by diagonalizing a Fock matrix; seeChapter 4). However, the SHM gives energy
levels in units of a parameter (b) that can be translated into actual quantities only by
comparing SHM results with experiment, and the EHM uses experimental ioniza-
tion energies to translate the Fock matrix elements into actual energy quantities.
Semiempirical calculations stand in contrast to empirical methods, like molecular
mechanics (Chapter 3), and theoretical methods, like ab initio calculations (Chapter
5 ). Molecular mechanics starts with a model of a molecule as balls and springs, a
model that works but whosetheoretical justificationlies outside molecular mechan-
ics. The ab initio method, like the H€uckel methods, starts with the Schr€odinger
equation but strictly ab initio calculations do not appeal to experiment, beyond
invoking, when actual quantities are needed, experimental values for Planck’s
constant, the charge on the electron and proton, and the masses of the electron
and atomic nuclei. These fundamental physical constants could be calculated only
by some deep theory of the origin and nature of our universe [ 1 ].
The H€uckel methods were discussed inChapter 4rather than here because
extensive application of these methods came before widespread use of ab initio
methods, and because the simple H€uckel, extended H€uckel and ab initio methods
form a conceptual progression in which the first two methods aid understanding of
the third in this hierarchy of complexity. The semiempirical methods treated in this
chapter are logically regarded as simplifications of the ab initio method, since they
use the SCF procedure (Chapter 5) to refine the Fock matrix, but do not evaluate
these matrix elementsab initio. The SHM was developed (1931) outside the realm
of SCF theory (which was invented for atoms: Hartree, 1928 [ 2 ]), as the first appli-
cation of the Schr€odinger equation to molecules of reasonable size, and the EHM is
a straightforward extension of this. In contrast, the methods of this chapter began as
a conscious attempt to provide practical alternatives to the ab initio approach, the
application of which to molecules of reasonable size understandably seemed
hopeless in the infancy of electronic computers. The PPP method, one of the first
SCF semiempirical methods, was published in 1953, just when the first electronic
computers began to be available to chemists [ 3 ]. Semiempirical calculations are
much less demanding of computer power than ab initio ones, because parameteri-
zation and approximations drastically reduce the number of integrals which must be
calculated. The pessimism with which the ab initio approach was viewed is clear in
the words of several pioneers of quantum chemistry:
C. A. Coulson, 1959: “I see little chance – and even less desirability – of dealing in this
accurate manner with systems containing more than 20 electrons...”[ 4 ]
M. J. S. Dewar^1 , 1969: “How then shall we proceed? The answer lies in abandoning
attempts to carry out rigorous a priori calculations.” [ 5 ].
Neither Coulson nor Dewar could have foreseen the enormous increase in com-
puter power that was to come over the next few decades. What Coulson meant by
(^1) Michael J. S. Dewar, born Ahmednagar, India, 1918. Ph.D. Oxford, 1942. Professor of chemistry
at Universities of London, Chicago, Texas at Austin, and University of Florida. Died Florida,
1997.
392 6 Semiempirical Calculations