Essentials of Computational Chemistry

152 5 SEMIEMPIRICAL IMPLEMENTATIONS OF MO THEORY
of 0.45, 0.35, and 0.38 D, respectively, for MNDO, AM1, and PM3 (Stewart 1989). PM3
seems to be somewhat more robust for compounds incorporating phosphorus.
An alternative measure of the charge distribution involves a partitioning into partial atomic
charges. While such partitioning is always arbitrary (see Chapter 9) simple methods tend to
give reasonably intuitive results when small basis sets are used, as is the case for the NDDO
models. While MNDO and AM1 present no particular issues for such analysis, PM3 tends to
predict nitrogen atoms to be too weakly electronegative. Thus, in the ammonium cation, PM3
predicts the charge on nitrogen to be +1.0 while the charge on each hydrogen is predicted
to be 0.0 (Storer et al. 1995).
Finally, some attention has been paid to the quality of the complete electrostatic potential
about the molecule at the NDDO level. This topic is discussed in Chapter 9, as are additional
details associated with the performance of semiempirical models in comparison to other levels
of electronic structure theory for a variety of more specialized properties.
5.7 Ongoing Developments in Semiempirical MO Theory
Semiempirical theory is still in widespread use today not because it competes effectively
with more sophisticated theories in terms of accuracy, but because it competes effectively in
terms of demand for computational resources. Indeed, if one has either an enormously large
molecule, or an enormously large number of small molecules to be compared at a consistent
level (the next section describes a particular example of this case), semiempirical theory is
the only practical option. Of course, with each improvement in technology, the size horizon
of the more sophisticated levels expands, but there seems little danger that chemists will not
always be able to imagine still larger systems meriting quantum chemical study. Therefore,
considerable interest remains in improving semiempirical models in a variety of directions.
We close this chapter with a brief overview of some of the most promising of these.
5.7.1 Use of Semiempirical Properties in SAR
This area is a development in the usage of NDDO models that emphasizes their utility for
large-scale problems. Structure–activity relationships (SARs) are widely used in the pharmaceutical
industry to understand how the various features of biologically active molecules
contribute to their activity. SARs typically take the form of equations, often linear equations,
that quantify activity as a function of variables associated with the molecules. The molecular
variables could include, for instance, molecular weight, dipole moment, hydrophobic surface
area, octanol–water partition coefficient, vapor pressure, various descriptors associated with
molecular geometry, etc. For example, Cramer, Famini, and Lowrey (1993) found a strong
correlation (r = 0.958) between various computed properties for 44 alkylammonium ions
and their ability to act as acetylcholinesterase inhibitors according to the equation
1
log
Ki
=−2.583 − 0.636
100
4.961
V + π − 2.234q+
0.1
(5.18)