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

Dispersion, static correlation, and delocalisation errors in density functional theory are considered from the unconventional perspective of the force on a nucleus in a stretched diatomic molecule. The electrostatic theorem of Feynman is used to relate errors in the forces to errors in the electron density distortions, which in turn are related to erroneous terms in the Kohn-Sham equations. For H(2), the exact dispersion force arises from a subtle density distortion; the static correlation error leads to an overestimated force due to an exaggerated distortion. For H(2)(+), the exact force arises from a delicate balance between attractive and repulsive components; the delocalisation error leads to an underestimated force due to an underestimated distortion. The net force in H(2)(+) can become repulsive, giving the characteristic barrier in the potential energy curve. Increasing the fraction of long-range exact orbital exchange increases the distortion, reducing delocalisation error but increasing static correlation error.