Essentials of Computational Chemistry

474 13 HYBRID QUANTAL/CLASSICAL MODELS
two QM atoms have been included in some studies and deliberately not included in
others. There is no strong consensus on which, if either, approach is better.
4. Torsional energies involving two or three MM atoms and two or one QM atoms,
respectively, are computed using the standard force-field formulation. Torsional energies
involving one MM atom and three QM atoms have, like bond angles, been included in
some studies and not in others.
5. Those MM point charges that are very close to the QM system, either coincidentally
or because the capping hydrogen atoms bring electron density out to the MM boundary
atoms, can have unphysically large influences on the electronic structure of the QM
region, even when those portions of the Fock operator involving the basis functions of
the capping atoms do not include their influence directly. As a result, some studies have
zeroed charges on near-boundary atoms, others have scaled them, and still others have
selectively kept and discarded particular interactions (Eurenius et al. 1996; Bakowies and
Thiel 1996). There is increasing evidence that it is better to maintain all QM/MM charge
interactions. Amara and Field (2003) have shown that these electrostatic interactions can
be made considerably more stable by replacing MM point charges near the QM/MM
boundary with spherical Gaussian charge distributions centered on the MM atoms in
question.
6. All remaining terms associated with HQM/MM and HMM are calculated in the usual way
according to Eq. (13.4).
The use of a hydrogen atom as a capping atom is clearly motivated by simplicity. It is a
reasonable choice based on other considerations as well, however. In general, the position
of the QM/MM boundary is selected so that it will not cut across any particularly polar
or polarizable bonds. This in principle allows the correct separation of the two electrons
in the (single) bond to the one that will remain in the QM region and the one that will
be eliminated in the MM region. In practice, then, the bonds that are inevitably cut in
biomolecules, for instance, are C–C bonds between sp 3 carbon atoms. Hydrogen is then a
reasonable choice for a capping atom because the electronegativities of H and C are not
too different. Nevertheless, a potentially better choice is a pseudo-halogen having seven
valence electrons and an electronegativity similar to that of carbon. The ‘lone pairs’ on such
a capping atom will then resemble the electrons from the other bonding orbitals that would
reside on the atom if the system were fully QM, which may offer a better representation of
the system; Zhang, Lee, and Yang (1999) have provided an initial description of a method
employing this protocol, using a pseudopotential for the core electrons that provides the
appropriate electronegativity behavior.
To date, the use of link atoms has been associated with extra instability in MD simulations
at the QM/MM level because of, inter alia, the stiff force constants maintaining linearity
of bonds crossing the boundary and the large electrostatic interactions involving atoms near
the boundary. Progress in this area, addressing the above and other issues, is expected to
continue briskly.