A chemical potential equalization method for molecular simulations

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Abstract
A formulation of the chemical potential (electronegativity) equalization principle is presented from the perspective of density‐functional theory. The resulting equations provide a linear‐response framework for describing the redistribution of electrons upon perturbation by an applied field. The method has two main advantages over existing electronegativity equalization and charge equilibration methods that allow extension to accurate molecular dynamics simulations. Firstly, the expansion of the energy is taken about the molecular ground state instead of the neutral atom ground states; hence, in the absence of an external field, the molecular charge distribution can be represented by static point charges and dipoles obtained from fitting to high‐level ab initio calculations without modification. Secondly, in the presence of applied fields or interactions with other molecules, the density response can be modeled accurately using basis functions. Inclusion of basis functions with dipolar or higher order multipolar character allows molecules or chemical groups to have correct local anisotropic polarizabilities. A modified semiempirical form of the hardness matrix has been introduced that can be evaluated efficiently using Gaussians, and requires only one parameter per basis function. Applications at two basis‐set levels demonstrate the method can accurately reproduce induced dipole moments and estimated chemical potentials obtained from density‐functional calculations for a variety of molecules. Inclusion of basis functions beyond the conventional spherical‐atom type is essential in some instances. The present formulation provides the foundation for a promising semi‐empirical model for polarization and charge transfer in molecular simulations.