border="1"
|+ Boat Transition state: QTS2 method
|-
! !! Arbitrary !! Boat-Like
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_secondtrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_properconformer_firsttrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Terminal C-C bond length (Angstrom)|| 2.02 || 2.14
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.38
|}

==== Endpiece: Comparing the Boat & Chair ====

To conclude this section of the study, the transition states will be optimised using the Intrinsic reaction coordinate (IRC) method. Arguably the defining feature of this approach is the ability to track the reaction coordinate from the transition state to a local minimum by taking minute steps along negative,steep gradients of the potential energy surface. This bears many favourable features for users to define at will namely defining how many steps to be taken in the calculation and the direction of the gradient should run from the transition state.

The IRC method was applied to the optimised chair conformer. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/a/a3/TSHYPOTHESIS_TRAILTWO_ForIRCcalculation_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_ForIRC_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

The same molecule was then further optimised to find a minimum under the HF/3-21G level of theory. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/d/d5/TSHYPOTHESIS_TRAILTWO_ForIRC_oi513.LOG here] 

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_PostIRC_Reopt.mol2</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC graphs oi513.png|thumb| figure 5: The Intrinsic Reaction Coordinates for the calculation. The convergence to a zero gradient indicates the structure optmisation has converged.]]

As seen by the the results of re-optimisation post-IRC, the conformer best represent that of the gauche2 state supported by the point group being C2. To allow activation energies to be calculated, a gauche 2 conformer was constructed and optimised under the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/5/51/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_HF312G_oi513.LOG here]) followed by the B3LYP/631G* level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/b/b8/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_REOPT_631GD_oi513.LOG here]) The thermochemical data can then be retrieved and be used as the reactants on the reaction coordinate pathway. Thus the difference in energy between the gauche2 conformer and the boat and chair transition states can be calculated

Lastly, optmised chair and boat structures were re-optimised under the a higher level of theory (B3LYP/6-31G*) with the resultant log files presented [https://wiki.ch.ic.ac.uk/wiki/images/3/34/TSHYPOTHESIS_TRAILTWO_ChairTS_631GdOpt_oi513.LOG here] and [https://wiki.ch.ic.ac.uk/wiki/images/5/5e/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_631Gd_reopt.LOG there] respectively

== The Diels Alder Cycloaddition: Computational Investigations ==

=== Overview ===

=== Simple Systems: S-cis butadiene and ethene ===

As an introduction to a cycloaddition, the reaction between ethene and butadiene was investigated.
setting the two vinyl protons in the same plane (i.e C1C2C3C4 dihedral angle = 0), the molecule was optmised under the Semi empirical am 1 method. Similarly, a molecule of cis-butadiene was optimised. The table below shows the results of optimisation

{| class="wikitable" border="1"
! !! Ethene !! S-cis butadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ethene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cisbutadiene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Point Group || C2v || d2h
|-
| HOMO || [[File:HOMO_ethene_oi513.png]] || [[File:HOMO butadiene.png]]
|-
| LUMO || [[File:LUMO_Ethene_oi513.png]] || [[File:LUMO_butadiene_oi513.png]]
|-
| LOG files || [https://wiki.ch.ic.ac.uk/wiki/images/f/fa/ETHENE_OPT_SEMIEM_AM1_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/64/CISBUTADIENE_OPT_SEMIEM_AM1_T1_oi513.LOG file]
|}

following reactant optimisation,the fragments were arranged into a guess transition state (using the same concepts explored in the cope rearrangement investigations. The terminal Carbons on each fragment was fixed to be 2.2 angstrom apart. The resultant TS structure had a single imaginary frequency confirming formation of a transition state. The log file for optmisation can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/UNDOCUMETEDTS_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents></uploadedFileContents>
</jmolApplet>UndocumetedTS_oi513.mol2</jmol>

[[File:HOMO_firstDA_oi513.png]|thumb| figure 6: HOMO of the Diels Alder between the two subtrates.]
[[File:LUMO_firstDA_oi513.png]|thumb| figure 7: LUMO of Diels Alder between the two subtrates]

=== Complex systems: Maelic anydride and Cyclohexadiene ===

Using the same concepts explored in the cycloaddition investigations with the two unfunctionalised alkenes, the properties of the Diels Alder reaction between Maleic anhydride and cyclohexa-1,3-diene was investigated. As we will see, the regiochemistry of the reaction comes into play as the arrangement of the two subtrates prior to bond making/breaking gives rise to two different trasnition states (an exo and an endo state). Obtaining Molecular orbital data for of the two states will account for differences in the observed energies of the transition states.

the two reactants were optimised under the Semi empirical am1 method. The results of the calculations are presented in the table below

{| class="wikitable" border="1"
Optmising the reactants
! !! Maelic anhydride !! Cyclohexadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>MAnydride_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cyclobutadiene_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|Point group || C2 || C1
|-
|HOMO || [[File:HOMO_MAnhydride_oi513.png]] || [[File:HOMO_butadiene_oi513.png]]
|-
|LUMO || [[File:LUMO_MAnhydride_oi513.png]] || [[File:LUMO_butadiene_oi513.png]]
|-
|LOG || [https://wiki.ch.ic.ac.uk/wiki/images/3/31/MANYDRIDE_OPT_SEMEM_AM1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/7/7a/CYCLOBUTADIENE_OPT_SEMEM_AM1_oi513.LOG file]
|}

As per routine, a guess transition structure had to be constructed using the optimised fragments. In this case, we have stereo-distinction between two possible transition states, and exo form and an endo form.

For both endo and exo forms, terminal C-C bond distances were set and fixed to 2.2 Angstrom and the molecule adapted to represent a postulated transition state fro the respective forms. an optimisation + frequency calculation was carried out an the results given below

{| class="wikitable" border="1"
! !! Exo transition state !! Endo Transition state
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess3_Exo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess_Endo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|HOMO || [[File:HOMO_secondDA_Exo_oi513.png]] || [[File:HOMO_secondDA_Endo_oi513]]
|-
|LUMO || [[File:LUMO_SecondDA_Exo_oi513.png]] || [[File:LUMO_secondDA_Endo_oi513]]
|-
|Imaginary frequency || cell || cell
|-
Log files || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/TSGUESS3_EXO_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/9/90/TSGUESS_ENDO_T1_oi513.LOG file]
|}

Geometry data for the two states was also collected. The results are presented below

{| class="wikitable" border="1"
! colspan="2"|Exo transition State !! ! colspan="3"|Endo Transition state
|-
| colspan="2"|[[File:NumberingforExotransitionstate_oi513.png]] || colspan="2"|[[File:NumberingofEndoTransitionstate_oi513]]
|-
|bond || values || bond || values
|-
| C1-C2 || 1.41 || C1-C2 || 1.49
|-
| C2-C3 || 1.49 || C4-C5 || 1.49
|-
| C5-C1 || 1.49 || C5-C1 || 1.41
|-
| C2-C9 || 2.17 || C1-C9 || 2.16
|-
| C1-C6 || 2.17 || C5-C6 || 2.16
|-
| C6-C7 || 1.34 || C6-C7 || 1.49
|-
| C7-C8 || 1.40 || C7-C8 || 1.52
|-
| C8-C9 || 1.39 || C8-C9 || 1.49
|-
| C9-C10 || 1.49 || C9-C10 || 1.39
|-
| C10-C11 || 1.52 || C10-C11 || 1.40
|-
| C11-C6 || 1.49 || C11-C6 || 1.49
|}
Lastly, thermochemical data was collated and the results given below

Exo

Sum of electronic and zero-point Energies= 0.134882
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.0991180.099118

Endo

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

Rep:Mod:Peebo

2015-12-18T11:12:39Z

Oi513: /* The Diels Alder Cycloaddition: Computational Investigations */

== Introduction ==

=== Overview ===
Fundamental to organic chemistry are pericyclic reactions that involve concerted movement of electrons through a cyclic transition state. Cycloadditions, a subset of pericyclic reactions, serve as a essential synthetic tool for organic chemists as a basis for accessing more complex structures in, for example, total synthesis of natural products [1]. In addition, sigmatropic rearrangements, and electrocyclic reactions are also a set of important pericyclic reactions that see Δσ 0 or ±1 respectively. For Diels alder and ene reactions, the initial arrangement of the fragments is brought into question when trying to understand the stereochemical outcome of the reaction. Other than these geometric factors, the frontier orbitals of the two fragments contain valuable information into predicting whether the two reactants may proceed to reach a product[2].

Robert Burns Woodward and Roald Hoffman established rules to explain whether a given pericyclic reaction may be thermally or photochemically allowed to give the said product. Naturally incorporated in their approach is considerations of the molecular orbitals involved in the reaction, the number of electrons, and the symmetry with respect to the connectivity between the two fragments. First applied to electrocyclic reactions [3], the two would then go on to publish more papers to fully develop their rules setting a universal foundation for understanding these class of reactions

Given the wealth factors that contribute towards going from reactants --> products, it is of the best interests to synthetic chemists to understand the mechanistic basis behind the reaction and therefore ,for example, the observed stereochemistry as opposed to whether a given reaction may be allowed or forbidden (in conjunction with Woodward-Hoffman rules). As such, computational methods into investigating diels alder reaction pathways have come to light[4][5] and have shown to provide insight into the optimal positioning of fragments and the structure and energy of Transition states. Studying transition states in particular are a huge advantage in computational studies; through this medium, calculations on energies of these states can be probes that would otherwise be immeasurable due to the fleeting nature of the transition state.

=== Experimental Aims ===
In this exercise, we first investigate the energies of varying 1-5 hexadiene conformers and investigate the possible cyclic transition states whilst it undergoes the cope rearrangement using the Hartree-Fock/3-21G and B3LYP/6-31G(d) levels of theory in addition to exploring Transition state optimization methods QTS2 and TS(Berny). Using similar methods, we then go on to develop our discussion of transition states by through investigating the regioselectivity of the Diels Alder reaction between maelic anhydride and 1-3 cyclohexadiene including molecular orbital interactions.

=== Brief note: Computational Methods ===

In this investigation, we explore different levels of theory to apply alongside our calculations as each have both advantageous features, and their respective drawbacks. Hatree fock method is used to determine both energies and quantum mechanical wavefunction of a multi-body system in state that has its probability density (position of the body in question) independent of time (i.e a stationary state). Amongst the appreciable number of approximations made by this method, the assumption that many electron wavefunction of the body in question will take the form of a just an isolated determinant (slater determinant) derived from a single electron wavefunction. Whist in theory this is entirely possible through linear combination of atomic orbitals, this naturally causes this approach to overlook the replusive interactions between the electrons in the system thus producing energies that are overestimated.

By virtue The Hohenberg-Kohn Theorems, the total energy of a ground state is exclusively dependent on electron density and distribution. Focusing in on this aspect and overlooking the electronic wavefunctions give rise to density functional theory. This method will aim to minimize energy via changes in electron density in a body. In addition to this, Electron correlations are taken into account and the mean field approximation is relaxed However, one key drawback in this theory is that it is not certain that using a more complicated basis set my necessarily produce a more accurate answer; the theory is not variational whereas the HF theory actively is.

== The Cope rearrangement: Computational Investigations ==

=== Overview ===

1-5 hexadiene provides a relatively simple system to observe a cope rearrangement. Through Woodward-Hoffmann analysis, we see that this [3,3] sigmatropic rearrangement is thermally allowed by virtue of the equation (4q + 2)s + (4r)a. Figure 2 provides one way in which the reaction can proceed via these rules with a single σ2s component and two π2a components. [[File:Computation_Coperearrangement.jpg|thumb|Figure 1: An overview of the cope rearrangement going through the cyclic 6M transition state.]]
During the concerted formation/dissociation of bonds, the transition state resembles that of a six membered ring which can exhibit a chair or boat topology (in line with the conformers of cyclohexane) These transition states represent energy maxima on the reaction pathway from reactants to products. On the other hand, 1-5 hexadiene exists in many conformers representing an energy minimum. In the following section, we obtain optimal structures for the diene on different levels of theory followed by locating the position of the TS on the potential energy surface. In doing this, we can appropriately deduce the activation energy involve in the cope rearrangement through the chair TS and boat TS pathways.

