where τα represents creation and annihilation operators for an α th -order electronic excitation. For example, with α = 1 (single electronic excitation), τa i = ĉ † a ĉi excites an electron from an occupied orbital i to an unoccupied orbital a. Similarly, α = 2 implies τab i j = ĉ † a ĉ † b ĉi ĉj which will excite two electrons i → a and j → b, respectively. The photon excitation operator is commonly written as the standard photonic ladder operator τn = ( â † ) n . It should be noted that this is not the only way to define the bosonic excitations. The authors of Ref. 78 defined an idempotent form of the excitation operator as τn = |n ⟩ ⟨0| for a finite number of Fock states { |n ⟩ } = { |0⟩, |1⟩, ..., |N F ⟩ }. However, the two cases are not formally equivalent, and a rigorous comparison of the quality of the results has not been performed.