Excited state methods for strongly-correlated systems: formulations based on the equation-of-motion approach

Abstract

Most research on solving the N-electron Schrödinger equation has focused on ground states; excited states are comparatively less studied, and represent a greater challenge for many ab initio methods. The challenge is exacerbated for systems with substantial multiconfigurational character (i.e., strongly-correlated systems) for which standard many-electron wavefunction methods relying on a single electronic configuration give qualitatively incorrect descriptions of electron correlation. This thesis explores approaches to molecular excited state properties that are computationally efficient, yet applicable to multiconfigurational systems. Specifically, we explore strategies that combine the Equation-of-Motion (EOM) approach with the types of correlated wavefunction ansätze that are suitable for strongly-correlated systems. While it is known that the EOM method provides a general strategy for computing electronic transition energies, the significant flexibility in how one formulates the EOM approach and how it can be applied as a post-processing tool for different wavefunctions is not always appreciated. We begin by reviewing the EOM approach, focussing on methods that can be formulated using the 1- and 2-electron reduced density matrices. We assess the accuracy of different EOM approaches for neutral and ionic excited states. We focus on EOM-based alternatives to the traditional extended Koopams’ Theorem for ionization energies and electron affinities as well as an EOM formulation for double ionization transitions that constitutes an extension of the hole-hole/particle-particle random phase approximation (RPA) to multideterminant wavefunction methods. Then we introduce FanEOM, an EOM extension of the Flexible Ansatz for N-electron Configuration Interaction (FANCI) [Comput. Theor. Chem. 1202, 113187 (2021)], and explore its application to spectroscopic properties. Using the EOM methods for electronic excitation and double ionization/double electron affinity transitions described in the initial part of this thesis (i.e., the extended random phase approximations, ERPA), we study adiabatic connection formulations (AC) for computing the residual dynamic correlation energy in correlated wavefunction methods. The key idea in these approaches is that the perturbation strength dependent 2-RDM that appears in the AC formula can be approximated through the solutions from the different variants of ERPA [Phys. Rev. Lett. 120, 013001 (2018)]. Finally, we present PyEOM, an open-source software package designed to help prototype and test EOM-based methods.