[[File:CompLab_Figure3_hexadieneconformers.jpg|thumb|Figure 3: Newman projections for hexadiene showing antiperiplanar and gauche arrangements of vinyl groups.150px]]
[[File:Complab_copeWoodwardHoffman.jpg|thumb|Figure 2: Woodward-Hoffmann analysis of the [3,3] sigmatropic rearrangement. the orbitals can "connect" through an suprafacial or antarafacial manner to make or break the bonds in the product.]]

=== Optimizing reactants and products ===

The substrate under investigation can adopt many different conformers with respect to the central C3-C4 bond as seen in figure 3. Within the conformers laid out in the diagram exists a subset of more isomers that differ in the exact positioning of the vinyl group relative to the rest of the molecule as opposed to just the other vinyl group. Initiative would serve to think the antiperiplanar set of isomers would be of lower energy than the gauche type isomers purely on the argument of steric repulsion between the two vinyl groups. Various conformers of Hexadiene the consist of gauche and antiperiplanr motifs were optimized and the results posted in the table below. The nomenclature of conformers are with respect to appendix 2

{| class="wikitable" border="1"
|+ Optimization of 1-5 hexadiene conformers
! placeholder !! Gauche3 !! Anti2 !! Anti1 !! Gauche(1)
|-
| Image || <jmol><jmolApplet>
<title></title>
<color>White</color>
<size>200</size>
<uploadedFileContents>Gauche3conformer.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet></jmol>|| <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet>react_anticonformer.mol2</jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_gaucheconformer.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy (Hartres) || -231.69266122 || -231.69253516 || -231.69260235 || -231.68771610
|-
| Point Group || C1 || Ci || C2 || C2
|-
| log || [https://wiki.ch.ic.ac.uk/wiki/images/c/c1/GAUCHE3CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/dd/REACT_ANTICONFORMER.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/6b/TRAILCONFORMER_TWO_ANTI1CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/REACT_GAUCHECONFORMER_oi513.LOG file]
|}

In comparison with literature reference values there is very good agreement. Interestingly, the lowest energy conformer reveals itself as a gauche type conformer which is contrary to initial predictions. Visualizing the molecular orbitals indicates favorable electronic interactions in the gauche3 setup; the two pi systems of the vinyl groups are in close enough proximity to yield a favourable in phase overlap which isn't possible in the anti conformation purely on the grounds of spacial arrangement. The gauche3 conformer serves as a balance between repulsive steric interactions and attractive molecular orbital-overlap interactions.

[[File:CompLab_Figure4_conformerorbitals.jpg|thumb|Figure 4: The orbitals HOMO of Gauche3 and Anti1 conformers on the left and right respectively of 1-5 hexadiene. As seen, there is a favourable in phase overlap between the the pi systems of the two vinyl groups]]

We can now approach the optimization of hexadiene on a different level of theory. The HF_3-21G optimized anti2 conformer of the alkene was then re-optimized under DFT_6-31G(d) level of theory. The geometrical differences arising form these two different methods of computation are summarized below.

{| class="wikitable" border="1"
|+anti conformer
|-
!colspan="4" style="text-align: left;"|[[File:anti2conformer_forrepresentingtheHF_321Glevel.png|600px]]
|-
|   ||   || HF/3-21G || B3LYP/6-31G*
|-
| rowspan="3" | Bond Lengths (Angstrom) || C1-C2 || 1.32 || 1.33
|-
| C2-C3 || 1.51 || 1.50
|-
| C3-C4 || 1.55 || 1.55
|-
| rowspan="3" | Bond Angles (Degrees) || C1-C2-C3 || 124.80 || 125.29
|-
| C2-C3-C4 || 111.34 || 112.65
|-
| C1-C2-C3-C4 || 114.63 || 118.58
|}

Being immediately observable is the increase in bond length with the B3LYP/6-31G* level of theory in comparison to HF/3-21G. Within the same level of theory however, the HF/3-21G method describes less of a distinction between bond lengths of C-C single bonds and C-C double bonds. This may also be detectable by running frequency calculations and visualizing the vibrations involving the C=C bonds in both conformers.

Frequency analysis of the B3LYP/6-31G* optimised structure was carried out. Gaussian carries out this procedure by applying the equation for force constants [[File:Force_constant_equation_oi513.png]] (where C = 1/2π) and preforming calculations to see a convergence in the force constant. The absence of imaginary frequencies would indicate that we have indeed reached a true minimum on the potential energy surface. A summary of the optimisation is given below

{| class="wikitable" border="1"
|+ Frequency calculations
! Frequency summary !! Spectrum
|-
| [[File:CompLab_SpectraofFrequencies_oi513.png]]|| [[File:CompLab SummaryofFrequencies oi513.png]]
|}

The thermodynamic properties were noted post-optimisation and printed as follows (units in Hartrees)

Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461864
Sum of electronic and thermal Enthalpies= -234.460920

=== Transition state investigations ===

==== Overview ====

Having processed information about the reaction reactants/products, we can now try to approach mining information about a different area on the potential energy surface; the transition states.

As eluded to earlier, the reaction proceeds via a 6 membered ring transition state that can exhibit a boat or chair toplogy. In this section, we aim to find these states on the potential energy surface, assess their energies and consequently determine the activation energy involved in both pathways. We will start by building and optimising the fragments of the transition states, and running further frequency/optimisation calculations.

Defining a transition state requires a degree of appreciation for the reaction mechanism being explored. In this case, the two allyl fragements that will be used need to exhibit sensible geometry to allow for a completed freq + opt calculation to be run to completion. Two different methods of computing the transition state are explored in this section. In the first method, the frozen coordinates approach is taken. This involves locking the reaction coordinate whilst minimisation of the rest of the molecule is performed (through any method of choice including Hf/3-21G, B3LYP/6-31G* levels of theory). Another optimsation can then be run which will optimize the rest of the molecule.

The second approach involves calculating the force constant along the reaction coordinate with both the number of steps along the coordinate and the direction to run the calculation both being defined by the user. In this approach however, It is important that the guess structure of the transition state is quite close to the actual case.

To start this investigation, the frozen coordinate methods were applied.

==== The Chair ====

After optimising an single allyl (CH2CHCH2) through the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/0/05/ALLYLFRAG_HF_321G_oi513.LOG here]), two of the said fragments were arranged in a chair conformation, with terminal C-C bond distance (between two fragements) set to 2.2 Å

<jmol><jmolApplet>
<title>HF/3-21G allyl fragment</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Allylfrag_HF_321g_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

This "guess" transition state was then run through an Frequency + Optimisation job (the log file of which can be located [https://wiki.ch.ic.ac.uk/wiki/images/0/0e/TSHYPOTHESIS_TRAILTWO_oi513.LOG here]) introducing the TS(Berny) optimisation method. This method works by employing the Berny algorithm. An approximate Hessian matrix (constituted by calculating second derivatives of energy) is developed using parameters of the initial structure including the valence force field. this approximation is then updated by calculating energies along the reaction pathway until a convergence is observed. Thus, the approximate matrix is a key factor in determining the success of the calculation. For most cases, using the approximate hessian serves well for the rest of the optimisation of the molecule, but in the cases where the the hessian changes dramatically, the force constant can be computed along every point of the reaction pathway. At the expense of time and computational power, the opitmisation will be able to find the local minimum.

<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

Inspection of the vibrations shows a single imaginary frequency (negative cm-1) at -817.94 cm-1 This "guess structure" method provides a reference/basis to which the frozen method can be compared with.

Imaginary frequencies are given such names due to the complex nature of their absolute values. Eigenvalues of hessian matrices correspond to squared harmonic oscillations of the normal vibration modes. thus a the square root of a negative eigenvalue gives rise a complex number with an imaginary component. Taking a simple plot of the harmonic oscillator (potential energy vs bond displacement), a negative second derivative would indicate that the geometry to which the reaction coordinate is abiding by is hitting a maximum (i.e. achieving transition state status). Thus if a transition state has been calculated, only one imaginary frequency should be as a result of the optimisation.

The frozen coordinate approach was then used to compute the transition. The (to be formed) bond between the terminal C's on both allyl fragments were strictly fixed/frozen to 2.2 Å followed by an optimisation. The log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/b/bb/TSBONDMODIFY_TCSET_COPY_TRAILONE_oi513.LOG here]. Having optimised the rest of the molecule with the mentioned bonds of interest fixed, the bonds will be accounted for in a second optimisation to which the log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/TSBONDMODIFY_TCSET_UNIDENTIFIEDDESTINATION_oi513.LOG here]

To summarize, the chair transition state has be investigated through a reference setup and an frozen coordinate setup. The table of results below give an account of the results of the two setups.

{| class="wikitable" border="1"
|+ Chair Transition State analysis
|-
| colspan="3" align="center"|[[File:CompLab_ChairTS_oi513.png]]
|-
! !! Guess TS !! Frozen TS
|-
| Terminal C-C Bond Length (Angstrom) || 2.02 || 2.02
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.39
|-
| C-C-C angle || 120.50 || 120.49
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSBondmodify_TCset_Unidentifieddestination_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==== The Boat ====

Having exhausted the chair TS, computations in the Boat conformer will be brought under investigation. In this section, more computational methods that investigate transition states will be explored. The QTS2 methods works by using user defined reactants and products and attempts to conceive new data points via interpolation such to find the transition state between them. The substrate was setup and labelled to depict reactants and product and was subsequently processed with the QTS2 method. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/c/c5/BOATTS_TWOMOLECULESETUP_SECONDTRAIL_oi513.LOG here]

Having run this initial calculation, the geometries of the reactants and products were edited to resemble that of a boat transition state. The same calculation was run again ( log file [https://wiki.ch.ic.ac.uk/wiki/images/5/53/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_oi513.LOG here]) The results of the two runs are summarized in the table below.

{| class="wikitable" border="1"
|+ Boat Transition state: QTS2 method
|-
! !! Arbitrary !! Boat-Like
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_secondtrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_properconformer_firsttrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Terminal C-C bond length (Angstrom)|| 2.02 || 2.14
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.38
|}

==== Endpiece: Comparing the Boat & Chair ====

To conclude this section of the study, the transition states will be optimised using the Intrinsic reaction coordinate (IRC) method. Arguably the defining feature of this approach is the ability to track the reaction coordinate from the transition state to a local minimum by taking minute steps along negative,steep gradients of the potential energy surface. This bears many favourable features for users to define at will namely defining how many steps to be taken in the calculation and the direction of the gradient should run from the transition state.

The IRC method was applied to the optimised chair conformer. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/a/a3/TSHYPOTHESIS_TRAILTWO_ForIRCcalculation_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_ForIRC_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

The same molecule was then further optimised to find a minimum under the HF/3-21G level of theory. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/d/d5/TSHYPOTHESIS_TRAILTWO_ForIRC_oi513.LOG here] 

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_PostIRC_Reopt.mol2</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC graphs oi513.png|thumb| figure 5: The Intrinsic Reaction Coordinates for the calculation. The convergence to a zero gradient indicates the structure optmisation has converged.]]

