Excitation Number: Characterizing Multiply Excited States

How many electrons are excited in an electronic transition? In this Letter, we introduce the excitation number eta to answer this question when the initial and final states are each modeled by a single-determinant wave function. We show that calculated eta values lie close to positive integers, leading to unambiguous assignments of the number of excited electrons. This contrasts with previous definitions of excitation quantities which can lead to mis-assignments. We consider several examples where eta provides improved excited-state characterizations.