The excitation propagator is of importance for the understanding of electronic excitation spectra, polarizabilities, indirect nuclear spin-spin coupling tensors, and many other quantities. It has been treated in higher order approximations 1 and is capable of yielding predictive results. An approach analogous to the one followed for the electron propagator is quite feasible.
A more accurate treatment of the equation of motion
is needed than what is done within the geometric approximation (RPA). The reference state is chosen as a single determinantal SCF state with the SCF spin orbital basis and the associated electron field operators being divided into occupied (labeled by indices a, b, c, ...) and unoccupied (labeled by indices p, q, r, ...). The superoperator hamiltonian is used again, and a basis of Boson-like operators
is employed. The hamiltonian is again partitioned into an unperturbed part and a perturbation as
but a different (but equivalent) way is chosen to proceed toward the perturbation expansion than what was done ...