Excitation Number: Characterizing Multiply Excited States

How many electrons are excited in an electronic transition? In this Letter, we introduce the excitation number η to answer this question when the initial and final states are each modeled by a single-determinant wave function. We show that calculated η 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 η provides improved excited-state characterizations.