The two faces of static correlation

Restricted Hartree-Fock (RHF) and UHF wavefunctions for beryllium-like ions with nuclear charge 3 <= Z <= 5 are found using a near-complete Slater basis set. The triplet (RHF --> UHF) instability and correlation energy are investigated as a function of Z and we find that the instability vanishes for Z > 4.5. We reproduce this surprising behavior using a minimal-basis model and, by comparing with the stretched H-2 molecule, conclude that static (also known as nondynamical, near-degeneracy, first-order, or strong) correlation comes in two flavors: one that can be captured by UHF and another that cannot. In the former (Type A), there is an absolute near-degeneracy; in the latter (Type B), there is a relative near-degeneracy. This dichotomy clarifies discussions of static correlation effects. (C) 2011 American Institute of Physics. [doi:10.1063/1.3570574]