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

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.

arXiv commentIncludes new kernels: a novel QV-MCP07 hybrid kernel that better estimates ultranonlocality, and the LRC and 2p2h kernels as better references for ultranonlocality. Miscellaneous typographical/syntactic changes

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Cited by in corpus (3)

• Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel
• First-principles wavevector- and frequency-dependent exchange-correlation kernel for jellium at all densities
• Exchange kernel $f_x^h(q,\omega )$ of electron liquid from the variational principle of McLachlan