Variational determination of the zero-flux surfaces of atoms in molecules

Abstract

A functional minimized by functions representing zero-flux surface sheets in curvilinear coordinates is proposed. A discrete version of this functional serves as the basis for a new variational approach to the determination of the zero-flux surfaces of atoms in molecules. Analytical expressions for the zero-flux surface sheets are obtained by solving a system of nonlinear equations for variational parameters of a trial function. The new method, which is computationally inexpensive, produces atomic surfaces that are 10–100 times more accurate than those afforded by the previously published algorithms. Results of numerical tests demonstrate that, when used in conjunction with an adaptive quadrature scheme, these surfaces yield atomic charges with errors smaller than 3 × 10-5 per atom. The numerous advantages of analytical representations for the atomic zero-flux surfaces are discussed.