论文标题
确切电子分解的几何潜力：含义，意义和应用
The Geometric Potential of the Exact Electron Factorization: Meaning, significance and application
论文作者
论文摘要
材料属性的理论和计算描述是最重要的科学和技术重要性的任务。电子电子相互作用的第一原则描述提出了巨大的挑战，通常通过将多电子问题转换为有效的单电子问题来应对。有不同的方法可以为多电子系统获得确切的单电子理论。紧急方法是确切的电子分解（EEF） - 多体系统的确切分解方法的分支之一。在EEF中，在所有其他电子的环境中，一个电子的schrödinger方程式被制定。环境的影响反映在代表环境能量的潜在$ v^{\ rm h} $中，并且在潜在的$ v^{\ rm g} $中，该$具有几何含义。在本文中，我们专注于$ v^{\ rm g} $，并详细研究其属性。我们研究了$ v^{\ rm g} $的几何起源，作为测量环境变化的度量，说明了环境状态的翻译和缩放是如何反映在$ v^{\ rm g} $中的，并解释了其对同性和异核模型模型系统的形状。基于EEF和密度功能理论之间的密切联系，我们还使用$ V^{\ rm g} $来为Pauli潜力提供了无轨道密度功能理论的替代解释。
The theoretical and computational description of materials properties is a task of utmost scientific and technological importance. A first-principles description of electron-electron interactions poses an immense challenge that is usually approached by converting the many-electron problem to an effective one-electron problem. There are different ways to obtain an exact one-electron theory for a many-electron system. An emergent method is the exact electron factorization (EEF) -- one of the branches of the Exact Factorization approach to many-body systems. In the EEF, the Schrödinger equation for one electron, in the environment of all other electrons, is formulated. The influence of the environment is reflected in the potential $v^{\rm H}$, which represents the energy of the environment, and in a potential $v^{\rm G}$, which has a geometrical meaning. In this paper, we focus on $v^{\rm G}$ and study its properties in detail. We investigate the geometric origin of $v^{\rm G}$ as a metric measuring the change of the environment, exemplify how translation and scaling of the state of the environment are reflected in $v^{\rm G}$, and explain its shape for homo- and heteronuclear diatomic model systems. Based on the close connection between the EEF and density functional theory, we also use $v^{\rm G}$ to provide an alternative interpretation to the Pauli potential in orbital-free density functional theory.
