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Inferring the one‐electron reduced density matrix of molecular crystals from experimental data sets through semidefinite programming
Author(s) -
De Bruyne Benjamin,
Gillet Jean-Michel
Publication year - 2020
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273319015870
Subject(s) - rdm , semidefinite programming , matrix (chemical analysis) , ab initio , density matrix , limit (mathematics) , statistical physics , crystal structure prediction , electron density , computer science , quantum , physics , electron , theoretical physics , quantum mechanics , mathematics , mathematical optimization , chemistry , molecule , mathematical analysis , computer network , chromatography
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.