Exact and Model Exchange-Correlation Potentials for Open-Shell Systems.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Conventional inverse density functional theory (DFT) methods struggle with open-shell systems due to assumptions of non-degenerate Kohn-Sham (KS) eigenvalues.
• Handling degenerate KS eigenvalues and fractional orbital occupancies is crucial for accurate electronic structure calculations in complex systems.

Purpose of the Study:

• To generalize the inverse DFT problem to accommodate degenerate KS eigenvalues and fractional orbital occupancies.
• To compute exact exchange-correlation (XC) potentials for open-shell systems and evaluate the accuracy of common DFT functionals.

Main Methods:

• Developed a generalized inverse DFT approach for systems with degenerate KS eigenvalues and ensemble-v-representable densities.
• Calculated exact XC potentials for Li, C, N, O atoms and CN, CH2 molecules using accurate ground-state densities from configuration interaction.
• Compared exact XC potentials against those derived from nonlocal (B3LYP, SCAN0) and local/semilocal (SCAN, PBE, PW92) XC functionals.

Main Results:

• Successfully generalized the inverse DFT problem to include degenerate KS eigenvalues and fractional orbital occupancies.
• Computed exact XC potentials for six open-shell systems.
• Observed substantial relative errors (10^-1 to 10^0) in model XC potentials from current DFT functionals, despite small density errors (10^-3 to 10^-2).

Conclusions:

• The generalized inverse DFT approach provides a robust framework for studying open-shell systems.
• Current DFT functionals exhibit significant inaccuracies in predicting exchange-correlation potentials for these systems.
• Further development of XC functionals is needed for reliable open-shell electronic structure calculations.