A polarizable fragment density model and its applications

Abstract

This work presented a new model, Polarizable Fragment Density Model (PFDM), for the fast energy estimation of peptides, proteins, or other large molecular systems. By introducing an analogous relation to the virial theorem, the kinetic energy in Kohn–Sham Density Functional Theory (DFT) is approximated to the corresponding potential energy multiplied by a scale factor. Furthermore, the error due to this approximation together with the exchange–correlation energy is approximated as a second order Taylor’s expansion about density. The PFDM energy is expressed as a functional of electronic density with system-dependent model parameters, such as a scaling factor c and a series of atomic pairwise KAB. The electron density in PFDM consists of a frozen part retaining chemical bonding information and a polarizable part to describe polarization effects, both of which are expanded as a linear expansion of Gaussian basis functions. The frozen density can be pre-calculated by fitting the DFT calculated density of fragments, as well as the polarizable density is optimized to solve PFDM energy. The PFDM energy is a quadratic function of the expansion coefficients of polarizable density and can be solved without expensive iteration process and numerical integrals. PFDM is especially suitable for the energy calculation of large molecular system with identical subunits, such as proteins, nucleic acids, and molecular clusters. Applying the PFDM method to the proteins, the results show that the accuracy is comparable to the PM6 semi-empirical method, and the efficiency is one order of magnitude faster than PM6.