A new chemical concept: Shape chemical potentials

Abstract

Within the density functional formalism, we introduce the shape chemical potential μ_i(^n) for subsystems, which in the limiting case of point subsystems, is a local chemical potential μ^n(r). It describes the electron withdrawing/donating ability of specified density fragments. The shape chemical potential does not equalize between subsystems, and provides a powerful new method to identify and describe local features of molecular systems. We explore the formal properties of μ_i(^n) especially with respect to discontinuities, and reconcile our results with Sanderson’s principle. We also perform preliminary calculations on model systems of atoms in molecules, and atomic shell structure, demonstrating how μ_i(^n) and μ^n(r), identify and characterize chemical features as regions of different shape chemical potential. We present arguments that shell structure, and other chemical features, are not ever obtainable within Thomas–Fermi-type theories.