Screening nature of the van der Waals density functional method: A review and analysis of the many-body physics foundation

Abstract

We review the screening nature and many-body physics foundation of the van der Waals density functional (vdW-DF) method [Berland K et al 2015 Rep. Prog. Phys. 78 066501], a systematic approach to construct truly nonlocal exchange-correlation energy density functionals. To that end we define and focus on a class of consistent vdW-DF versions that adhere to the Lindhard screening logic of the full method formulation. The consistent-exchange vdW-DF-cx version [Berland K and Hyldgaard P 2014 Phys. Rev. B 89 035412] and its spin extension [Thonhauser T et al 2015 Phys. Rev. Lett. 115 136402] represent the first examples of this class; in general, consistent vdW-DFs reflect a concerted expansion of a formal recast of the adiabatic-connection formula [Hyldgaard P et al 2014 Phys. Rev. B 90 075148], an exponential summation of contributions to the local-field response, and the Dyson equation. We argue that the screening emphasis is essential because the exchange-correlation energy reflects an effective electrodynamics set by a long-range interaction. Two consequences are that (1) there are, in principle, no wiggle room in how one balances exchange and correlation, for example, in vdW-DF-cx, and that (2) consistent vdW-DFs have a formal structure that allows them to incorporate vertex-correction effects, at least in the case of levels that experience recoil-less interactions (for example, near the Fermi surface). We explore the extent to which the strictly nonempirical vdW-DF-cx formulation can serve as a systematic extension of the constraint-based semilocal functionals. For validation, we provide a complete survey of vdW-DF-cx performance for broad molecular processes, for the full set of 55 benchmarks in GMTKN55 [Goerigk L et al 2017 Phys. Chem. Chem. Phys. 19 32184] and comparing to the quantum-chemistry calculations that are summarized in that paper. We also provide new vdW-DF-cx results for metal surface energies and work functions that we compare to experiment. Finally, we use the screening insight to separate the vdW-DF nonlocal-correlation term into pure-vdW-interaction and local-field-susceptibility effects and present tools to compute and map the binding signatures.