As seen by the the results of re-optimisation post-IRC, the conformer best represent that of the gauche2 state supported by the point group being C2. To allow activation energies to be calculated, a gauche 2 conformer was constructed and optimised under the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/5/51/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_HF312G_oi513.LOG here]) followed by the B3LYP/631G* level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/b/b8/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_REOPT_631GD_oi513.LOG here]) The thermochemical data can then be retrieved and be used as the reactants on the reaction coordinate pathway. Thus the difference in energy between the gauche2 conformer and the boat and chair transition states can be calculated

Lastly, optmised chair and boat structures were re-optimised under the a higher level of theory (B3LYP/6-31G*) with the resultant log files presented [https://wiki.ch.ic.ac.uk/wiki/images/3/34/TSHYPOTHESIS_TRAILTWO_ChairTS_631GdOpt_oi513.LOG here] and [https://wiki.ch.ic.ac.uk/wiki/images/5/5e/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_631Gd_reopt.LOG there] respectively

== The Diels Alder Cycloaddition: Computational Investigations ==

=== Overview ===

=== Simple Systems: S-cis butadiene and ethene ===

As an introduction to a cycloaddition, the reaction between ethene and butadiene was investigated.
setting the two vinyl protons in the same plane (i.e C1C2C3C4 dihedral angle = 0), the molecule was optmised under the Semi empirical am 1 method. Similarly, a molecule of cis-butadiene was optimised. The table below shows the results of optimisation

{| class="wikitable" border="1"
! !! Ethene !! S-cis butadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ethene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cisbutadiene_Opt_SemiEm_Am1_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Point Group || C2v || d2h
|-
| HOMO || [[File:HOMO_ethene_oi513.png]] || [[File:HOMO butadiene.png]]
|-
| LUMO || [[File:LUMO_Ethene_oi513.pnh]] || [[File:LUMO_butadiene_oi513.png]]
|-
| LOG files || [https://wiki.ch.ic.ac.uk/wiki/images/f/fa/ETHENE_OPT_SEMIEM_AM1_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/64/CISBUTADIENE_OPT_SEMIEM_AM1_T1_oi513.LOG file]
|}

following reactant optimisation,the fragments were arranged into a guess transition state (using the same concepts explored in the cope rearrangement investigations. The terminal Carbons on each fragment was fixed to be 2.2 angstrom apart. The resultant TS structure had a single imaginary frequency confirming formation of a transition state. The log file for optmisation can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/UNDOCUMETEDTS_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents></uploadedFileContents>
</jmolApplet>UndocumetedTS_oi513.mol2</jmol>

[[File:HOMO_firstDA_oi513.png]|thumb| figure 6: HOMO of the Diels Alder between the two subtrates.]
[[File:LUMO_firstDA_oi513.png]|thumb| figure 7: LUMO of Diels Alder between the two subtrates]

=== Complex systems: Maelic anydride and Cyclohexadiene ===

Using the same concepts explored in the cycloaddition investigations with the two unfunctionalised alkenes, the properties of the Diels Alder reaction between Maleic anhydride and cyclohexa-1,3-diene was investigated. As we will see, the regiochemistry of the reaction comes into play as the arrangement of the two subtrates prior to bond making/breaking gives rise to two different trasnition states (an exo and an endo state). Obtaining Molecular orbital data for of the two states will account for differences in the observed energies of the transition states.

the two reactants were optimised under the Semi empirical am1 method. The results of the calculations are presented in the table below

{| class="wikitable" border="1"
Optmising the reactants
! !! Maelic anhydride !! Cyclohexadiene
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>MAnydride_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>Cyclobutadiene_Opt_SemEm_Am1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|Point group || C2 || C1
|-
|HOMO || [[File:HOMO_MAnhydride_oi513.png]] || [[File:HOMO_butadiene_oi513.png]]
|-
|LUMO || [[File:LUMO_MAnhydride_oi513.png]] || [[File:LUMO_butadiene_oi513.png]]
|-
|LOG || [https://wiki.ch.ic.ac.uk/wiki/images/3/31/MANYDRIDE_OPT_SEMEM_AM1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/7/7a/CYCLOBUTADIENE_OPT_SEMEM_AM1_oi513.LOG file]
|}

As per routine, a guess transition structure had to be constructed using the optimised fragments. In this case, we have stereo-distinction between two possible transition states, and exo form and an endo form.

For both endo and exo forms, terminal C-C bond distances were set and fixed to 2.2 Angstrom and the molecule adapted to represent a postulated transition state fro the respective forms. an optimisation + frequency calculation was carried out an the results given below

{| class="wikitable" border="1"
! !! Exo transition state !! Endo Transition state
|-
|Jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess3_Exo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSGuess_Endo_T1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
|HOMO || [[File:HOMO_secondDA_Exo_oi513.png]] || [[File:HOMO_secondDA_Endo_oi513]]
|-
|LUMO || [[File:LUMO_SecondDA_Exo_oi513.png]] || [[File:LUMO_secondDA_Endo_oi513]]
|-
|Imaginary frequency || cell || cell
|-
Log files || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/TSGUESS3_EXO_T1_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/9/90/TSGUESS_ENDO_T1_oi513.LOG file]
|}

Geometry data for the two states was also collected. The results are presented below

{| class="wikitable" border="1"
! colspan="2"|Exo transition State !! ! colspan="3"|Endo Transition state
|-
| colspan="2"|[[File:NumberingforExotransitionstate_oi513.png]] || colspan="2"|[[File:NumberingofEndoTransitionstate_oi513]]
|-
|bond || values || bond || values
|-
| C1-C2 || 1.41 || C1-C2 || 1.49
|-
| C2-C3 || 1.49 || C4-C5 || 1.49
|-
| C5-C1 || 1.49 || C5-C1 || 1.41
|-
| C2-C9 || 2.17 || C1-C9 || 2.16
|-
| C1-C6 || 2.17 || C5-C6 || 2.16
|-
| C6-C7 || 1.34 || C6-C7 || 1.49
|-
| C7-C8 || 1.40 || C7-C8 || 1.52
|-
| C8-C9 || 1.39 || C8-C9 || 1.49
|-
| C9-C10 || 1.49 || C9-C10 || 1.39
|-
| C10-C11 || 1.52 || C10-C11 || 1.40
|-
| C11-C6 || 1.49 || C11-C6 || 1.49
|}
Lastly, thermochemical data was collated and the results given below

Exo

Sum of electronic and zero-point Energies= 0.134882
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.0991180.099118

Endo

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

File:TSGUESS ENDO T1 oi513.LOG

2015-12-18T11:04:28Z

Oi513:

File:TSGUESS3 EXO T1 oi513.LOG

2015-12-18T11:03:51Z

Oi513:

File:CYCLOBUTADIENE OPT SEMEM AM1 oi513.LOG

2015-12-18T10:58:17Z

Oi513:

File:MANYDRIDE OPT SEMEM AM1 oi513.LOG

2015-12-18T10:57:24Z

Oi513:

File:UNDOCUMETEDTS oi513.LOG

2015-12-18T10:43:17Z

Oi513:

File:ETHENE OPT SEMIEM AM1 T1 oi513.LOG

2015-12-18T10:41:41Z

Oi513:

File:CISBUTADIENE OPT SEMIEM AM1 T1 oi513.LOG

2015-12-18T10:40:54Z

Oi513:

File:UndocumetedTS oi513.mol2

2015-12-18T10:38:41Z

Oi513:

File:TSGuess Endo T1.mol2

2015-12-18T10:38:15Z

Oi513: Oi513 uploaded a new version of File:TSGuess Endo T1.mol2

File:TSGuess3 Exo T1.mol2

2015-12-18T10:37:44Z

Oi513:

File:TSGuess Endo T1.mol2

2015-12-18T10:37:26Z

Oi513:

File:MAnydride Opt SemEm Am1.mol2

2015-12-18T10:36:58Z

Oi513:

File:Cyclobutadiene Opt SemEm Am1.mol2

2015-12-18T10:36:45Z

Oi513:

File:Cisbutadiene Opt SemiEm Am1 T1.mol2

2015-12-18T10:36:24Z

Oi513: Oi513 uploaded a new version of File:Cisbutadiene Opt SemiEm Am1 T1.mol2

File:NumberingofEndoTransitionstate oi513.png

2015-12-18T10:35:30Z

Oi513:

File:NumberingforExotransitionstate oi513.png

2015-12-18T10:35:14Z

Oi513:

File:LUMO SecondDA Exo oi513.png

2015-12-18T10:35:01Z

Oi513:

File:LUMO secondDA Endo oi513.png

2015-12-18T10:34:47Z

Oi513:

File:LUMO MAnhydride oi513.png

2015-12-18T10:34:13Z

Oi513:

File:LUMO firstDA oi513.png

2015-12-18T10:33:57Z

Oi513:

File:LUMO Ethene oi513.png

2015-12-18T10:33:41Z

Oi513:

File:LUMO Cyclodiene oi513.png

2015-12-18T10:33:26Z

Oi513:

File:LUMO butadiene oi513.png

2015-12-18T10:33:10Z

Oi513:

File:HOMO secondDA Exo oi513.png

2015-12-18T10:32:53Z

Oi513:

File:HOMO secondDA Endo oi513.png

2015-12-18T10:32:36Z

Oi513:

File:HOMO MAnhydride oi513.png

2015-12-18T10:32:21Z

Oi513:

File:HOMO firstDA oi513.png

2015-12-18T10:32:05Z

Oi513:

File:HOMO ethene oi513.png

2015-12-18T10:31:54Z

Oi513:

File:HOMO Cylodiene oi513.png

2015-12-18T10:31:40Z

Oi513:

File:HOMO butadiene.png

2015-12-18T10:28:44Z

Oi513:

File:Ethene Opt SemiEm Am1 T1.mol2

2015-12-18T10:17:34Z

Oi513:

File:Cisbutadiene Opt SemiEm Am1 T1.mol2

2015-12-18T10:17:19Z

Oi513:

Rep:Mod:Peebo

2015-12-18T10:15:42Z

Oi513: /* Transition state investigations */

== Introduction ==

=== Overview ===
Fundamental to organic chemistry are pericyclic reactions that involve concerted movement of electrons through a cyclic transition state. Cycloadditions, a subset of pericyclic reactions, serve as a essential synthetic tool for organic chemists as a basis for accessing more complex structures in, for example, total synthesis of natural products [1]. In addition, sigmatropic rearrangements, and electrocyclic reactions are also a set of important pericyclic reactions that see Δσ 0 or ±1 respectively. For Diels alder and ene reactions, the initial arrangement of the fragments is brought into question when trying to understand the stereochemical outcome of the reaction. Other than these geometric factors, the frontier orbitals of the two fragments contain valuable information into predicting whether the two reactants may proceed to reach a product[2].

Robert Burns Woodward and Roald Hoffman established rules to explain whether a given pericyclic reaction may be thermally or photochemically allowed to give the said product. Naturally incorporated in their approach is considerations of the molecular orbitals involved in the reaction, the number of electrons, and the symmetry with respect to the connectivity between the two fragments. First applied to electrocyclic reactions [3], the two would then go on to publish more papers to fully develop their rules setting a universal foundation for understanding these class of reactions

Given the wealth factors that contribute towards going from reactants --> products, it is of the best interests to synthetic chemists to understand the mechanistic basis behind the reaction and therefore ,for example, the observed stereochemistry as opposed to whether a given reaction may be allowed or forbidden (in conjunction with Woodward-Hoffman rules). As such, computational methods into investigating diels alder reaction pathways have come to light[4][5] and have shown to provide insight into the optimal positioning of fragments and the structure and energy of Transition states. Studying transition states in particular are a huge advantage in computational studies; through this medium, calculations on energies of these states can be probes that would otherwise be immeasurable due to the fleeting nature of the transition state.

=== Experimental Aims ===
In this exercise, we first investigate the energies of varying 1-5 hexadiene conformers and investigate the possible cyclic transition states whilst it undergoes the cope rearrangement using the Hartree-Fock/3-21G and B3LYP/6-31G(d) levels of theory in addition to exploring Transition state optimization methods QTS2 and TS(Berny). Using similar methods, we then go on to develop our discussion of transition states by through investigating the regioselectivity of the Diels Alder reaction between maelic anhydride and 1-3 cyclohexadiene including molecular orbital interactions.

