Using Atomic Confining Potentials for Geometry Optimization and Vibrational Frequency Calculations in Quantum-Chemical Models of Enzyme Active Sites

Quantum-chemical
studies of enzymatic reaction mechanisms sometimes
use truncated active-site models as simplified alternatives to mixed
quantum mechanics molecular mechanics (QM/MM) procedures. Eliminating
the MM degrees of freedom reduces the complexity of the sampling problem,
but the trade-off is the need to introduce geometric constraints in
order to prevent structural collapse of the model system during geometry
optimizations that do not contain a full protein backbone. These constraints
may impair the efficiency of the optimization, and care must be taken
to avoid artifacts such as imaginary vibrational frequencies. We introduce
a simple alternative in which terminal atoms of the model system are
placed in soft harmonic confining potentials rather than being rigidly
constrained. This modification is simple to implement and straightforward
to use in vibrational frequency calculations, unlike iterative constraint-satisfaction
algorithms, and allows the optimization to proceed without constraint
even though the practical result is to fix the anchor atoms in space.
The new approach is more efficient for optimizing minima and transition
states, as compared to the use of fixed-atom constraints, and also
more robust against unwanted imaginary frequencies. We illustrate
the method by application to several enzymatic reaction pathways where
entropy makes a significant contribution to the relevant reaction
barriers. The use of confining potentials correctly describes reaction
paths and facilitates calculation of both vibrational zero-point and
finite-temperature entropic corrections to barrier heights.