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Related Concept Videos

X-ray Crystallography02:18

X-ray Crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
Determination of Crystal Structures01:29

Determination of Crystal Structures

In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an organic...

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Updated: Jun 13, 2026

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
08:44

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

Published on: August 22, 2017

Characterizing the space of interatomic distance distribution functions consistent with solution scattering data.

Paritosh A Kavathekar1, Bruce A Craig, Alan M Friedman

  • 1Department of Computer Science, Dartmouth College, Hanover, NH 03755, USA.

Journal of Bioinformatics and Computational Biology
|April 20, 2010
PubMed
Summary
This summary is machine-generated.

Researchers developed a new method for analyzing molecular structures in solution using scattering data. This approach accepts multiple valid distance distribution curves, avoiding overfitting and improving structural analysis without crystallization.

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Analysis of SEC-SAXS data via EFA deconvolution and Scatter
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Analysis of SEC-SAXS data via EFA deconvolution and Scatter
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Area of Science:

  • Structural biology
  • Biophysics
  • Biochemistry

Background:

  • Neutron and X-ray scattering provide methods for studying macromolecular structures in solution without crystallization.
  • Elucidating three-dimensional structures from solution scattering data is challenging due to the ill-conditioned nature of the problem.
  • Overfitting observed scattering data is a risk when determining interatomic distance distributions, P(r).

Purpose of the Study:

  • To address the ill-posed problem of determining interatomic distance distributions (P(r)) from solution scattering data.
  • To develop a novel approach that avoids overfitting by accepting multiple consistent P(r) curves.
  • To enable more robust structural analysis of molecules in solution.

Main Methods:

  • Proposed a new approach by accepting multiple alternative P(r) curves instead of seeking a single best fit.
  • Applied linear constraints to ensure computed P(r) curves are consistent with experimental data, enforcing smoothness and probability distribution properties.
  • Utilized linear programming to sample the space of all consistent P(r) curves, described as a polytope.
  • Generated ensembles of P(r) curves from experimental and simulated scattering data.

Main Results:

  • Demonstrated an efficient method for generating diverse ensembles of realistic P(r) curves.
  • Successfully avoided the risk of overfitting by considering multiple valid solutions.
  • Showcased the approach's effectiveness on both experimental and simulated scattering data.
  • The method precisely describes the space of all consistent P(r) curves.

Conclusions:

  • The developed linear programming approach offers a robust way to analyze solution scattering data.
  • Accepting multiple P(r) curves enhances the reliability of structural elucidation without crystallization.
  • This method provides a more comprehensive understanding of macromolecular structures in their native solution state.