=== Brief note: Computational Methods ===

In this investigation, we explore different levels of theory to apply alongside our calculations as each have both advantageous features, and their respective drawbacks. Hatree fock method is used to determine both energies and quantum mechanical wavefunction of a multi-body system in state that has its probability density (position of the body in question) independent of time (i.e a stationary state). Amongst the appreciable number of approximations made by this method, the assumption that many electron wavefunction of the body in question will take the form of a just an isolated determinant (slater determinant) derived from a single electron wavefunction. Whist in theory this is entirely possible through linear combination of atomic orbitals, this naturally causes this approach to overlook the replusive interactions between the electrons in the system thus producing energies that are overestimated.

By virtue The Hohenberg-Kohn Theorems, the total energy of a ground state is exclusively dependent on electron density and distribution. Focusing in on this aspect and overlooking the electronic wavefunctions give rise to density functional theory. This method will aim to minimize energy via changes in electron density in a body. In addition to this, Electron correlations are taken into account and the mean field approximation is relaxed However, one key drawback in this theory is that it is not certain that using a more complicated basis set my necessarily produce a more accurate answer; the theory is not variational whereas the HF theory actively is.

== The Cope rearrangement: Computational Investigations ==

=== Overview ===

1-5 hexadiene provides a relatively simple system to observe a cope rearrangement. Through Woodward-Hoffmann analysis, we see that this [3,3] sigmatropic rearrangement is thermally allowed by virtue of the equation (4q + 2)s + (4r)a. Figure 2 provides one way in which the reaction can proceed via these rules with a single σ2s component and two π2a components. [[File:Computation_Coperearrangement.jpg|thumb|Figure 1: An overview of the cope rearrangement going through the cyclic 6M transition state.]]
During the concerted formation/dissociation of bonds, the transition state resembles that of a six membered ring which can exhibit a chair or boat topology (in line with the conformers of cyclohexane) These transition states represent energy maxima on the reaction pathway from reactants to products. On the other hand, 1-5 hexadiene exists in many conformers representing an energy minimum. In the following section, we obtain optimal structures for the diene on different levels of theory followed by locating the position of the TS on the potential energy surface. In doing this, we can appropriately deduce the activation energy involve in the cope rearrangement through the chair TS and boat TS pathways.

[[File:CompLab_Figure3_hexadieneconformers.jpg|thumb|Figure 3: Newman projections for hexadiene showing antiperiplanar and gauche arrangements of vinyl groups.150px]]
[[File:Complab_copeWoodwardHoffman.jpg|thumb|Figure 2: Woodward-Hoffmann analysis of the [3,3] sigmatropic rearrangement. the orbitals can "connect" through an suprafacial or antarafacial manner to make or break the bonds in the product.]]

=== Optimizing reactants and products ===

The substrate under investigation can adopt many different conformers with respect to the central C3-C4 bond as seen in figure 3. Within the conformers laid out in the diagram exists a subset of more isomers that differ in the exact positioning of the vinyl group relative to the rest of the molecule as opposed to just the other vinyl group. Initiative would serve to think the antiperiplanar set of isomers would be of lower energy than the gauche type isomers purely on the argument of steric repulsion between the two vinyl groups. Various conformers of Hexadiene the consist of gauche and antiperiplanr motifs were optimized and the results posted in the table below. The nomenclature of conformers are with respect to appendix 2

{| class="wikitable" border="1"
|+ Optimization of 1-5 hexadiene conformers
! placeholder !! Gauche3 !! Anti2 !! Anti1 !! Gauche(1)
|-
| Image || <jmol><jmolApplet>
<title></title>
<color>White</color>
<size>200</size>
<uploadedFileContents>Gauche3conformer.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet></jmol>|| <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet>react_anticonformer.mol2</jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_gaucheconformer.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy (Hartres) || -231.69266122 || -231.69253516 || -231.69260235 || -231.68771610
|-
| Point Group || C1 || Ci || C2 || C2
|-
| log || [https://wiki.ch.ic.ac.uk/wiki/images/c/c1/GAUCHE3CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/dd/REACT_ANTICONFORMER.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/6b/TRAILCONFORMER_TWO_ANTI1CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/REACT_GAUCHECONFORMER_oi513.LOG file]
|}

In comparison with literature reference values there is very good agreement. Interestingly, the lowest energy conformer reveals itself as a gauche type conformer which is contrary to initial predictions. Visualizing the molecular orbitals indicates favorable electronic interactions in the gauche3 setup; the two pi systems of the vinyl groups are in close enough proximity to yield a favourable in phase overlap which isn't possible in the anti conformation purely on the grounds of spacial arrangement. The gauche3 conformer serves as a balance between repulsive steric interactions and attractive molecular orbital-overlap interactions.

[[File:CompLab_Figure4_conformerorbitals.jpg|thumb|Figure 4: The orbitals HOMO of Gauche3 and Anti1 conformers on the left and right respectively of 1-5 hexadiene. As seen, there is a favourable in phase overlap between the the pi systems of the two vinyl groups]]

We can now approach the optimization of hexadiene on a different level of theory. The HF_3-21G optimized anti2 conformer of the alkene was then re-optimized under DFT_6-31G(d) level of theory. The geometrical differences arising form these two different methods of computation are summarized below.

{| class="wikitable" border="1"
|+anti conformer
|-
!colspan="4" style="text-align: left;"|[[File:anti2conformer_forrepresentingtheHF_321Glevel.png|600px]]
|-
|   ||   || HF/3-21G || B3LYP/6-31G*
|-
| rowspan="3" | Bond Lengths (Angstrom) || C1-C2 || 1.32 || 1.33
|-
| C2-C3 || 1.51 || 1.50
|-
| C3-C4 || 1.55 || 1.55
|-
| rowspan="3" | Bond Angles (Degrees) || C1-C2-C3 || 124.80 || 125.29
|-
| C2-C3-C4 || 111.34 || 112.65
|-
| C1-C2-C3-C4 || 114.63 || 118.58
|}

Being immediately observable is the increase in bond length with the B3LYP/6-31G* level of theory in comparison to HF/3-21G. Within the same level of theory however, the HF/3-21G method describes less of a distinction between bond lengths of C-C single bonds and C-C double bonds. This may also be detectable by running frequency calculations and visualizing the vibrations involving the C=C bonds in both conformers.

Frequency analysis of the B3LYP/6-31G* optimised structure was carried out. Gaussian carries out this procedure by applying the equation for force constants [[File:Force_constant_equation_oi513.png]] (where C = 1/2π) and preforming calculations to see a convergence in the force constant. The absence of imaginary frequencies would indicate that we have indeed reached a true minimum on the potential energy surface. A summary of the optimisation is given below

{| class="wikitable" border="1"
|+ Frequency calculations
! Frequency summary !! Spectrum
|-
| [[File:CompLab_SpectraofFrequencies_oi513.png]]|| [[File:CompLab SummaryofFrequencies oi513.png]]
|}

The thermodynamic properties were noted post-optimisation and printed as follows (units in Hartrees)

Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461864
Sum of electronic and thermal Enthalpies= -234.460920

=== Transition state investigations ===

==== Overview ====

Having processed information about the reaction reactants/products, we can now try to approach mining information about a different area on the potential energy surface; the transition states.

As eluded to earlier, the reaction proceeds via a 6 membered ring transition state that can exhibit a boat or chair toplogy. In this section, we aim to find these states on the potential energy surface, assess their energies and consequently determine the activation energy involved in both pathways. We will start by building and optimising the fragments of the transition states, and running further frequency/optimisation calculations.

Defining a transition state requires a degree of appreciation for the reaction mechanism being explored. In this case, the two allyl fragements that will be used need to exhibit sensible geometry to allow for a completed freq + opt calculation to be run to completion. Two different methods of computing the transition state are explored in this section. In the first method, the frozen coordinates approach is taken. This involves locking the reaction coordinate whilst minimisation of the rest of the molecule is performed (through any method of choice including Hf/3-21G, B3LYP/6-31G* levels of theory). Another optimsation can then be run which will optimize the rest of the molecule.

The second approach involves calculating the force constant along the reaction coordinate with both the number of steps along the coordinate and the direction to run the calculation both being defined by the user. In this approach however, It is important that the guess structure of the transition state is quite close to the actual case.

To start this investigation, the frozen coordinate methods were applied.

==== The Chair ====

After optimising an single allyl (CH2CHCH2) through the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/0/05/ALLYLFRAG_HF_321G_oi513.LOG here]), two of the said fragments were arranged in a chair conformation, with terminal C-C bond distance (between two fragements) set to 2.2 Å

<jmol><jmolApplet>
<title>HF/3-21G allyl fragment</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Allylfrag_HF_321g_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

This "guess" transition state was then run through an Frequency + Optimisation job (the log file of which can be located [https://wiki.ch.ic.ac.uk/wiki/images/0/0e/TSHYPOTHESIS_TRAILTWO_oi513.LOG here]) introducing the TS(Berny) optimisation method. This method works by employing the Berny algorithm. An approximate Hessian matrix (constituted by calculating second derivatives of energy) is developed using parameters of the initial structure including the valence force field. this approximation is then updated by calculating energies along the reaction pathway until a convergence is observed. Thus, the approximate matrix is a key factor in determining the success of the calculation. For most cases, using the approximate hessian serves well for the rest of the optimisation of the molecule, but in the cases where the the hessian changes dramatically, the force constant can be computed along every point of the reaction pathway. At the expense of time and computational power, the opitmisation will be able to find the local minimum.

<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

Inspection of the vibrations shows a single imaginary frequency (negative cm-1) at -817.94 cm-1 This "guess structure" method provides a reference/basis to which the frozen method can be compared with.

Imaginary frequencies are given such names due to the complex nature of their absolute values. Eigenvalues of hessian matrices correspond to squared harmonic oscillations of the normal vibration modes. thus a the square root of a negative eigenvalue gives rise a complex number with an imaginary component. Taking a simple plot of the harmonic oscillator (potential energy vs bond displacement), a negative second derivative would indicate that the geometry to which the reaction coordinate is abiding by is hitting a maximum (i.e. achieving transition state status). Thus if a transition state has been calculated, only one imaginary frequency should be as a result of the optimisation.

The frozen coordinate approach was then used to compute the transition. The (to be formed) bond between the terminal C's on both allyl fragments were strictly fixed/frozen to 2.2 Å followed by an optimisation. The log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/b/bb/TSBONDMODIFY_TCSET_COPY_TRAILONE_oi513.LOG here]. Having optimised the rest of the molecule with the mentioned bonds of interest fixed, the bonds will be accounted for in a second optimisation to which the log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/TSBONDMODIFY_TCSET_UNIDENTIFIEDDESTINATION_oi513.LOG here]

To summarize, the chair transition state has be investigated through a reference setup and an frozen coordinate setup. The table of results below give an account of the results of the two setups.

{| class="wikitable" border="1"
|+ Chair Transition State analysis
|-
| colspan="3" align="center"|[[File:CompLab_ChairTS_oi513.png]]
|-
! !! Guess TS !! Frozen TS
|-
| Terminal C-C Bond Length (Angstrom) || 2.02 || 2.02
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.39
|-
| C-C-C angle || 120.50 || 120.49
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TSBondmodify_TCset_Unidentifieddestination_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==== The Boat ====

Having exhausted the chair TS, computations in the Boat conformer will be brought under investigation. In this section, more computational methods that investigate transition states will be explored. The QTS2 methods works by using user defined reactants and products and attempts to conceive new data points via interpolation such to find the transition state between them. The substrate was setup and labelled to depict reactants and product and was subsequently processed with the QTS2 method. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/c/c5/BOATTS_TWOMOLECULESETUP_SECONDTRAIL_oi513.LOG here]

Having run this initial calculation, the geometries of the reactants and products were edited to resemble that of a boat transition state. The same calculation was run again ( log file [https://wiki.ch.ic.ac.uk/wiki/images/5/53/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_oi513.LOG here]) The results of the two runs are summarized in the table below.

