Rep:Ss2310:Module 3

Module 3

Cope Rearrangement: [3,3] sigmatropic shift

The above mechanism shows that there is a flow of 6 electrons during the rearrangement process. According to the Huckel rule (4n+2) this means that the intermediate transition state possesses aromatic character and is therefore more stabilised energetically due to favourable delocalisation. Interestingly, the intermediate also has higher symmetry than either the reactant or product.

Optimising 'anti' 1,5-hexadiene

The first step taken was to draw 1,5-hexadiene in Guassview and ensure that central 4 carbons had anti-periplanar conformation. Structure was 'cleaned' and then optimised. The calculation set-up was as follows: 1. Job Type: Optimisation 2. Method: Hartree-Fock, 3-21G basis set 3. Link 0: mem%500MB 4. Once the job had completed the chk file was opened.

**Table summarising 'anti' and 'gauche' 1,5-hexadiene conformations**
Conformer	Energy(a.u.)	Point group (Symmetrised)	Dipole moment (Debeye)	Structure
anti 2	-231.69253529	Ci	0.0002	Link to optimised 1,5-hexadiene (anti2) [1]
gauche 2	-231.69166696	C2	0.3799	Link to optimised 1,5-hexadiene (gauche2)[2]

Job convergence information:

(i) Anti 2

         Item               Value     Threshold  Converged?
 Maximum Force            0.000034     0.000450     YES
 RMS     Force            0.000007     0.000300     YES
 Maximum Displacement     0.001226     0.001800     YES
 RMS     Displacement     0.000346     0.001200     YES
 Predicted change in Energy=-1.334886D-08
 Optimization completed.
    -- Stationary point found.

(ii) Gauche 2

        Item               Value     Threshold  Converged?
 Maximum Force            0.000118     0.000450     YES
 RMS     Force            0.000024     0.000300     YES
 Maximum Displacement     0.001511     0.001800     YES
 RMS     Displacement     0.000383     0.001200     YES
 Predicted change in Energy=-8.082607D-08
 Optimization completed.
    -- Stationary point found.

Lowest Energy Conformation

**Lowest energy 'anti' and 'gauche' 1,5-hexadiene conformations**
Conformer	Energy(a.u.)	Point group (Symmetrised)	Dipole moment (Debeye)	Structure
anti 1	-231.69260235	C2	0.2021	Link to optimised 1,5-hexadiene (anti1) [3]
gauche 1	-231.68771617	C2	0.4557	Link to optimised 1,5-hexadiene (gauche1)[4]

Job convergence information:

(i) anti 1

         Item               Value     Threshold  Converged?
 Maximum Force            0.000056     0.000450     YES
 RMS     Force            0.000010     0.000300     YES
 Maximum Displacement     0.001565     0.001800     YES
 RMS     Displacement     0.000459     0.001200     YES
 Predicted change in Energy=-2.090792D-08
 Optimization completed.
    -- Stationary point found.

(ii) gauche 1

         Item               Value     Threshold  Converged?
 Maximum Force            0.000008     0.000450     YES
 RMS     Force            0.000002     0.000300     YES
 Maximum Displacement     0.000242     0.001800     YES
 RMS     Displacement     0.000084     0.001200     YES
 Predicted change in Energy=-1.777507D-09
 Optimization completed.
    -- Stationary point found.

Structure Comparison and Identification When comparing the experimentally calculated values to those stated in Appendix 1, there is close agreement in the values up to approximately 5d.p. The second lowest energy conformers (anti and gauche 2) have total Hartree/atomic unit energies of -231.69253529 and -231.69166696. The stated values for anti 2 and gauche 2 are -231.69254 and -231.69167. There is also a change in energy of -1.334886D-08 and -8.082607D-08 when optimising from the starting structure. The large difference between the anti and gauche conformers can be rationalised when taking into account the unfavourable repulsion between the C2H5 groups when lying at 60 degrees (gauche) to each other. This interaction is repulsive and creates a higher energy barrier compared to the eclipsed anti-periplanar conformer.

Ci anti2 1,5-hexadiene optimisation using B3LYP/6-31G* Basis Set

Reoptimised 3-21G structure using higher B3LYP/6-31G* basis set. Calculation was carried out as follows: 1. Job: Optimisation 2. Method: Selected DFT and B3LYP 3. Link 0: Changed chk file name to that of DFT opt file.

