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

Abstract

The energy of an atomic or molecular systemundergoing Coulomb interactions is well known atthe integer numbers of its neutral or ionic configurations.Nevertheless, the physical domains (atoms in molecules)inside the whole molecular system possess a non-integernumber of particles due to the electron exchange with itssurrounding. Hence, the dependence of the energy, thedensity matrix and their marginal distributions (reduceddensity matrices) with the number of particles becomea problem of fundamental importance in the descriptionof the electron distribution, its properties and transformations.In this work, we present a rigorous mathematical andphysical basis for the treatment of this problem within thegrand-canonical statistical distribution of few particles.In this context, the derivatives of the energy and the densityreferred as chemical descriptors (especially chemicalpotential and hardness) are analyzed in both cases, whenthe system is isolated and when it is subject to the interactionwith an environment. The ground state energy convexitydependence with the number of particles of these systemssimplifies the description.