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Related Concept Videos

Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Gauss's Law01:07

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
Gauss's Law in Dielectrics01:17

Gauss's Law in Dielectrics

Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...

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Equibiaxial Stretching Device for High Magnification Live-Cell Confocal Fluorescence Microscopy
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Radial gausslets.

Steven R White1

  • 1Department of Physics and Astronomy, University of California, Irvine, Irvine, California 92697, USA.

The Journal of Chemical Physics
|June 1, 2026
PubMed
Summary
This summary is machine-generated.

Researchers developed new radial gausslets for atomic basis sets, improving computational efficiency for electronic structure calculations. This compact basis set offers diagonal electron-electron interaction terms, enhancing accuracy in quantum chemistry simulations.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Atomic Physics

Background:

  • Gausslets offer a unique basis set for electronic structure, enabling two-index/diagonal electron-electron interactions.
  • Traditional gausslets are limited to Cartesian coordinates due to their one-dimensional origin, restricting their application in three-dimensional atomic systems.

Purpose of the Study:

  • To generalize the gausslet construction to the radial coordinate in three dimensions for atomic basis sets.
  • To create a compact radial basis with diagonal interaction terms for efficient electronic structure calculations.

Main Methods:

  • Developed a novel construction for radial gausslets in three dimensions.
  • Applied Hartree-Fock and exact diagonalization methods to atomic systems using the new radial basis set.

Main Results:

  • Successfully generalized gausslets to radial coordinates, creating a compact basis set.
  • The new radial gausslets exhibit diagonal electron-electron interaction terms.
  • Demonstrated the accuracy of the radial gausslet construction in atomic system calculations.

Conclusions:

  • The generalized radial gausslets provide a compact and efficient basis set for electronic structure calculations.
  • This advancement overcomes the coordinate limitations of previous gausslet formulations.
  • The method shows promise for accurate quantum chemistry simulations of atomic systems.