Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Reduced Mass Coordinates: Isolated Two-body Problem01:12

Reduced Mass Coordinates: Isolated Two-body Problem

1.3K
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
1.3K
Electronic Structure of Atoms02:28

Electronic Structure of Atoms

21.3K

An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
21.3K
Electron Configuration of Multielectron Atoms03:26

Electron Configuration of Multielectron Atoms

40.8K
The alkali metal sodium (atomic number 11) has one more electron than the neon atom. This electron must go into the lowest-energy subshell available, the 3s orbital, giving a 1s22s22p63s1 configuration. The electrons occupying the outermost shell orbital(s) (highest value of n) are called valence electrons, and those occupying the inner shell orbitals are called core electrons. Since the core electron shells correspond to noble gas electron configurations, we can abbreviate electron...
40.8K
Electron Orbital Model01:18

Electron Orbital Model

67.7K
Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...
67.7K
Electron Microscope Tomography and Single-particle Reconstruction01:07

Electron Microscope Tomography and Single-particle Reconstruction

2.4K
Transmission electron microscopy (TEM) can be used to determine the 3D structure of biological samples with the help of techniques such as electron microscope tomography and single-particle reconstruction. While single-particle reconstruction can examine macromolecules and macromolecular complexes in vitro conditions only, tomography permits the study of cell components or small cells in vivo.
Electron Tomography
Electron tomography can be performed either in TEM or STEM (scanning transmission...
2.4K
Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

11.4K
The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
 
where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient...
11.4K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Pierre J. Becker (1942-2024).

Acta crystallographica. Section A, Foundations and advances·2025
Same author

Intrusion of quantum crystallography into classical lands.

Acta crystallographica Section B, Structural science, crystal engineering and materials·2025
Same author

5-Fluoro-1,2,3-triazole motif in peptides and its electronic properties.

Organic & biomolecular chemistry·2022
See all related articles

Related Experiment Video

Updated: Jun 30, 2025

Author Spotlight: Optimizing Cryo-EM Analysis with CryoSieve for Enhanced Particle Selection Efficiency
06:41

Author Spotlight: Optimizing Cryo-EM Analysis with CryoSieve for Enhanced Particle Selection Efficiency

Published on: May 10, 2024

1.6K

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

Sizhuo Yu1, Jean Michel Gillet1

  • 1CentraleSupélec, CNRS, Laboratoire SPMS, Université Paris-Saclay, F91190 Gif-sur-Yvette, France.

Acta Crystallographica. Section A, Foundations and Advances
|March 21, 2024
PubMed
Summary

Researchers reconstructed a one-electron reduced density matrix (1-RDM) for crystalline urea using X-ray data. This quantum crystallography method improves accuracy, even with incomplete or corrupted experimental data.

Keywords:
Compton scatteringX-ray diffractionquantum crystallographyreduced density matrix

More Related Videos

Single Particle Cryo-Electron Microscopy: From Sample to Structure
11:52

Single Particle Cryo-Electron Microscopy: From Sample to Structure

Published on: May 29, 2021

8.5K
Structure of HIV-1 Capsid Assemblies by Cryo-electron Microscopy and Iterative Helical Real-space Reconstruction
12:38

Structure of HIV-1 Capsid Assemblies by Cryo-electron Microscopy and Iterative Helical Real-space Reconstruction

Published on: August 9, 2011

17.4K

Related Experiment Videos

Last Updated: Jun 30, 2025

Author Spotlight: Optimizing Cryo-EM Analysis with CryoSieve for Enhanced Particle Selection Efficiency
06:41

Author Spotlight: Optimizing Cryo-EM Analysis with CryoSieve for Enhanced Particle Selection Efficiency

Published on: May 10, 2024

1.6K
Single Particle Cryo-Electron Microscopy: From Sample to Structure
11:52

Single Particle Cryo-Electron Microscopy: From Sample to Structure

Published on: May 29, 2021

8.5K
Structure of HIV-1 Capsid Assemblies by Cryo-electron Microscopy and Iterative Helical Real-space Reconstruction
12:38

Structure of HIV-1 Capsid Assemblies by Cryo-electron Microscopy and Iterative Helical Real-space Reconstruction

Published on: August 9, 2011

17.4K

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.