Computational Environment For Many Electron Systems

Abstract The computational treatment of many‐electron systems capable of exchanging electrons and nuclei with the environment represents one of the outermost frontiers in simulation methodology. The exchanging process occurs in a large variety of natural and artificially induced phenomena which are of major relevance to several leading fields of academic research and modern technology. In this Progress Report, an overview of problems in current materials science and chemical physics is presented where the corresponding computational approaches require the concept of an electronic system with open boundaries. Quantum and quantum/classical computational techniques treat the exchange of electrons with the environment at different computational efficiency, conceptual rigorousness, and numerical accuracy. The overall emerging picture shows a rich availability of interesting ideas, some with a higher weight on the pragmatic side, others with higher weight on the conceptual side; possible combinations, in perspective, may push the field much beyond its current frontiers.Abstract The computational treatment of many‐electron systems capable of exchanging electrons and nuclei with the environment represents one of the outermost frontiers in simulation methodology. The exchanging process occurs in a large variety of natural and artificially induced phenomena which are of major relevance to several leading fields of academic research and modern technology. In this Progress Report, an overview of problems in current materials science and chemical physics is presented where the corresponding computational approaches require the concept of an electronic system with open boundaries. Quantum and quantum/classical computational techniques treat the exchange of electrons with the environment at different computational efficiency, conceptual rigorousness, and numerical accuracy. The overall emerging picture shows a rich availability of interesting ideas, some with a higher weight on the pragmatic side, others with higher weight on the conceptual side; possible combinations, in perspective, may push the field much beyond its current frontiers.

arXiv:1902.07523Advanced Theory and SimulationsAug 12, 201815 citations

Numerical simulation of many electron systems

Robert L. Sugar

Nuclear Physics B - Proceedings SupplementsApr 1, 19881 citation

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

Jakub Kocák, Eli Kraisler, Axel Schild

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.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.

arXiv:2010.14885Oct 28, 20202 citations

Many-electron systems

Springer eBooksApr 6, 20080 citations

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

Jakub Kocák, Eli Kraisler, Axel Schild

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 Schr\"odinger equation for one electron, in the environment of all other electrons, is formulated. The influence of the environment is reflected in the potential ${v}^{\mathrm{H}}$ , which represents the energy of the environment, and in a potential ${v}^{\mathrm{G}}$ , which has a geometrical meaning. In this paper, we focus on ${v}^{\mathrm{G}}$ and study its properties in detail. We investigate the geometric origin of ${v}^{\mathrm{G}}$ as a metric measuring the change of the environment, exemplify how translation and scaling of the state of the environment are reflected in ${v}^{\mathrm{G}}$ , 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 ${v}^{\mathrm{G}}$ to provide an alternative interpretation to the Pauli potential in orbital-free density functional theory.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 Schr\"odinger equation for one electron, in the environment of all other electrons, is formulated. The influence of the environment is reflected in the potential ${v}^{\mathrm{H}}$, which represents the energy of the environment, and in a potential ${v}^{\mathrm{G}}$, which has a geometrical meaning. In this paper, we focus on ${v}^{\mathrm{G}}$ and study its properties in detail. We investigate the geometric origin of ${v}^{\mathrm{G}}$ as a metric measuring the change of the environment, exemplify how translation and scaling of the state of the environment are reflected in ${v}^{\mathrm{G}}$, 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 ${v}^{\mathrm{G}}$ to provide an alternative interpretation to the Pauli potential in orbital-free density functional theory.

Physical Review ResearchJan 17, 202310 citations

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.

{v}^{\mathrm{H}}