Computational Chemistry

Chapter 6

Semiempirical Calculations

Current “ab initio” methods were limited to very inaccurate calculations

for very small molecules.

M.J.S. Dewar,A Semiempirical Life, 1992

AbstractSemiempirical quantum mechanical calculations are based on the
Schr€odinger equation. This chapter deals with SCF semiempirical methods, in
which repeated diagonalization of the Fock matrix refines the wavefunction and
molecular energy. These calculations are much faster than ab initio ones, mainly
because the number of integrals to be dealt with is greatly reduced by ignoring some
and approximating others with the help of experimental quantities, or values from
high-level ab initio or DFT calculations. In order of increasing sophistication, these
SCF semiempirical procedures have been developed: PPP (Pariser-Parr-Pople),
CNDO (complete neglect of differential overlap), INDO (intermediate neglect of
differential overlap), and NDDO (neglect of diatomic differential overlap). Today
the most popular SCF semiempirical methods are AM1 and PM3, which are
carefully parameterized to reproduce experimental quantities (primarily heats of
formation). Recent extensions of AM1 (RM1) and PM3 (PM6) seem to represent
substantial improvements and are likely to soon become the standard semiempirical
methods.

6.1 Perspective..............................................................

We have already seen examples of semiempirical methods, inChapter 4: the simple
H€uckel method (SHM, Erich H€uckel, ca. 1931) and the extended H€uckel method
(EHM, Roald Hoffmann, 1963). These are semiempirical (“semi-experimental”)
because they combine physical theory with experiment. Both methods start with the
Schr€odinger equation (theory) and derive from this a set of secular equations which
may be solved for energy levels and molecular orbital coefficients (most efficiently

E.G. Lewars,Computational Chemistry,
DOI 10.1007/978-90-481-3862-3_6,#Springer ScienceþBusiness Media B.V. 2011

391