|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Position-dependent exact-exchange energy for slabs and semi-infinite jellium | | C. M. Horowitz
; L. A. Constantin
; C. R. Proetto
; J. M. Pitarke
; | | Date: |
6 Nov 2009 | | Abstract: | 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 $varepsilon_{x}^{ ext{Slab}}(z o infty) o - e^{2}/2z$, {it
independent} of the bulk electron density, which is exactly half the
corresponding exact-exchange potential $V_{x}(z o infty) o - e^2/z$ [Phys.
Rev. Lett. {f 97}, 026802 (2006)] of density-functional theory, as occurs in
the case of finite systems. The fitting of $varepsilon_{x}^{ ext{Slab}}(z)$
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 $varepsilon_{x}^{ ext{SI}}(z)$ is somehow different.
As in the case of jellium slabs $varepsilon_{x}^{ ext{SI}}(z o infty)$ 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
$varepsilon_{x}^{ ext{Slab}}(z)$ and $varepsilon_{x}^{ ext{SI}}(z)$ only
coincide in the low-density limit ($r_s o infty$), where the
density-dependent coefficient of the semi-infinite jellium approaches the slab
{it universal} coefficient 1/2. | | Source: | arXiv, 0911.1338 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER