suite carries it. AM1/d was modified and parameterized for P, S and Cl to give a
variant called AM1* [ 69 ].
6.2.5.6 PM3 and Extensions (PM3(tm), PM5, and PM6)
PM3, parametric method 3, is a variation of AM1 differing mainly in how the para-
meterization is done. There were no explicit PM1 and PM2 because the developer
(below) considered the first two viable parameterized methods of this type to be
MNDO and AM1. When PM3 was first published [ 41 ], those two parameterizations of
MNDO-type methods had been carried out, and PM3 was at first called MNDO-PM3,
meaning MNDO parametric method 3. Three papers [ 41 , 70 , 71 ] define the PM3
method. The Dewar school’s approach to parameterization was a painstaking one
(Section6.2.5.4), making liberal use of chemical intuition. The developer of PM3,
J. J. P. Stewart, employed a faster, more algorithmic approach, “several orders of
magnitude faster than those previously employed.” [ 41 ]. Although it is based on AM1,
PM3 did not enjoy Dewar’s blessing. The reasons for this appear to be at least twofold:
(1) Dewar felt (on the basis of very early results [ 72 ]) that PM3 represented at best an
only marginal improvement over AM1, and that a new semiempirical method should
make previous ones essentially obsolete, as MNDO made MINDO/3 obsolete, and
AM1 largely replaced MNDO. Stewart defended his approach [ 73 ] with the rejoinder,
inter alia, that if PM3 was only a marginal improvement over AM1, then AM1 was
only a marginal improvement over MNDO. (2) Dewar objected strongly to any
proliferation of computational chemistry methods, whether it be in the realm of
ab initio basis sets [ 74 ] or of semiempirical methods [ 72 , 74 ].
For compounds containing H, C, N, O, F, Cl, Br, and I, Holder et al. reported [ 75 ]
that PM3 calculations gave an absolute mean error in heat of formation of 22 kJ mol"^1
for 408 compounds (cf. 27 kJ mol"^1 for AM1), and Dewar et al. reported an absolute
mean error in bond lengths of 0.022 A ̊for 344 bonds (cf. 0.027 for AM1), 2.8for 146
angles (cf. 2.3for AM1) [ 76 ], and 0.40 D for 196 compounds (cf. 0.35 D for AM1)
[ 76 ]. PM3 and AM1 are the most widely-used semiempirical method nowadays.
PM3(tm) is a version (1996, 1997) parameterized with d orbitals for geome-
tries, but not for heats of formation, dipolemoments,orionizationenergies,for
transition metals [ 77 ]. It was evaluated ca. 2000 by Bosque and Maseras [ 78 ], who
also briefly mentioned 11 earlier (1996–1999) publications testing this method.
The consensus seems to be that the method tends to be good for geometries but not
for energies, and that “its reliability hastobeprovedonacasebycasebasis”[ 78 ].
There have since been many published tests of PM3(tm), a few of which are given
in reference [ 79 ].
The designation PM4 is said to have been reserved for “a separate, collaborative
parameterization effort” [ 80 ], and the results of this do not appear to have been
published. PM5 was an improvement of PM3 that appeared in MOPAC2002 [ 58 ].
An idea of the accuracy of PM5 compared to MNDO, AM1, and PM3 is given by
this information on errors in the MOPAC2002 manual [ 81 ] (I converted kcal mol"^1
to kJ mol"^1 ):
410 6 Semiempirical Calculations