{| class="wikitable" border="1"
|+ Boat Transition state: QTS2 method
|-
! !! Arbitrary !! Boat-Like
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_secondtrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_properconformer_firsttrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Terminal C-C bond length (Angstrom)|| 2.02 || 2.14
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.38
|}

==== Endpiece: Comparing the Boat & Chair ====

To conclude this section of the study, the transition states will be optimised using the Intrinsic reaction coordinate (IRC) method. Arguably the defining feature of this approach is the ability to track the reaction coordinate from the transition state to a local minimum by taking minute steps along negative,steep gradients of the potential energy surface. This bears many favourable features for users to define at will namely defining how many steps to be taken in the calculation and the direction of the gradient should run from the transition state.

The IRC method was applied to the optimised chair conformer. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/a/a3/TSHYPOTHESIS_TRAILTWO_ForIRCcalculation_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_ForIRC_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

The same molecule was then further optimised to find a minimum under the HF/3-21G level of theory. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/d/d5/TSHYPOTHESIS_TRAILTWO_ForIRC_oi513.LOG here] 

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_PostIRC_Reopt.mol2</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC graphs oi513.png|thumb| figure 5: The Intrinsic Reaction Coordinates for the calculation. The convergence to a zero gradient indicates the structure optmisation has converged.]]

As seen by the the results of re-optimisation post-IRC, the conformer best represent that of the gauche2 state supported by the point group being C2. To allow activation energies to be calculated, a gauche 2 conformer was constructed and optimised under the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/5/51/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_HF312G_oi513.LOG here]) followed by the B3LYP/631G* level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/b/b8/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_REOPT_631GD_oi513.LOG here]) The thermochemical data can then be retrieved and be used as the reactants on the reaction coordinate pathway. Thus the difference in energy between the gauche2 conformer and the boat and chair transition states can be calculated

Lastly, optmised chair and boat structures were re-optimised under the a higher level of theory (B3LYP/6-31G*) with the resultant log files presented [https://wiki.ch.ic.ac.uk/wiki/images/3/34/TSHYPOTHESIS_TRAILTWO_ChairTS_631GdOpt_oi513.LOG here] and [https://wiki.ch.ic.ac.uk/wiki/images/5/5e/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_631Gd_reopt.LOG there] respectively

== The Diels Alder Cycloaddition: Computational Investigations ==

=== Overview ===

=== Simple Systems: S-cis butadiene and ethene ===

As an introduction to a cycloaddition, the reaction between ethene and butadiene was investigated.
setting the two vinyl protons in the same plane (i.e C1C2C3C4 dihedral angle = 0), the molecule was optmised under the Semi empirical am 1 method. Similarly, a molecule of cis-butadiene was optimised. The table below shows the results of optimisation

{| class="wikitable" border="1"
! !! Ethane !! S-cis butadiene
|-
|Jmol || cell || cell
|-
| Point Group || cell || cell
|-
| HOMO || cell || cell
|-
| LUMO || cell || cell
|-
| LOG files || cell || cell
|}

following reactant optimisation,the fragments were arranged into a guess transition state (using the same concepts explored in the cope rearrangement investigations. The terminal Carbons on each fragment was fixed to be 2.2 angstrom apart. The resultant TS structure had a single imaginary frequency confirming formation of a transition state. The log file for optmisation can be found here.

jmol file of the transition state

insert image of HOMO and LUMO 

animate frequency

The geometrical data was also extracted from the transition state, they are presented in the table below

{| class="wikitable" border="1"
! Carbon Atoms !! Bond Lenghts (Angstrom)
|-
|cell || cell
|}

=== Complex systems: Maelic anydride and Cyclohexadiene ===

Using the same concepts explored in the cycloaddition investigations with the two unfunctionalised alkenes, the properties of the Diels Alder reaction between Maleic anhydride and cyclohexa-1,3-diene was investigated. As we will see, the regiochemistry of the reaction comes into play as the arrangement of the two subtrates prior to bond making/breaking gives rise to two different trasnition states (an exo and an endo state). Obtaining Molecular orbital data for of the two states will account for differences in the observed energies of the transition states.

the two reactants were optimised under the Semi empirical am1 method. The results of the calculations are presented in the table below

{| class="wikitable" border="1"
Optmising the reactants
! !! Maelic anhydride !! Cyclohexadiene
|-
|Jmol || cell || cell
|-
|Point group || cell || cell
|-
|HOMO || cell || cell
|-
|LUMO || cell || cell
|-
|LOG || cell || cell
|}

As per routine, a guess transition structure had to be constructed using the optimised fragments. In this case, we have stereo-distinction between two possible transition states, and exo form and an endo form.

For both endo and exo forms, terminal C-C bond distances were set and fixed to 2.2 Angstrom and the molecule adapted to represent a postulated transition state fro the respective forms. an optimisation + frequency calculation was carried out an the results given below

{| class="wikitable" border="1"
! !! Exo transition state !! Endo Transition state
|-
|Jmol || cell || cell
|-
|HOMO || cell || cell
|-
|LUMO || cell || cell
|-
|Imaginary frequency || cell || cell
|-
Log files || cell || cell
|}

Geometry data for the two states was also collected. The results are presented below

{| class="wikitable" border="1"
! colspan="2"|Exo transition State !! ! colspan="3"|Endo Transition state
|-
|bond || values || bond || values
|-
| C1-C2 || 1.49 || C1-C2 || 1.41
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|}
Lastly, thermochemical data was collated and the results given below

Exo

Sum of electronic and zero-point Energies= 0.134882
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.0991180.099118

Endo

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

Rep:Mod:Peebo

2015-12-18T10:08:42Z

Oi513: /* Transition state investigations */

== Introduction ==

=== Overview ===
Fundamental to organic chemistry are pericyclic reactions that involve concerted movement of electrons through a cyclic transition state. Cycloadditions, a subset of pericyclic reactions, serve as a essential synthetic tool for organic chemists as a basis for accessing more complex structures in, for example, total synthesis of natural products [1]. In addition, sigmatropic rearrangements, and electrocyclic reactions are also a set of important pericyclic reactions that see Δσ 0 or ±1 respectively. For Diels alder and ene reactions, the initial arrangement of the fragments is brought into question when trying to understand the stereochemical outcome of the reaction. Other than these geometric factors, the frontier orbitals of the two fragments contain valuable information into predicting whether the two reactants may proceed to reach a product[2].

Robert Burns Woodward and Roald Hoffman established rules to explain whether a given pericyclic reaction may be thermally or photochemically allowed to give the said product. Naturally incorporated in their approach is considerations of the molecular orbitals involved in the reaction, the number of electrons, and the symmetry with respect to the connectivity between the two fragments. First applied to electrocyclic reactions [3], the two would then go on to publish more papers to fully develop their rules setting a universal foundation for understanding these class of reactions

Given the wealth factors that contribute towards going from reactants --> products, it is of the best interests to synthetic chemists to understand the mechanistic basis behind the reaction and therefore ,for example, the observed stereochemistry as opposed to whether a given reaction may be allowed or forbidden (in conjunction with Woodward-Hoffman rules). As such, computational methods into investigating diels alder reaction pathways have come to light[4][5] and have shown to provide insight into the optimal positioning of fragments and the structure and energy of Transition states. Studying transition states in particular are a huge advantage in computational studies; through this medium, calculations on energies of these states can be probes that would otherwise be immeasurable due to the fleeting nature of the transition state.

=== Experimental Aims ===
In this exercise, we first investigate the energies of varying 1-5 hexadiene conformers and investigate the possible cyclic transition states whilst it undergoes the cope rearrangement using the Hartree-Fock/3-21G and B3LYP/6-31G(d) levels of theory in addition to exploring Transition state optimization methods QTS2 and TS(Berny). Using similar methods, we then go on to develop our discussion of transition states by through investigating the regioselectivity of the Diels Alder reaction between maelic anhydride and 1-3 cyclohexadiene including molecular orbital interactions.

=== Brief note: Computational Methods ===

In this investigation, we explore different levels of theory to apply alongside our calculations as each have both advantageous features, and their respective drawbacks. Hatree fock method is used to determine both energies and quantum mechanical wavefunction of a multi-body system in state that has its probability density (position of the body in question) independent of time (i.e a stationary state). Amongst the appreciable number of approximations made by this method, the assumption that many electron wavefunction of the body in question will take the form of a just an isolated determinant (slater determinant) derived from a single electron wavefunction. Whist in theory this is entirely possible through linear combination of atomic orbitals, this naturally causes this approach to overlook the replusive interactions between the electrons in the system thus producing energies that are overestimated.

By virtue The Hohenberg-Kohn Theorems, the total energy of a ground state is exclusively dependent on electron density and distribution. Focusing in on this aspect and overlooking the electronic wavefunctions give rise to density functional theory. This method will aim to minimize energy via changes in electron density in a body. In addition to this, Electron correlations are taken into account and the mean field approximation is relaxed However, one key drawback in this theory is that it is not certain that using a more complicated basis set my necessarily produce a more accurate answer; the theory is not variational whereas the HF theory actively is.

== The Cope rearrangement: Computational Investigations ==

=== Overview ===

1-5 hexadiene provides a relatively simple system to observe a cope rearrangement. Through Woodward-Hoffmann analysis, we see that this [3,3] sigmatropic rearrangement is thermally allowed by virtue of the equation (4q + 2)s + (4r)a. Figure 2 provides one way in which the reaction can proceed via these rules with a single σ2s component and two π2a components. [[File:Computation_Coperearrangement.jpg|thumb|Figure 1: An overview of the cope rearrangement going through the cyclic 6M transition state.]]
During the concerted formation/dissociation of bonds, the transition state resembles that of a six membered ring which can exhibit a chair or boat topology (in line with the conformers of cyclohexane) These transition states represent energy maxima on the reaction pathway from reactants to products. On the other hand, 1-5 hexadiene exists in many conformers representing an energy minimum. In the following section, we obtain optimal structures for the diene on different levels of theory followed by locating the position of the TS on the potential energy surface. In doing this, we can appropriately deduce the activation energy involve in the cope rearrangement through the chair TS and boat TS pathways.

[[File:CompLab_Figure3_hexadieneconformers.jpg|thumb|Figure 3: Newman projections for hexadiene showing antiperiplanar and gauche arrangements of vinyl groups.150px]]
[[File:Complab_copeWoodwardHoffman.jpg|thumb|Figure 2: Woodward-Hoffmann analysis of the [3,3] sigmatropic rearrangement. the orbitals can "connect" through an suprafacial or antarafacial manner to make or break the bonds in the product.]]

=== Optimizing reactants and products ===

The substrate under investigation can adopt many different conformers with respect to the central C3-C4 bond as seen in figure 3. Within the conformers laid out in the diagram exists a subset of more isomers that differ in the exact positioning of the vinyl group relative to the rest of the molecule as opposed to just the other vinyl group. Initiative would serve to think the antiperiplanar set of isomers would be of lower energy than the gauche type isomers purely on the argument of steric repulsion between the two vinyl groups. Various conformers of Hexadiene the consist of gauche and antiperiplanr motifs were optimized and the results posted in the table below. The nomenclature of conformers are with respect to appendix 2

{| class="wikitable" border="1"
|+ Optimization of 1-5 hexadiene conformers
! placeholder !! Gauche3 !! Anti2 !! Anti1 !! Gauche(1)
|-
| Image || <jmol><jmolApplet>
<title></title>
<color>White</color>
<size>200</size>
<uploadedFileContents>Gauche3conformer.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet></jmol>|| <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet>react_anticonformer.mol2</jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_gaucheconformer.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy (Hartres) || -231.69266122 || -231.69253516 || -231.69260235 || -231.68771610
|-
| Point Group || C1 || Ci || C2 || C2
|-
| log || [https://wiki.ch.ic.ac.uk/wiki/images/c/c1/GAUCHE3CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/dd/REACT_ANTICONFORMER.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/6b/TRAILCONFORMER_TWO_ANTI1CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/REACT_GAUCHECONFORMER_oi513.LOG file]
|}

In comparison with literature reference values there is very good agreement. Interestingly, the lowest energy conformer reveals itself as a gauche type conformer which is contrary to initial predictions. Visualizing the molecular orbitals indicates favorable electronic interactions in the gauche3 setup; the two pi systems of the vinyl groups are in close enough proximity to yield a favourable in phase overlap which isn't possible in the anti conformation purely on the grounds of spacial arrangement. The gauche3 conformer serves as a balance between repulsive steric interactions and attractive molecular orbital-overlap interactions.

