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Register a new userFirst-principles wavevector- and frequency-dependent exchange-correlation kernel for jellium and related metals
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Aaron D. Kaplan
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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. All exact constraints satisfied by the recent MCP07 kernel [A. Ruzsinszky, et al., Phys. Rev. B 101, 245135 (2020)] are maintained in the new tightly-constrained 2021 (TC21) kernel, while others are added.
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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, $lim_{qto 0}f_{xc}(n,q,omega) = -alpha(omega)e^2/q^2$, 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.
The position-dependent exact-exchange energy per particle $varepsilon_x(z)$ (defined as the interaction between a given electron at $z$ and its exact-exchange hole) at metal surfaces is investigated, by using either jellium slabs or the semi-infinite (SI) jellium model. For jellium slabs, we prove analytically and numerically that in the vacuum region far away from the surface $varepsilon_{x}^{text{Slab}}(z to infty) to - e^{2}/2z$, {it independent} of the bulk electron density, which is exactly half the corresponding exact-exchange potential $V_{x}(z to infty) to - e^2/z$ [Phys. Rev. Lett. {bf 97}, 026802 (2006)] of density-functional theory, as occurs in the case of finite systems. The fitting of $varepsilon_{x}^{text{Slab}}(z)$ to a physically motivated image-like expression is feasible, but the resulting location of the image plane shows strong finite-size oscillations every time a slab discrete energy level becomes occupied. For a semi-infinite jellium, the asymptotic behavior of $varepsilon_{x}^{text{SI}}(z)$ is somehow different. As in the case of jellium slabs $varepsilon_{x}^{text{SI}}(z to infty)$ has an image-like behavior of the form $propto - e^2/z$, but now with a density-dependent coefficient that in general differs from the slab universal coefficient 1/2. Our numerical estimates for this coefficient agree with two previous analytical estimates for the same. For an arbitrary finite thickness of a jellium slab, we find that the asymptotic limits of $varepsilon_{x}^{text{Slab}}(z)$ and $varepsilon_{x}^{text{SI}}(z)$ only coincide in the low-density limit ($r_s to infty$), where the density-dependent coefficient of the semi-infinite jellium approaches the slab {it universal} coefficient 1/2.
Measuring the transport of electrons through a graphene sheet necessarily involves contacting it with metal electrodes. We study the adsorption of graphene on metal substrates using first-principles calculations at the level of density functional theory. The bonding of graphene to Al, Ag, Cu, Au and Pt(111) surfaces is so weak that its unique ultrarelativistic electronic structure is preserved. The interaction does, however, lead to a charge transfer that shifts the Fermi level by up to 0.5 eV with respect to the conical points. The crossover from p-type to n-type doping occurs for a metal with a work function ~5.4 eV, a value much larger than the work function of free-standing graphene, 4.5 eV. We develop a simple analytical model that describes the Fermi level shift in graphene in terms of the metal substrate work function. Graphene interacts with and binds more strongly to Co, Ni, Pd and Ti. This chemisorption involves hybridization between graphene $p_z$-states and metal d-states that opens a band gap in graphene. The graphene work function is as a result reduced considerably. In a current-in-plane device geometry this should lead to n-type doping of graphene.
The dynamical exchange-correlation kernel $f_{xc}$ of a non-uniform electron gas is an essential input for the time-dependent density functional theory of electronic systems. The long-wavelength behavior of this kernel is known to be of the form $f_{xc}= alpha/q^2$ where $q$ is the wave vector and $alpha$ is a frequency-dependent coefficient. We show that in the limit of weak non-uniformity the coefficient $alpha$ has a simple and exact expression in terms of the ground-state density and the frequency-dependent kernel of a {it uniform} electron gas at the average density. We present an approximate evaluation of this expression for Si and discuss its implications for the theory of excitonic effects.
We compute the thermal conductivity of water within linear response theory from equilibrium molecular dynamics simulations, by adopting two different approaches. In one, the potential energy surface (PES) is derived on the fly from the electronic ground state of density functional theory (DFT) and the corresponding analytical expression is used for the energy flux. In the other, the PES is represented by a deep neural network (DNN) trained on DFT data, whereby the PES has an explicit local decomposition and the energy flux takes a particularly simple expression. By virtue of a gauge invariance principle, established by Marcolongo, Umari, and Baroni, the two approaches should be equivalent if the PES were reproduced accurately by the DNN model. We test this hypothesis by calculating the thermal conductivity, at the GGA (PBE) level of theory, using the direct formulation and its DNN proxy, finding that both approaches yield the same conductivity, in excess of the experimental value by approximately 60%. Besides being numerically much more efficient than its direct DFT counterpart, the DNN scheme has the advantage of being easily applicable to more sophisticated DFT approximations, such as meta-GGA and hybrid functionals, for which it would be hard to derive analytically the expression of the energy flux. We find in this way, that a DNN model, trained on meta-GGA (SCAN) data, reduce the deviation from experiment of the predicted thermal conductivity by about 50%, leaving the question open as to whether the residual error is due to deficiencies of the functional, to a neglect of nuclear quantum effects in the atomic dynamics, or, likely, to a combination of the two.
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