Asymptotic behavior of the Kohn-Sham exchange potential at a metal surface

Abstract

The asymptotic structure of the Kohn-Sham exchange potential $v_x(\mathbf{r})$ in the classically forbidden region of a metal surface is investigated, together with that of the Slater exchange potential $V_x^S(\mathbf{r})$ and those of the approximate Krieger-Li-Iafrate $V_x^{KLI}(\mathbf{r})$ and Harbola-Sahni $W_x(\mathbf{r})$ exchange potentials. Particularly, the former is shown to have the form of $v_x(z\to \infty )=-{\alpha }_x/z$ with ${\alpha }_x$ a constant dependent only of bulk electron density. The same result in previous work is thus confirmed; in the meanwhile controversy raised recently gets resolved. The structure of the exchange hole ${\rho }_x(\mathbf{r},{\mathbf{r}}^{\prime })$ is examined, and the delocalization of it in the metal bulk when the electron is at large distance from the metal surface is demonstrated with analytical expressions. The asymptotic structures of $v_x(\mathbf{r})$, $V_x^S(\mathbf{r})$, $V_x^{KLI}(\mathbf{r})$, and $W_x(\mathbf{r})$ at a slab metal surface are also investigated. Particularly, $v_x(z\to \infty )=-1/z$ in the slab case. The distinction in this respect between the semi-infinite and the slab metal surfaces is elucidated.

arXiv comment15 pages

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Cited by in corpus (4)

• Semilocal density functional theory with correct surface asymptotics
• Approximations to the exact exchange potential: KLI versus semilocal
• Exact "exact exchange" potential of two- and one-dimensional electron gases beyond the asymptotic limit
• Asymptotics of the metal-surface Kohn-Sham exact exchange potential revisited