Accurate and Efficient
Treatment of Continuous Solute
Charge Density in the Mean-Field QM/MM Free Energy Calculation
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Abstract
QM/MM free energy calculation is computationally demanding
because
of the need for an excessive number of electronic structure calculations.
A practical approach for reducing the computational cost is that based
on mean field approximation, which calculates the QM wave function
in the presence of a partially or totally averaged potential of the
MM environment. For obtaining the latter potential, it is common to
first represent the QM molecule in terms of point charges and then
perform statistical sampling of MM molecules. However, the point charge
approximation has the drawback that it tends to overestimate electrostatic
(ES) interactions at short-range, which may give rise to a divergence
problem in the self-consistent iterations. In this paper, we thus
consider a more accurate and robust implementation of mean-field QM/MM
method based on continuous QM charge density, here utilizing the following
combination: (i) grid-based treatment of ES potential generated by
the QM molecule, which allows for an efficient sampling of MM molecules
in the presence of QM charge density, and (ii) adaptation of the QM/MM-Ewald
method to the mean-field framework for eliminating cutoff errors in
the long-range ES interactions. As a numerical test, we apply the
obtained method to several benchmark reactions in aqueous solution,
and show that the density-based method essentially eliminates the
divergence problem while providing the free energy profile consistent
with experiment. In addition, we test the utility of a recently proposed
screened charge model for the QM charge density and show that the
latter also performs well for the free energy calculation. These results
suggest that explicit inclusion of charge penetration effects is beneficial
for improving the accuracy and stability of the mean-field QM/MM calculation