Extended solids are frequently simulated as finite systems with periodic boundary conditions, which due to the long-range nature of the Coulomb interaction may lead to slowly decaying finite- size errors. In the case of Quantum-Monte-Carlo simulation
s, which are based on real space, both real-space and momentum-space solutions to this problem exist. Here, we describe a hybrid method which using real-space data models the spherically averaged structure factor in momentum space. We show that (i) by integration our hybrid method exactly maps onto the real-space model periodic Coulomb-interaction (MPC) method and (ii) therefore our method combines the best of both worlds (real-space and momentum-space). One can use known momentum-resolved behavior to improve convergence where MPC fails (e.g., at surface-like systems). In contrast to pure momentum-space methods, our method only deals with a simple single-valued function and, hence, better lends itself to interpolation with exact small-momentum data as no directional information is needed. By virtue of integration, the resulting finite-size corrections can be written as an addition to MPC.
A still open issue in many-body theory is the asymptotic behavior of the exchange-correlation energy and potential in the vacuum region of a metal surface. Here we report a numerical study of the position-dependent exchange-correlation energy for jel
lium slabs, as obtained by combining the formally exact adiabatic-connection-fluctuation-dissipation theorem with either time-dependent density-functional theory or an inhomogeneous Singwi-Tosi-Land-Sjolander approach. We find that the inclusion of correlation allows to obtain well-converged semi-infinite-jellium results (independent of the slab thickness) that exhibit an image-like asymptotic behavior close to the classical image potential $V_{im}(z)=-e^2/4z$.
A long-standing puzzle in density-functional theory is the issue of the long-range behavior of the Kohn-Sham exchange-correlation potential at metal surfaces. As an important step towards its solution, it is proved here, through a rigurouos asymptoti
c analysis and accurate numerical solution of the Optimized-Effective-Potential integral equation, that the Kohn-Sham exact exchange potential decays as $ln(z)/z$ far into the vacuum side of an {it extended} semi-infinite jellium. In contrast to the situation in {it localized} systems, like atoms, molecules, and slabs, this dominant contribution does not arise from the so-called Slater potential. This exact-exchange result provides a strong constraint on the suitability of approximate correlation-energy functionals.
In a recent Letter we introduced Hellmann-Feynman operator sampling in diffusion Monte Carlo calculations. Here we derive, by evaluating the second derivative of the total energy, an efficient method for the calculation of the static density-response
function of a many-electron system. Our analysis of the effect of the nodes suggests that correlation is described correctly and we find that the effect of the nodes can be dealt with.
We present a detailed study of the coupling-constant-averaged exchange-correlation hole density at a jellium surface, which we obtain in the random-phase approximation (RPA) of many-body theory. We report contour plots of the exchange-only and exchan
ge-correlation hole densities, the integration of the exchange-correlation hole density over the surface plane, the on-top correlation hole, and the energy density. We find that the on-top correlation hole is accurately described by local and semilocal density-functional approximations. We also find that for electrons that are localized far outside the surface the main part of the corresponding exchange-correlation hole is localized at the image plane.
We propose a generalized gradient approximation (GGA) for the angle- and system-averaged exchange-correlation hole of a many-electron system. This hole, which satisfies known exact constraints, recovers the PBEsol (Perdew-Burke-Ernzerhof for solids)
exchange-correlation energy functional, a GGA that accurately describes the equilibrium properties of densely packed solids and their surfaces. We find that our PBEsol exchange-correlation hole describes the wavevector analysis of the jellium exchange-correlation surface energy in agreement with a sophisticated time-dependent density-functional calculation (whose three-dimensional wavevector analysis we report here).
We report first-principles calculations of acoustic surface plasmons on the (0001) surface of Be, as obtained in the random-phase approximation of many-body theory. The energy dispersion of these collective excitations has been obtained along two sym
metry directions. Our results show a considerable anisotropy of acoustic surface plasmons, and underline the capability of experimental measurements of these plasmons to {it map} the electron-hole excitation spectrum of the quasi two-dimensional Shockley surface state band that is present on the Be(0001) surface.
After the early suggestion by John Pendry to probe unoccupied bands at surfaces through the time reversal of the photoemission process, the inverse-photoemission technique yielded the first conclusive experimental evidence for the existence of image-
potential bound states at metal surfaces and has led over the last two decades to an active area of research in condensed-matter and surface physics. Here we describe the current status of the many-body theory of inelastic lifetimes of these image-potential states and also the Shockley surface states that exist near the Fermi level in the projected bulk band gap of simple and noble metals. New calculations of the self-energy and lifetime of surface states on Au surfaces are presented as well, by using the $GWGamma$ approximation of many-body theory.
Due to the strongly nonlocal nature of $f_{xc}({bf r},{bf r},omega)$ the {em scalar} exchange and correlation (xc) kernel of the time-dependent density-functional theory (TDDFT), the formula for Q the friction coefficient of an interacting electron g
as (EG) for ions tends to give a too large value of Q for heavy ions in the medium- and low-density EG, if we adopt the local-density approximation (LDA) to $f_{xc}({bf r},{bf r},omega)$, even though the formula itself is formally exact. We have rectified this unfavorable feature by reformulating the formula for Q in terms of the {em tensorial} xc kernel of the time dependent current-density functional theory, to which the LDA can be applied without intrinsic difficulty. Our numerical results find themselves in a considerably better agreement with the experimental stopping power of Al and Au for slow ions than those previously obtained within the LDA to the TDDFT.
We report many-body calculations of the self-energy and lifetime of Shockley and image states on the (100) and (111) surfaces of Cu that go beyond the $GW$ approximation of many-body theory. The self-energy is computed in the framework of the GWGamma
approximation by including short-range exchange-correlation (XC) effects both in the screened interaction W (beyond the random-phase approximation) and in the expansion of the self-energy in terms of W (beyond the GW approximation). Exchange-correlation effects are described within time-dependent density-functional theory from the knowledge of an adiabatic nonlocal XC kernel that goes beyond the local-density approximation.
