Van der Waals density functional: Self-consistent potential and the nature of the van der Waals bond

TL;DR

This paper derives a self-consistent exchange-correlation potential for the van der Waals density functional, enabling accurate ground state calculations and insights into the nature of van der Waals bonds.

Contribution

It introduces a self-consistent potential for the nonlocal van der Waals functional, validating previous perturbative approaches and enabling geometry optimizations.

Findings

Self-consistent potential has little effect on equilibrium separations.

Results agree with wave-function calculations.

The approach facilitates geometry relaxations and bond analysis.

Abstract

We derive the exchange-correlation potential corresponding to the nonlocal van der Waals density functional [M. Dion, H. Rydberg, E. Schroder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)]. We use this potential for a self-consistent calculation of the ground state properties of a number of van der Waals complexes as well as crystalline silicon. For the latter, where little or no van der Waals interaction is expected, we find that the results are mostly determined by semilocal exchange and correlation as in standard generalized gradient approximations (GGA), with the fully nonlocal term giving little effect. On the other hand, our results for the van der Waals complexes show that the self-consistency has little effect at equilibrium separations. This finding validates previous calculations with the same functional that treated the fully nonlocal term as a post GGA perturbation. A comparison of our results with wave-function calculations demonstrates the usefulness of our approach. The exchange-correlation potential also allows us to calculate Hellmann-Feynman forces, hence providing the means for efficient geometry relaxations as well as unleashing the potential use of other standard techniques that depend on the self-consistent charge distribution. The nature of the van der Waals bond is discussed in terms of the self-consistent bonding charge.