Bilinear Constraints upon the Correlation Contribution to the Electron–Electron Repulsion Energy as a Functional of the One-Electron Reduced Density Matrix

2019 ◽  
Vol 15 (9) ◽  
pp. 4862-4872 ◽  
Author(s):  
Jerzy Cioslowski ◽  
Zsuzsanna É. Mihálka ◽  
Ágnes Szabados
Keyword(s):  
Density Matrix ◽  
Reduced Density Matrix ◽  
Repulsion Energy ◽  
Electron Repulsion ◽  
Bilinear Constraints ◽  
The One ◽  
Reduced Density

scholarly journals Insights into one-body density matrices using deep learning

2020 ◽  
Vol 224 ◽  
pp. 265-291 ◽  
Author(s):  
Jack Wetherell ◽  
Andrea Costamagna ◽  
Matteo Gatti ◽  
Lucia Reining
Keyword(s):  
Deep Learning ◽  
Density Matrix ◽  
Reduced Density Matrix ◽  
Body Density ◽  
Density Matrices ◽  
Learning Constraints ◽  
The One ◽  
Reduced Density

Deep-learning constraints of the one-body reduced density matrix from its compressibility to enable efficient determination of key observables.

scholarly journals Entropic entanglement criteria for fermion systems

2013 ◽  
Vol 32 (1) ◽  
Author(s):  
Claudia Zander
Keyword(s):  
Density Matrix ◽  
Reduced Density Matrix ◽  
Total System ◽  
Mixed States ◽  
Fermion Systems ◽  
The One ◽  
Reduced Density ◽  
Global Density

Entanglement criteria for general (pure or mixed) states of systems consisting of N identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system and the entropy of the one-particle, reduced density matrix.

On the Inference of the One-Particle Density Matrix from Position and Momentum-Space Form Factors

1993 ◽  
Vol 48 (1-2) ◽  
pp. 211-220
Author(s):  
Hartmut Schmider ◽  
Vedene H. Smith, Jr. ◽  
Wolf Weyrich
Keyword(s):  
Density Matrix ◽  
Electron Correlation ◽  
Momentum Space ◽  
Space Form ◽  
Particle Density ◽  
Form Factors ◽  
Reduced Density Matrix ◽  
Expectation Values ◽  
The One ◽  
Reduced Density

Abstract A modification of a recently developed method for the least-squares reconstruction of a one-particle reduced density matrix from experimentally accessible expectation values is applied to the test systems of atomic beryllium and neon. The improvement of the resulting matrices through inclusion of electron correlation is demonstrated. Their quality is judged by comparison of the moments of the position and momentum densities and of the spherically averaged density matrix in a suitable representation.

scholarly journals Inferring the one-electron reduced density matrix of molecular crystals from experimental data sets through semidefinite programming

2020 ◽  
Vol 76 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Benjamin De Bruyne ◽  
Jean-Michel Gillet
Keyword(s):  
Density Matrix ◽  
Semidefinite Programming ◽  
Ab Initio ◽  
Molecular Crystals ◽  
Reduced Density Matrix ◽  
Data Sets ◽  
Mathematical Framework ◽  
Reconstruction Methods ◽  
The One ◽  
Reduced Density

Constructing a quantum description of crystals from scattering experiments is of great significance to explain their macroscopic properties and to evaluate the pertinence of theoretical ab initio models. While reconstruction methods of the one-electron reduced density matrix have already been proposed, they are usually tied to strong assumptions that limit and may introduce bias in the model. The goal of this paper is to infer a one-electron reduced density matrix (1-RDM) with minimal assumptions. It has been found that the mathematical framework of semidefinite programming can achieve this goal. Additionally, it conveniently addresses the nontrivial constraints on the 1-RDM which were major hindrances for the existing models. The framework established in this work can be used as a reference to interpret experimental results. This method has been applied to the crystal of dry ice and provides very satisfactory results when compared with periodic ab initio calculations.

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