介观体系中密度泛函理论电离势定理的失效
Breakdown of the ionization potential theorem of density functional theory in mesoscopic systems
摘要：
Kohn-Sham（KS）密度泛函理论（DFT）的IP定理指出最高占据分子轨道（HOMO）$ε_{HOMO}$的能量等于第一电离势（IP）的负值，从而赋予KS哈密顿量的一个本征值以物理意义。我们仔细检查的事实，即IP定理的有效性依赖于电子密度$n({\bf r})$，远离系统，由HOMO只确定，作为$n({\bf r}) \underset{r\to\infty}{\sim} e^{- 2 \sqrt{-2 ε_{HOMO}} r}$的行为。虽然这种行为总是适用于有限系统，但它不适用于介观系统，如准二维（Q2 D）电子气或Q2 D晶体。我们表明，这导致违反后一类系统的IP定理。这一发现有很强的KS价带的作用，相对于在介观情况下的功函数问题的影响。基于我们的研究结果，我们引入了IP能带结构的概念，作为一个可观察的替代其非物理KS对应。给出了一种用DFT量确定IP能带结构的实用方法。
英文摘要：
The IP-theorem of the Kohn-Sham (KS) density functional theory (DFT) states that the energy of the highest occupied molecular orbital (HOMO) $ε_{HOMO}$ equals the negative of the first ionization potential (IP), thus ascribing a physical meaning to one of the eigenvalues of the KS hamiltonian. We scrutinize the fact that the validity of the IP-theorem relies critically on the electron density $n({\bf r})$, far from the system, to be determined by HOMO only, behaving as $n({\bf r}) \underset{r\to\infty}{\sim} e^{- 2 \sqrt{-2 ε_{HOMO}} r}$. While this behavior always holds for finite systems, it does not hold for mesoscopic ones, such as quasi-two-dimensional (Q2D) electron gas or Q2D crystals. We show that this leads to the violation of the IP-theorem for the latter class of systems. This finding has a strong bearing on the role of the KS valence band with respect to the work-function problem in the mesoscopic case. Based on our results, we introduce a concept of the IP band structure as an observable alternative to its unphysical KS counterpart. A practical method of the determination of IP band structure in terms of DFT quantities is provided.
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