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Related Concept Videos

Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

1.7K
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...
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Gauss's Law01:07

Gauss's Law

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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.
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Line, Surface, and Volume Integrals01:15

Line, Surface, and Volume Integrals

2.3K
A line integral for a vector field is defined as the integral of the dot product of a vector function with an infinitesimal displacement vector along a prescribed path. If the prescribed path is closed, the integrals reduce to a closed-line integral. The closed-contour integral of the vector field is referred to in terms of the circulation of the vector field around the closed path. A vector with zero circulation around every closed path is called a conservative field, while one with non-zero...
2.3K
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

7.9K
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...
7.9K
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

7.4K
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...
7.4K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

7.5K
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,...
7.5K

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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GBasis: A Python library for evaluating functions, functionals, and integrals expressed with Gaussian basis

Taewon David Kim1, Leila Pujal2, Michelle Richer2

  • 1Department of Chemistry & Chemical Biology, McMaster University, Hamilton, Ontario L8S-4L8, Canada.

The Journal of Chemical Physics
|July 30, 2024
PubMed
Summary
This summary is machine-generated.

GBasis is a new Python library for quantum chemistry computations using Gaussian basis functions. It offers features for evaluating molecular properties and integrals, with a focus on usability and sustainable development.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Molecular Modeling

Background:

  • Gaussian basis functions are fundamental in quantum chemistry for representing atomic and molecular orbitals.
  • Efficient computation of molecular properties and integrals is crucial for advancing theoretical chemistry.
  • Existing tools may lack flexibility or comprehensive features for advanced calculations.

Purpose of the Study:

  • To introduce GBasis, a free and open-source Python library for molecular property computations.
  • To provide a flexible and extensible tool for evaluating functions and integrals based on Gaussian basis sets.
  • To facilitate high-performance computations through an interface with the Libcint C package.

Main Methods:

  • Development of a Python library utilizing Gaussian basis functions.
  • Implementation of functions for evaluating molecular orbitals, electron density, and density matrices.
  • Computation of overlap, one-electron, and two-electron integrals.
  • Inclusion of arbitrary-order derivative calculations and various Coulomb interactions.
  • Provision of a Python interface to the high-performance Libcint C package.

Main Results:

  • GBasis enables evaluation of arbitrary-order derivatives of density matrices.
  • The library supports a wide range of screened Coulomb interactions.
  • GBasis facilitates the evaluation of overlap integrals for numerous Gaussians in high dimensions.
  • A seamless Python interface to Libcint ensures high performance when needed.

Conclusions:

  • GBasis is a versatile and user-friendly Python library for quantum chemistry.
  • It offers advanced features for molecular property computations and integral evaluations.
  • The library adheres to sustainable software development principles, ensuring maintainability and extensibility.