One-Electron Density Matrices and Related Observables

Weyrich, Wolf

doi:10.1007/978-3-642-61478-1_14

Cited by 8 publications

(3 citation statements)

References 53 publications

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“…In previous studies, 17,18 the position and momentum spin densities were reconstructed separately using experimental magnetic structure factors (MSFs) and magnetic Compton profiles (MCPs), respectively. In the present work, the spin electron distributions in both spaces, i.e., the entire spin-resolved one-electron-reduced density matrix [29][30][31][32][33][34][35][36] (1-SRDM) elements, are simultaneously reconstructed from the theoretical MSFs and MCPs using the joint refinement model. 37 The aim of the present work is therefore to (1) reproduce the magnetic and electronic properties of a YTiO 3 crystal from a simple molecular model with limited basis sets and (2) assess the added value of the combination of MSFs and MCPs to reconstruct the entire 1-SRDM.…”

Section: Introductionmentioning

confidence: 99%

Joint refinement model for the spin resolved one-electron reduced density matrix of YTiO3 using magnetic structure factors and magnetic Compton profiles data

Gueddida

Zhu

Kibalin

et al. 2018

The Journal of Chemical Physics

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In this paper, we propose a simple cluster model with limited basis sets to reproduce the unpaired electron distributions in a YTiO ferromagnetic crystal. The spin-resolved one-electron-reduced density matrix is reconstructed simultaneously from theoretical magnetic structure factors and directional magnetic Compton profiles using our joint refinement algorithm. This algorithm is guided by the rescaling of basis functions and the adjustment of the spin population matrix. The resulting spin electron density in both position and momentum spaces from the joint refinement model is in agreement with theoretical and experimental results. Benefits brought from magnetic Compton profiles to the entire spin density matrix are illustrated. We studied the magnetic properties of the YTiO crystal along the Ti-O-Ti bonding. We found that the basis functions are mostly rescaled by means of magnetic Compton profiles, while the molecular occupation numbers are mainly modified by the magnetic structure factors.

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Section: Introductionmentioning

confidence: 99%

Joint refinement model for the spin resolved one-electron reduced density matrix of YTiO3 using magnetic structure factors and magnetic Compton profiles data

Gueddida

Zhu

Kibalin

et al. 2018

The Journal of Chemical Physics

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“…Furthermore, the 1-RDM encapsulates momentum space information through a 6D Fourier-Dirac transform (Weyrich, 1996),…”

Section: -Rdm Reconstruction Using Least-squares Fittingmentioning

confidence: 99%

N-representable one-electron reduced density matrix reconstruction with frozen core electrons

Yu,

Gillet

2024

Acta Cryst Sect A

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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.

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“…Quantum Crystallography has its roots in the seminal work of Clinton and Massa, in the sense of constraining the refinement of experimentally‐determined crystallographic X‐ray structure factors to quantum mechanical requirements such as N ‐representability and the generation of density matrices or of wavefunctions . The term itself, “Quantum Crystallography”, has been coined in 1995 by Lulu Huang, Lou Massa, and Jerome Karle who fleshed it out with extensive applications subsequently .…”

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confidence: 99%

Quantum crystallography: From the intersection to the union of crystallography and quantum mechanics

Matta

2018

J Comput Chem

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One-Electron Density Matrices and Related Observables

Cited by 8 publications

References 53 publications

Joint refinement model for the spin resolved one-electron reduced density matrix of YTiO3 using magnetic structure factors and magnetic Compton profiles data

Joint refinement model for the spin resolved one-electron reduced density matrix of YTiO3 using magnetic structure factors and magnetic Compton profiles data

N-representable one-electron reduced density matrix reconstruction with frozen core electrons

Quantum crystallography: From the intersection to the union of crystallography and quantum mechanics

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