Molecular modeling and quantum pharmacology calculations have emerged as extremely
important techniques in modern medicinal chemistry. A review of drug design papers in the
Journal of Medicinal Chemistry and of pharmaceutically relevant papers in the Journal of
the American Chemical Society, covering the year 2000, reveals that 43% of these papers
included computational chemistry techniques in their design and analyses of drug molecule
action. Clearly the dawn of the 21st century has emphasized the exponentially growing
importance of molecular modeling and quantum pharmacology in drug design. Accordingly,
a basic understanding of medicinal chemistry in the modern era requires an appreciation of
the fundamentals of quantum mechanics, molecular mechanics, and the other techniques of
computational chemistry as applied to drug design. The medicinal chemist who uses com-
mercially available computer programs to design drugs should not treat them as merely
“black boxes,” and should have some insight into their conceptual basis.
1.6.1 Methods of Quantum Pharmacology for Molecular Geometry
Optimization: Quantum Mechanics, Molecular
Mechanics, QM/MM CalculationsThe first and foremost goal of quantum pharmacology is to predict and determine the
optimal geometry of drug molecules and drug receptors. This is best achieved by using
a “mechanics” method that permits the geometry of a molecule to be expressed as a
function of energy. By minimizing this energy function, one can ascertain the optimal
geometry of the molecule. Quantum mechanics and molecular mechanics are the
dominant “mechanics” methods in quantum pharmacology (see figure 1.12).
1.6.1.1 Quantum Mechanics
TheSchrödinger equation is the centrepiece of quantum mechanics and lies at the heart
of much of modern science. In its simplest form, the Schrödinger equation may be
represented as
whereψis the wave function,Eis the energy of the system, and H(the “Hamiltonian
operator”) is the shorthand notation for a mathematical operator function that operates on
other mathematical functions. Once the wavefunction is known for a particular system,
then any physical property may in principle be determined for that system. However,ψis
just a normal mathematical function; it has no special mathematical properties.
If the system being studied is a simple hydrogen atom with a single electron outside
of a positively charged nucleus, the Schrödinger equation may be solved exactly. The
wavefunctions which satisfy the Schrödinger equation for this simple hydrogen atom
are called orbitals; a hydrogenic atomic orbital is therefore the three-dimensional mathe-
matical function from which one may calculate the energy and other properties of a single
electron. For single atoms that contain multiple electrons (polyelectronic mono-atomic
systems), the wavefunction for the atom (ψ) is a product of one-electron wavefunctions
(χi), one for each electron. For molecules that contain multiple atoms (polyelectronic,
polyatomic molecular systems) the wave function for the molecule (Ψ) is a product of
one-electron wavefunctions (φi), where φis a three-dimensional mathematical function
44 MEDICINAL CHEMISTRY
Hψ=Eψ (1.7)