If ∆P hole is dominated by a single NTO, it follows that so is ∆P elec , which is a consequence of the correspondence between amplitudes x ia and elements of the one-particle density matrix that was discussed in Section 2.3. As a result, for single-excitation theories (only), the NTOs are equivalent to excited-state natural orbitals. For CIS wave functions, the corresponding eigenvalues in the natural orbital basis (natural occupation numbers) can be specified in terms of the singular values of the transition amplitudes: