Essentials of Computational Chemistry

146 5 SEMIEMPIRICAL IMPLEMENTATIONS OF MO THEORY
c that modify the potential of mean force between the two atoms. Simultaneous optimization
of the original MNDO parameters with the Gaussian parameters led to markedly improved
performance, although the Gaussian form of Eq. (5.16) is sufficiently force-field-like in
nature that one may quibble about this method being entirely quantum mechanical in nature.
Since the report for the initial four elements, AM1 parameterizations for B, F, Mg, Al, Si,
P, S, Cl, Zn, Ge, Br, Sn, I, and Hg have been reported. Because AM1 calculations are so fast
(for a quantum mechanical model), and because the model is reasonably robust over a large
range of chemical functionality, AM1 is included in many molecular modeling packages,
and results of AM1 calculations continue to be reported in the chemical literature for a wide
variety of applications.
5.5.3 PM3
One of the authors on the original AM1 paper and a major code developer in that effort, James
J. P. Stewart, subsequently left Dewar’s labs to work as an independent researcher. Stewart
felt that the development of AM1 had been potentially non-optimal, from a statistical point of
view, because (i) the optimization of parameters had been accomplished in a stepwise fashion
(thereby potentially accumulating errors), (ii) the search of parameter space had been less
exhaustive than might be desired (in part because of limited computational resources at the
time), and (iii) human intervention based on the perceived ‘reasonableness’ of parameters had
occurred in many instances. Stewart had a somewhat more mathematical philosophy, and felt
that a sophisticated search of parameter space using complex optimization algorithms might
be more successful in producing a best possible parameter set within the Dewar-specific
NDDO framework.
To that end, Stewart set out to optimize simultaneously parameters for H, C, N, O, F,
Al, Si, P, S, Cl, Br, and I. He adopted an NDDO functional form identical to that of AM1,
except that he limited himself to two Gaussian functions per atom instead of the four in
Eq. (5.16). Because his optimization algorithms permitted an efficient search of parameter
space, he was able to employ a significantly larger data set in evaluating his penalty function
than had been true for previous efforts. He reported his results in 1989; as he considered his
parameter set to be the third of its ilk (the first two being MNDO and AM1), he named it
Parameterized Model 3 (PM3; Stewart 1989).
There is a possibility that the PM3 parameter set may actually be the global minimum in
parameter space for the Dewar-NDDO functional form. However, it must be kept in mind
that even if it is the global minimum, it is a minimum for a particular penalty function, which
is itself influenced by the choice of molecules in the data set, and the human weighting of
the errors in the various observables included therein (see Section 2.2.7). Thus, PM3 will
not necessarily outperform MNDO or AM1 for any particular problem or set of problems,
although it is likely to be optimal for systems closely resembling molecules found in the
training set. As noted in the next section, some features of the PM3 parameter set can lead
to very unphysical behaviors that were not assessed by the penalty function, and thus were
not avoided. Nevertheless, it is a very robust NDDO model, and continues to be used at
least as widely as AM1.