**Comparing 1,5-hexadiene anti2 opt conformers using (3-21G) and (6-31G*)**
Basis Set	Energy(a.u.)	Point group	Dipole moment (Debeye)	Structure
3-21G	-231.69253529	Ci	0.0002	Link to 3-21G basis set opt)[5]
6-31G*	-234.55970424	Ci	0.0000	*Link to 6-31G basis set opt** [6]

The overall geometry does not change significantly but there is a slight rotation of the central two carbons (C3 and C4). Using the higher 6-31G* basis set has resulted in a lower energy conformer -234.55970424 when compared to the simpler 3-21G basis set which gives an energy of -231.69253529. Interestingly, after optimising at this higher level, Gaussian now states that there is no longer a dipole moment and hence no accumulation of positive/negative charge at a one particular point on the molecule.

Anti 2 HF/3-21G Thermochemistry information:

 Sum of electronic and zero-point Energies=           -231.539539
 Sum of electronic and thermal Energies=              -231.532566
 Sum of electronic and thermal Enthalpies=            -231.531621
 Sum of electronic and thermal Free Energies=         -231.570913

When comparing the experimental results to those states, the energy values for 'Sum of electronic and zero-point Energies' are both -231.539539 hartree. There is also an agreement up to 6d.p in the overall Electronic Energy values at -231.692535 and -231.69253529 respectively for stated and experimental values. There is also agreement between the experimentally calculated values of -231.532566 hartree for 'Sum of electronic and thermal Energies' and the literature stated values of -231.532566 hartree.

Low frequencies ---   -2.6036   -1.8534   -1.5120    0.0004    0.0008    0.0008
 Low frequencies ---   71.3545   85.7097  116.2084

First Frequency Value: 71.35cm^-1

Job convergence information: (i) 3-21G

         Item               Value     Threshold  Converged?
 Maximum Force            0.000034     0.000450     YES
 RMS     Force            0.000007     0.000300     YES
 Maximum Displacement     0.001226     0.001800     YES
 RMS     Displacement     0.000346     0.001200     YES
 Predicted change in Energy=-1.334886D-08
 Optimization completed.
    -- Stationary point found.

(i) 6-31G*

        Item               Value     Threshold  Converged?
 Maximum Force            0.000079     0.000450     YES
 RMS     Force            0.000019     0.000300     YES
 Maximum Displacement     0.000471     0.001800     YES
 RMS     Displacement     0.000196     0.001200     YES
 Predicted change in Energy=-8.950676D-08
 Optimization completed.
    -- Stationary point found

6-31G* anti2 1,5-hexadiene Frequency Analysis

After re-optimising the HF/3-21G anti 2 structure to 6-31G*, a frequency analysis was also carried out and results compared to the given values. The calculation was carried out as follows: 1. Gaussian calculation set-up, Job Type: Frequency 2. Change chk. file name under Link 0 tab so that it is not overwritten. 3. Ensure that 'scrf=(solvent=water,check)' is not part of the method and then submit job. 4. Open log file once job was run and visualise vibrations.

Link to anti2 1,5-hexadiene 6-31G* frequency file: [7]

 First Frequency value: 93.84cm<sup>-1</sup>

The absence of a negative frequency values shows that imaginary frequencies are absent in this structure.

 Low frequencies ---   -0.0008   -0.0008   -0.0006   21.2228   29.2342   63.2481
 Low frequencies ---   93.8433  101.9293  138.2437

 Sum of electronic and zero-point Energies=           -234.469219
 Sum of electronic and thermal Energies=              -234.461966
 Sum of electronic and thermal Enthalpies=            -234.461021
 Sum of electronic and thermal Free Energies=         -234.500370

The 'Electronic energy' experimental value is -234.55970424 hartree which is lower than the -234.611710 hartree value states for anti 2 when running a frequency analysis at the higher basis set B3LYP/6-31G* theoretical set-up. The values for'Sum of electronic and zero-point Energies' are in agreement up to 4d.p. with the experimental calculation of -234.469219 compared to -234.469203, which suggests that the experimentally determined structure had a higher than expected potential energy at 0K when including the zero-point vibrational energy. Similarly, there is also agreement of up to 4d.p in hartree when comparing 'Sum of electronic and thermal Energies' with previously stated values of -234.461856 which is again slightly lower than the experimentally determined value of -234.461966. This may suggest that the experimental conformer experienced greater contributions in terms of translational, rotational, and vibrational energy modes due to not having undergone an ideal optimisation.

