Analysis of Static Correlation using Atomic Populations of Effectively Localized Electrons (APELE)

Abstract

Static or nondynamic correlation is an effect where the single-reference approximation fails to adequately describe a molecular system.1 Systems dominated by nondynamic correlation require multi-reference (MR) methods, such as full-configuration interaction (FCI) or multi-configurational self-consistent field theory (MCSCF), which are impractical for most systems due to their high computational complexity. Most functionals in Density Functional Theory (DFT) fail to describe such systems due to the ever-elusive exchange-correlation term (EXC).2,3 In order to avoid using MR methods a number of diagnostics have been proposed that allow the user to determine the quality of their single-reference solution.4{7 It has been show through preliminary tests that some of these diagnostics prove not to be size-extensive, while simultaneously being computationally complex themselves. Using the Kong-Proynov ‘16 / Becke ‘13 (KP16/B13) functional, atomic populations of effectively localized electrons (APELE) are generated and compared against current diagnostics to estimate nondynamic correlation.1,8 It is also shown that the APELE method is size-extensive and correlates well with wave-function based diagnostics.