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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...
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The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
X-ray Diffraction of Biological Samples01:10

X-ray Diffraction of Biological Samples

X-ray diffraction or XRD is an analytical tool that utilizes X-rays to study ordered structures such as crystalline organic and inorganic samples, polycrystalline materials, proteins, carbohydrates, and drugs.
According to Bragg's law, when X-rays strike the sample positioned on a stage, the rays are  scattered by the electron clouds around the sample atoms. The  X-ray diffraction or scattering is caused by constructive interference of the X-ray waves that reflect off the internal crystal...
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...
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...

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Modeling electron density distributions from X-ray diffraction to derive optical properties: constrained wavefunction

Daniel D Hickstein1, Jacqueline M Cole, Michael J Turner

  • 1Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom.

The Journal of Chemical Physics
|August 17, 2013
PubMed
Summary
This summary is machine-generated.

X-ray constrained wavefunction refinement accurately predicts optical properties from X-ray diffraction data. This method, superior to multipole refinement, enables the design of advanced optical materials.

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Area of Science:

  • Materials Science
  • Crystallography
  • Computational Chemistry

Background:

  • Designing advanced optical materials requires linking molecular structure to solid-state optical properties.
  • X-ray diffraction provides crucial structural data, but electron density alone is insufficient for calculating nonlinear optical properties.
  • Multipole refinement has been standard for electron density determination, but has limitations.

Purpose of the Study:

  • To compare multipole refinement with X-ray constrained wavefunction refinement for analyzing nonlinear optical materials.
  • To assess the reliability of calculating optical properties from experimentally derived wavefunctions.
  • To demonstrate the potential of X-ray constrained wavefunction refinement for molecular engineering of optical materials.

Main Methods:

  • Applied both multipole refinement and X-ray constrained wavefunction refinement to four molecules with nonlinear optical properties.
  • Analyzed electron density distributions and wavefunctions generated by each method.
  • Calculated molecular dipole moment, polarizability, hyperpolarizability, and refractive index from experimental wavefunctions.

Main Results:

  • Both methods yielded comparable figures of merit and similar electron densities.
  • X-ray constrained wavefunction refinement's electron density accuracy depends on nuclear positions.
  • Using Hirshfeld atom refinement coordinates improved wavefunction accuracy in the X-ray constrained wavefunction method.
  • Experimentally derived optical properties closely matched ab initio calculations.

Conclusions:

  • Experimental wavefunctions can be reliably obtained from X-ray diffraction data.
  • Optical properties can be accurately calculated from these experimental wavefunctions.
  • X-ray constrained wavefunction refinement facilitates the development of custom optical materials.