First-principles wavevector- and frequency-dependent exchange-correlation kernel for jellium at all densities

Abstract

We propose a spatially and temporally nonlocal exchange-correlation (xc) kernel for the spin-unpolarized fluid phase of ground-state jellium, for use in time-dependent density functional and linear response calculations. The kernel is constructed to satisfy known properties of the exact xc kernel, to accurately describe the correlation energies of bulk jellium, and to satisfy frequency-moment sum rules at a wide range of bulk jellium densities, including those low densities that display strong correlation and symmetry breaking. These effects are easier to understand in the simple jellium model than in real systems. All exact constraints satisfied by the recent MCP07 kernel [A. Ruzsinszky, et al., Phys. Rev. B 101, 245135 (2020)] are maintained in the new revised MCP07 (rMCP07) kernel, while others are added. The revision $f_{\mathrm{xc}}^{rMCP07}(q,\omega )$ differs from MCP07 only for non-zero frequencies $\omega$. Only at densities much lower than those of real bulk metals is the frequency dependence of the kernel important for the correlation energy of jellium. As the wavevector $q$ tends to zero, the kernel has a $-4\pi \alpha (\omega )/q^2$ divergence whose frequency-dependent ultranonlocality coefficient $\alpha (\omega )$ vanishes in jellium, and is predicted by rMCP07 to be extremely small for the real metals Al and Na.}

(1st revision) Changes to the TC21 model, new App. F discussing numerical methods. (2nd revision) Revisions in response to peer comments. Refocused discussion around building a kernel for jellium, rather than for metals/materials. (3rd revision) Name change of kernel, TC21 --> rMCP07; added details of QMC calculations; added CP07 and Richardson-Ashcroft correlation energies

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• QMC-consistent static spin and density local field factors for the uniform electron gas
• Low-energy peak in the one-particle spectral function of the electron gas at metallic densities
• Strengths and limitations of the adiabatic exact-exchange kernel for total energy calculations
• Viscous current-induced forces
• Exchange kernel $f_x^h(q,\omega )$ of electron liquid from the variational principle of McLachlan
• Viscous AC current-driven nanomotors
• Many-body interactions in the dielectric theory of stopping power of solids for classical and quantum projectiles