On the non-integer number of particles in molecular system domains: treatment and description

Abstract

The energy of an atomic or molecular system undergoing Coulomb interactions is well known at the integer numbers of its neutral or ionic confi gurations. Nevertheless, the physical domains (atoms in molecules) inside the whole molecular system possess a non-integer number of particles due to the electron exchange with its surrounding. Hence, the dependence of the energy, the density matrix and their marginal distributions (reduced density matrices) with the number of particles become a problem of fundamental importance in the description of the electron distribution, its properties and transformations. In this work, we present a rigorous mathematical and physical basis for the treatment of this problem within the grand-canonical statistical distribution of few particles. In this context, the derivatives of the energy and the density referred as chemical descriptors (especially chemical potential and hardness) are analyzed in both cases, when the system is isolated and when it is subject to the interaction with an environment. The ground state energy convexity dependence with the number of particles of these systems simplifi es the description.

Published as part of the special collection of articles “Festschrift in honour of P. R. Surjan”.