Toward a General Non-Local Polarizability Density Functional for van der Waals Dispersion Interactions

Density-functional theory (DFT), while being a workhorse for electronic-structure calculations, struggles with describing van der Waals (vdW) dispersion interactions stemming from long-range electron correlations. Determining the correlation energy using the adiabatic connection fluctuation-dissipation theorem via a non-local polarizability density gives a general framework to tackle this problem [1], but a robust general formalism is yet to be found. Here, we present a unified formula for the non-local polarizability density based on the second-order perturbation theory expression for the polarizability. We analyze this function for the quantum harmonic oscillator and particle in a box, as two elementary model systems, and identify efficient numerical approximations. The electromagnetic coupling of two harmonic oscillators, treated non locally, is also considered. Our model studies along with prior work on semi-local polarizability functionals [2] pave the way toward developing a unified non-local polarizability functional for molecules and materials.

[1] Hermann and Tkatchenko, Phys. Rev. Lett. 124, 146401 (2020)
[2] Vydrov and Van Voorhis, Phys. Rev. Lett. 103, 063004 (2009)