Optimising 'Chair' and 'Boat' Transition Structures

An allyl fragment (CH2CHCH2) was drawn and then optimised using the HF/3-21G level of theory. A new GaussView window was then opened and the allyl structure copied into it twice. The two fragments were then manipulated in such a way that they were orientated in a chair (C_2h) transition state. Once this was done, the guess molecule was copied and pasted into a New MolGroup window and a TS optimisation set up using the HF/3-21G method. This time the calculation was carried out as follows:

1. Job Type: Opt+Freq 2. Optimisation: TS (Berny), Force constants: Once 3. Additional keywords: Opt=NoEigen. 4. Submitted the job and once finished, visualised the vibrations

Optimised Chair (C_2h) conformation

Link to optimised 'Chair' transition state file [8]

Job convergence information:

        Item               Value     Threshold  Converged?
 Maximum Force            0.000010     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000625     0.001800     YES
 RMS     Displacement     0.000176     0.001200     YES
 Predicted change in Energy=-3.648416D-08
 Optimization completed.
    -- Stationary point found.

Results Summary:

Imaginary Frequency Magnitude: -817.93cm^-1

The chair transition structure was optimised again using the 'frozen coordinate' method. Like before, the guess structure was copied and pasted into a New GaussView window. This time the Redundant Coord Editor option was selected from the Edit menu. The 'Add Unidentified' tab was used to selected the terminal carbons that were involved in bond forming/breaking during the rearrangement process. Once the two pairs have been chosen, 'Bond' was specified below instead of 'Unidentified' and the option to Free Coordinates instead of adding them was chosen. At this point, the bonds were NOT set at the optimal distance of 2.2 Angstroms but instead this was achieved by using the 'bond' tool in the main GaussView window.This time the calculation was run slightly differently:

1. Job Type: Optimisation, to a minimum not a TS (Berny). 2. Check that the keyword 'Opt=ModRedundant' is part of the input line and submit the job.

The chk. file was opened once the calculation had run and the bond distances themselves (previously set to 2.2 Angstroms' were now optimised. The same set-up was used as before but this time when selecting terminal carbon atoms, the option 'derivative' was chosen instead of 'add'. A TS (Berny) optimisation was run but the force constants are set to 'Never'.

Link to 'frozen coordinate' chair opt file: [9]

Job convergence information:

        Item               Value     Threshold  Converged?
 Maximum Force            0.000014     0.000450     YES
 RMS     Force            0.000005     0.000300     YES
 Maximum Displacement     0.000206     0.001800     YES
 RMS     Displacement     0.000063     0.001200     YES
 Predicted change in Energy=-1.637393D-08
 Optimization completed.
    -- Stationary point found.

Results Summary:

Thermochemistry information:

 Sum of electronic and zero-point Energies=           -231.466701
 Sum of electronic and thermal Energies=              -231.461341
 Sum of electronic and thermal Enthalpies=            -231.460397
 Sum of electronic and thermal Free Energies=         -231.495207

The 3-21G Chair experimental optimisation has an electronic energy of -231.61932245 which agrees to 6d.p with the literature value of -231.619322. Interestingly, the frozen co-ordinate optimisation approach results in a lower energy value of -231.61932239, differing only in the last two decimal places. In terms of 'Sum of electronic and zero-point Energies' there is close agreement between the literature and experimental values up to 5d.p with results of -231.466705 hartree and -231.466701 hartree respectively. Similarly,for 'Sum of electronic and thermal Energies', the experimental value was -231.461341 hartree compared to a theoretical value of -231.461346 in Appendix 2.

Optimised Boat (C_2v) conformation

To optimise the boat conformation, the QST2 method was used. This allowed us to locate the reactants and products and find the transition state between the two by interpolation. Firstly, the chk. file belonging the anti 2 Ci optimised molecule was opened and copied into a new MolGroup. From the File menu, selected 'New' and 'Add to MolGroup'. This brought up a new window, where the molecule was again copied and pasted. Clicking the arrow in the window bar, allowed both molecules to be seen. The individual atoms on each molecule were renumbered by selecting 'Edit' and 'Atom List'. The two structures were then orientated as shown below.

