Gaussians (an STO-3G basis set) as in standard ab initio calculations (Section5.3.2).
This is in contrast to AM1, where the two-center two-electron integrals are calcu-
lated from the one-center two-electron integrals, which are estimated spectroscopi-
cally. As Holder and Evleth point out in a brief but lucid outline of the basis of AM1
and SAM1 [ 86 ], a key distinguishing feature of each semiempirical method is how it
calculates the two-electron repulsion integrals. Since the NDDO approximation
discards all the three- and four-center two-electron integrals, the number of two-
electron integrals to be calculated is greatly reduced. This, and the limitation to
valence electrons, makes SAM1 only about twice as slow as AM1 [ 86 ].
One of the main reasons for developing SAM1 was to improve the treatment of
hydrogen bonding (this was also a primary reason for developing AM1 from
MNDO; evidently success there was only limited [ 63 ]). SAM1 is indeed an
improvement over AM1 in this respect, and “appears to be the first semiempirical
parameterization to handle a wide variety of [hydrogen bonded] systems correctly”;
in fact, it was said that “The results from SAM1 for virtually every system has
improved over AM1 and PM3, fulfilling the criteria for SAM1 to be a reasonable
successor to AM1 and PM3 for general purpose semiempirical calculations” [ 86 ].
An extensive list of experimental heats of formation compared with those calcu-
lated by SAM1, AM1 and PM3 has been published [ 75 ]. Actually, despite its
apparent generally significant superiority over AM1, there have been relatively
few publications using SAM1. This is probably because the program is at present
available only in the commercial semiempirical package AMPAC [ 57 ], and
because the latest “PMX”, the fully semiempirical PM6, appears to be so powerful.
That the parameterization of SAM1 has not been fully disclosed in the open
literature may also play a role – researchers are perhaps uncomfortable about
using a black box.
6.3 Applications of Semiempirical Methods................................
A good, brief overview of the performance of MNDO, AM1 and PM3 as of ca. 1999
is given by Levine [ 87 ]. Hehre has compiled a very useful book comparing AM1
with molecular mechanics (Chapter 3), ab initio (Chapter 5) and DFT (Chapter 7)
methods for calculating geometries and other properties [ 88 ], and an extensive
collection of AM1 and PM3 geometries is to be found in Stewart’s second PM3
paper [ 70 ].
6.3.1 Geometries.......................................................
Many of the general remarks on molecular geometries in Section5.5.1, preceding
the discussion of results of specifically ab initio calculations, apply also to semi-
empirical calculations. Geometry optimizations of large biomolecules like proteins
412 6 Semiempirical Calculations