Geometric potential of the exact electron factorization: Meaning, significance, and application

• Published in: Physical review research Vol. 5; no. 1; p. 013016
• Main Authors: Kocák, Jakub, Kraisler, Eli, Schild, Axel
• Format: Journal Article
• Language: English
• Published: American Physical Society 01.01.2023
• ISSN: 2643-1564; 2643-1564
• DOI: 10.1103/PhysRevResearch.5.013016

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^{H}, which represents the energy of the environment, and in a potential v^{G}, which has a geometrical meaning. In this paper, we focus on v^{G} and study its properties in detail. We investigate the geometric origin of v^{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^{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^{G} to provide an alternative interpretation to the Pauli potential in orbital-free density functional theory.