Essentials of Computational Chemistry

13.2 BOUNDARIES THROUGH SPACE 463
Table 13.2 Computed dipole moments (D) of the nucleic acid bases in the gas phase and in aqueous
solution
Nucleic acid base 〈|µ|〉AM1 a
Gas Aqueous solution
a 〈|µ|〉AM1/TIP3P
〈|µ|〉AM1−SM2 b
Adenine 2.2 3.8 3.1
Cytosine 6.3 9.4 9.0
Guanine 6.2 9.4 8.5
Thymine 4.2 5.9 6.2
Uracil 4.3 6.2 6.4
a Gao 1994.
b Cramer and Truhlar 1992, 1993.
be applied to those atoms were they to be in the MM region (like the AOC model).
Another option is to develop separate transferable LJ parameters to be used for the QM
fragment whenever the particular QM/MM choice has been made (see, for example,
Martin et al. 2002). The data in Table 13.2 were determined using such a procedure,
with the parameters thus being part of the definition of the AM1/TIP3P model (Gao and
Xia 1992).
3. Where necessary, determine system properties as ensemble expectation values (for the
data in Table 13.2, a MC sampling scheme was employed, but MD methods are equally
applicable). Every time the coordinates of any atom in the system change, i.e., at each
time step in a MD trajectory or following an accepted MC move of either a QM or MM
atom, recompute the QM wave function (since at least one term in the operator involving
the relative positions of the QM electrons and the MM atoms must be different). Note
the contrast with the AOC method, where only internal moves in the QM system’s
coordinates necessitate a recomputation of the wave function.
4. At each simulation step, the property or properties of interest are included in the ensemble
average. For Table 13.2, the property is the evaluation of the dipole moment operator
as an electronic expectation value over the QM subsystem. Thus, the QM/MM result
for this case is an MC ensemble expectation value of a quantum mechanical operator
expectation value.
A different application of the AM1/TIP3P model nicely illustrates the ability of QM/MM
models to permit the analysis of quantities not typically simultaneously available to either
pure QM or MM models. Gao (1994) employed the AM1/TIP3P model to determine the
PMF for the Claisen rearrangement in water, a reaction already discussed in some detail
in the context of pure continuum or explicit solvation models in Section 12.5.1 (see also
Section 11.1.2). Similarly to the pure MM simulation, the computational protocol involved
FEP along the gas-phase reaction coordinate using λ to drive the structure of the initial allyl
vinyl ether through the TS to the unsaturated aldehyde product. At the AM1/TIP3P level,
the same increase in hydrogen bonding to the ether oxygen noted in the pure MM study was
observed. In the QM/MM model, however, the effect of this increased hydrogen bonding on