With single particle Green`s function (or electron propagator) techniques electron removal and attachment energies are calculated directly. This avoids the sometimes inaccurate process of separately determining the total electronic energies of the neutral and an ionic state and subtracting one large number from another to obtain a relatively small value, i.e. the ionization potential (IP) or electron affinity (EA) of a molecule. Traditionally these Green`s function methods used a single determinant wavefunction as the “zeroth order” initial state which was improved with Møller-Plesset perturbation theory. Although these perturbative Green`s function methods have been very  successful, they are limited in applicability. Perturbative approaches usually cannot handle reliably (or at all) systems with initial states that are open shell and/or highly correlated (non-dynamical correlation) for either IPs or EAs.

We specifically designed the multiconfigurational spin tensor electron propagator method (MCSTEP) and its predecessor the multiconfigurational electron propagator method (MCEP) to provide accurate IPs and EAs for systems that cannot be accurately handled by perturbational approaches to single particle Green`s function methods, namely when the initial state is open shell and/or has non-dynamical correlation that must be accounted for. In addition, of course, the goal is to also be able to provide accurate IPs and EAs for systems with closed shell initial states without non-dynamical correlation  i.e., those systems that could be handled as well by  perturbational Green`s function methods.

In this article I will first review the theory behind the multiconfigurational spin-tensor electron propagator method. Since the introduction of MCSTEP over ten years ago, several accurate MCSTEP atomic and molecular IPs and EAs have been determined. I will summarized several of the more significant calculations to date. Finally I will indicate what current research is going on with the method which will allow for rapid and accurate IP calculations for all inner and outer valence IPs - including both principal and shake- up IPs.