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Recent advances in quantum crystallography have shown that, beyond conventional charge density refinement, a one‐electron reduced density matrix (1‐RDM) satisfying N‐representability conditions can be reconstructed using jointly experimental X‐ray structure factors and directional Compton profiles (DCP) through semidefinite programming. So far, such reconstruction methods for 1‐RDM, not constrained to idempotency, have been tested only on a toy model system (CO2). In this work, a new method is assessed on crystalline urea [CO(NH2)2] using static (0 K) and dynamic (50 K) artificial experimental data. An improved model, including symmetry constraints and frozen core‐electron contribution, is introduced to better handle the increasing system complexity. Reconstructed 1‐RDMs, deformation densities and DCP anisotropy are analysed, and it is demonstrated that the changes in the model significantly improve the reconstruction quality, even when there is insufficient information and data corruption. The robustness of the model and the strategy are thus shown to be well adapted to address the reconstruction problem from actual experimental scattering data. [ABSTRACT FROM AUTHOR]

This article retraces different methods that have been explored to account for the atomic thermal motion in the reconstruction of one‐electron reduced density matrices from experimental X‐ray structure factors (XSF) and directional Compton profiles (DCP). Attention has been paid to propose the simplest possible model, which obeys the necessary N‐representability conditions, while accurately reproducing all available experimental data. The deconvolution of thermal effects makes it possible to obtain an experimental static density matrix, which can directly be compared with theoretical 1‐RDM (reduced density matrix). It is found that above a 1% statistical noise level, the role played by Compton scattering data becomes negligible and no accurate 1‐RDM is reachable. Since no thermal 1‐RDM is available as a reference, the quality of an experimentally derived temperature‐dependent matrix is difficult to assess. However, the accuracy of the obtained static 1‐RDM, through the performance of the refined observables, is strong evidence that the Semi‐Definite Programming method is robust and well adapted to the reconstruction of an experimental dynamical 1‐RDM. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The spectrum of the undulator radiation of beamline P01 at Petra III has been measured after passing a multiple reflection channel-cut polarimeter. Odd and even harmonics up to the 15th order, as well as Compton peaks which were produced by the high harmonics in the spectrum, could been measured. These additional contributions can have a tremendous influence on the performance of the polarimeter and have to be taken into account for further polarimeter designs. [ABSTRACT FROM AUTHOR]