of electrons and electron properties. Molecular mechanics, on the other hand, does not
consider electrons explicitly. In molecular mechanics, atoms are regarded as distensible
balls, bearing charge, and connected to other distensible balls via springs. The mathe-
matics of molecular mechanics is thus rapid and trivial, which makes the technique
ideal for the treatment of pharmaceutically relevant macromolecules.
The term molecular mechanicsrefers to a heavily parameterized calculational
method that leads to accurate geometries and accurate relative energies for different
conformations of molecules. The molecular mechanics procedure employs the funda-
mental equations of vibrational spectroscopy, and represents a natural evolution of the
notions that atoms are held together by bonds and that additional interactions exist
between nonbonded atoms. The essential idea of molecular mechanics is that a mole-
cule is a collection of particles held together by elastic or harmonic forces, which can
be defined individually in terms of potential energy functions. The sum of these vari-
ous potential energy equations comprises a multidimensional energy function termed
theforce field, which describes the restoring forces acting on a molecule when the
minimal potential energy is perturbed. The force field approach supposes that bonds
have natural lengths and angles, and that molecules relax their geometries to assume
these values. The incorporation of van der Waals potential functions and electrostatic
terms allows the inclusion of steric interactions and electrostatic effects. In strained
systems, molecules will deform in predictable ways, with strain energies that can be
readily calculated. Thus molecular mechanics uses an empirically derived set of
simple classical mechanical equations, and is in principle well suited to provide
accurate a priori structures and energies for drugs, peptides, or other molecules of
pharmacological interest.
Molecular mechanics lies conceptually between quantum mechanics and classical
mechanics, in that data obtained from quantum mechanical calculations are incorpo-
rated into a theoretical framework established by the classical equations of motion. The
Born–Oppenheimer approximation, used in quantum mechanics, states that Schrödinger’s
equation can be separated into a part that describes the motion of electrons and a part
that describes the motion of nuclei, and that these can be treated independently.
Quantum mechanics is concerned with the properties of electrons; molecular mechan-
ics is concerned with the nuclei, while electrons are treated in a classical electrostatic
manner.
The heart of quantum mechanics is the Schrödinger equation; the heart of molecular
mechanics is the force field equation. A typical molecular mechanics force field is
shown below:
General form of a force field equation:
Specific force field equation (AMBER):
DRUG MOLECULES: STRUCTURE AND PROPERTIES 47V=Vr+Vθ+Vω+Vinv+Vnb+Vhb+Vcross (1.8)Vr=∑
kr(r−r 0 )^2 (1.9)Vθ=∑
kθ(θ−θ 0 )^2 (1.10)