structures; PM3 has been reported to tend to give more reliable structures, and AM1
better energies [ 110 ]. Neither AM1 nor PM3 are generally reliable in modelling
hydrogen bonds [ 126 , 127 ], and the reclusive SAM1 appears to be the semiempiri-
cal method of choice here [ 86 ]. Recently, PM6 (Section6.2.5.6) has been said to
represent an improvement in the treatment of hydrogen bonds.
In general, the accuracy of semiempirical methods, particularly in energetics,
falls short of that of current routine ab initio methods (this may not have been the
case when AM1 was developed, in 1985 [ 125 ]). Parameters may not be available
for the elements in the molecules one is interested in, and obtaining new parame-
ters is something rarely done by people not actively engaged in developing new
methods. Semiempirical errors are less systematic than ab initio, and thus harder to
correct for. Clark has soberly warned that “All parameterized techniques can
interpolate and none can extrapolate consistently and well”, thus we can expect
on occasion “a catastrophic failure”; but semiempirical methods “will do what they
are designed to do” [ 11 ].
6.5 Summary................................................................
Semiempirical 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 the molecular
energy. The simple and extended H€uckel methods, in contrast, need only one matrix
diagonalization because their Fock matrix elements are not calculated using a
wavefunction guess (Chapter 4). 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 (“empiri-
cal”) quantities, and, nowadays, results from high-level ab initio or DFT calcula-
tions. In order of increasing sophistication, these SCF semiempirical procedures
have been developed: PPP (Pariser-Parr-Pople), CNDO (complete neglect of dif-
ferential overlap), INDO (intermediate neglect of differential overlap), and NDDO
(neglect of diatomic differential overlap). The PPP method is limited topelectrons,
while CNDO, INDO and NDDO use all the valence electrons. All four use the ZDO
(zero differential overlap) approximation, which sets the differential of the overlap
integral equal to zero; this greatly reduces the number of integrals to be calculated.
Traditionally, these methods were parameterized mostly using experimental quan-
tities (usually ionization energies and electron affinities), but also (PPP and CNDO)
making some use of results of minimal-basis-set (i.e. low-level) ab initio calcula-
tions. Of these original methods, only versions of INDO parameterized to reproduce
experimental UV spectra (INDO/S and its variant ZINDO/S) are much used
nowadays. Today the most popular SCF semiempirical methods are AM1 (Austin
method 1) and PM3 (parametric method 3), which are NDDO-based, carefully
parameterized to reproduce experimental quantities (primarily heats of formation).
6.5 Summary 437