Recipe of polarized one-electron potential optimization for development of polarizable force fields

Polarized one-electron potential (POP) optimization is a powerful and practical method to determine multicenter dipole polarizabilities that can be used for constructing polarizable force fields. The POP optimization is similar to the widely used electrostatic potential (ESP) optimization to determine the partial charges of molecules. However, while the ESP optimization targets the electrostatic potentials on a molecular surface, the POP optimization targets the change of electrostatic potentials on molecular surfaces which are induced by the field of a test charge on the molecular surface. Since only additional one-electron integrals for the test charge are required for the estimation of the surface potentials, the change of electrostatic potentials has been named polarized one-electron potentials. We show that in the POP optimization, both an explicitly interacting polarizability model and an implicitly interacting polarizability model can be used for the determination of the multicenter polarizabilities. In the explicitly interacting model, intramolecular induced dipole-induced dipole interaction is mutually included in the process of the POP optimization, but the interaction is not included in the implicitly interacting model. In the implicitly interacting polarizability model, a combined model of isotropic atom polarization and anisotropic bond polarization is shown to provide the best fitting results for nucleic acid bases which show large polarization anisotropy. A simple scaling model to the chemical bond has been newly proposed for the explicitly interacting polarizability model. We show that the simple model can be applied to molecular simulations without any damping of exponential type in the intramolecular induced dipole interaction. A detailed procedure for determination of the multicenter dipole polarizability by the POP optimization is also presented.