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arXiv 0812.0742cond-mat.str-elcond-mat.other
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密度泛函理论强相互作用极限下的电子零点振荡

Electronic zero-point oscillations in the strong-interaction limit of density functional theory

Paola Gori-Giorgi, Giovanni Vignale, Michael Seidl

摘要:

科恩-沙姆密度泛函理论中的交换相关能可以精确地用电子-电子排斥算符的期望值的变化来表示,在多电子哈密顿量中,同一算符乘以一个在0(科恩-沙姆系统)和1(物理系统)之间变化的实参数$λ$。在这个过程中,通常被称为绝热连接,单电子密度保持固定的适当的本地单体势。密度泛函理论的强相互作用极限被定义为极限$λ\to\infty$,结果证明,就像相反的非相互作用Kohn-Sham极限($λ\to 0$)一样,它在数学上比物理($λ=1$)情况简单,并且可以用来建立一个近似的交换相关能的$λ\to 0$和$λ\to\infty$之间的插值公式。在这里,我们将$λ\to\infty$极限[Phys. Rev. A { \bf 75},042511(2007)]的精确处理扩展到下一个主导项,描述严格关联电子的零点振荡,并以小球形原子为例进行数值计算。我们还提出了一个改进的近似泛函的零点项和一个修正的插值公式的交换相关能量满足更精确的约束。

英文摘要:

The exchange-correlation energy in Kohn-Sham density functional theory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron hamiltonian, this same operator is multiplied by a real parameter $λ$ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is kept fixed by a suitable local one-body potential. The strong-interaction limit of density functional theory, defined as the limit $λ\to\infty$, turns out to be, like the opposite non-interacting Kohn-Sham limit ($λ\to 0$) mathematically simpler than the physical ($λ=1$) case, and can be used to build an approximate interpolation formula between $λ\to 0$ and $λ\to\infty$ for the exchange-correlation energy. Here we extend the exact treatment of the $λ\to\infty$ limit [Phys. Rev. A {\bf 75}, 042511 (2007)] to the next leading term, describing zero-point oscillations of strictly correlated electrons, with numerical examples for small spherical atoms. We also propose an improved approximate functional for the zero-point term and a revised interpolation formula for the exchange-correlation energy satisfying more exact constraints.

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