Computational Chemistry

MNDO AM1 PM3 PM5

Heat of formation 77 50 42 25 kJ mol"^1

Bond length 0.066 0.053 0.065 0.051 A ̊

Bond angle 6.298 5.467 5.708 5.413

As of mid-2009 the latest version of the PMx series was PM6, which Stewart has
described in detail in a long paper [ 82 ]; in this paper, which also gives a brief
history of NDDO methods, it was explicitly said that PM4 and PM5 were “unpub-
lished”, presumably meaning that the details of their parameterization had not been
revealed. PM6 is available in Gaussian 09 [ 55 ], AMPAC 9 [ 57 ], and MOPAC2009
[ 58 ]. It appears to be a major improvement over PM3 and AM1 and will likely be
the standard general-purpose semiempirical method for some years, except in those
program suites which retain PM3 and AM1 without introducing PM6. A brief
summary of the performance of PM6, from the MOPAC2009 brochure [ 83 ]
(much more detail is given in [ 82 ], mainly for the parameterization for heats of
formation) indicates that this method:

1. Was parameterized with data from over 9,000 compounds; experimental and
   ab initio data were used, so unlikeearlierNDDOmethods(MNDO,AM1,
   PM3; ca. 1975–1990) the parameterization is not purely empirical. Only about
   500 compounds were used for PM3.


2. Gives better heats of formation (from tests on 1,373 compounds) than those from
   B3LYP/6-31G (a DFT method), PM3, HF/6-31G, and AM1: the average
   unsigned errors for PM6 and those four methods were 20.0 (PM6), 21.7, 26.2,
   30.8, and 41.9 kJ mol"^1. Using a version of NDDO specially parameterized just
   for heats of formation and somewhat more accurate for this purpose than PM6
   (average unsigned errors 16.1 versus 20.0 kJ mol"^1 ), several errors were identi-
   fied in a survey of ca. 1,300 compounds in the NIST Chemistry WebBook
   database [ 84 ].


3. Treats hydrogen bonds better than PM3 and AM1.


4. Is parameterized for all main group and transition elements.

Some other information on the accuracy of PM6 is available from the
MOPAC2009 manual [ 85 ]:

PM6 PM3 AM1

Bond length 0.091 0.104 0.130 A ̊

Bond angle 7.86 8.50 8.77

Dipole moment 0.85 0.72 0.67 D

Ionization energy 0.50 0.68 0.63 eV

6.2.5.7 SAM1

SAM1 (semi ab initio method number 1) was the last semiempirical method to be
reported (1993, [ 76 ]) by Dewar’s group. SAM1 is essentially a modification of
AM1 in which the two-electron integrals are calculated ab initio using contracted

6.2 The Basic Principles of SCF Semiempirical Methods 411