representing the energy and properties of an individual electron within the molecule, and
where these unknown molecular orbitals φmay be represented as a linear combination
of known atomic orbital functions (χi).
In quantum pharmacology, the goal is to determine the wavefunction Ψfor the drug
molecule so that the energy and properties of the drug may be calculated. However,
Schrödinger’s equation may be exactly solved only for the hydrogen atom. It is not
possible to provide an exact mathematical solution for the wavefunction of an entire
molecule. Accordingly, quantum mechanics calculations that provide approximate, but
not exact, solutions for the drug molecule wavefunction are employed; these approxi-
mate methods are called molecular orbital calculations.
In molecular orbital calculations, the molecular orbitals φare represented as a linear
combination of atomic orbital functions (χi). A variety of different mathematical func-
tions may be used to represent these atomic orbital functions. If a very sophisticated
mathematical function is used, then the resulting answer is higher in quality, providing
very accurate energies and geometries for the drug molecule being studied; however,
such calculations may be extremely expensive in terms of computer time required. If a
DRUG MOLECULES: STRUCTURE AND PROPERTIES 45Figure 1.12 Determining the properties of drug molecules. Drug molecules may have their
properties ascertained by either experimental or theoretical methods. Although experimental meth-
ods, especially X-ray crystallography, are the “gold standard” methods, calculational approaches
tend to be faster and do provide high quality information. Nonempirical techniques, such as
ab initio quantum mechanics calculations, provide accurate geometries and electron distribution
properties for drug molecules.