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Module 3: The Transistion State

Objectives

In module 1 relative energies of conformers were investigated. In this module we can move on to investigate how reactions take place i.e. bonds forming and bonds breaking. This can be done, using molecular orbital methods, numerically solving the Schrodinger equation to find transistion structures on the local shape of a potential energy surface . For this module 3 different reactions will be investigated; the Cope Rearrangement of 1,5-hexadiene and the Diels-Alder Cycloadditions of cis-butadiene with ethylene and Cyclohexa-1,3-diene with with maleic anhydride.

The Cope Rearrangement Tutorial

In the following exercise computational methods will be used in order to investigate the [3,3]-sigmatropic shift rearrangement 1,5-hexadiene.

Cope Rearrangement

Optimisation of Reactants and Produtcs

1,5-hexadiene can exist in either an anti or gauche conformation. The optimised structures of the reactants and products need to be determined before any further investigation into the transition state structures. Therefore the anti and gauche conformers were visualised and optimised using GaussView 5.0 and their relative energies recorded.

anti and gauche conformers

ANTI anti optimisation File Name anti1_5_hexadiene_optimisation File Type .chk Calculation Type FOPT Calculation Method RHF Basis Set 3-21G Charge 0 Spin Singlet Total Energy -231.69253528 a.u. RMS Gradient Norm 0.00001891 a.u. Imaginary Freq Dipole Moment 0.0000 Debye Point Group

Symmetrize? Point Group = Ci

Energy given in table -231.69254, in agreement with my energy Total Energy -231.69253528

GAUCHE

HF/3-21G

File Name gauche1_5hexadiene_optimisation File Type .chk Calculation Type FOPT Calculation Method RHF Basis Set 3-21G Charge 0 Spin Singlet Total Energy -231.69266118 a.u. RMS Gradient Norm 0.00001742 a.u. Imaginary Freq Dipole Moment 0.3404 Debye Point Group

Symmetrized.. Point Group = C1

gauche conformer optimised with low level basis set HF/3-21G.jpg

Run anti2 again with B3LYP/6-31G*

anti2 high level optimisation File Name anti1_5_hexadiene_optimisation_highlevel File Type .chk Calculation Type FOPT Calculation Method RB3LYP Basis Set 6-31G(D) Charge 0 Spin Singlet Total Energy -234.61171027 a.u. RMS Gradient Norm 0.00000985 a.u. Imaginary Freq Dipole Moment 0.0000 Debye Point Group

anti conformer optimised with low level basis set HF/3-21G.jpg
anti conformer optimised with high level basis set B3LYP/6-31G*.jpg

Torsion Angles (high level) C 1,2,3,4 118.54991 C 2,3,4,5 180.0 C 3,4,5,6 118.54991

Torsion Angles (low level) C 1,2,3,4 114.66878 C 2,3,4,5 180.0 C 3,4,5,6 114.66878

Vibrational analysis of anti2

B3LYP/6-31G*

Modes all positive and real

Sum of electronic and zero-point Energies= -234.469203 Sum of electronic and thermal Energies= -234.461856 Sum of electronic and thermal Enthalpies= -234.460912 Sum of electronic and thermal Free Energies= -234.500777

Freq analysis ran at lower basis set for activation energies [later].

Sum of electronic and zero-point Energies= -231.539539 Sum of electronic and thermal Energies= -231.532565 Sum of electronic and thermal Enthalpies= -231.531621 Sum of electronic and thermal Free Energies= -231.570916

Optimising the Chair and Boat Transistion Structures

Chair and Boat Transition State Structures

Chair Optimised to a TS (Berny)

Chair optimised to TS (Berny)

C-C [terminal] = 2.02055 Imaginary vibration at 817.9cm-1 Optimised using frozen method

imaginary freq 817.9cm-1
imaginary freq 818cm-1


Boat

imaginary freq 840cm-1
Total Energy along IRC
RMS Gradient along IRC

The Diels-Alder Cycloaddition

Diels Alder Cycloaddition of cis-butadiene and ethylene

Optimisation and Analysis of cis-butadiene and ethylene

cis butadiene opt File Name cis-butadiene-opt File Type .chk Calculation Type FOPT Calculation Method RPDDG Basis Set ZDO Charge 0 Spin Singlet Total Energy 0.04616719 a.u. RMS Gradient Norm 0.00013689 a.u. Imaginary Freq Dipole Moment 0.0407 Debye Point Group

Optimised cis-butadiene
Optimised Ethylene

cis-butadiene

HOMO - anti-symmetric, E =
LUMO - symmetric, E =

ethylene

HOMO - symmetric, E =
LUMO - anti-symmetric, E =

Optimisation and Analysis of Transistion State

The Transition State was modelled using GaussView and optimised. A frequency calculation was also carried out in order to confirm the transition state had reached a minima. An imaginary frequency at -956cm-1 confirms this minima and is shown below. This frequency corresponds to the forming of the 2 new σ bonds. The next lowest frequency is at 147cm-1 which corresponds to the rocking motion of the ethylene hydrogens.

Imaginary Frequency at -956cm-1
Low Frequency at 147cm-1