Dynamic QM/MM: A Hybrid Approach to Simulating Gas–Liquid Interactions - Multiscale Molecular Methods in Applied Chemistry - page 49

site also becomes a seed atom, since this radical site is considered to be a reactive
atom. The radius of the QM region around a seed atom (or the distance from the
seed atom to atoms treated as MM) was defined as the distance where the forces
between the atoms are less than 1

10 7 hartree/bohr, at which point the
differences between MM and QM forces are thought to be negligible. This was
empirically determined to be 10.0, 10.0, 12.0, 12.5 bohr for F, O, H, and C,
respectively, when interacting with methane. We also found it convenient to do an
assessment on which atoms should or should not be in the reactive region only
every ten time steps, since this involves a distance search and, for 10-a.u. time
steps, the atoms have not moved very far. Throughout much of the simulation it is
common to have between 75 and 150 atoms within the reactive region(s). Given
the effort associated with QM calculations at each time step, the use of a
computationally efficient semiempirical QM method such as MSINDO is clearly
desirable.

2.3 Issues with Dynamic Partitioning

It must be noted that the instantaneous switching of an atom in and out of the
reactive region has raised concern in the past [ 21 ]. This is because from one time
step to the next there will inevitably be an abrupt change in the forces on that
atom. In dynamics studies this discontinuity can influence the integration with
respect to time and conceivably lead to nonphysical behavior. To circumvent
this we use a more robust integration method (a sixth order predictor-corrector
algorithm) that is not available in TINKER. This integration technique should
help dampen out any fluctuations in the force/position changes that would lead
to discontinuities when atoms are switched back and forth between the MM and
QM regions.
Recently other groups have designed algorithms that include dynamically
moving QM regions to model explicit solvent interactions. Morokuma et al. have
extended their multilevel ONIOM technique to include the exchange of solvent
(ONION-XS) molecules dynamically throughout the simulation [ 23 ]. They imple-
mented a fifth order polynomial switching function to accommodate the instanta-
neous change in forces and potentials on atoms changing from one level to the next
in the ONIOM regime. This technique extends the “Hot Spot” method that Rode
et al. originally used [ 46 ] by not only smoothing out the differences in forces of
atoms that are in a defined “buffer” region between the various levels, but also
smoothing out the forces for all atoms in the QM region when any atom crosses in
or out of the buffer region. In addition, the ONIOM-XS method uses the same
switching function algorithm to smooth the potential energy for the atoms in the
QM and buffer regions. However, knowing how large the buffer region needs to be
for each chemical system is uncertain. Furthermore, it has been demonstrated that
when multiple molecular groups are in the buffer region the ONIOM-XS method is
no longer able to remove all discontinuities in the potential [ 23 ].