Transferability of parameters of strictly local geminals' wave function and possibility of sequential derivation of molecular mechanics

Abstract

The problem of substantiation of molecular mechanics (MM) remains actual due to growing popularity of hybrid quantum/classical (QM/MM) schemes. Recently proposed deductive molecular mechanics (DMM) seems to be a natural tool to derive mechanistic models of molecular energy (classical force fields) from a suitable quantum mechanical (QM) description of molecular structure. It is based on an assumption that the trial wave function underlying the MM description is one of the antisymmetrized product of strictly local geminals (SLG). A proof of transferability of electronic structure parameters (ESPs) in this approximation is an essential component of a logical framework for the transition from the QM to an MM description because it allows constructing expressions for potential energy surfaces by proper consideration of the response of the ESPs to the variations of geometry parameters. In the present article the ESPs defining density matrix elements and basis one-electron states (hybrid orbitals-HOs) in the SLG approximation are formally considered. The transferability of the density matrix elements with respect to the parameters of molecular electronic structure and the linear response relations for the HOs are proven to take place under very nonrestrictive conditions. Special attention is paid to numerical estimates of the ESPs' features giving an "experimental" support to approximate expressions for the molecular energy.