Accurate and Efficient Treatment of Continuous Solute Charge Density in the Mean-Field QM/MM Free Energy Calculation.

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.