Progress towards understanding ultranonlocality through the wavevector and frequency dependence of approximate exchange-correlation kernels

TL;DR

This paper investigates the wavevector and frequency dependence of approximate exchange-correlation kernels in TDDFT, revealing the limitations of the MCP07 kernel in capturing optical properties and exploring the ultranonlocality coefficient in various materials.

Contribution

It analyzes the wavevector and frequency dependence of approximate xc kernels, especially MCP07, in describing ultranonlocality in inhomogeneous electron gases.

Findings

MCP07 accurately predicts UEG ground-state energies.

Strong frequency dependence of the ultranonlocality coefficient is demonstrated.

Imposing exact constraints influences the shape of the ultranonlocality coefficient.

Abstract

In the framework of time-dependent density functional theory (TDDFT), the exact exchange-correlation (xc) kernel $f_{xc}(n,q,\omega)$ determines the ground-state energy, excited-state energies, lifetimes, and the time-dependent linear density response of any many-electron system. The recently developed MCP07 xc kernel $f_{xc}(n,q,\omega)$ of A. Ruzsinszky et al. [Phys. Rev. B 101, 245135 (2020)] yields excellent uniform electron gas (UEG) ground-state energies and plausible plasmon lifetimes. As MCP07 is constructed to describe $f_{xc}$ of the UEG, it cannot capture optical properties of real materials. To verify this claim, we follow Nazarov et al. [Phys. Rev. Lett. 102, 113001 (2009)] to construct the long-range, dynamic xc kernel, $\lim_{q\to 0}f_{xc}(n,q,\omega) = -\alpha(\omega)e^2/q^2$, of a weakly inhomogeneous electron gas, using MCP07 and other common xc kernels. The strong wavevector and frequency dependence of the "ultranonlocality" coefficient $\alpha(\omega)$ is demonstrated for a variety of simple metals and semiconductors. We examine how imposing exact constraints on an approximate kernel shapes $\alpha(\omega)$. Comparisons to kernels derived from correlated-wavefunction calculations are drawn.