Generalized Christoffel?Darboux formulae and the frontier Kohn?Sham molecular orbitals

Abstract

The Christoffel–Darboux formula for classical orthogonal polynomials is generalized to arbitrary sets of orthogonal functions in three dimensions, yielding an explicit link between frontier Kohn–Sham molecular orbitals and the Kohn–Sham density matrix. Methods using this result could significantly accelerate Kohn–Sham density functional theory calculations, as only a subset of the Kohn–Sham equations would need to be addressed. The result can also be seen as an explicit justification for the utility of frontier molecular orbital theory.