几何势及精确电子因式分解与密度泛函理论的关系
On the Geometric Potential and the Relationship between the Exact Electron Factorization and Density Functional Theory
摘要：
对于多电子体系，精确单电子理论有不同的方法，精确电子因式分解（EEF）就是其中之一。在EEF中，构造了一个电子在其他电子环境中的薛定谔方程。环境提供了出现在这个方程中的势：一个标量势$v^{\rm H}$代表环境的能量，另一个标量势$v^{\rm G}$以及一个具有几何意义的矢量势。通过用无相互作用的Kohn-Sham（KS）体系代替相互作用的多电子体系，我们展示了EEF与密度泛函理论的关系，并解释了Hartree交换关联势和Pauli势.特别是，我们表明，从EEF的观点，泡利势并不代表费米子和玻色子之间的差异非相互作用系统，但它对应于$v^{\rm G}$和部分$v^{\rm H}$（费米子）KS系统。然后，我们详细研究了$v^{\rm G}$的含义：它的几何起源作为衡量环境变化的度量。此外，它的行为的一个简单的模型的同质和heteronucler双原子的研究和解释的帮助下，一个两态模型。通过这种方式，我们提供了一个物理解释的EEF和DFT中出现的单电子势。
英文摘要：
There are different ways to obtain an exact one-electron theory for a many-electron system, and the exact electron factorization (EEF) is one of them. In the EEF, the Schrödinger equation for one electron in the environment of other electrons is constructed. The environment provides the potentials that appear in this equation: A scalar potential $v^{\rm H}$ representing the energy of the environment and another scalar potential $v^{\rm G}$ as well as a vector potential that have geometric meaning. By replacing the interacting many-electron system with the non-interacting Kohn-Sham (KS) system, we show how the EEF is related to density functional theory (DFT) and we interpret the Hartree-exchange-correlation potential as well as the Pauli potential in terms of the EEF. In particular, we show that from the EEF viewpoint, the Pauli potential does not represent the difference between a fermionic and a bosonic non-interacting system, but that it corresponds to $v^{\rm G}$ and partly to $v^{\rm H}$ for the (fermionic) KS system. We then study the meaning of $v^{\rm G}$ in detail: Its geometric origin as a metric measuring the change of the environment is presented. Additionally, its behavior for a simple model of a homo- and heteronucler diatomic is investigated and interpreted with the help of a two-state model. In this way, we provide a physical interpretation for the one-electron potentials that appear in the EEF and in DFT.
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