Dispersion, static correlation, and delocalisation errors in density functional theory: an electrostatic theorem...

Area of Science:

• Computational chemistry
• Quantum mechanics
• Materials science

Background:

• Density functional theory (DFT) is a cornerstone of modern computational chemistry.
• Accurate prediction of molecular properties relies on minimizing errors in DFT, such as static correlation, dispersion, and delocalization.
• Understanding these errors is crucial for developing more reliable theoretical models.

Purpose of the Study:

• To investigate the origins of dispersion, static correlation, and delocalization errors in DFT.
• To analyze these errors from the perspective of nuclear forces in stretched diatomic molecules.
• To establish a link between errors in electron density and erroneous forces within the Kohn-Sham framework.

Main Methods:

• Utilized the electrostatic theorem of Feynman to connect force errors with electron density distortions.
• Examined the behavior of forces and density distortions in stretched H(2) and H(2)(+) molecules.
• Investigated the impact of varying the fraction of long-range exact orbital exchange on these errors.

Main Results:

• Dispersion forces in H(2) arise from subtle electron density distortions.
• Static correlation errors in DFT lead to overestimated forces due to exaggerated density distortions.
• Delocalization errors in DFT result in underestimated forces due to underestimated density distortions.
• The interplay of forces in H(2)(+) can create a repulsive barrier in the potential energy curve.
• Increasing long-range exact orbital exchange reduces delocalization error but exacerbates static correlation error.

Conclusions:

• The study provides an unconventional yet insightful view of DFT errors through the lens of nuclear forces.
• The findings highlight the complex relationship between electron density, molecular forces, and common DFT approximations.
• This work offers a foundation for developing improved DFT functionals that better capture electron correlation and delocalization effects.