The calculation was set-up as follows:

1. Job Type: Opt+Freq 2. Optimisation: TS (QST2).

Failed opt job:

Link to optimised boat transition structure: [10]

However, the job fails because rotation about the central atoms of the allyl fragment was not considered and hence simply translated it, instead of optimisation. This time, the central C-C-C-C dihedral angle must be adjusted to take this problem into account. Therefore, the dihedral angle for the reactant molecule of atoms C2-C3-C4-C5 was set to 0.0. Then the C2-C3-C4 and C3-C4-C5 angles were selected and reduced to 100 degrees. Once the optimisation set-up was run again, the following structure was formed.

Successful opt job:

Link to optimised boat transition structure: [11]

Results Summary:

Imaginary Frequency Magnitude:-840.00cm^-1

Thermochemistry information:

 Sum of electronic and zero-point Energies=           -231.450929
 Sum of electronic and thermal Energies=              -231.445301
 Sum of electronic and thermal Enthalpies=            -231.444357
 Sum of electronic and thermal Free Energies=         -231.479774

The 3-21G optimised boat conformer has an experimental electronic energy of -231.66280246 which is much higher than the literature value of -231.602802 which suggests that the optimisation using the QST2 method did not work fully. The experimental values for the optimised boat transition state correspond to the literature values stated in Appendix 2. Both 'Sum of electronic and zero-point Energies' and 'Sum of electronic and thermal Energies' have values of -231.450929 hartree and -231.445301 hartree. There is a small discrepancy in the 'Sum of electronic and thermal Energies' information of 0.000001 hartree.

Chair: Intrinsic reaction coordinate

In order to locate the local minimum on a potential energy surface, an Intrinsic Reaction Coordinate calculation was carried out. This is achieved by geometrically moving towards a point where the slope of the energy surface is steepest until a minimum is located. The calculation was set-up as follows: (i) Job type: IRC, forward only, compute 50 steps (ii) Method: Hartree-fock, 3-21G (iii) Link O: Specify - chair_optimised.chk file (iv) Solvation: none (v) General: Write connectivity ticked, Guess: Read checkpoint file

Once the job had run, the chk. file was opened. The IRC gradient had not yet reached zero which meant that a minimum had not been located. One way to solve this was to select the last point on the graph, copy the corresponding structure into a new GaussView window and run another minimisation. Whilst this approach is fastest, there is a danger of locating the wrong minimum

File:LAPTOPRUN CHAIR IRC - COPY.LOG

Results Summary:

Job convergence information:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000010     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000300     0.001800     YES
 RMS     Displacement     0.000091     0.001200     YES
 Predicted change in Energy=-2.407459D-09
 Optimization completed.
    -- Stationary point found

Table overview of reaction co-ordinate structural changes
	Structure 1	Structure 11	Structure 22
Image
Analysis	This first structure shows us the initial C_2h geometry with partial double bonds. There is a clear plane of symmetry passing vertically through the structure	As the calculation progresses, the bottom two terminal carbons form a bond and rotate outwards slightly. In contrast, the opposite terminal carbons become further apart and rotate in the same direction	This structure corresponds to the halfway point of the IRC calculation. There are structural similarities to both the reactants (slide 1) and final minimum (slide 44). The top terminal carbons are now further apart with their bonds parallel to one another.
	Structure 33	Structure 44	Intrinsic Reaction Co-ordinate Plot
Image			IRC plot
Analysis	The distance between the terminal carbons increases with the middle (C3-C4) bond remaining stationary. The partial bonds have now formed into two double bonds at either end of the diene structure	The bonds connecting (C1-C2-C3) and (C4-C5-C6) are no longer parallel and are angled outwards. The two allyl groups are now connecting at a single point (C3-C4).	The IRC plot shows that the gradient of the slope is tending to zero. When the first derivative of the energy tends to zero, this corresponds to a local minima. This means that there are minimal or no forces acting on the structure.

Activation Energies

The activation energies for both the chair and boat transition states were then calculated using a frequency analysis at B3LYP/6-31G* level of theory. Both structures were first optimised using the higher basis set and then the Job Type was changed to Freq.

Re-opt info for chair at 6-31G(d)

Link to optimisation file: [12]

Job convergence information:

       Item               Value     Threshold  Converged?
 Maximum Force            0.000011     0.000450     YES
 RMS     Force            0.000002     0.000300     YES
 Maximum Displacement     0.000177     0.001800     YES
 RMS     Displacement     0.000031     0.001200     YES
 Predicted change in Energy=-3.140358D-09
 Optimization completed.
    -- Stationary point found.

