Self-consistent polarization of the boundary in the redistributed charge and dipole scheme for combined quantum-mechanical and molecular-mechanical calculations

The recently developed redistributed charge (RC) and redistributed charge and dipole (RCD) schemes are electrostatic-embedding schemes to treat a quantum-mechanical/molecular- mechanical (QM/MM) boundary that passes through covalent bonds. In the RC and RCD schemes, the QM subsystem is polarized by the MM subsystem, but the MM subsystem is not polarized by the QM one; this results in an unbalanced treatment of the electrostatic interactions. In the work reported here, we developed improved schemes, namely, the polarized-boundary RC scheme (PBRC) and the polarized-boundary RCD (PBRCD) scheme, by adding self-consistent mutual polarization of the boundary region of the MM subsystem to the previous schemes. The mutual polarizations are accounted for in the polarized-boundary calculations by adjusting the boundary-region MM point charges according to the principles of electronegativity equalization and charge conservation until the charge distributions in both the QM subsystem and the polarizable region of the MM subsystem converge. In particular, we implemented three literature parametrizations of electronegativity equalization: the original electronegativity equalization method (EEM) by Mortier and co-workers, the charge equalization (QEq) method proposed by Rappe and Goddard, and a modified version of the QEq method by Bakowies and Thiel. The PBRC and PBRCD schemes were tested by calculating proton affinities for small organic compounds and capped amino acids. As compared to full-QM calculations, the PBRC and PBRCD schemes produced more accurate proton affinities, on average, than the original RC and RCD methods; the mean unsigned error in proton affinities is reduced from about 5 kcal/mol to 3 kcal/mol with little change in geometry. The improvement is encouraging and illustrates the importance of mutual polarization of the QM and MM subsystems in treating reactions where noticeable charge transfer occurs in the QM subsystem.