Numerical analysis of the complete active-space extended Koopmans's theorem.

Area of Science:

• Quantum Chemistry
• Computational Chemistry

Background:

• The extended Koopmans's theorem (EKT) is a method for calculating ionization energies (IEs).
• Accurate IE calculations are crucial for understanding atomic and molecular electronic structures.

Purpose of the Study:

• To assess the numerical accuracy of EKT for reproducing FCI and CAS-CI ionization energies.
• To investigate the convergence behavior of EKT IEs with varying basis set and active space sizes.

Main Methods:

• Calculated ionization energies using EKT for atomic and molecular systems.
• Compared EKT results with FCI and CAS-CI reference values.
• Analyzed the impact of basis set size and diffuse functions on EKT accuracy.

Main Results:

• FCI EKT IEs demonstrate convergence towards exact values with increasing basis set size.
• CAS-CI EKT IEs do not consistently improve with larger basis sets or active spaces.
• FCI EKT IEs can be systematically improved using diffuse functions, as noted by Davidson et al.

Conclusions:

• EKT shows promise for accurate IE calculations, particularly for FCI systems.
• The accuracy of CAS-CI EKT IEs is sensitive to basis set choice and active space definition.
• Further studies on diffuse function optimization are needed for precise CAS-CI EKT IE predictions in molecular spectroscopy.