Atomic Charges via Electronegativity Equalization: Generalizations and Perspectives

Abstract

Abstract Since the atomic point charges came into wide use as the electrostatic part of modern molecular force fields, dozens of empirical and semiempirical charge calculation methods were developed over the last few decades. Many of them employ electronegativity equalization, one of the DFT cornerstone principles. We show that algebraically all known electronegativity equalization schemes can be divided into two different groups with respect to the underlying mathematical formalism and the degree to which electronegativity is equalized. Methods of the first group are based on the generalized hardness matrix formalism and provide complete electronegativity equalization, whereas another group of methods invokes the Laplacian matrix formalism and results in a redistribution of electronegativity rather than complete equalization. A new principle of electronegativity relaxation is introduced. Electronegativity identified with electrical potential is viewed as a harmonic function satisfying a discrete Laplace equation with Dirichlet boundary conditions. A Markov chain formalism for solving such equations is developed. Some numerical results of chemical interest are discussed. Application of atomic charges in different areas of molecular modeling is overviewed.