6.3.7 Some General Remarks..........................................
AM1 and PM3 have become extremely useful not only because they allow quantum
mechanical calculations to be done on molecules which are still too big for ab initio
or DFT (Chapter 7) methods, but also as adjuncts to these latter methods, since they
often allow a relatively rapid survey of a problem, such as an exploration of
a potential energy surface: one can locate minima and transition states, then use
the semiempirical structures as inputs for initial geometries, wavefunctions and
Hessians (Sections 2.4 and 5.2.3.6.5) in a higher-level geometry optimization, size
permitting. If geometry optimizations are not feasible, single-point calculations on
AM1 or PM3 geometries, which are usually reasonably good, will likely give
improved relative energies. The time is well past when semiempirical calculations
were regarded by many as “worthless” [ 118 ], or, at best, a poor substitute for ab
initio calculations. In fact, in his thoughtful review Tim Clark, a major worker in the
field of developing semiempirical methods, has described “The NDDO-approxima-
tion [as] one of the most successful and least appreciated in modern theoretical
chemistry” [ 11 ]. Recall that modern general-purpose semiempirical methods are
based on NDDO (Section6.2.5). In his book which focusses on ab initio and density
functional methods, Bachrach says that faster computers and more efficient algo-
rithms will make semiempirical methods less important [ 119 ]; a more extreme view
was recently expressed by the president of a major computational chemistry
software company, who told this author that he thought semiempirical methods
would soon be replaced by DFT; and a rather dismissive rejection of the general
enterprise of employing the semiempirical approach in science came from the
mathematician John von Neumann [ 120 ]: “With four parameters I can cover an
elephant, and with five I can make him wiggle his trunk.” Elephants aside, Clark
rejects the opinion of “pundits [who] predict the demise” of modern semiempirical
methods. He makes the interesting point that Dewar (Section6.2.5.1and [ 24 ]) may
have made a mistake in “trying to match” the ab initio methods of the time “on its
own ground”, namely achieving good geometries and energies for small molecules,
instead of concentrating on the forte of semiempirical methods, large molecules.
This review [ 11 ] is commended to the reader. A caveat is in order regarding the
application of semiempirical methods to large biomolecules: the most popular
program suites for studying proteins and nucleic acids, AMBER [ 121 ] and
CHARMM/CHARMm [ 121 ], use molecular mechanics (MM,Chapter 3). One
seems justified in being sceptical [e.g. [ 122 ]) of the appropriateness of semiempiri-
cal methods for geometry optimization of such biomolecules, since the relevant
MM forcefields have been very carefully parameterized for them and are much
faster. A useful procedure would be to optimize the molecule with MM, then perform
a single-point (unchanged geometry) semiempirical calculation to obtain a wavefunc-
tion, from which electronic properties like charges can be calculated.
The philosophical divide we saw in, for example, the exchange between Dewar
and Halgren, Kleir and Lipscomb (6.2.5.1), persists. One gets the impression that
certain journals are reluctant to publish purely theoretical semiempirical papers;
6.3 Applications of Semiempirical Methods 435