We derive a formal definition of the number of excited electrons within multiconfigurational wavefunctions by introducing the excited-electron number operator in the formalism of second quantization. This operator measures deviations in orbital occupations relative to a chosen reference configuration, ensuring a symmetric and non-redundant count of electronic promotions. Its expectation value provides a continuous and physically meaningful descriptor, capturing both single- and higher-order excitations while remaining applicable to correlated superpositions of determinants. Furthermore, we demonstrate that the operator can be decomposed into excitation-order contributions, offering a systematic partitioning of excited-state character. This theoretical formulation establishes a consistent and generalizable foundation for quantifying excitation strength in electronic-structure theory.
Cristian Guerra (Wed,) studied this question.