Essentials of Computational Chemistry

5.7 ONGOING DEVELOPMENTS IN SEMIEMPIRICAL MO THEORY 153
where Ki is the inhibition constant, V is the molecular volume, π derives from the molecular
polarizability, q + is the largest positive charge on a hydrogen atom, and all of the variables
on the r.h.s. of Eq. (5.18) were computed at the MNDO level.
Once a SAR is developed, it can be used to prioritize further research efforts by focusing
first on molecules predicted by the SAR to have the most desirable activity. Thus, if a drug
company has a database of several hundred thousand molecules that it has synthesized over
the years, and it has measured molecular properties for those compounds, once it identifies
a SAR for some particular bio-target, it can quickly run its database through the SAR to
identify other molecules that should be examined. However, this process is not very useful
for identifying new molecules that might be better than any presently existing ones. It can be
quite expensive to synthesize new molecules randomly, so how can that process be similarly
prioritized?
One particularly efficient alternative is to develop SARs not with experimental molecular
properties, but with predicted ones. Thus, if the drug company database is augmented with
predicted values, and a SAR on predicted values proves useful based on data for compounds
already assayed, potential new compounds can be examined in a purely computational fashion
to evaluate whether they should be priority targets for synthesis. In 1998, Beck et al. (1998)
optimized the geometries of a database of 53 000 compounds with AM1 in 14 hours on a
128-processor Origin 2000 computer. Such speed is presently possible only for semiempirical
levels of theory. Once the geometries and wave functions are in hand, it is straightforward
(and typically much faster) to compute a very wide variety of molecular properties in order
to survey possible SARs. Note that for the SAR to be useful, the absolute values of the
computed properties do not necessarily need to be accurate – only their variation relative to
their activity is important.
5.7.2 d Orbitals in NDDO Models
To extend NDDO methods to elements having occupied valence d orbitals that participate
in bonding, it is patently obvious that such orbitals need to be included in the formalism.
However, to accurately model even non-metals from the third row and lower, particularly
in hypervalent situations, d orbitals are tremendously helpful to the extent they increase the
flexibility with which the wave function may be described. As already mentioned above,
the d orbitals present in the SINDO1 and INDO/S models make them extremely useful for
spectroscopy. However, other approximations inherent in the INDO formalism make these
models poor choices for geometry optimization, for instance. As a result, much effort over
the last decade has gone into extending the NDDO formalism to include d orbitals.
Thiel and Voityuk (1992, 1996) described the first NDDO model with d orbitals included,
called MNDO/d. For H, He, and the first-row atoms, the original MNDO parameters are
kept unchanged. For second-row and heavier elements, d orbitals are included as a part of
the basis set. Examination of Eqs. (5.12) to (5.14) indicates what is required parametrically
to add d orbitals. In particular, one needs Ud and βd parameters for the one-electron integrals,
additional one-center two-electron integrals analogous to those in Eq. (5.11) (there are