The electrostatic potential of dynamic charge densities

Abstract

A procedure to derive the electrostatic potential (ESP) for dynamic charge densities obtained from structure models or maximum-entropy densities is introduced. The ESP essentially is obtained by inverse Fourier transform of the dynamic structure factors of the total charge density corresponding to the independent atom model, the multipole model or maximum-entropy densities, employing dedicated software that will be part of the BayMEM software package. Our approach is also discussed with respect to the Ewald summation method. It is argued that a meaningful ESP can only be obtained if identical thermal smearing is applied to the nuclear (positive) and electronic (negative) parts of the dynamic charge densities. The method is applied to structure models of dl-serine at three different temperatures of 20, 100 and 298K. The ESP at locations near the atomic nuclei exhibits a drastic reduction with increasing temperature, the largest difference between the ESP from the static charge density and the ESP of the dynamic charge density being at T = 20K. These features demonstrate that zero-point vibrations are sufficient for changing the spiky nature of the ESP at the nuclei into finite values. On 0.5eÅ-3 isosurfaces of the electron densities (taken as the molecular surface relevant to intermolecular interactions), the dynamic ESP is surprisingly similar at all temperatures, while the static ESP of a single molecule has a slightly larger range and is shifted towards positive potential values.The electrostatic potential (ESP) is computed for dynamic charge densities corresponding to multipole models and maximum-entropy densities. Convergence of the reciprocal-space summation is guaranteed by the Gaussian form of the Debye-Waller factor. Applications to serine demonstrate only a weak temperature dependence of the ESP on molecular surfaces relevant to intermolecular interactions.