From Wavefunction Sign Structure to Static Correlation

Abstract

A variational nodal partition of the correlation energy is introduced, $E_{\mathrm{cor}}=E_{\mathrm{sym}}+E_{\mathrm{stat}}$, relative to a chosen mean-field correlation baseline and its associated single-determinant node. Static correlation $E_{\mathrm{stat}}$ is the negative of the energy penalty incurred when the many-electron wavefunction is constrained to that reference node rather than the exact one. This nodal term isolates the antisymmetric, sign-structure component of correlation, while the complementary symmetric term $E_{\mathrm{sym}}$ necessarily contains dynamic correlation together with a distinct strong but nodeless contribution. The resulting state-based, method-independent framework clarifies the relation between dynamic, nondynamic, strong, and static correlation, places earlier node-based decompositions on rigorous footing, and explains why single-determinant fixed-node diffusion Monte Carlo can be highly accurate in some systems yet fail in others.