A practical use of self-energy shift for the description of orbital relaxation

Plots of the three lowest singlet excitation energies (in eV) of formaldehyde with the 6-311(2+, 2+)G∗∗ basis set. The first state is of valence type whereas upper two states are of Rydberg type for which the CIS(D) method yields too low values relative to the CCSD values and experimental data. This difficulty is remedied by the modified CIS(D) method with the second-order self-energy shift (denoted as CIS(D)SS(2)) by keeping an accuracy for the valence state.