Essentials of Computational Chemistry

6
Ab Initio Implementations of
Hartree–Fock Molecular Orbital
Theory
6.1 Ab Initio Philosophy
The fundamental assumption of HF theory, that each electron sees all of the others as an
average field, allows for tremendous progress to be made in carrying out practical MO calculations.
However, neglect of electron correlation can have profound chemical consequences
when it comes to determining accurate wave functions and properties derived therefrom. As
noted in the preceding chapter, the development of semiempirical theories was motivated
in part by the hope that judicious parameterization efforts could compensate for this feature
of HF theory. While such compensation has no rigorous foundation, to the extent it permits
one to make accurate chemical predictions, it may have great practical utility.
Early developers of so-called ‘ab initio’ (Latin for ‘from the beginning’) HF theory, however,
tended to be less focused on making short-term predictions, and more focused on long-term
development of a rigorous methodology that would be worth the wait (a dynamic tension
between the need to make predictions now and the need to make better predictions tomorrow
is likely to characterize computational chemistry well into the future). Of course, the ultimate
rigor is the Schrödinger equation, but that equation is insoluble in a practical sense for all
but the most simple of systems. Thus, HF theory, in spite of its fairly significant fundamental
assumption, was adopted as useful in the ab initio philosophy because it provides a very well
defined stepping stone on the way to more sophisticated theories (i.e., theories that come
closer to accurate solution of the Schrödinger equation). To that extent, an enormous amount
of effort has been expended on developing mathematical and computational techniques to
reach the HF limit, which is to say to solve the HF equations with the equivalent of an
infinite basis set, with no additional approximations. If the HF limit is achieved, then the
energy error associated with the HF approximation for a given system, the so-called electron
correlation energy Ecorr, can be determined as
Ecorr = E − EHF
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)
(6.1)