Role of the generalized pauli constraints in the quantum chemistry of excited states

Abstract

The Pauli exclusion principle requires that spin orbitals have occupations between zero and one. For pure quantum systems, however, the occupations of the spin orbitals are constrained by additional inequalities known as the generalized Pauli constraints. If the occupation numbers saturate (or nearly saturate) the generalized Pauli constraints, then the occupation numbers are said to be pinned (or quasi‐pinned) to the constraints. Here, we assess the complexity of electron correlation of excited states from the pinning or quasi‐pinning of the occupation numbers to the generalized Pauli constraints where the degree of pinning encodes information about the structure of the wave function including correlation and entanglement. Results are presented for three‐ and four‐electron atoms and molecules, the five‐electron cyclopentadienyl radical, and the seven‐electron Fenna‐Matthews‐Olson complex in green‐sulfur bacteria. The data shows that even when the ground‐state occupation numbers are pinned, the occupation numbers of excited states manifest pinned, quasi‐pinned, and unpinned behavior, reflecting the complexity of electron correlation and entanglement in excited states. © 2016 Wiley Periodicals, Inc.