Results Summary:

 Low frequencies --- -565.5826    0.0009    0.0009    0.0010   21.9110   27.1727
 Low frequencies ---   39.7535  194.4806  267.9169

Thermochemistry data:

 Sum of electronic and zero-point Energies=           -234.414929
 Sum of electronic and thermal Energies=              -234.409008
 Sum of electronic and thermal Enthalpies=            -234.408064
 Sum of electronic and thermal Free Energies=         -234.443815

The experimental thermochemistry values are slightly for 6-31G* optimised chair conformer closely agree than those given in Appendix 2. The experimental electronic energy is -234.55698303 which agrees to 6d.p with the stated figure of -234.556983. For example, the 'Sum of electronic and zero-point Energies' for experimental and theoretical are -234.414929 hartree and -234.414919 hartree. Similarly, the 'Sum of electronic and thermal Energies' show a discrepancy between stated and calculated values with -234.408998 hartree and -234.409008 hartree respectively.

Re-opt info for boat at 6-31G(d)

Link to optimisation file: [13]

Job convergence information:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000028     0.000450     YES
 RMS     Force            0.000008     0.000300     YES
 Maximum Displacement     0.000636     0.001800     YES
 RMS     Displacement     0.000093     0.001200     YES
 Predicted change in Energy=-7.644997D-08
 Optimization completed.
    -- Stationary point found.

Results Summary:

Low frequencies --- -530.9265   -8.8127   -0.0003    0.0006    0.0007   15.4957
 Low frequencies ---   17.3620  135.3052  261.7740

Thermochemistry data:

Sum of electronic and zero-point Energies=           -234.402335
Sum of electronic and thermal Energies=              -234.396001
Sum of electronic and thermal Enthalpies=            -234.395057
Sum of electronic and thermal Free Energies=         -234.431745

The boat transition state energy values show a similar discrepancy as the chair conformer. The experimental 6-31G* optimisation method gave an experimental electronic energy of -234.54309280 compared to the value in Appendix 2 of -234.543093. However, for the corresponding values the experimental values are lower than that of the literature values in Appendix 2. For example, the 'Sum of electronic and zero-point Energies' is -234.402335 hartree compared to -234.402340 hartree. Also, the 'Sum of electronic and thermal Energies' have a difference also of -234.396001 hartree compared to a theoretical energy value of -234.396006.

Diels-Alder Rearrangement: [4+2] cycloaddition

The above mechaniss demonstrates the movement of 6 electrons when breaking pi bonds and forming two new sigma bonds and a pi bond. Specifically, 4 electrons come from the conjugated diene (e.g. cis-butadiene or cyclohexa-1,3-diene ) and 2 electrons from a dienophile (e.g. ethylene or maleic anhydride) when taking part in the thermally allowed [4+2] cycloaddition.

Building cis-Butadiene

A molecule of cis-butadiene was built in Gaussian and optimised using the semi-empirical, AM1 method.In order to visualise the MOs a frequency calculation was carried out. Once the job had completed, the chk. file was opened, 'Edit' tab selected and 'MO' option chosen. 1,3-butadiene can take two planar structures: 'cis' and 'trans', with the trans structure being less sterically hindered.

Link to optimised cis-butadiene file: [14]

Job convergence info:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000025     0.000450     YES
 RMS     Force            0.000011     0.000300     YES
 Maximum Displacement     0.000318     0.001800     YES
 RMS     Displacement     0.000128     0.001200     YES
 Predicted change in Energy=-8.152974D-09
 Optimization completed.
    -- Stationary point found.

Results Summary:

Low Frequencies of Diels-Alder reaction:

 Low frequencies --- -480.6077  -12.2005   -5.2043    0.0012    0.0012    0.0012
 Low frequencies ---   21.7095  136.3436  220.7358

Imaginary Frequency values: 1  -480.61   8.4073

Results Summary for Frequency:

HOMO and LUMO of cis-butadiene
	HUMO orbital	LUMO orbital
Orbital no.	Eleven	Twelve
Energy values	-0.34382	-0.01708
Nodes	One	Two
Delocalisation	There are four carbon p orbitals - these are split into two pairs which are in phase. There is a greater extent of delocalisation over the molecule as a result of these in-phase interactions	In the LUMO arrangement of orbitals, there is instead just one pair of p orbitals overlapping and 2 nodes. Therefore, the extent of delocalisation over the molecule is less than that of the HOMO due to unfavourable orbital overlap.

