Density Functional Theory and Optimal Transportation with Coulomb Cost
Density Functional Theory and Optimal Transportation with Coulomb Cost
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DOI：
10.1002/cpa.21437
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发表时间：
2013-04-01
影响因子：
3
通讯作者：
Klueppelberg, Claudia
中科院分区：
文献类型：
--
作者：
Cotar, Codina;Friesecke, Gero;Klueppelberg, Claudia
本文基于最优运输的观点，提出了密度泛函理论中交换相关泛函的新见解。我们表明，在两个电子的情况下，在半经典极限下，确切的交换相关泛函减少到一个非常有趣的泛函，它取决于与给定密度相关的最优输运映射T。在物理文献中，基于形式论证，极限问题已经被提出，但迄今为止，它似乎还没有被解释为最优输运问题。由于上述极限是强相关的，极限泛函产生了对电子相关性的洞察。我们证明了任意数量的电子和每个电子的最优映射的存在唯一性，并明确地确定了径向对称情况下的最优映射。(c) 2012 Wiley期刊有限公司
We present here novel insight into exchange-correlation functionals in density functional theory, based on the viewpoint of optimal transport. We show that in the case of two electrons and in the semiclassical limit, the exact exchange-correlation functional reduces to a very interesting functional that depends on an optimal transport map T associated with a given density . The limit problem has been suggested, on grounds of formal arguments, in the physics literature, but it appears that it has not hitherto been interpreted as an optimal transport problem. Since the above limit is strongly correlated, the limit functional yields insight into electron correlations. We prove the existence and uniqueness of such an optimal map for any number of electrons and each and determine the map explicitly in the case when is radially symmetric. (c) 2012 Wiley Periodicals, Inc.