Abstract
Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the non-locality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the image-like surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to the ones at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.
Highlights
The exact form of the potential felt by an electron leaving from or approaching a metal surface is of great importance for a variety of physical phenomena, including the interpretation of image states[1], modeling quantum-transport[2], low-energy electron diffraction (LEED)[3], scanning tunneling microscopy[4,5], and inverse or two-photon photoemission spectroscopy[6,7]
The asymptotic form of this image potential is −1/(4(z −z0)), with z being the distance from the surface, and z0 representing the position of the so-called image plane[8], and should be reproduced by any computational method aiming at an accurate description of the surface physics
Within Kohn-Sham (KS) density-functional theory (DFT)[9,10], which is the most used computational method for electronic structure calculations in theoretical solidstate physics, the shape of the image potential is dictated by the properties of the effective Kohn-Sham (KS) potential
Summary
The exact form of the potential felt by an electron leaving from or approaching a metal surface is of great importance for a variety of physical phenomena, including the interpretation of image states[1], modeling quantum-transport[2], low-energy electron diffraction (LEED)[3], scanning tunneling microscopy[4,5], and inverse or two-photon photoemission spectroscopy[6,7]. Within Kohn-Sham (KS) density-functional theory (DFT)[9,10], which is the most used computational method for electronic structure calculations in theoretical solidstate physics, the shape of the image potential is dictated by the properties of the effective Kohn-Sham (KS) potential This depends on the employed approximation for the exchange-correlation (XC) functional Exc[ρ], which gives the XC potential via the relation vxc(r). We show that the issue can be instead solved at the meta-GGA level of theory, employing an exact condition which yields the correct image-like asymptotic behavior of both εxc and vxc at metal surfaces. This condition can be implemented in any meta-GGA functional, keeping its original accuracy for ground-state properties not related to surface asymptotics. An accurate KS-DFT method with correct metal-surface asymptotic can be obtained for application in many surface science problems
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