activation and reaction energies, and the errors in absolute energies were, ca. 1970,
commonly in the region of a 1,000 kJ mol"^1. Cancellation (actually not as untrust-
worthy as Dewar thought –Section 5.5.2) could not, he held, be relied on to provide
chemically useful relative energies (reaction and activation energies), say with
errors of no more than some tens of kilojoules per mole. The exchange with
Halgren, Kleir and Lipscomb nicely illustrates the viewpoint difference [ 28 ]: one
side held that even when inaccurate, ab initio calculations can teach us something
fundamental, while semiempirical calculations, no matter how good, do not con-
tribute to fundamental theory. Dewar focussed on the study of reactions of “real”
chemical interest. Toward the end of his career as an active chemist, he coauthored
a review of pericyclic reactions such as the Cope and Diels-Alder processes,
defending the results of AM1 (below) studies [ 30 ]. The divergence of these con-
clusions from those of other workers engendered a rebuke from Houk and
Li [ 31 ]. Interestingly, the high-accuracy “ab initio” methods that in recent years
have achieved chemical accuracy (Section 5.5.2.2b), considered to be about
10 kJ mol"^1 , employ some empirical parameters, a fact that would have amused
Dewar (Section 6.1, footnote).
In contrast to the viewpoint of the ab initio school, Dewar regarded the semiem-
pirical method not merely as an approximation to ab initio calculations, but rather
as an approach that, carefully parameterized, could give results far superior to those
from ab initio calculations, at least for the foreseeable future: “The situation [ca.
1992] could be changed only by a huge increase in the speed of computers, larger
than anything likely to be attained before the end of the century, or by the
development of some fundamentally better ab initio approach” [ 32 ]. The conscious
decision to strive for experimental accuracy rather than merely to reproduce low-
level ab initio results (note the remarks in connection with Eq.6.12) was clearly
stated several times [ 27 , 29 , 33 ] in the course of the development of these semiem-
pirical methods: “We set out to parametrize [semiempirical methods] in an entirely
different manner, to reproduce the results of experiment rather than those of
dubious ab initio calculations” [ 33 ]. Of the several experimental parameters that
the Dewar methods are designed to reproduce, probably the two most important are
geometry and heat of formation. As with ab initio calculations, optimized geome-
tries are found by an algorithm which uses first and second derivatives of energy
with respect to geometric parameters to locate stationary points (Section 2.4). The
method of finding heats of formation is described below.
6.2.5.2 Heats of Formation (Enthalpies of Formation) from Semiempirical
Electronic Energies
For heat of formation the procedure encoded in the methods is the following [ 34 ]. As
with ab initio calculations, SCF-type semiempirical calculations initially give elec-
tronic energiesESE; these are calculated using Eq.6.2. Inclusion of the core–core
repulsionVCC, which is necessary for geometry optimization, gives the total semi-
empirical energyEtotalSE, normally expressed in atomic units (hartrees), as in an ab
6.2 The Basic Principles of SCF Semiempirical Methods 401