Rep:Mod:NBCPHY

Optimizing the Reactants and Products

Anti 1 optimisation

Name	anti-1	gauche-1	anti-2	anti-2
Structure
Calculation type	FOPT	FOPT	FOPT	FOPT
Calculation Method	RHF	RHF	RHF	RB3LYP
Basis Set	3-21G	3-21G	3-21G	6-31G(d)
Point Group	C1	C2	Ci	Ci
Energy/ a.u.	-231.69097054	-231.68771610	-231.69253528	-234.61171035
.log File	here	here	here	here

anti-2 conformer

Anti-1 conformer has a lower energy compared to that of gauche-1 conformer, therefore it is more stable. This is because anti-1 adopted antiperiplanar conformation for the four central carbon atoms, two alkene groups are far apart so there is less steric interactions between them.

Based on the description above, a conformer in antiperiplanar conformation should be lower in energy. The lowest energy conformation of 1,5-hexadiene is predicted to be anti-2 conformer. Because the two alkene groups are heading toward opposite direction, steric interaction between two groups is expected to be the minimum. Final energy of anti-2 conformer given in the appendix table is -231.69254 a.u., which is the same as experimental value (-231.69253528 a.u.), considering only 5 decimal places are given in the appendix table.

Anti-2 Frequency Analysis

Structure
Calculation type	FREQ
Calculation Method	RB3LYP
Basis Set	6-31G(d)
Point Group	Ci
Energy/ a.u.	-234.61171035
Sum of electronic and zero-point energies	234.469204
Sum of electronic and thermal energies	234.461857
Sum of electronic and thermal enthalpies	234.460913
Sum of electronic and thermal free energies	234.500777
.log File	here

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Optimizing the "Chair" and "Boat" Transition Structures

Chair and Boat T.S.

Chair and Boat T.S. Optimisation

Method	Hessian	Frozen coordinate method (Bond)	Frozen coordinate method (Derivative)	TS (QST2)
Structure	chair	chair	chair	boat
Calculation type	FREQ	FREQ	FREQ	FREQ
Calculation Method	RHF	RHF	RHF	RHF
Basis Set	3-21G	3-21G	3-21G	3-21G
Point Group	C2h	C2h	C2h	C2v
Energy/ a.u.	-231.61932208	-231.61518535	-231.61932232	-231.60280222
Transition bond distances/ Å	2.02	2.20	2.02	2.14
.log File	here	here	here	here

Hessian Method: Vibration at 818 cm^-1 ( imaginary frequency )

As it can be seen on the left, Hessian method gives an imaginary frequency of 818 cm^-1 and the vibration corresponding to the Cope rearrangement of 1,5-hexadiene.

For chair transition structure of 1,5-hexadiene, both of the Hessian and the frozen coordinate methods give the same bond forming/breaking bond lengths of 2.02 Å. It worked in both ways in this case because of the reasonable assumption for transition structure geometry. However, if it is a more complex molecule, it'll be difficult to predict its transition structure using the Hessian method (deviation of curvature are larger), which makes the frozen coordinate method a more ideal choice.

QST2 Method: Vibration at 840 cm^-1 ( imaginary frequency )

QST2 method was used to find the boat transition structure, vibration corresponding to the only imaginary frequency (840 cm^-1) is visualized.

IRC Method

In this step, reaction coordinate is computed in the forward direction only because of its symmetry, also, the number of points along the IRC is set to 50. A normal minimization (HF/3-21G) is carried out after IRC. The following result is obtained for chair structure.

IRC

Structure	chair	chair
Calculation type	FREQ	FOPT
Calculation Method	RHF	RHF
Basis Set	3-21G	3-21G
Point Group	C2	C2
Energy/ a.u.	-231.69157819	-231.69166702
.log File	here	here

Reoptimize Boat and Chair T.S.

Both chair and boat structures are reoptimized using B3LYP/6-31G(d) level of theory, giving the table below.

Reoptimize Boat and Chair T.S.

Structure
Calculation type	FREQ	FREQ
Calculation Method	RB3LYP	RB3LYP
Basis Set	6-31G(d)	6-31G(d)
Point Group	C2h	C2v
Energy/ a.u.	-234.55698249	-234.54309287
.log File	here	here

Energies

Summary of Energies / hartree

	HF/3-21G				HF/6-31G*
	Electronic Energy	Sum of Electronic and Zero-point Energies	Sum of Electronic and Thermal Energies	.log file	Electronic Energy	Sum of Electronic and Zero-point Energies	Sum of Electronic and Thermal Energies	.log file
		at 0 K	at 298.15 K			at 0 K	at 298.15 K
Chair T.S.	-231.619322	-231.466705	-231.461346	here	-234.556982	-234.414934	-234.409011	here
Boat T.S.	-231.602802	-231.450930	-231.445302	here	-234.543093	-234.402345	-234.396011	here
Reactant (anti2)	-231.692535	-231.539540	-231.532566	here	-234.611710	-234.469204	-234.461857	here

