Essentials of Computational Chemistry

13.2 BOUNDARIES THROUGH SPACE 459
approach ignores the effect solvent has on coordinates other than the reaction coordinate,
and on the solute wave function, but it nevertheless may legitimately be referred to as a
‘weakly coupled’ QM/MM calculation. We now proceed to consider increasingly tightly
coupled protocols for joining the two regions.
13.2.1 Unpolarized Interactions
A significant issue with modern force fields is that it can be difficult to simultaneously
address both generality and suitability for use in condensed-phase simulations. For example,
the MMFF94 force field is reasonably robust for gas-phase conformational analysis over a
broad range of chemical functional groups, but erroneously fails to predict a periodic box of
n-butane to be a liquid at −0.5 ◦ C (Kaminski and Jorgensen 1996). The OPLS force field, on
the other hand, is very accurate for condensed-phase simulations of molecules over which it
is defined, but it is an example of a force field whose parameterization is limited primarily
to functionality of particular relevance to biomolecules, so it is not obvious how to include
arbitrary solutes in the modeling endeavor.
Kaminski and Jorgensen (1998) have proposed one particularly simple QM/MM approach
to address this problem, which they refer to as AM1/OPLS/CM1 (AOC). In AOC, Monte
Carlo calculations are carried out for solute molecules represented by the AM1 Hamiltonian
embedded in periodic boxes of solvent molecules represented by the OPLS force field. Thus,
HQM in Eq. (13.1) is simply the AM1 energy for the solute, and HMM is evaluated for all
solvent–solvent interactions using the OPLS force field. The QM/MM interaction energy
is computed in a fashion closely resembling the standard approach for MM non-bonded
interactions
HQM/MM =
solute
i
solvent
j
CM1 αqi qj
rij
+ 4εij
σ 12
ij
r 12
ij
−
6 σij r6
ij
(13.2)
where the Lennard–Jones parameters are determined from the usual combining rules
(Eqs. (2.30) and (2.31)) assuming the solute atoms have ε and σ values characteristic
for their atomic type in the OPLS force field. The single feature that is quantum mechanical
is that the solute charges are determined from the CM1 charge model applied to the
AM1 wave function (see Section 9.1.3.4). For charged molecules, the constant α is 1.0,
while for neutral molecules, it is 1.2 to approximate the effect of solvent polarization on
the gas-phase charge distribution.
The choice of AM1 as a particularly efficient level of electronic-structure theory is motivated
by the large number of QM calculations potentially required in the MC sampling. In
the standard AOC MC protocol, moves of solute internal coordinates are attempted every
50 MC steps, and accepted or rejected according to the standard Metropolis protocol as
described in Section 3.4.2. If the move is accepted, the QM energy and CM1 charges are
updated and used in Eq. (13.2) until the next accepted change of solute geometry. Note that
QM calculations are not required unless a solute move is being attempted.
The AOC method successfully predicts the effects of polar solvents on rotameric equilibria
for 1,2-dichloroethane and 2-furfural, as illustrated in Table 13.1. However, it is not very