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

Area of Science:

• Quantum Crystallography
• Materials Science
• Computational Chemistry

Background:

• Conventional charge density refinement has limitations.
• Reconstructing a one-electron reduced density matrix (1-RDM) offers a more detailed electronic structure description.
• Previous 1-RDM reconstruction methods were limited to simple systems and lacked robustness.

Purpose of the Study:

• To develop and assess a novel method for reconstructing the 1-RDM of crystalline urea.
• To improve the accuracy and robustness of 1-RDM reconstruction using experimental data.
• To investigate the impact of symmetry constraints and frozen core approximations on reconstruction quality.

Main Methods:

• Utilized semidefinite programming to reconstruct the 1-RDM from X-ray structure factors and directional Compton profiles (DCP).
• Applied an improved model incorporating symmetry constraints and frozen core-electron contributions.
• Tested the method using static (0 K) and dynamic (50 K) artificial experimental data for crystalline urea.

Main Results:

• The improved model significantly enhanced the quality of reconstructed 1-RDMs, deformation densities, and DCP anisotropy.
• The method demonstrated robustness and accuracy even with insufficient information and data corruption.
• Successful reconstruction of the 1-RDM for a more complex system (urea) compared to previous studies (CO2).

Conclusions:

• The developed method and strategy are well-suited for reconstructing 1-RDMs from experimental scattering data.
• The incorporation of symmetry and frozen core approximations is crucial for handling complex systems.
• This approach advances the application of quantum crystallography for detailed electronic structure analysis.