The derivative discontinuity of the exchange-correlation functional

Area of Science:

• Electronic structure theory
• Quantum mechanics
• Computational chemistry

Background:

• The derivative discontinuity is a fundamental property of electronic energy in quantum systems.
• It arises from the integer nature of electrons and affects total energy calculations.
• Understanding this discontinuity is vital for accurate electronic structure theory and density functional theory (DFT).

Purpose of the Study:

• To investigate the failure of approximate exchange-correlation functionals in DFT.
• To highlight the importance of the derivative discontinuity in the exact electronic structure of molecules.
• To explore the implications of derivative discontinuity for various quantum systems and models.

Main Methods:

• Analysis of models including hydrogen systems (varying electrons/nuclear charge) and the 1D Hubbard model (1DHM).
• Comparison of approximate DFT functionals with exact results from Full Configuration Interaction (FCI).
• Investigation of derivative discontinuity at constant particle number (N).

Main Results:

• Approximate DFT functionals, including hybrids, fail to capture the derivative discontinuity.
• This leads to significant errors: incorrect total energies (e.g., H2, H2+), missing band gaps in Mott insulators (e.g., stretched H2, 1DHM), and incorrect densities (e.g., HZ molecule).
• The exact particle behavior, including derivative discontinuity, is essential for describing electron transfer processes.

Conclusions:

• Current approximate DFT functionals are fundamentally flawed due to missing the derivative discontinuity.
• Accurate description of electron behavior, particularly derivative discontinuity, is critical for real-world systems and electron transfer.
• Addressing derivative discontinuity presents a significant challenge for developing improved DFT exchange-correlation functionals.