Development of Multiconfigurational Green’s Function Approaches

Abstract

With Green’s function or propagator techniques electronic excitation energies, ionization potentials, electron affinities, electronic transition probabilities, and other response properties can be calculated. These techniques have several significant advantages over more conventional ab initio approaches to electronic energy difference calculations such as ΔMCSCF, ΔCI, and A coupled cluster (ΔCC). Included among these are: 1) For excitation, ionization, and attachment energies propagator techniques mimic Δ full CI at a small fraction of the computer time and cost; 2) The polarization propagator is the correct linear response of a system with a fully optimized (for both orbitals and state expansion coefficients) wavefunction to an external perturbation (e.g. an electromagnetic field) so response properties such as frequency dependent polarizabilities are calculated reliably and accurately, and 3) The length, velocity, and acceleration forms of the oscillator strength are equal in the limit of a complete basis set of orbitals.

We have been developing, studying, and applying both single-particle multiconfigurational Green’s function and the particle-hole multiconfigurational Green’s function. MC based techniques are necessary for application to highly correlated systems where more traditional perturbational approaches are inadequate. We have furthermore been formulating tensor-coupled Green’s function approaches so that these methods can be correctly applied to open shell atoms and molecules.

In this talk I will review our MC Green’s function techniques. The single-particle approaches are known as the multiconfigurational electron propagator (MCEP) and the multiconfigurational spin tensor electron propagator (MCSTEP). The p-h multiconfigurational Green’s function approach is equivalent to the multiconfigurational linear response (MCLR) or the multiconfiguration time-dependent Hartree-Fock (MCTDHF). I will present and discuss several examples using these methods including for the ionization potentials of NH₂, the excitation energies of CH+, the polarizability of acetylene, and the transition moments between excited triplet states of N₂. In a final example I will discuss the tensor coupled MCTDHF with application to O₂