[[File:CompLab_Figure4_conformerorbitals.jpg|thumb|Figure 4: The orbitals HOMO of Gauche3 and Anti1 conformers on the left and right respectively of 1-5 hexadiene. As seen, there is a favourable in phase overlap between the the pi systems of the two vinyl groups]]

We can now approach the optimization of hexadiene on a different level of theory. The HF_3-21G optimized anti2 conformer of the alkene was then re-optimized under DFT_6-31G(d) level of theory. The geometrical differences arising form these two different methods of computation are summarized below.

{| class="wikitable" border="1"
|+anti conformer
|-
!colspan="4" style="text-align: left;"|[[File:anti2conformer_forrepresentingtheHF_321Glevel.png|600px]]
|-
|   ||   || HF/3-21G || B3LYP/6-31G*
|-
| rowspan="3" | Bond Lengths (Angstrom) || C1-C2 || 1.32 || 1.33
|-
| C2-C3 || 1.51 || 1.50
|-
| C3-C4 || 1.55 || 1.55
|-
| rowspan="3" | Bond Angles (Degrees) || C1-C2-C3 || 124.80 || 125.29
|-
| C2-C3-C4 || 111.34 || 112.65
|-
| C1-C2-C3-C4 || 114.63 || 118.58
|}

Being immediately observable is the increase in bond length with the B3LYP/6-31G* level of theory in comparison to HF/3-21G. Within the same level of theory however, the HF/3-21G method describes less of a distinction between bond lengths of C-C single bonds and C-C double bonds. This may also be detectable by running frequency calculations and visualizing the vibrations involving the C=C bonds in both conformers.

Frequency analysis of the B3LYP/6-31G* optimised structure was carried out. Gaussian carries out this procedure by applying the equation for force constants [[File:Force_constant_equation_oi513.png]] (where C = 1/2π) and preforming calculations to see a convergence in the force constant. The absence of imaginary frequencies would indicate that we have indeed reached a true minimum on the potential energy surface. A summary of the optimisation is given below

{| class="wikitable" border="1"
|+ Frequency calculations
! Frequency summary !! Spectrum
|-
| [[File:CompLab_SpectraofFrequencies_oi513.png]]|| [[File:CompLab SummaryofFrequencies oi513.png]]
|}

The thermodynamic properties were noted post-optimisation and printed as follows (units in Hartrees)

Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461864
Sum of electronic and thermal Enthalpies= -234.460920

=== Transition state investigations ===

==== Overview ====

Having processed information about the reaction reactants/products, we can now try to approach mining information about a different area on the potential energy surface; the transition states.

As eluded to earlier, the reaction proceeds via a 6 membered ring transition state that can exhibit a boat or chair toplogy. In this section, we aim to find these states on the potential energy surface, assess their energies and consequently determine the activation energy involved in both pathways. We will start by building and optimising the fragments of the transition states, and running further frequency/optimisation calculations.

Defining a transition state requires a degree of appreciation for the reaction mechanism being explored. In this case, the two allyl fragements that will be used need to exhibit sensible geometry to allow for a completed freq + opt calculation to be run to completion. Two different methods of computing the transition state are explored in this section. In the first method, the frozen coordinates approach is taken. This involves locking the reaction coordinate whilst minimisation of the rest of the molecule is performed (through any method of choice including Hf/3-21G, B3LYP/6-31G* levels of theory). Another optimsation can then be run which will optimize the rest of the molecule.

The second approach involves calculating the force constant along the reaction coordinate with both the number of steps along the coordinate and the direction to run the calculation both being defined by the user. In this approach however, It is important that the guess structure of the transition state is quite close to the actual case.

To start this investigation, the frozen coordinate methods were applied.

==== The Chair ====

After optimising an single allyl (CH2CHCH2) through the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/0/05/ALLYLFRAG_HF_321G_oi513.LOG here]), two of the said fragments were arranged in a chair conformation, with terminal C-C bond distance (between two fragements) set to 2.2 Å

<jmol><jmolApplet>
<title>HF/3-21G allyl fragment</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Allylfrag_HF_321g_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

This "guess" transition state was then run through an Frequency + Optimisation job (the log file of which can be located [https://wiki.ch.ic.ac.uk/wiki/images/0/0e/TSHYPOTHESIS_TRAILTWO_oi513.LOG here]) introducing the TS(Berny) optimisation method. This method works by employing the Berny algorithm. An approximate Hessian matrix (constituted by calculating second derivatives of energy) is developed using parameters of the initial structure including the valence force field. this approximation is then updated by calculating energies along the reaction pathway until a convergence is observed. Thus, the approximate matrix is a key factor in determining the success of the calculation. For most cases, using the approximate hessian serves well for the rest of the optimisation of the molecule, but in the cases where the the hessian changes dramatically, the force constant can be computed along every point of the reaction pathway. At the expense of time and computational power, the opitmisation will be able to find the local minimum.

<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

Inspection of the vibrations shows a single imaginary frequency (negative cm-1) at -817.94 cm-1 This "guess structure" method provides a reference/basis to which the frozen method can be compared with.

Imaginary frequencies are given such names due to the complex nature of their absolute values. Eigenvalues of hessian matrices correspond to squared harmonic oscillations of the normal vibration modes. thus a the square root of a negative eigenvalue gives rise a complex number with an imaginary component. Taking a simple plot of the harmonic oscillator (potential energy vs bond displacement), a negative second derivative would indicate that the geometry to which the reaction coordinate is abiding by is hitting a maximum (i.e. achieving transition state status). Thus if a transition state has been calculated, only one imaginary frequency should be as a result of the optimisation.

The frozen coordinate approach was then used to compute the transition. The (to be formed) bond between the terminal C's on both allyl fragments were strictly fixed/frozen to 2.2 Å followed by an optimisation. The log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/b/bb/TSBONDMODIFY_TCSET_COPY_TRAILONE_oi513.LOG here]. Having optimised the rest of the molecule with the mentioned bonds of interest fixed, the bonds will be accounted for in a second optimisation to which the log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/TSBONDMODIFY_TCSET_UNIDENTIFIEDDESTINATION_oi513.LOG here]

To summarize, the chair transition state has be investigated through a reference setup and an frozen coordinate setup. The table of results below give an account of the results of the two setups.

{| class="wikitable" border="1"
|+ Chair Transition State analysis
|-
| colspan="3" align="center"|[[File:CompLab_ChairTS_oi513.png]]
|-
! !! Guess TS !! Frozen TS
|-
| Terminal C-C Bond Length (Angstrom) || 2.02 || 2.02
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.39 ||
|-
| C-C-C angle || 120.50 || 120.49
|-
| animated frequency ||
<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || cell
|-
|}

==== The Boat ====

Having exhausted the chair TS, computations in the Boat conformer will be brought under investigation. In this section, more computational methods that investigate transition states will be explored. The QTS2 methods works by using user defined reactants and products and attempts to conceive new data points via interpolation such to find the transition state between them. The substrate was setup and labelled to depict reactants and product and was subsequently processed with the QTS2 method. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/c/c5/BOATTS_TWOMOLECULESETUP_SECONDTRAIL_oi513.LOG here]

Having run this initial calculation, the geometries of the reactants and products were edited to resemble that of a boat transition state. The same calculation was run again ( log file [https://wiki.ch.ic.ac.uk/wiki/images/5/53/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_oi513.LOG here]) The results of the two runs are summarized in the table below.

{| class="wikitable" border="1"
|+ Boat Transition state: QTS2 method
|-
! !! Arbitrary !! Boat-Like
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_secondtrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_properconformer_firsttrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Terminal C-C bond length (Angstrom)|| 2.02 || 2.14
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.38
|-
| Animated frequency || cell || cell
|}

==== Endpiece: Comparing the Boat & Chair ====

To conclude this section of the study, the transition states will be optimised using the Intrinsic reaction coordinate (IRC) method. Arguably the defining feature of this approach is the ability to track the reaction coordinate from the transition state to a local minimum by taking minute steps along negative,steep gradients of the potential energy surface. This bears many favourable features for users to define at will namely defining how many steps to be taken in the calculation and the direction of the gradient should run from the transition state.

The IRC method was applied to the optimised chair conformer. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/a/a3/TSHYPOTHESIS_TRAILTWO_ForIRCcalculation_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_ForIRC_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

The same molecule was then further optimised to find a minimum under the HF/3-21G level of theory. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/d/d5/TSHYPOTHESIS_TRAILTWO_ForIRC_oi513.LOG here] 

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_PostIRC_Reopt.mol2</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC graphs oi513.png|thumb| figure 5: The Intrinsic Reaction Coordinates for the calculation. The convergence to a zero gradient indicates the structure optmisation has converged.]]

As seen by the the results of re-optimisation post-IRC, the conformer best represent that of the gauche2 state supported by the point group being C2. To allow activation energies to be calculated, a gauche 2 conformer was constructed and optimised under the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/5/51/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_HF312G_oi513.LOG here]) followed by the B3LYP/631G* level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/b/b8/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_REOPT_631GD_oi513.LOG here]) The thermochemical data can then be retrieved and be used as the reactants on the reaction coordinate pathway. Thus the difference in energy between the gauche2 conformer and the boat and chair transition states can be calculated

Lastly, optmised chair and boat structures were re-optimised under the a higher level of theory (B3LYP/6-31G*) with the resultant log files presented [https://wiki.ch.ic.ac.uk/wiki/images/3/34/TSHYPOTHESIS_TRAILTWO_ChairTS_631GdOpt_oi513.LOG here] and [https://wiki.ch.ic.ac.uk/wiki/images/5/5e/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_631Gd_reopt.LOG there] respectively

== The Diels Alder Cycloaddition: Computational Investigations ==

=== Overview ===

=== Simple Systems: S-cis butadiene and ethene ===

As an introduction to a cycloaddition, the reaction between ethene and butadiene was investigated.
setting the two vinyl protons in the same plane (i.e C1C2C3C4 dihedral angle = 0), the molecule was optmised under the Semi empirical am 1 method. Similarly, a molecule of cis-butadiene was optimised. The table below shows the results of optimisation

{| class="wikitable" border="1"
! !! Ethane !! S-cis butadiene
|-
|Jmol || cell || cell
|-
| Point Group || cell || cell
|-
| HOMO || cell || cell
|-
| LUMO || cell || cell
|-
| LOG files || cell || cell
|}

following reactant optimisation,the fragments were arranged into a guess transition state (using the same concepts explored in the cope rearrangement investigations. The terminal Carbons on each fragment was fixed to be 2.2 angstrom apart. The resultant TS structure had a single imaginary frequency confirming formation of a transition state. The log file for optmisation can be found here.

jmol file of the transition state

insert image of HOMO and LUMO 

animate frequency

The geometrical data was also extracted from the transition state, they are presented in the table below

{| class="wikitable" border="1"
! Carbon Atoms !! Bond Lenghts (Angstrom)
|-
|cell || cell
|}

=== Complex systems: Maelic anydride and Cyclohexadiene ===

Using the same concepts explored in the cycloaddition investigations with the two unfunctionalised alkenes, the properties of the Diels Alder reaction between Maleic anhydride and cyclohexa-1,3-diene was investigated. As we will see, the regiochemistry of the reaction comes into play as the arrangement of the two subtrates prior to bond making/breaking gives rise to two different trasnition states (an exo and an endo state). Obtaining Molecular orbital data for of the two states will account for differences in the observed energies of the transition states.

the two reactants were optimised under the Semi empirical am1 method. The results of the calculations are presented in the table below

{| class="wikitable" border="1"
Optmising the reactants
! !! Maelic anhydride !! Cyclohexadiene
|-
|Jmol || cell || cell
|-
|Point group || cell || cell
|-
|HOMO || cell || cell
|-
|LUMO || cell || cell
|-
|LOG || cell || cell
|}

As per routine, a guess transition structure had to be constructed using the optimised fragments. In this case, we have stereo-distinction between two possible transition states, and exo form and an endo form.

