simpler mathematical function is used, it may be calculated more rapidly, but will
provide a cruder approximation of the numerical properties of the atomic orbital func-
tion that it endeavours to represent. Classically, the most obvious types of mathemati-
cal functions used to represent atomic orbitals are called Slater-type orbitals. If one
uses Slater-type functions for each atomic orbital which is filled (e.g., for carbon using
1s, 2s, and 2p atomic orbitals), then the resulting set of functions is termed the basis set.
The term basis set applies to a set of mathematical functions used to describe the shape
of the orbitals in an atom.
Molecular orbital calculations may be broadly divided into two types:ab initio and
semi-empirical. The termab initio is an unfortunate choice of words since it gives a
mistaken idea of quality; nevertheless, it is used universally for molecular orbital wave-
function calculations that explicitly consider all electrons within the drug molecule. Ab
initio calculations may be done at a variety of basis set levels. The higher the basis set
level, the more likely will the calculation reproduce experimental observations, such as
bond lengths determined from X-ray crystallographic methods. Not surprisingly, the
current medicinal chemistry literature contains numerous examples in which quantum
pharmacology calculations using ab initio methods have been employed to understand
the properties of drug molecules.
Despite the length of time required for their completion, ab initio calculations are
themselves not always successful in reproducing experimental observations and do
require prolonged calculational times. To address these potential problems, consider-
able effort has been expended to devise the so-called semi-empiricalmolecular orbital
calculations. Semi-empirical methods employ a variety of approximations and assump-
tions to reduce the complexity of the mathematics and thus the time required for a cal-
culation. Typically, semi-empirical calculations consider only valence shell electrons.
Core electrons, such as 1s electrons, are ignored under the assumption that they play
little if any role in biological and biochemical processes. To compensate for ignoring
core electrons, empirically derived parameters are incorporated into the calculations;
these “fudge factors” help the semi-empirical calculation to reproduce experimental
results while neglecting to calculate a number of difficult integral equations that would
be present in the ab initio mathematical formulation. It is not uncommon for semi-
empirical calculations to run 2 to 3 times faster than ab initio calculations. There are a
number of types of semi-empirical calculations. Historically, CNDO (complete neglect
of differential overlap) and INDO (intermediate neglect of differential overlap) para-
meterizations were used. These first methods were somewhat crude and proved to be of
little value in medicinal chemistry and quantum pharmacology. More recently, parame-
terizations such as AM1 and PM3 yield impressive results when compared with a range
of experimental observables. AM1 and PM3 semi-empirical calculations have been
used successfully over the past 5 to 10 years to model a variety of drugs and drug–
receptor interactions, and their utility in quantum pharmacology calculations continues
to be explored and expanded.
1.6.1.2 Molecular Mechanics
Molecular mechanics is based on the principles of classical mechanics, rather than
those of quantum mechanics. Quantum mechanics is based on an explicit consideration
46 MEDICINAL CHEMISTRY