Summary of Activation Energies / kcal/mol

	HF/3-21G	HF/3-21G	B3LYP/6-31G*	B3LYP/6-31G*	Expt.
	at 0 K	at 298.15 K	at 0 K	at 298.15 K	at 0 K
ΔE (Chair)	45.70	44.69	34.05	33.16	33.5 ± 0.5
ΔE (Boat)	55.60	54.76	41.95	41.32	44.7 ± 2.0

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The Diels Alder Cycloaddition

Cis-butadiene

Cis-butadiene Summary

Structure
HOMO	Anti-symmetric
LUMO	Symmetric
Calculation type	FREQ
Calculation Method	RAM1
Basis Set	ZDO
Point Group	C2v
Energy/ a.u.	0.04879770
.log File	here

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Ethylene+Cis-butadiene Transition Structure

Ethylene+Butadiene Cycloaddition T.S.

Structure
HOMO	Anti-symmetric
LUMO	Symmetric
Calculation type	FREQ
Calculation Method	RAM1
Basis Set	ZDO
Point Group	C1
Energy/ Hartree	0.11165476
Sum of electronic and zero-point energies /Hartree	0.253276
Sum of electronic and thermal energies /Hartree	0.259453
Sum of electronic and thermal enthalpies /Hartree	0.260397
Sum of electronic and thermal free energies /Hartree	0.224016
Partly formed σ C-C bond lengths /Å	2.12
.log File	here

Vibration at -956 cm^-1 (imaginary frequency)

Vibration at 147 cm^-1

Typical sp³ and sp² C-C bond lengths 1.51 Å

Van der Waals radius of the C atom:1.70 Å

Partly formed σ C-C bond lengths in the transition state (2.12 Å) is shorter than two Van der Waals radius of C atoms combined (3.4 Å), indicating the presence of interaction in the transition state between two carbon atoms. However, partly formed σ C-C bond length is longer than a typical sp³ and sp² C-C bond length (1.51 Å), which means there is no bond formed yet between two carbon atoms.

As it can be seen on the right, the formation of the two bonds is synchronous at the imaginary frequency of -956 cm^-1. The blue arrows in the graph represent displacement vectors. It is obvious that the formation of the two bonds is asynchronous at the lowest positive frequency of 147 cm^-1. This is because only the imaginary frequency (a negative value) corresponds to the minimum energy of transition state.

Butadiene HOMO

Ethylene LUMO

HOMO of the transition structure is anti-symmetric, which is formed by two anti-symmetric orbitals. Therefore the HOMO of butadiene and LUMO of ethylene are used to form this orbital, because they are all anti-symmetric. Reaction is allowed because HOMO of butadiene and LUMO of ethylene have the same symmetry property (anti-symmetric), there is a significant overlap density.

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Regioselectivity Study of Diels-Alder Reaction

Cyclohexa-1,3-diene Reaction With Maleic Anhydride

	Endo	Exo
Structure
HOMO
LUMO
Calculation type	FREQ	FREQ
Calculation Method	RAM1	RAM1
Basis Set	ZDO	ZDO
Point Group	CS	CS
Energy/ a.u.	-0.05150480	-0.05041984
Relative Energy /kcal/mol	0	0.68
.log File	here	here

Exo HOMO:NO secondary orbital overlap

Endo HOMO:Secondary orbital overlap

Endo structure is formed when the maleic anhydride molecule is faced toward the cyclohexa-1,3-diene, exo is formed when maleic anhydride molecule is faced away from cyclohexa-1,3-diene. Endo structure is favored because there are less steric interactions between -(C=O)-O-(C=O)- fragment and the remainder of the system. Secondary orbital overlap effect is another reason for the tendency to form endo structure. It can be seen on the diagram that there are through-space bonding interactions between -(C=O)-O-(C=O)- fragment and the remainder of the system in the HOMO of endo structure, but there are no such interactions in HOMO of exo structure.

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Further Study

What effects have been neglected in these calculations of Diels Alder transition states?

AM1 belongs to Zero Differential Overlap (ZDO) method, in which electrons involving two-center charge distributions are neglected.

In order to obtain a more accurate approximation of transition structures, the endo and exo structures are reoptimised using B3LYP/6-31G(d) method, and the following result is obtained.

Cyclohexa-1,3-diene Reaction With Maleic Anhydride

	Endo	Exo
Structure
Calculation type	FREQ	FREQ
Calculation Method	RB3LYP	RB3LYP
Basis Set	6-31G(d)	6-31G(d)
Energy/ a.u.	-612.68339673	-612.67931096
Relative Energy /kcal/mol	0	2.56
.log File	here	here

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