Essentials of Computational Chemistry

472 13 HYBRID QUANTAL/CLASSICAL MODELS
frozen region
flexible region
Figure 13.5 An application of a hybrid MO/MO philosophy to the indicated RNA trimer proceeds
using correlated levels of electronic structure theory for various tautomers and protonation states of
the central base pair, this pair then representing the small system in the MO/MO analog of Eq. (13.6),
and semiempirical theory for both the small system and the frozen-geometry larger system
An alternative is to force those atoms common to the large and small models (i.e., all of
the atoms in the small model except the capping hydrogens) to occupy the same coordinate
locations in all three energy evaluations. Within this set of restraints, one may then write
down fairly simple expressions for the gradients as sums of QM and MM gradients from the
small and large systems, noting that there are some details associated with the capping atoms
in the small system and the alignment of bonds to capping atoms with bonds in the full system
(see, for example, Vreven et al. 2003 and Swart 2003). Maseras and Morokuma (1995) were
the first to provide such gradient expressions, referring to the optimization approach as the
integrated molecular orbital molecular mechanics method (IMOMM).
Subsequently, Humbel, Sieber, and Morokuma (1996) generalized the IMOMM optimization
scheme to the case where two different levels of QM theory were used instead of a
QM/MM approach, and Svensson, Humbel, and Morokuma (1996) examined the relative efficacy
of different combinations of levels for prototype problems. Corchado and Truhlar (1998)
later proposed a refinement of that methodology to improve computed vibrational frequencies
and Rickard et al. (2003) showed that a combination of MP2 and HF theories permits the
calculation of high-quality NMR chemical shifts within the high-level system.