Validation of Koopmans' theorem for density functional theory binding energies

Area of Science:

• Quantum Chemistry
• Computational Physics
• Solid State Physics

Background:

• Core-level binding energies (BEs) are influenced by initial state (electrostatic potential at the nucleus) and final state (electron response to core-hole) effects.
• Koopmans' theorem (KT) rigorously relates initial state BEs to Hartree-Fock (HF) orbital energies (-ε).
• KT is frequently applied using Kohn-Sham (KS) orbital energies, despite theoretical limitations.

Purpose of the Study:

• To evaluate the validity of using Koopmans' theorem with Kohn-Sham orbital energies for core-level binding energy calculations.
• To determine if shifts in KS orbital energies can accurately represent shifts in initial state BEs.
• To provide theoretical justification for the widespread use of KT with KS energies in computational studies.

Main Methods:

• Review of theoretical frameworks for core-level binding energies, including initial and final state effects.
• Analysis of the rigorous application of Koopmans' theorem within Hartree-Fock theory.
• Investigation of the relationship between Kohn-Sham orbital energies and initial state contributions to binding energy shifts.

Main Results:

• The direct application of Koopmans' theorem using Kohn-Sham orbital energies does not accurately yield absolute initial state contributions to BEs.
• Shifts in initial state BEs relative to a reference value are accurately predicted by shifts in Kohn-Sham orbital energies.
• This demonstrates that the initial state component of BE shifts can be reliably obtained using KT with KS orbital energies.

Conclusions:

• Koopmans' theorem, when applied with Kohn-Sham orbital energies, is validated for calculating shifts in initial state binding energies.
• This finding supports the extensive body of research that utilizes KT with KS energies to analyze initial state contributions to BE shifts.
• The study reconciles theoretical shortcomings with practical computational methodologies in core-level spectroscopy.