The extended Koopmans' theorem for orbital-optimized methods: accurate computation of ionization potentials

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• The extended Koopmans' theorem (EKT) is a method for calculating ionization potentials (IPs).
• Standard non-variational methods require complex calculations for EKT, involving analytic gradients and relaxed density matrices.
• Orbital-optimized methods simplify EKT computations by providing readily available, symmetric matrices and addressing N-representability issues.

Purpose of the Study:

• To present and evaluate the extended Koopmans' theorem (EKT) within orbital-optimized theoretical frameworks.
• To compare the performance of orbital-optimized methods against standard methods for ionization potential calculations.
• To demonstrate the accuracy and applicability of orbital-optimized EKT for diverse chemical systems.

Main Methods:

• Implementation of EKT for orbital-optimized second- and third-order Møller-Plesset perturbation theory.
• Application of EKT to orbital-optimized coupled-electron pair approximation (OCEPA(0)).
• Calculation of ionization potentials for second- and third-row atoms and closed- and open-shell molecules.

Main Results:

• Orbital-optimized methods provide a natural and stable framework for EKT calculations.
• The OCEPA(0) method with the aug-cc-pVTZ basis set yields highly accurate lowest IPs for atoms (MAE 0.11 eV) and closed-shell molecules (MAE 0.15 eV).
• Performance comparisons show orbital-optimized methods are advantageous over standard post-Hartree-Fock approaches.

Conclusions:

• Orbital-optimized methods are the preferred choice for EKT-based ionization potential studies.
• The developed orbital-optimized EKT methods provide accurate and reliable results for a wide range of chemical species.
• This work establishes a robust computational strategy for electronic structure investigations.