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Register a new userSimple dynamic exchange-correlation kernel of the uniform electron gas
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We propose a simple dynamic exchange-correlation kernel of the uniform electron gas. We model the reduction of the electron-electron interaction due to short-range exchange-correlation effects by introducing a frequency-dependent error-function effective interaction. By imposing the fulfillment of the compresibility and the third-frequency-moment sum rules, as well as the correct asymptotic behavior at large wave vectors, we find an accurate and simple dynamic exchange-correlation kernel that accurately reproduces the wave-vector analysis and the imaginary-frequency analysis of the correlation energy of the uniform electron gas.
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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.
In our previous study [Phys. Rev. B 86, 201104 (2012)] we introduced the so called quasi-non-uniform gradient-level exchange-correlation approximation (QNA) and demonstrated its strength in producing highly accurate equilibrium volumes for metals and their alloys within the density-functional theory. In this paper we extend the scheme to include the accuracy of bulk modulus as an additional figure of merit and show that this scheme is flexible enough as to allow the computation of accurate equilibrium volumes and bulk moduli at the same time. The power and feasibility of this scheme is demonstrated on NiAl and FeV binary alloys.
We develop a scheme for building the scalar exchange-correlation (xc) kernel of time-dependent density functional theory (TDDFT) from the tensorial kernel of time-dependent {em current} density functional theory (TDCDFT) and the Kohn-Sham current density response function. Resorting to the local approximation to the kernel of TDCDFT results in a nonlocal approximation to the kernel of TDDFT, which is free of the contradictions that plague the standard local density approximation (LDA) to TDDFT. As an application of this general scheme, we calculate the dynamical xc contribution to the stopping power of electron liquids for slow ions to find that our results are in considerably better agreement with experiment than those obtained using TDDFT in the conventional LDA.
Density matrix quantum Monte Carlo (DMQMC) is used to sample exact-on-average $N$-body density matrices for uniform electron gas systems of up to 10$^{124}$ matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the $k$-space configuration path-integral formalism disagree by up to $sim$$10$% at certain reduced temperatures $T/T_F le 0.5$ and densities $r_s le 1$. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that DMQMC can calculate free energies directly and present exact free energies for $T/T_F ge 1$ and $r_s le 2$.
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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