The evaluation of MCRPA (MCTDHF) electronic excitation energies, oscillator strengths, and polarizabilities: Application to O2

We derive the multiconfigurational random phase approximation (MCRPA) by requiring the equivalence between the length and velocity forms of the oscillator strength. The MCRPA is also justified in terms of the equations of motion (EOM) formalism. The final equations and techniques developed are the same as the multiconfigurational time dependent Hartree-Fock (MCTDHF). We explicitly demonstrate the validity of the energy-weighted sum rule for the MCRPA-MCTDHF. A modification of our previously derived MCTDHF technique is introduced. This involves the incorporation of additional CI states from different symmetry blocks than the symmetry block of the MCSCF reference state into the MCRPA equations. For a 50 STO calculation on O2 molecule, our results for the low-lying vertical excitation energies are in excellent agreement with experiment and with large-scale CI. Oscillator strengths, frequency dependent polarizabilities, and the energy weighted sum rule are also reported.