cis-Butadiene and Ethylene Transition state

The next step after visualising the MOs of cis-butadiene was to carry out an optimisation of the transition state pathway. An approximate transition structure that had an envelope-like form was drawn in GaussView. This was carried out by first using a bicyclo structure and then removing the extra fragment CH2CH2 below. The remaining ethylene fragment was positioned at a distance of 2.2 Angstroms from the cis-butadiene and a dotted bond drawn between the terminal carbons. An optimisation and then frequency calculation using semi-empirical AM1 theory was carried out on the structure. The presence of a Diels-Alder transition state could be confirmed due to the imaginary frequency value of -480cm^-1 obtained in the 'Vibrations' list. This result is indicative of a transition state as a 'minimum' value would be positive (i.e. square root of a positive energy slope) whereas this imaginary (i.e. square root of a negative energy slope)

Link to optimised TS: [ http://hdl.handle.net/10042/21315]

Job convergence info:

        Item               Value     Threshold  Converged?
 Maximum Force            0.000026     0.000450     YES
 RMS     Force            0.000009     0.000300     YES
 Maximum Displacement     0.000563     0.001800     YES
 RMS     Displacement     0.000227     0.001200     YES
 Predicted change in Energy=-2.092648D-08
 Optimization completed.
    -- Stationary point found

Results Summary:

We can confirm that a transition state has been located due to the presence of an imaginary frequency value: -480cm^-1

In the lowest energy conformation, there is totally symmetric orbital overlap between the p orbitals. The second-highest energy arrangement is having two pairs of p orbitals overlapping with 1 node. The next highest orbital conformation is the LUMO with just one pair of p orbitals overlapping with 2 nodes. The highest energy conformation has no favourable interactions between the p orbitals and has 3 nodes.The favourable overlap between the diene and dienophile is why it is important that butadiene is orientated in the cis position despite the trans conformation being more thermodynamically stable due to less electronic repulsion. Diels-Alder undergoes 'cis' [4+2] cycloaddition. As seen in the mechanism diagram previously, the transition state has a cyclic, 6-member form which suggests that bond forming/breaking is concerted in this reaction.

cis-Butadiene and ethylene MO interactions^[1]

↑ http://web.chem.ucsb.edu/~kalju/chem109C/DielsAlder.html

HOMO and LUMO of cis-butadiene and ethylene transition structure
	HOMO orbital	LUMO orbital
Orbital no.	23	24
Energy values	-0.22099	-0.00622
Nodes	One node present where there is a change in phase.	Two nodes present
Delocalisation	The pi MO is asymmetric with respect to the plane of symmetry. The electrons from this orbital move into the LUMO of the ethylene during the reaction. This allows for the formation of a new carbon-carbon bond.	The LUMO is symmetric with respect to the plane of symmetry. As the ethylene HOMO is also symmetric this interaction is 'allowed' due to favourable overlap. However, compared to the HOMO orbital, the lobes of the butadiene p orbitals are much smaller which suggests a greater disparity in energy between the diene and dienophile.

. In addition, the lowest energy orbital arrangement for butadiene would be totally symmetric with no nodes. There would be extensive delocalisation over the entire molecule. The highest energy orbital arrangement would be asymmetric with 3 nodes present. As bonds are being formed and broken at the same time, this mechanism is symmetric and synchronous.

Synchronous definition^[1]

↑ http://www.annualreviews.org/doi/abs/10.1146/annurev.pc.39.100188.001241

Studying regioselectivity of Diels-Alder

This last calculation was an opportunity to investigate the regioselectivity preferences for the Diels-Alder mechanism. This is simply the preference of one chemical bond direction when forming a product over an alternative method. The presence of EWG such as carbonyls on the dienophile (maleic anhydride) lower the HOMO/LUMO orbitals and result in a stronger interaction with the cyclohexa-1,3-diene orbitals.

Link to optimised Endo structure:[15]

Vibration

Job Convergence info:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000136     0.000450     YES
 RMS     Force            0.000026     0.000300     YES
 Maximum Displacement     0.000705     0.001800     YES
 RMS     Displacement     0.000145     0.001200     YES
 Predicted change in Energy=-9.332376D-08
 Optimization completed.
    -- Stationary point found.