For both endo and exo forms, terminal C-C bond distances were set and fixed to 2.2 Angstrom and the molecule adapted to represent a postulated transition state fro the respective forms. an optimisation + frequency calculation was carried out an the results given below

{| class="wikitable" border="1"
! !! Exo transition state !! Endo Transition state
|-
|Jmol || cell || cell
|-
|HOMO || cell || cell
|-
|LUMO || cell || cell
|-
|Imaginary frequency || cell || cell
|-
Log files || cell || cell
|}

Geometry data for the two states was also collected. The results are presented below

{| class="wikitable" border="1"
! colspan="2"|Exo transition State !! ! colspan="3"|Endo Transition state
|-
|bond || values || bond || values
|-
| C1-C2 || 1.49 || C1-C2 || 1.41
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|}
Lastly, thermochemical data was collated and the results given below

Exo

Sum of electronic and zero-point Energies= 0.134882
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.0991180.099118

Endo

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

Rep:Mod:Peebo

2015-12-18T09:59:58Z

Oi513: /* Transition state investigations */

== Introduction ==

=== Overview ===
Fundamental to organic chemistry are pericyclic reactions that involve concerted movement of electrons through a cyclic transition state. Cycloadditions, a subset of pericyclic reactions, serve as a essential synthetic tool for organic chemists as a basis for accessing more complex structures in, for example, total synthesis of natural products [1]. In addition, sigmatropic rearrangements, and electrocyclic reactions are also a set of important pericyclic reactions that see Δσ 0 or ±1 respectively. For Diels alder and ene reactions, the initial arrangement of the fragments is brought into question when trying to understand the stereochemical outcome of the reaction. Other than these geometric factors, the frontier orbitals of the two fragments contain valuable information into predicting whether the two reactants may proceed to reach a product[2].

Robert Burns Woodward and Roald Hoffman established rules to explain whether a given pericyclic reaction may be thermally or photochemically allowed to give the said product. Naturally incorporated in their approach is considerations of the molecular orbitals involved in the reaction, the number of electrons, and the symmetry with respect to the connectivity between the two fragments. First applied to electrocyclic reactions [3], the two would then go on to publish more papers to fully develop their rules setting a universal foundation for understanding these class of reactions

Given the wealth factors that contribute towards going from reactants --> products, it is of the best interests to synthetic chemists to understand the mechanistic basis behind the reaction and therefore ,for example, the observed stereochemistry as opposed to whether a given reaction may be allowed or forbidden (in conjunction with Woodward-Hoffman rules). As such, computational methods into investigating diels alder reaction pathways have come to light[4][5] and have shown to provide insight into the optimal positioning of fragments and the structure and energy of Transition states. Studying transition states in particular are a huge advantage in computational studies; through this medium, calculations on energies of these states can be probes that would otherwise be immeasurable due to the fleeting nature of the transition state.

=== Experimental Aims ===
In this exercise, we first investigate the energies of varying 1-5 hexadiene conformers and investigate the possible cyclic transition states whilst it undergoes the cope rearrangement using the Hartree-Fock/3-21G and B3LYP/6-31G(d) levels of theory in addition to exploring Transition state optimization methods QTS2 and TS(Berny). Using similar methods, we then go on to develop our discussion of transition states by through investigating the regioselectivity of the Diels Alder reaction between maelic anhydride and 1-3 cyclohexadiene including molecular orbital interactions.

=== Brief note: Computational Methods ===

In this investigation, we explore different levels of theory to apply alongside our calculations as each have both advantageous features, and their respective drawbacks. Hatree fock method is used to determine both energies and quantum mechanical wavefunction of a multi-body system in state that has its probability density (position of the body in question) independent of time (i.e a stationary state). Amongst the appreciable number of approximations made by this method, the assumption that many electron wavefunction of the body in question will take the form of a just an isolated determinant (slater determinant) derived from a single electron wavefunction. Whist in theory this is entirely possible through linear combination of atomic orbitals, this naturally causes this approach to overlook the replusive interactions between the electrons in the system thus producing energies that are overestimated.

By virtue The Hohenberg-Kohn Theorems, the total energy of a ground state is exclusively dependent on electron density and distribution. Focusing in on this aspect and overlooking the electronic wavefunctions give rise to density functional theory. This method will aim to minimize energy via changes in electron density in a body. In addition to this, Electron correlations are taken into account and the mean field approximation is relaxed However, one key drawback in this theory is that it is not certain that using a more complicated basis set my necessarily produce a more accurate answer; the theory is not variational whereas the HF theory actively is.

== The Cope rearrangement: Computational Investigations ==

=== Overview ===

1-5 hexadiene provides a relatively simple system to observe a cope rearrangement. Through Woodward-Hoffmann analysis, we see that this [3,3] sigmatropic rearrangement is thermally allowed by virtue of the equation (4q + 2)s + (4r)a. Figure 2 provides one way in which the reaction can proceed via these rules with a single σ2s component and two π2a components. [[File:Computation_Coperearrangement.jpg|thumb|Figure 1: An overview of the cope rearrangement going through the cyclic 6M transition state.]]
During the concerted formation/dissociation of bonds, the transition state resembles that of a six membered ring which can exhibit a chair or boat topology (in line with the conformers of cyclohexane) These transition states represent energy maxima on the reaction pathway from reactants to products. On the other hand, 1-5 hexadiene exists in many conformers representing an energy minimum. In the following section, we obtain optimal structures for the diene on different levels of theory followed by locating the position of the TS on the potential energy surface. In doing this, we can appropriately deduce the activation energy involve in the cope rearrangement through the chair TS and boat TS pathways.

[[File:CompLab_Figure3_hexadieneconformers.jpg|thumb|Figure 3: Newman projections for hexadiene showing antiperiplanar and gauche arrangements of vinyl groups.150px]]
[[File:Complab_copeWoodwardHoffman.jpg|thumb|Figure 2: Woodward-Hoffmann analysis of the [3,3] sigmatropic rearrangement. the orbitals can "connect" through an suprafacial or antarafacial manner to make or break the bonds in the product.]]

=== Optimizing reactants and products ===

The substrate under investigation can adopt many different conformers with respect to the central C3-C4 bond as seen in figure 3. Within the conformers laid out in the diagram exists a subset of more isomers that differ in the exact positioning of the vinyl group relative to the rest of the molecule as opposed to just the other vinyl group. Initiative would serve to think the antiperiplanar set of isomers would be of lower energy than the gauche type isomers purely on the argument of steric repulsion between the two vinyl groups. Various conformers of Hexadiene the consist of gauche and antiperiplanr motifs were optimized and the results posted in the table below. The nomenclature of conformers are with respect to appendix 2

{| class="wikitable" border="1"
|+ Optimization of 1-5 hexadiene conformers
! placeholder !! Gauche3 !! Anti2 !! Anti1 !! Gauche(1)
|-
| Image || <jmol><jmolApplet>
<title></title>
<color>White</color>
<size>200</size>
<uploadedFileContents>Gauche3conformer.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet></jmol>|| <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_anticonformer.mol2</uploadedFileContents>
</jmolApplet>react_anticonformer.mol2</jmol> || <jmol><jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>react_gaucheconformer.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy (Hartres) || -231.69266122 || -231.69253516 || -231.69260235 || -231.68771610
|-
| Point Group || C1 || Ci || C2 || C2
|-
| log || [https://wiki.ch.ic.ac.uk/wiki/images/c/c1/GAUCHE3CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/dd/REACT_ANTICONFORMER.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/6/6b/TRAILCONFORMER_TWO_ANTI1CONFORMER_oi513.LOG file] || [https://wiki.ch.ic.ac.uk/wiki/images/d/d0/REACT_GAUCHECONFORMER_oi513.LOG file]
|}

In comparison with literature reference values there is very good agreement. Interestingly, the lowest energy conformer reveals itself as a gauche type conformer which is contrary to initial predictions. Visualizing the molecular orbitals indicates favorable electronic interactions in the gauche3 setup; the two pi systems of the vinyl groups are in close enough proximity to yield a favourable in phase overlap which isn't possible in the anti conformation purely on the grounds of spacial arrangement. The gauche3 conformer serves as a balance between repulsive steric interactions and attractive molecular orbital-overlap interactions.

[[File:CompLab_Figure4_conformerorbitals.jpg|thumb|Figure 4: The orbitals HOMO of Gauche3 and Anti1 conformers on the left and right respectively of 1-5 hexadiene. As seen, there is a favourable in phase overlap between the the pi systems of the two vinyl groups]]

We can now approach the optimization of hexadiene on a different level of theory. The HF_3-21G optimized anti2 conformer of the alkene was then re-optimized under DFT_6-31G(d) level of theory. The geometrical differences arising form these two different methods of computation are summarized below.

{| class="wikitable" border="1"
|+anti conformer
|-
!colspan="4" style="text-align: left;"|[[File:anti2conformer_forrepresentingtheHF_321Glevel.png|600px]]
|-
|   ||   || HF/3-21G || B3LYP/6-31G*
|-
| rowspan="3" | Bond Lengths (Angstrom) || C1-C2 || 1.32 || 1.33
|-
| C2-C3 || 1.51 || 1.50
|-
| C3-C4 || 1.55 || 1.55
|-
| rowspan="3" | Bond Angles (Degrees) || C1-C2-C3 || 124.80 || 125.29
|-
| C2-C3-C4 || 111.34 || 112.65
|-
| C1-C2-C3-C4 || 114.63 || 118.58
|}

Being immediately observable is the increase in bond length with the B3LYP/6-31G* level of theory in comparison to HF/3-21G. Within the same level of theory however, the HF/3-21G method describes less of a distinction between bond lengths of C-C single bonds and C-C double bonds. This may also be detectable by running frequency calculations and visualizing the vibrations involving the C=C bonds in both conformers.

Frequency analysis of the B3LYP/6-31G* optimised structure was carried out. Gaussian carries out this procedure by applying the equation for force constants [[File:Force_constant_equation_oi513.png]] (where C = 1/2π) and preforming calculations to see a convergence in the force constant. The absence of imaginary frequencies would indicate that we have indeed reached a true minimum on the potential energy surface. A summary of the optimisation is given below

{| class="wikitable" border="1"
|+ Frequency calculations
! Frequency summary !! Spectrum
|-
| [[File:CompLab_SpectraofFrequencies_oi513.png]]|| [[File:CompLab SummaryofFrequencies oi513.png]]
|}

The thermodynamic properties were noted post-optimisation and printed as follows (units in Hartrees)

Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461864
Sum of electronic and thermal Enthalpies= -234.460920

=== Transition state investigations ===

==== Overview ====

Having processed information about the reaction reactants/products, we can now try to approach mining information about a different area on the potential energy surface; the transition states.

As eluded to earlier, the reaction proceeds via a 6 membered ring transition state that can exhibit a boat or chair toplogy. In this section, we aim to find these states on the potential energy surface, assess their energies and consequently determine the activation energy involved in both pathways. We will start by building and optimising the fragments of the transition states, and running further frequency/optimisation calculations.

