DENSITY AND REDUCED DENSITY MATRICES FUNCTIONALS FOR SYSTEMS WITH NON-INTEGER NUMBER OF PARTICLES: THE CASE OF NON-CONVEX E vs N

MIRANDA-QUINTANA, RAMÓN A.; BOCHICCHIO, ROBERTO

La Habana - Varadero

Congreso; Seminars on Molecular Modeling IX (SEADIM9); 2013

Universidad de La Habana

The study of quantum open systems, which possess the particular characteristic of having fractional electron numbers, has proven of great help in understanding molecular structures and chemical reactivity. Up to now, attempts to describe these systems have almost exclusively been done using density functional theory (DFT) techniques. Recently, a new approach to study open systems based on grand-canonical density matrices (DMs) has been proposed. This treatment allows extending the DFT results for the energy of systems with non-integer electron numbers to arbitrary state functions. However, these works rely on the assumption that the energy of the system is a convex function of the number of particles. This property, empirically proven for isolated Coulomb systems (e.g. atoms and molecules), it is not expected to hold for interacting reagents or for species imbedded in some environment. In this work we analyze quantum open systems without the assumption of convex E vs N. Particularly, we discuss the constrained-search functionals of the density and 1- and 2-reduced density matrices (RDMs) for these systems. Taking into account the recently described contracting mapping relating grand-canonical DMs and their associated RDMs and the loss of information on partial contractions we show that functionals of the 2-RDM for these systems must depend on the number of particles.