Can the Kohn-Sham gap be larger than the fundamental gap?

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• The Kohn-Sham (KS) approach is a cornerstone of density functional theory (DFT) for electronic structure calculations.
• A common assumption is that the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO-LUMO) gap from exact KS theory underestimates the fundamental gap.
• The fundamental gap represents the energy difference between the first excited state and the ground state.

Purpose of the Study:

• To investigate the relationship between the exact Kohn-Sham gap and the fundamental gap.
• To challenge the prevailing assumption regarding the underestimation of the fundamental gap by the exact KS gap.
• To provide numerical evidence for cases where the exact KS gap exceeds the fundamental gap.

Main Methods:

• Utilizing the Hubbard dimer as a simplified, yet relevant, model system.
• Employing numerical calculations based on the Hubbard model Hamiltonian.
• Comparing the calculated exact Kohn-Sham gap with the fundamental gap for the model system.

Main Results:

• Demonstrated numerically that the exact Kohn-Sham gap can be larger than the fundamental gap.
• Provided a counterexample to the widely held belief about the KS gap underestimation.
• The Hubbard dimer model serves as a crucial test case for theoretical predictions.

Conclusions:

• The assumption that the exact Kohn-Sham HOMO-LUMO gap always underestimates the fundamental gap is not universally true.
• The Hubbard dimer model highlights the importance of rigorous numerical verification of theoretical assumptions in electronic structure.
• Further investigations are warranted to understand the conditions under which the exact KS gap can exceed the fundamental gap.