Previous studies by one of the authors showed that doubly excited configurations contribute to the electron density evolved using the RT-TDHF method and that the resonance energy is affected by the superposition of the Hartree-Fock and the doubly excited configurations. To determine the direction of the peak shifts, the excitation energies of S 0 → S 1 and S 1 → S 2 transitions were calculated using the SA-CASSCF method, where the S 2 state corresponds to a doubly excited state with nearly double occupation of the LUMO. The resulting S 0 → S 1 excitation energies show a similar trend as with CIS and LR-TDHF: decreasing excitation energies with increasing system size (∆E S0→S1 = 9.24, 7.23, 5.92 eV). The energies for the next transition are smaller: ∆E S1→S2 = 3.97, 1.18, 1.29 eV, respectively. Given the energetically lower-lying S 1 → S 2 transition compared to the S 0 → S 1 transition, the resonance peaks are expected to shift towards lower energies as the population of the LUMO increases and the contribution of the doubly excited configuration increases.