Defining a transition state requires a degree of appreciation for the reaction mechanism being explored. In this case, the two allyl fragements that will be used need to exhibit sensible geometry to allow for a completed freq + opt calculation to be run to completion. Two different methods of computing the transition state are explored in this section. In the first method, the frozen coordinates approach is taken. This involves locking the reaction coordinate whilst minimisation of the rest of the molecule is performed (through any method of choice including Hf/3-21G, B3LYP/6-31G* levels of theory). Another optimsation can then be run which will optimize the rest of the molecule.

The second approach involves calculating the force constant along the reaction coordinate with both the number of steps along the coordinate and the direction to run the calculation both being defined by the user. In this approach however, It is important that the guess structure of the transition state is quite close to the actual case.

To start this investigation, the frozen coordinate methods were applied.

==== The Chair ====

After optimising an single allyl (CH2CHCH2) through the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/0/05/ALLYLFRAG_HF_321G_oi513.LOG here]), two of the said fragments were arranged in a chair conformation, with terminal C-C bond distance (between two fragements) set to 2.2 Å

<jmol><jmolApplet>
<title>HF/3-21G allyl fragment</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Allylfrag_HF_321g_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

This "guess" transition state was then run through an Frequency + Optimisation job (the log file of which can be located [https://wiki.ch.ic.ac.uk/wiki/images/0/0e/TSHYPOTHESIS_TRAILTWO_oi513.LOG here]) introducing the TS(Berny) optimisation method. This method works by employing the Berny algorithm. An approximate Hessian matrix (constituted by calculating second derivatives of energy) is developed using parameters of the initial structure including the valence force field. this approximation is then updated by calculating energies along the reaction pathway until a convergence is observed. Thus, the approximate matrix is a key factor in determining the success of the calculation. For most cases, using the approximate hessian serves well for the rest of the optimisation of the molecule, but in the cases where the the hessian changes dramatically, the force constant can be computed along every point of the reaction pathway. At the expense of time and computational power, the opitmisation will be able to find the local minimum.

<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

Inspection of the vibrations shows a single imaginary frequency (negative cm-1) at -817.94 cm-1 This "guess structure" method provides a reference/basis to which the frozen method can be compared with.

Imaginary frequencies are given such names due to the complex nature of their absolute values. Eigenvalues of hessian matrices correspond to squared harmonic oscillations of the normal vibration modes. thus a the square root of a negative eigenvalue gives rise a complex number with an imaginary component. Taking a simple plot of the harmonic oscillator (potential energy vs bond displacement), a negative second derivative would indicate that the geometry to which the reaction coordinate is abiding by is hitting a maximum (i.e. achieving transition state status). Thus if a transition state has been calculated, only one imaginary frequency should be as a result of the optimisation.

The frozen coordinate approach was then used to compute the transition. The (to be formed) bond between the terminal C's on both allyl fragments were strictly fixed/frozen to 2.2 Å followed by an optimisation. The log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/b/bb/TSBONDMODIFY_TCSET_COPY_TRAILONE_oi513.LOG here]. Having optimised the rest of the molecule with the mentioned bonds of interest fixed, the bonds will be accounted for in a second optimisation to which the log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/4/44/TSBONDMODIFY_TCSET_UNIDENTIFIEDDESTINATION_oi513.LOG here]

To summarize, the chair transition state has be investigated through a reference setup and an frozen coordinate setup. The table of results below give an account of the results of the two setups.

{| class="wikitable" border="1"
|+ Chair Transition State analysis
|-
| colspan="3" align="center"|[[File:CompLab_ChairTS_oi513.png]]
|-
! !! Guess TS !! Frozen TS
|-
| rowspan="2" | Bond Length || cell || cell
|-
| cell || cell
|-
| C-C-C angle || cell || cell
|-
| animated frequency ||
<jmol><jmolApplet>
<title>Guess Transition state vibration mode</title>
<color>white</color>
<size>200</size>
<script>frame 1; vibration 2;</script>
<uploadedFileContents>TShypothesis_trailtwo_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || cell
|-
|}

==== The Boat ====

Having exhausted the chair TS, computations in the Boat conformer will be brought under investigation. In this section, more computational methods that investigate transition states will be explored. The QTS2 methods works by using user defined reactants and products and attempts to conceive new data points via interpolation such to find the transition state between them. The substrate was setup and labelled to depict reactants and product and was subsequently processed with the QTS2 method. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/c/c5/BOATTS_TWOMOLECULESETUP_SECONDTRAIL_oi513.LOG here]

Having run this initial calculation, the geometries of the reactants and products were edited to resemble that of a boat transition state. The same calculation was run again ( log file [https://wiki.ch.ic.ac.uk/wiki/images/5/53/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_oi513.LOG here]) The results of the two runs are summarized in the table below.

{| class="wikitable" border="1"
|+ Boat Transition state: QTS2 method
|-
! !! Arbitrary !! Boat-Like
|-
| jmol || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_secondtrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol> || <jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>BoatTS_Twomoleculesetup_properconformer_firsttrail_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>
|-
| Terminal C-C bond length (Angstrom)|| 2.02 || 2.14
|-
| C1-C2/C2-C3 bond length || 1.39 || 1.38
|-
| Animated frequency || cell || cell
|}

==== Endpiece: Comparing the Boat & Chair ====

To conclude this section of the study, the transition states will be optimised using the Intrinsic reaction coordinate (IRC) method. Arguably the defining feature of this approach is the ability to track the reaction coordinate from the transition state to a local minimum by taking minute steps along negative,steep gradients of the potential energy surface. This bears many favourable features for users to define at will namely defining how many steps to be taken in the calculation and the direction of the gradient should run from the transition state.

The IRC method was applied to the optimised chair conformer. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/a/a3/TSHYPOTHESIS_TRAILTWO_ForIRCcalculation_oi513.LOG here].

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_ForIRC_oi513.mol2</uploadedFileContents>
</jmolApplet></jmol>

The same molecule was then further optimised to find a minimum under the HF/3-21G level of theory. The resultant log file can be found [https://wiki.ch.ic.ac.uk/wiki/images/d/d5/TSHYPOTHESIS_TRAILTWO_ForIRC_oi513.LOG here] 

<jmol><jmolApplet>
<color>white</color>
<size>200</size>
<uploadedFileContents>TShypothesis_trailtwo_PostIRC_Reopt.mol2</uploadedFileContents>
</jmolApplet></jmol>

[[File:IRC graphs oi513.png|thumb| figure 5: The Intrinsic Reaction Coordinates for the calculation. The convergence to a zero gradient indicates the structure optmisation has converged.]]

As seen by the the results of re-optimisation post-IRC, the conformer best represent that of the gauche2 state supported by the point group being C2. To allow activation energies to be calculated, a gauche 2 conformer was constructed and optimised under the HF/3-21G level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/5/51/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_HF312G_oi513.LOG here]) followed by the B3LYP/631G* level of theory (log file [https://wiki.ch.ic.ac.uk/wiki/images/b/b8/CONFORMERMATCHFORPOSTIRCCALC_GAUCHE2CONFORMER_REOPT_631GD_oi513.LOG here]) The thermochemical data can then be retrieved and be used as the reactants on the reaction coordinate pathway. Thus the difference in energy between the gauche2 conformer and the boat and chair transition states can be calculated

Lastly, optmised chair and boat structures were re-optimised under the a higher level of theory (B3LYP/6-31G*) with the resultant log files presented [https://wiki.ch.ic.ac.uk/wiki/images/3/34/TSHYPOTHESIS_TRAILTWO_ChairTS_631GdOpt_oi513.LOG here] and [https://wiki.ch.ic.ac.uk/wiki/images/5/5e/BOATTS_TWOMOLECULESETUP_PROPERCONFORMER_FIRSTTRAIL_631Gd_reopt.LOG there] respectively

== The Diels Alder Cycloaddition: Computational Investigations ==

=== Overview ===

=== Simple Systems: S-cis butadiene and ethene ===

As an introduction to a cycloaddition, the reaction between ethene and butadiene was investigated.
setting the two vinyl protons in the same plane (i.e C1C2C3C4 dihedral angle = 0), the molecule was optmised under the Semi empirical am 1 method. Similarly, a molecule of cis-butadiene was optimised. The table below shows the results of optimisation

{| class="wikitable" border="1"
! !! Ethane !! S-cis butadiene
|-
|Jmol || cell || cell
|-
| Point Group || cell || cell
|-
| HOMO || cell || cell
|-
| LUMO || cell || cell
|-
| LOG files || cell || cell
|}

following reactant optimisation,the fragments were arranged into a guess transition state (using the same concepts explored in the cope rearrangement investigations. The terminal Carbons on each fragment was fixed to be 2.2 angstrom apart. The resultant TS structure had a single imaginary frequency confirming formation of a transition state. The log file for optmisation can be found here.

jmol file of the transition state

insert image of HOMO and LUMO 

animate frequency

The geometrical data was also extracted from the transition state, they are presented in the table below

{| class="wikitable" border="1"
! Carbon Atoms !! Bond Lenghts (Angstrom)
|-
|cell || cell
|}

=== Complex systems: Maelic anydride and Cyclohexadiene ===

Using the same concepts explored in the cycloaddition investigations with the two unfunctionalised alkenes, the properties of the Diels Alder reaction between Maleic anhydride and cyclohexa-1,3-diene was investigated. As we will see, the regiochemistry of the reaction comes into play as the arrangement of the two subtrates prior to bond making/breaking gives rise to two different trasnition states (an exo and an endo state). Obtaining Molecular orbital data for of the two states will account for differences in the observed energies of the transition states.

the two reactants were optimised under the Semi empirical am1 method. The results of the calculations are presented in the table below

{| class="wikitable" border="1"
Optmising the reactants
! !! Maelic anhydride !! Cyclohexadiene
|-
|Jmol || cell || cell
|-
|Point group || cell || cell
|-
|HOMO || cell || cell
|-
|LUMO || cell || cell
|-
|LOG || cell || cell
|}

As per routine, a guess transition structure had to be constructed using the optimised fragments. In this case, we have stereo-distinction between two possible transition states, and exo form and an endo form.

For both endo and exo forms, terminal C-C bond distances were set and fixed to 2.2 Angstrom and the molecule adapted to represent a postulated transition state fro the respective forms. an optimisation + frequency calculation was carried out an the results given below

{| class="wikitable" border="1"
! !! Exo transition state !! Endo Transition state
|-
|Jmol || cell || cell
|-
|HOMO || cell || cell
|-
|LUMO || cell || cell
|-
|Imaginary frequency || cell || cell
|-
Log files || cell || cell
|}

Geometry data for the two states was also collected. The results are presented below

{| class="wikitable" border="1"
! colspan="2"|Exo transition State !! ! colspan="3"|Endo Transition state
|-
|bond || values || bond || values
|-
| C1-C2 || 1.49 || C1-C2 || 1.41
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|-
| cell ||
|}
Lastly, thermochemical data was collated and the results given below

Exo

Sum of electronic and zero-point Energies= 0.134882
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145826
Sum of electronic and thermal Free Energies= 0.0991180.099118

Endo

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

File:TSHYPOTHESIS TRAILTWO ChairTS 631GdOpt oi513.LOG

2015-12-18T09:53:45Z

Oi513:

File:BOATTS TWOMOLECULESETUP PROPERCONFORMER FIRSTTRAIL 631Gd reopt.LOG

2015-12-18T09:52:40Z

Oi513:

File:CONFORMERMATCHFORPOSTIRCCALC GAUCHE2CONFORMER REOPT 631GD oi513.LOG

2015-12-18T09:43:29Z

Oi513:

File:CONFORMERMATCHFORPOSTIRCCALC GAUCHE2CONFORMER HF312G oi513.LOG

2015-12-18T09:42:25Z

Oi513:

File:IRC graphs oi513.png

2015-12-18T09:39:35Z

Oi513:

File:TSHYPOTHESIS TRAILTWO ForIRCcalculation oi513.LOG

2015-12-18T09:38:06Z

Oi513:

File:TShypothesis trailtwo PostIRC Reopt.mol2

2015-12-18T09:33:55Z

Oi513: