According to Grimme and Neese, vertical excitation energies at the double-hybrid level are obtained by first solving the TD(A)-DFT eigenvalue problem with only the hybrid portion of the DHDF (∆E TD(A)-hybrid in Eq. 3), and then adding Head-Gordon and co-workers' CIS(D) perturbative correction (∆ CIS(D) ): ∆E TD(A)-DHDF = ∆E TD(A)-hybrid + a C ∆ CIS(D) .