Koopmans' theorem and selection rules for one-electron ionization processes in orbitally degenerate systems

Area of Science:

• Quantum Chemistry
• Atomic Physics

Background:

• One-electron ionization processes in orbitally degenerate systems, like pN atoms, are classified into allowed and forbidden categories based on selection rules (SRs).
• Koopmans' theorem (KT) is typically applied to SR-allowed processes, with its validity for forbidden processes being less understood.

Purpose of the Study:

• To analyze the validity of Koopmans' theorem (KT) for one-electron ionization processes forbidden by selection rules (SRs).
• To develop an extension of KT to estimate ionization energies (IEs) for SR-forbidden processes.
• To investigate the impact of Hund's rule violations on KT validity for cation states.

Main Methods:

• Analysis of the variational condition underlying Koopmans' theorem for SR-allowed and SR-forbidden processes.
• Development of an extended Koopmans' theorem formulation.
• Application of the extended KT to ionization processes in carbon, nitrogen, and oxygen atoms.
• Comparison of theoretical IEs with experimental data and ΔSCF calculations.

Main Results:

• The general formulation of KT in Hartree-Fock implicitly assumes SR-allowed processes, limiting its applicability.
• An extended KT formulation is developed, providing a more complex relationship for SR-forbidden processes.
• The extended KT accurately estimates IEs for both SR-allowed and SR-forbidden processes in C, N, and O atoms.
• The study highlights the importance of considering SRs and Hund's rule violations for accurate IE predictions.

Conclusions:

• Koopmans' theorem requires extension to accurately describe ionization processes forbidden by selection rules.
• The developed extended KT provides a more comprehensive approach to calculating ionization energies in complex atomic systems.
• The findings contribute to a deeper understanding of ionization dynamics and the limitations of theoretical models.