Computational Chemistry

believed (e.g. from quantum mechanical calculations on simple systems, or from
chemical intuition) to approximate those in the transition state, and with appropriate
angles and dihedrals also constrained. With luck this will take the input structure to
a point on the potential energy surface near the saddle point. For example, an
approximation to the geometry of the transition state for formation of cyclohexene
in the Diels–Alder reaction of butadiene with ethene can be achieved (Fig.3.11) by
essentially building a boat conformation of cyclohexene, constraining the two
forming C/C bonds to about 2.1 A ̊, and optimizing, using the CH 2 bridge (later
removed) to avoid twisting and to maintainCssymmetry; optimization with a
dihedral constraint removes steric conflict between two hydrogens and gives a
reasonable starting structure for, say, an ab initio optimization.
The most sophisticated approach to locating a transition state with MM would be
to use an algorithm that optimizes the input structure to a true saddle point, that is to
a geometry characterized by a Hessian with one and only one negative eigenvalue
(Chapter 2 ). To do this the MM program would have to be able not only to calculate
second derivatives, but should also be parameterized for the partial bonds in
transition states. This is a feature lacking in standard MM forcefields, which are
not, in general, used to calculate transition states.
MM has been used to study the transition states involved in SN2 reactions,
hydroborations, cycloadditions (mainly the Diels–Alder reaction), the Cope and
Claisen rearrangements, hydrogen transfer, esterification, nucleophilic addition to

H 2 C

3

C2v

C

H H

C

H H

make a C / C double bond;

set constraints on two C / C

bonds

constrain to

(2.1 Å)

constrain to

(2.1 Å)

butadiene

ethene

H

HH

H

H H

H

H

H

H

2.1 Å

2.1 Å

2.1 Å

2.1 Å

2.1 Å

2.1 Å

from

start with chair cyclohexane attach a CH 2 1,4

Cf. the transition state

12

4

optimize

optimize optimize

5

C

H H

6

H HH H

remove CH 2 , set 1, 2, 3, 4 dihedral to 0

2 14 3

7

H

H

H H

Cs

Cs

Fig. 3.11Using molecular mechanics to get the (approximate) transition state for the Diels–Alder
reaction of butadiene with ethene. This procedure gives a structure with the desirable Cs, rather
than a lower, symmetry

3.3 Examples of the Use of Molecular Mechanics 63