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

The theoretical and computational description of materials properties is a task utmost scientific technological importance. A first-principles electron-electron interactions poses an immense challenge that usually approached by converting the many-electron problem to effective one-electron problem. There are different ways obtain exact theory for system. An emergent method electron factorization (EEF) -- one branches approach many-body systems. In EEF, Schr\"odinger equation electron, in environment all other electrons, formulated. influence reflected potential ${v}^{\mathrm{H}}$, which represents energy environment, ${v}^{\mathrm{G}}$, has geometrical meaning. this paper, we focus on ${v}^{\mathrm{G}}$ study its detail. We investigate geometric origin as metric measuring change exemplify how translation scaling state explain shape homo- heteronuclear diatomic model Based close connection between EEF density functional theory, also use provide alternative interpretation Pauli orbital-free theory.