Grand-Canonical Interpolation Models

62We analyze the physical grounds of common approaches used to model the dependency of the ground state energy on the number of electrons in molecular systems (E vs. N models). We elaborate on a recent result indicating that smooth interpolation models are inconsistent with the popular grand ensemble approach to open quantum systems, and we illustrate this discrepancy using the parabolic and exponential E vs. N models. Unlike most previous considerations of this problem, we explicitly account for the possibility of degenerate ground states and nonconvexity of the energy. This chapter analyzes the physical grounds of common approaches used to model the dependency of the ground state energy on the number of electrons in molecular systems (E vs. N models). It elaborates on a result indicating that smooth interpolation models are inconsistent with the popular grand ensemble approach to open quantum systems, and illustrates this discrepancy using the parabolic and exponential E vs. N models. The chapter explains the possibility of degenerate ground states and nonconvexity of the energy. More relevant to the present work, the Perdew, Parr, Levy, and Balduz (PPLB) paper revealed that noninteger electron number can be regarded as the time-average of an open system. The chapter presents a thorough discussion of interpolation models and the grand canonical treatment, including the t-neglected issue of degenerate ground-state energies. It focuses on interpolation models: models that estimate the properties of a system with a noninteger electron number by interpolating its properties at integer values.