A simple definition of the number of excited electrons

Abstract

We introduce a formal and computationally accessible definition of the number of excited electrons within multiconfigurational wavefunctions by constructing the operator _ex in the framework of second quantization. The expectation value 〈_ex〉 quantifies the extent of electronic promotion relative to a chosen reference configuration, offering a continuous measure of excitation strength applicable to correlated and state-averaged wavefunctions. Through applications to representative photochemical systems, 〈_ex〉 proves sensitive to static correlation in ground states and yields values consistent with single- and multi-electron promotions in low-lying excited states. In dissociation processes, the descriptor reflects the gradual weakening or strengthening of correlation associated with bond breaking, whereas in pericyclic reactions it provides insight into the symmetry-allowed or -forbidden nature of the transformation: low 〈_ex〉 values for the ground-state [4+2] cycloaddition and high, variable values for the excited-state [2+2] pathway. Overall, 〈_ex〉 offers a coherent and quantitative approach for following changes in electronic structure during photochemical processes.