The Multiconfigurational Spin-Tensor Electron Propagator Method (MCSTEP)

Abstract

Abstract With electron propagator (also known as single particle Green's function) techniques vertical 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 then 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 electron propagator/Green's function (GF) methods used a single determinant wavefunction as the “zero order” initial state which was improved with Moller–Plesset perturbation theory often obtained via diagrammatic techniques. Although these usual perturbative electron propagator/GF methods have been very successful, they are limited in applicability. Usual 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 usual perturbational approaches to electron propagator/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 usual perturbational electron propagator/GF methods. In this article I will first review the theory behind the multiconfigurational spin-tensor electron propagator method. Since the introduction of MCSTEP over fifteen years ago, several accurate MCSTEP atomic and molecular IPs and EAs have been determined. I will summarize some of the more significant calculations to date. An electron propagator method using a multiconfigurational second-order perturbation theory wavefunction as the initial state in the fermion operator block (block 1) in the MCSTEP matrix equations was initially developed by Heryadi and Yeager. In the other blocks an MCSCF wavefunction is the initial state. This new method is called EPCASPT2 and should be viewed as an extension of MCSTEP. In this article I will review the theory behind EPCASPT2 and some of the recent calculations done using a CASPT2 wavefunction as the initial state in the electron propagator. We compare our results with the results of the calculations using MCSTEP, full configuration interaction, and the multireference configuration interaction method with the same geometries and basis sets.