applied to those one-center two-electron integrals, (rs|tu), withfr,fs,ft, andfuall
on the same atom; obviously, these repulsion integrals should be the most impor-
tant. Although more accurate than CNDO, INDO is nowadays used mostly only for
calculating UV spectra, in specially parameterized versions called INDO/S and
ZINDO/S [ 20 ].
6.2.5 The Neglect of Diatomic Differential Overlap (NDDO)
Methods
NDDO [ 21 ] goes beyond INDO in that the ZDO approximation (Section 6.2.1,
point (3)) is not applied to orbitals on the same atom, i.e. ZDO is used only for
atomic orbitals on different atoms. NDDO is the basis of the currently popular
semiempirical methods developed by M. J. S. Dewar and by coworkers who took up
the torch: MNDO, AM1 and PM3 (as well as SAM1, PM5, and PM6). NDDO
methods are the gold standard in general-purpose semiempirical methods, and the
rest of this chapter concentrates on them.
6.2.5.1 NDDO-Based Methods from the Dewar Group: MNDO, AM1, PM3
and SAM1, and Related Methods – Preliminaries
SCF-type (seeSection 6.1) semiempirical theories are based to a large extent on the
approximate molecular orbital theory (see the book of this title [ 10 ]) developed by
Pople and coworkers. The Pople school, however, went on to concentrate on the
development of ab initio methods, and indeed it is for his contributions to these,
which are largely encapsulated in the Gaussian series of programs [ 22 ], that Pople
was awarded the 1998 Nobel Prize in chemistry [ 23 ] (shared with Walter Kohn, a
pioneer in density functional theory; seeChapter 7). In contrast, Dewar pursued the
semiempirical approach almost exclusively [ 24 ], and continued till the end of his
career to stoutly maintain that at least as far as molecules of real chemical interest
go his semiempirical methods were superior to ab initio ones (“There is clearly little
point in using a procedure that requires thousands of times more computing time
than ours do if it is no better than ours, let alone one that is inferior.”) [ 25 ]. The
rivalry between the Dewar school and the adherents of the ab initio approach began
relatively early in the development of Dewar methods (see e.g. [ 26 – 28 ]), intensified
to actual polemic [ 29 ], and is passionately described from an unabashedly partisan
viewpoint in Dewar’s autobiography [ 24 ]. The ab initio versus Dewar semiem-
pirical controversy was largely rooted in a difference of viewpoints and in a focus
by Dewar on the inability of ab initio calculations to give reasonably accurate
absolute molecular energies (here we can take this to mean the atomization energy).
In the absence of error cancellation, errors in absolute energies lead to errors in
400 6 Semiempirical Calculations