This constitutes another proof that the transformation to NTOs distills a given excitation into the smallest possible number of occupied/virtual orbital pairs. In a well-defined sense, the NTO basis is the best choice for conceptualizing excited states in terms of a one-electron promotion from an occupied MO into a virtual MO. Note that the NTOs are state-specific, so this optimal basis changes from one excited state to the next. (State-averaged NTOs have been suggested as a compact basis for correlated wave function expansions. ) In Eqs. (3.1) and (3.2), we have written the eigenvalues of ∆P elec and ∆P hole as λ 2 r in order to emphasize the correspondence with x 2 ia in the canonical MO basis, whereas the singular values λ r in Eq. (3.4) are the amplitudes themselves, rotated into the NTO basis.