Results Summary:

Link to frequency 'Endo' file: [16]

Thermochemistry values:

 Sum of electronic and zero-point Energies=           -605.414905
 Sum of electronic and thermal Energies=              -605.405479
 Sum of electronic and thermal Enthalpies=            -605.404535
 Sum of electronic and thermal Free Energies=         -605.450133

Table Summarising HOMO and LUMO 'Endo' orbitals

Analysis	The HOMO of this product is orbital number 47 which has an energy of -0.32441.This is lower and hence more stable than the Exo HOMO which has an energy of -0.32324. There is extensive delocalisation between the maleic anhydride and cyclohexa-1,3-diene structures. There is one node passing vertically along the plane of symmetry. The is contribution from both the pi bonds and the carbonyl atoms which leads to larger, more delocalised lobes.	The LUMO of this product is orbital number 48 which has an energy of 0.07338. This is higher than the Exo LUMO which has an energy of 0.05808, which suggests that a flow of electron density from HOMO-LUMO is highly unlikely. There is unfavourable interaction between the two structures - this can be seen by the change of phase when the carbons interact. There are two nodes - one vertically along the plane of symmetry and one between the dienophile and diene.

Link to Exo opt+freq structure:File:ENDO FREQ 1 SS2310.LOG

Vibration

Job convergence info:

       Item               Value     Threshold  Converged?
 Maximum Force            0.000108     0.000450     YES
 RMS     Force            0.000010     0.000300     YES
 Maximum Displacement     0.000463     0.001800     YES
 RMS     Displacement     0.000119     0.001200     YES
 Predicted change in Energy=-2.546980D-08
 Optimization completed.
    -- Stationary point found.

Results Summary:

Link to freq and opt 'Exo' conformer:File:ENDO FREQ 1 SS2310.LOG

Thermochemistry values:

 Sum of electronic and zero-point Energies=           -605.408138
 Sum of electronic and thermal Energies=              -605.398678
 Sum of electronic and thermal Enthalpies=            -605.397734
 Sum of electronic and thermal Free Energies=         -605.443689

Table Summarising HOMO and LUMO 'Exo' orbitals
	HOMO orbital	LUMO orbital
Analysis	The HOMO is in orbital 47 with an energy of -0.323234 which is higher than that of the Endo HOMO. This corresponds to the prediction that Exo will be higher in energy due to lacking secondary orbital interactions. There is favourable overlap between the carbon orbitals due to the primary interaction. However, the lobes are smaller which indicates that the extent of delocalisation is not as great. This makes sense considering the sterically unhindered arrangement of both structures	The LUMO is in orbital 48 with an energy of 0.05808 which is less than that of the Endo conformer. This suggests that it may be easier for electrons to flow from the HOMO to the corresponding LUMO orbital in the Exo conformer. Again, the smaller-sized lobes indicate that the delocalisation over both molecules is less than that of the Endo conformer. There is significantly less contribution towards bonding from the cyclohexa-1,3-diene as can be seen from the smaller lobes.Even more significantly, there is no contribution towards bonding from the sp3 carbons of cyclohexa-1,3-diene (opposite the electron-rich double bond).

Endo vs Exo Summary:

As the bonds are being formed and broken simultaneously, this is another example of a concerted, synchronous mechanism between an electron-rich diene (cyclohexa-1,3-diene) and an electron-poor dienophile with EWG (maleic anhydride). The orbitals fit the requirement that the there is favourable overlap due to matching symmetry and correct regioselective arrangement (cis-conformer for diene). The Endo product is the kinetically-favoured, major product of the reaction due to secondary orbital interactions between 4 carbon p orbitals despite the thermodynamically-favoured Exo product being sterically more favourable. This suggests that the secondary orbital interactions, when the EWG is below the diene, are sufficiently able to stabilised the structure and lower energy, even when compared to the Exo conformer. The transition energy values for both the Exo and Endo conformer are very close which suggests that the intermediate, transition structures are similar. However, the results of -605.61036757 and -605.60359123 hartree for the Endo and Exo respectively do not agree with the theory that the Endo will experience a lower energy. This may be due to an error in how the calculation was run in Gaussian, due to positioning of the original molecule.

[Diels-Alder_MO_interactions-1] ttp://web.chem.ucsb.edu/~kalju/chem109C/DielsAlder.html

[Dewar_definition_of_synchronous-2] ttp://www.annualreviews.org/doi/abs/10.1146/annurev.pc.39.100188.001241

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