Thus the desired quantity, the heat of formation of the molecule, can be cal-
culated from the experimental heats of formation of the atoms and the semiempiri-
cal energies of the atoms and the molecule. The calculation using Eq.6.13is
automatically done by the program using stored values for atomic heats of forma-
tion and semiempirical atomic energies, and the “freshly calculated” calculated
molecular energy, and one normally never seesEtotalSEðMÞ. These calculations are for
the gas phase, and if one wants the heat of formation of a liquid or a solid, then the
experimental heat of vaporization or sublimation must be taken into account. Note
that this procedure is conceptually almost the same as the atomization method for
ab initio calculation of heats of formation (Section5.5.2.2c). However, the purpose
here is to obtain the heat of formation at room temperature (298 K) from the
molecular “total semiempirical energy”, the electronic energy plus core–core
repulsion; in the ab initio atomization method the 0 K heat of formation is
calculated with the aid of the molecular energy including ZPE (the 0 K heat of
formation can be corrected to 298 K – see Section5.5.2.2c). The semiempirical
procedure involves some approximations. The ZPE of the molecule is not used (so a
frequency calculation is not needed for this), and the increase in thermal energy
from 0 to 298 K is not calculated. Thus ifEtotalSEðMÞwere fully analogous to the ab
initio 0 K electronic energy plus internuclear repulsion then the calculated atomi-
zation energy would be at 0 K, not 298 K, and furthermore would employ a frozen-
nucleus approximation to the true 0 K energy. The good news is thatEtotalSEðMÞis
parameterized (below) to reproduceDH*f298ðMÞ; to the extent that this parameteri-
zation succeeds the neglect of ZPE and of the 0–298 K increase in thermal energy
are overcome, and electron correlation is also implicitly taken into account. The key
to obtaining reasonably accurate heats of formation from these methods is thus their
parameterization to give the values ofESEðAiÞandEtotalSEðMÞused in Eq.6.13. This
parameterization, which is designed to also give reasonable geometries and dipole
moments, is discussed below.
6.2.5.3 MINDO
The first (1967) of the Dewar-type methods was PNDDO [ 35 ], partial NDDO),
but because further development of the NDDO approach turned out to be
“unexpectedly formidable” [ 33 ], Dewar’s group temporarily turned to INDO,
creating MINDO/1 [ 36 ] (modified INDO, version 1). The third version of this
method, MINDO/3, was said [ 33 ] “[to have] so far survived every test without
serious failure”, and it became the first widely-used Dewar-type method. Keeping
their promise to return to NDDO the group soon came up with MNDO (modified
NDDO). MINDO/3 was made essentially obsolete by MNDO, except perhaps for
the study of carbocations (Clark has summarized the strengths and weaknesses
of MINDO/3, and the early work on MNDO [ 37 ]). MNDO (and MNDOC and
MNDO/d) and its descendants, the very popular AM1 and PM3, are discussed
below. Briefly mentioned are a modification of AM1 called SAM1 and an
6.2 The Basic Principles of SCF Semiempirical Methods 403