A time-dependent variation–perturbation method for the calculation of transition properties and its relation to the random phase approximation

A time−dependent variation−perturbation (VP) formulation is presented for the simultaneous calculation of the ground state correlation function and the excited state wave function of an atomic or molecular system. The wave functions are chosen for the optimal calculation of transition properties with a relatively small number of molecular integrals. The VP equations so obtained for a singlet system are identical with the equations in the random phase approximation (RPA). On the other hand, if the ground state is a singlet and the excited state a triplet, the VP and RPA equations are different. The latter assumes a ground state correlation function with an open shell component, which is a poor approximation for a closed shell ground state. The orthonormalization condition in the VP scheme is different from that in the RPA. The consequence of this difference is discussed. It is also pointed out that the RPA excitation energy actually contains part of the ground state correlation energy; hence the RPA excitation energy is always lower than the corresponding values in the Tamm−Dancoff approximation and the self−consistent RPA. A variational formulation of the time−dependent problem gives a set of equations which resembles the higher RPA equations.