Geometry-dependent atomic charge calculations using charge equilibration method with empirical two-center Coulombic terms

Abstract

The calculation of atomic charges plays an important role in the non-bonded interaction terms of energy functions for molecular mechanics and molecular dynamics methods. Since the electronic states vary with changing molecular conformations, different atomic charges are required for different conformers. Although the charge equilibration (QEq) method was proposed by Rappé and Goddard as a technique for easily calculating atomic charges that depend on the molecular conformation, this method utilizes the two-center Coulombic integrals of Slater type orbitals, which have unrealistic values for small interatomic distances. In this study, we instead calculated the atomic charges for 87 compounds using QEq methods in combination with five types of empirical equations to calculate the two-center Coulombic terms, and investigated which equation gives the most appropriate charges. As a result, it was found that the DasGupta–Huzinaga equation and the Ohno–Klopman equation are effective for the calculations of QEq charges and that the Ohno–Klopman equation with QEq/PD parameters derived by Bakowies and Thiel are best for calculating dipole moments. It was also discovered that both the quantitative and qualitative derivation of appropriate charges for compounds that contain formal charges or aromatic five-membered hetero-rings is not always possible using QEq methods.