Essentials of Computational Chemistry

5
Semiempirical Implementations
of Molecular Orbital Theory
5.1 Semiempirical Philosophy
In the last chapter, the full formalism of Hartree–Fock theory was developed. While this
theory is impressive as a physical and mathematical construct, it has several limitations in a
practical sense. Particularly during the early days of computational chemistry, when computational
power was minimal, carrying out HF calculations without any further approximations,
even for small systems with small basis sets, was a challenging task.
In spite of the technical hurdles, however, many chemists recognized the potentially
critical role that theory could play in furthering experimental progress on any number of
fronts. And the interests of that population of chemists were by no means restricted to
molecules composed of only a small handful of atoms. Accepting HF theory as a framework,
several research groups turned their attention to implementations of the theory that would
make it more tractable, and perhaps more accurate, for molecules of moderate size. These
steps ‘sideways’, if you will, led to a certain bifurcation of effort in the area of molecular
orbital theory (although certainly some research groups pursued topics in both directions)
that persists to this day. Semiempirical calculations continue to appear in large numbers
in the chemical literature; since there will always be researchers interested in molecules
that exceed the size of those practically accessible by ab initio methods, semiempirical
levels of MO theory are certain to continue to be developed and applied. This chapter
describes the underlying approximations of semiempirical methods (organizing them roughly
in chronological order of appearance) and provides detailed comparisons between methods
now in common use for the prediction of various chemical properties. Section 5.7 describes
recent developments in the area of improving/extending semiempirical models.
5.1.1 Chemically Virtuous Approximations
Let us consider how one might go about making formal Hartree–Fock theory less computationally
intensive without necessarily sacrificing its accuracy. The most demanding step
Essentials of Computational Chemistry, 2nd Edition Christopher J. Cramer
© 2004 John Wiley & Sons, Ltd ISBNs: 0-470-09181-9 (cased); 0-470-09182-7 (pbk)