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Register a new userAdiabatic-Connection-Fluctuation-Dissipation approach to the long-range behavior of the exchange-correlation energy at metal surfaces: A numerical study for jellium slabs
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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 jellium 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 $V_{im}(z)=-e^2/4z$.
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An adiabatic-connection fluctuation-dissipation theorem approach based on a range separation of electron-electron interactions is proposed. It involves a rigorous combination of short-range density functional and long-range random phase approximations. This method corrects several shortcomings of the standard random phase approximation and it is particularly well suited for describing weakly-bound van der Waals systems, as demonstrated on the challenging cases of the dimers Be$_2$ and Ne$_2$.
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 exchange-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.
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.
Exact-exchange self-consistent calculations of the Kohn-Sham potential, surface energy, and work function of jellium slabs are reported in the framework of the Optimized Effective Potential (OEP) scheme of Density Functional Theory. In the vacuum side of the jellium surface and at a distance $z$ that is larger than the slab thickness, the exchange-only Kohn-Sham potential is found to be image-like ($sim -e^2/z$) but with a coefficient that differs from that of the classical image potential $V_{im}(z)=-e^2/4z$. The three OEP contributions to the surface energy (kinetic, electrostatic, and exchange) are found to oscillate as a function of the slab thickness, as occurs in the case of the corresponding calculations based on the use of single-particle orbitals and energies obtained in the Local Density Approximation (LDA). The OEP work function presents large quantum size effects that are absent in the LDA and which reflect the intrinsic derivative discontinuity of the exact Kohn-Sham potential.
Nonadiabatic effects that arise from the concerted motion of electrons and atoms at comparable energy and time scales are omnipresent in thermal and light-driven chemistry at metal surfaces. Excited (hot) electrons can measurably affect molecule-metal reactions by contributing to state-dependent reaction probabilities. Vibrational state-to-state scattering of NO on Au(111) has been one of the most studied examples in this regard, providing a testing ground for developing various nonadiabatic theories. This system is often cited as the prime example for the failure of electronic friction theory, a very efficient model accounting for dissipative forces on metal-adsorbed molecules due to the creation of hot electrons in the metal. However, the exact failings compared to experiment and their origin from theory are not established for any system, because dynamic properties are affected by many compounding simulation errors of which the quality of nonadiabatic treatment is just one. We use a high-dimensional machine learning representation of electronic structure theory to minimize errors that arise from quantum chemistry. This allows us to perform a comprehensive quantitative analysis of the performance of nonadiabatic molecular dynamics in describing vibrational state-to-state scattering of NO on Au(111) and compare directly to adiabatic results. We find that electronic friction theory accurately predicts elastic and single-quantum energy loss, but underestimates multi-quantum energy loss and overestimates molecular trapping at high vibrational excitation. Our analysis reveals that multi-quantum energy loss can potentially be remedied within friction theory, whereas the overestimation of trapping constitutes a genuine breakdown of electronic friction theory. Addressing this overestimation for dynamic processes in catalysis and surface chemistry will require more sophisticated theories.
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