  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.
