Computational Chemistry

the most widely-used method for computing the geometries and energies of
large biological molecules like proteins and nucleic acids (although recently semi-
empirical (Chapter 6 ) and even ab initio (Chapter 5 ) methods have begun to be
applied to these large molecules.

3.2 The Basic Principles of Molecular Mechanics

3.2.1 Developing a Forcefield............................................

The potential energy of a molecule can be written

E¼

X

bonds

Estretchþ

X

angles

Ebendþ

X

dihedrals

Etorsionþ

X

pairs

Enonbond (*3.1)

whereEstretchetc. are energy contributions from bond stretching, angle bending,
torsional motion (rotation) around single bonds, and interactions between atoms or
groups which are nonbonded (not directly bonded together). The sums are over all
the bonds, all the angles defined by three atoms A–B–C, all the dihedral angles
defined by four atoms A–B–C–D, and all pairs of significant nonbonded interac-
tions. The mathematical form of these terms and the parameters in them constitute a
particular forcefield. We can make this clear by being more specific; let us consider
each of these four terms.

∆ l = l – leq

∆ a = a – aeq

aeq

a

+

leq

l

0 ∆ l or ∆ a

energy

Fig. 3.2Changes in bond lengths or in bond angles result in changes in the energy of a molecule.
Such changes are handled by theEstretchandEbendterms in the molecular mechanics forcefield.
The energy is approximately a quadratic function of the change in bond length or angle

48 3 Molecular Mechanics