Numerical Analysis of the Complete Active-Space Extended Koopmans's Theorem

TL;DR

This paper assesses the numerical accuracy of the extended Koopmans's theorem (EKT) in calculating ionization energies of atomic and molecular systems, highlighting the importance of basis set and active space choices for precision.

Contribution

It provides a detailed analysis of how basis set size, active space, and diffuse functions influence the accuracy of EKT-derived ionization energies, especially for CAS-CI methods.

Findings

FCI EKT ionization energies improve with larger basis sets.

CAS-CI EKT energies do not always improve with increased basis or active space.

Diffuse functions significantly enhance the accuracy of EKT ionization energies.

Abstract

We investigate the numerical accuracy of the extended Koopmans's theorem (EKT) in reproducing the full configuration interaction (FCI) and complete active-space configuration interaction (CAS-CI) ionization energies (IEs) of atomic and molecular systems calculated as the difference between the energies of N and (N - 1) electron states. In particular, we study the convergence of the EKT IEs to their exact values as the basis set and the active space sizes vary. We find that the first FCI EKT IEs approach their exact counterparts as the basis set size increases. However, increasing the basis set or the active space sizes do not always lead to more accurate CAS-CI EKT IEs. Our investigation supports the Davidson et al.'s observation [E. R. Davidson, et al., J. Chem. Phys. 155, 051102 (2021)] that the FCI EKT IEs can be systematically improved with arbitrary numerical accuracy by supplementing the basis set with diffuse functions of appropriate symmetry which allow the detached electron to travel far away from the reference system. By changing the exponent and the center of the diffuse functions, our results delineate a complex pattern for the CAS-CI EKT IE of LiH which can be important for the spectroscopic studies of small molecules.