Essentials of Computational Chemistry

5.7 ONGOING DEVELOPMENTS IN SEMIEMPIRICAL MO THEORY 157
test set. Such a reparameterization of a semiempirical Hamiltonian for a focused set of
molecules is completely analogous to the targeted parameterization of a force field, and the
usual caveats apply with respect to application of a focused model to anything other than
molecules falling within the target category.
5.7.4 Linear Scaling
As already touched upon in Section 2.4.2, the development of methods that scale linearly with
respect to system size opens the door to the modeling of very large systems with maximal
computational efficiency. Because the NDDO approximation is already rather efficient when
it comes to forming the Fock matrix (because so many integrals are assumed to be zero,
etc.), it serves as an excellent basis on which to build a linear-scaling QM model. Such
models have been reported; the details associated with achieving linear scaling are sufficiently
technical that interested readers are referred to the original literature (van der Vaart et al.
2000; Khandogin, Hu, and York 2000; see also Stewart 1996).
It is worth a pause, however, to consider how such models should best be used. Part of
the motivation for developing linear scaling models has been to permit QM calculations
to be carried out on biomolecules, e.g., proteins or polynucleic acids. However, one may
legitimately ask whether there is any point in such a calculation, beyond demonstrating that
it can be done. Because of the relatively poor fashion with which semiempirical models
handle non-bonded interactions, there is every reason to expect that such models would be
disastrously bad at predicting biomolecular geometries – or at the very least inferior to the
far more efficient force fields developed and optimized for this exact purpose.
Instead, the virtue of the semiempirical models when applied to such molecules tends to
be that they permit the charge distribution to be predicted more accurately given a particular
structure. To the extent that biomolecules often employ charge–charge interactions to
enhance reactivity and or specificity in the reaction and recognition of smaller molecules,
such predictions can be quite useful. Since the QM calculation intrinsically permits polarization
of the overall electronic structure, it is capable of showing greater sensitivity to
group–group interactions as they modify the charge distribution than is the case for the
typical fixed-atomic-charge, non-polarizable force field.
Of course, one may also be interested in the modeling of a bond-making/bond-breaking
reaction that takes place within a very large molecular framework, in which case the availability
of appropriate force-field models is extremely limited and one must perforce resort to
some QM approach in practice. Recognition of the complementary strengths and weaknesses
of QM and MM models has led to extensive efforts to combine them in ways that allow
maximum advantage to be taken of the good points of both; such QM/MM hybrid models
are the subject of Chapter 13.
5.7.5 Other Changes in Functional Form
Two modifications to the fundamental forms of modern NDDO functions have been reported
recently that merit particular attention. First, Weber and Thiel (2000) have reconsidered the