acceptable is a matter of judgment. Dewar et al. chose to call their modified MNDO
method AM1, rather than MNDO/2, because they felt that their methods were being
confused (presumably because of the “INDO” and “NDO” components of the
appellations) with “grossly inaccurate” [ 60 ] ZDO SCF semiempirical methods
like CNDO and INDO.
Dewar et al. reported [ 60 ] that AM1 calculations on compounds containing
nitrogen and/or oxygen gave an absolute mean error in heats of formation of
25 kJ mol"^1 for 80 compounds, “generally satisfactory” agreement with experiment
for the geometries of 138 molecules, absolute mean error in dipole moment of
0.26 D for 46 compounds, and absolute mean error in ionization energy of 0.40 eV
for 29 compounds. These results are slightly better than those for MNDO, but the
real advantages of AM1 over MNDO were said [ 60 ] to lie in its better treatment of
crowded molecules, four-membered rings, activation energies, and hydrogen bond-
ing. Nevertheless, misrepresentations of hydrogen bonding remain a problem with
AM1 [ 63 ]. AM1 and PM3 (below) are the most widely-used semiempirical methods
nowadays, and are available in practically all commercial program suites which
have not made a point of being strictly devoted to some other method(s) than
semiempirical ones.
A fairly recent reparameterization of AM1, called RM1 (for Recife, a city in
Brazil where three of the four authors work; by analogy with Austin method 1) is
said to be better than AM1 and PM3 and to be “at least very competitive” with PM5
(PM3, PM5 and PM6: see below) [ 64 ]. RM1 keeps “the mathematical structure and
qualities of AM1, while significantly improving its quantitative accuracy with the
help of today’s computers and also of the more advanced techniques available for
nonlinear optimization.” RM1 can be implemented in the AM1 software without
changing the code, other than altering the parameters. For 1,736 species considered
in the parameterization some average errors were:
Heat of formation (kJ mol"^1 /kcal mol"^1 ):
AM1 47/11.15, PM3 33/7.98, PM5 25/6.03, RM1 24/5.77
Bond length (A ̊):
AM1 0.036, PM3 0.029, PM5 0.037, RM1 0.027
Bond angle (degrees):
AM1 5.88, PM3 6.98, PM5 9.83, RM1 6.82
The impetus behind RM1 was to make calculations on big biomolecules more
accurate. RM1 is available in Spartan ‘06 [ 56 ] and later versions and in AMPAC 9.0
[ 57 ] and MOPAC2009 [ 58 ].
Another variation of AM1 is AM1/d. This is similar in structure to MNDO/d; d
functions appear to have been first introduced into AM1 to parameterize it for
molybdenum [ 65 ], and other parameterizations seem to have been done on an as-
needed basis, e.g. for magnesium [ 66 ] and for phosphoryl transfer reactions [ 67 ].
AM1/d was available in an early version of MOPAC [ 58 ], WinMOPAC v.2.0
(reported in a study of the reaction of ethene with oxygen atoms on a silver surface)
[ 68 ], and in MOPAC2000 [ 58 ] but it is unclear if any current commercial program
6.2 The Basic Principles of SCF Semiempirical Methods 409