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Register a new userExact dynamical exchange-correlation kernel of a weakly inhomogeneous 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.
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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.
The full three dimensional dispersion of the pi-bands, Fermi velocities and effective masses are measured with angle resolved photoemission spectroscopy and compared to first-principles calculations. The band structure by density-functional theory strongly underestimates the slope of the bands and the trigonal warping effect. Including electron-electron calculation on the level of the GW approximation, however, yields remarkable agreement in the vicinity of the Fermi level. This demonstrates the breakdown of the independent electron picture in semi-metallic graphite and points towards a pronounced role of electron correlation for the interpretation of transport experiments and double-resonant Raman scattering for a wide range of carbon based materials.
Quantum Monte Carlo simulations of interacting electrons in solids often use Slater-Jastrow trial wave functions with Jastrow factors containing one- and two-body terms. In uniform systems the long-range behavior of the two-body term may be deduced from the random-phase approximation (RPA) of Bohm and Pines. Here we generalize the RPA to nonuniform systems. This gives the long-range behavior of the inhomogeneous two-body correlation term and provides an accurate analytic expression for the one-body term. It also explains why Slater-Jastrow trial wave functions incorporating determinants of Hartree-Fock or density-functional orbitals are close to optimal even in the presence of an RPA Jastrow factor. After adjusting the inhomogeneous RPA Jastrow factor to incorporate the known short-range behavior, we test it using variational Monte Carlo calculations. We find that the most important aspect of the two-body term is the short-range behavior due to electron-electron scattering, although the long-range behavior described by the RPA should become more important at high densities.
In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. We obtain exact benchmark solutions for two electrons on four-site extended Hubbard lattices over a wide range of interaction strengths, and compare exact xc potentials and magnetic fields with approximations obtained from orbital-dependent xc functionals. The xc magnetic fields turn out to play an increasingly important role as systems becomes more and more correlated and the electrons begin to localize; the effects of the xc torques, however, remain relatively minor. The approximate xc functionals perform overall quite well, but tend to favor symmetry-broken solutions for strong interactions.
Density functional theory is generalized to incorporate electron-phonon coupling. A Kohn-Sham equation yielding the electronic density $n_U(mathbf{r})$, a conditional probability density depending parametrically on the phonon normal mode amplitudes $U={U_{mathbf{q}lambda}}$, is coupled to the nuclear Schrodinger equation of the exact factorization method. The phonon modes are defined from the harmonic expansion of the nuclear Schrodinger equation. A nonzero Berry curvature on nuclear configuration space affects the phonon modes, showing that the potential energy surface alone is generally not sufficient to define the phonons. An orbital-dependent functional approximation for the non-adiabatic exchange-correlation energy reproduces the leading-order nonadiabatic electron-phonon-induced band structure renormalization in the Frohlich model.
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