Essentials of Computational Chemistry

13
Hybrid Quantal/Classical Models
13.1 Motivation
An interest in understanding solvent structure represents one example of a situation that
requires the explicit representation of a large system, as described in detail in the preceding
chapter. For reasons of efficiency, such representation is most typically carried out at the
molecular mechanics level. The chief drawback of the MM level of theory, however, is that
it is almost never appropriate for the description of processes involving bond-making or
bond-breaking, i.e., chemical reactions. To adequately model such processes, QM methods
are required. However, the region of space within which significant changes in electronic
structure occur along the course of a reaction coordinate is often relatively small compared
to the size of the reacting system as a whole. For instance, a very large enzyme may catalyze
the conversion of its substrate from one molecule to another, but the volume of space within
which bonds are being made and broken is usually limited to the relatively small active site.
The remainder of the enzyme may be important for maintaining its structure, recognizing
other enzymes with which it works, folding, etc., but fails to exert any quantum mechanical
influence on the catalytic active site.
Thus, from a modeling perspective, we may regard the situation in the abstract as described
by Figure 13.1. Within a limited region, we wish to make use of the tools of quantum
mechanics to accurately model an electronic-structure problem, while in the surrounding
region the explicit representation of the supersystem is important, but the level of model
applied can be reduced in complexity owing to the more simply understood influence of the
outer region on the process as a whole. When the level applied to the outer system is MM,
the complete Hamiltonian for the system must be some kind of hybrid of QM and MM
methodologies, defining a so-called QM/MM technique. Put in a disarmingly simple fashion
Hcomplete = HQM + HMM + HQM/MM
(13.1)
where HQM accounts for the full interaction energy of all quantum mechanical particles
with one other, HMM accounts for the full interaction energy of all classical particles with
one other, and HQM/MM accounts for the energy of all interactions between one quantum
mechanical particle and one classical particle. Methods for the evaluation of the first two
Essentials of Computational Chemistry, 2nd Edition Christopher J. Cramer
© 2004 John Wiley & Sons, Ltd ISBNs: 0-470-09181-9 (cased); 0-470-09182-7 (pbk)