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Experimental reconstruction of one-electron reduced density matrices for molecular crystals

Sizhuo Yu

Published Jun 8, 2026• 0 citations
OpenAlex

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

Benjamin De Bruyne, Jean‐Michel Gillet

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.

Acta Crystallographica Section A Foundations and Advances•Dec 9, 2019•13 citations

Inferring crystal electronic properties from experimental data sets through Semidefinite Programming

Benjamin De Bruyne, Jean‐Michel Gillet

Constructing a quantum description of crystals from scattering experiments is of paramount importance 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. We have 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.

arXiv:1904.08757•Apr 11, 2019•0 citations
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.
Constructing a quantum description of crystals from scattering experiments is of paramount importance 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. We have 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.