Essentials of Computational Chemistry

458 13 HYBRID QUANTAL/CLASSICAL MODELS
MM
QM
Figure 13.1 In large systems that require explicit representation, understanding bond-making/bond-breaking
processes can often be accomplished using a quantum mechanical representation of
only a portion of the full system, with a molecular mechanics representation of the rest
terms on the r.h.s. of Eq. (13.1) have already been the subject of much discussion in preceding
chapters – the devil for a hybrid method is in the details of the final term, and those are the
subject of this chapter.
Many QM/MM modeling schemes have been described with varying levels of formalism.
In terms of classification, perhaps the most fundamental distinction is whether or not the
boundary separating the QM region from the MM region in Figure 13.1 cuts across any
chemical bonds. If it does not, the coupling of the QM and MM regions can be represented
with a reasonable degree of simplicity. If so clean a separation is not practical, however,
e.g., the QM region consists of the substrate for a large enzyme and at least one atom from
a side chain residue in the active site (that serves to accept a proton from the substrate, for
example), then more complicated coupling schemes must be employed to stitch together the
distinct subspaces.
13.2 Boundaries Through Space
In some sense, the simplest example of what might be called a QM/MM approach with a
through-space boundary has already been alluded to in Section 12.2.5 and illustrated with the
specific example of the Claisen rearrangement in Section 12.5.1. To evaluate the PMF for a
reaction in solution, one useful approach is to compute the reaction coordinate using a QM
method in the gas phase, and then determine changes in solvation free energy as the system
is driven from one end of the coordinate to the other by the coupling parameter λ. Forthe
FEP calculations themselves, the reacting system is represented classically (e.g., using fixed
geometries, partial atomic point charges, and van der Waals parameters), but the gas-phase
energies to which the solvation free energies are added, and also often the atomic partial
charges, are taken from the antecedent QM calculations. As has already been emphasized, this