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Gauss's Law: Planar Symmetry01:27

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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...
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The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
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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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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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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...
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Material-Specific Optimization of Gaussian Basis Sets against Plane Wave Data.

Yanbing Zhou1, Emanuel Gull2, Dominika Zgid1

  • 1Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States.

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|August 27, 2021
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Summary
This summary is machine-generated.

This study introduces a material-specific Gaussian basis optimization for solids, improving simulation accuracy by tailoring basis sets to material properties. This method enhances total and band energies compared to standard plane wave calculations.

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Area of Science:

  • Computational materials science
  • Quantum chemistry
  • Solid-state physics

Background:

  • Elemental basis sets in periodic systems can lack material specificity, leading to simulation inaccuracies.
  • Vastly different physical and chemical properties arise from different spatial arrangements of elements.
  • Existing methods may not adequately account for material-specific electronic structures.

Purpose of the Study:

  • To develop a material-specific Gaussian basis optimization scheme for solids.
  • To enhance the accuracy of electronic structure calculations in periodic systems.
  • To address the limitations of element-independent basis sets.

Main Methods:

  • A novel optimization scheme that minimizes total energy and optimizes band energies simultaneously.
  • Utilizes reference plane wave calculations for band energy optimization.
  • Incorporates a condition number check for the overlap matrix.

Main Results:

  • Generated material-specific Gaussian basis sets for diamond, graphite, and silicon.
  • Demonstrated improved accuracy compared to existing basis sets for these materials.
  • Successfully applied the scheme to existing basis sets for MoS2 and NiO, yielding enhanced results.

Conclusions:

  • The proposed material-specific Gaussian basis optimization scheme significantly improves simulation accuracy for solids.
  • This method provides a more reliable approach for electronic structure calculations in periodic materials.
  • The optimization scheme offers a pathway to more precise predictions of material properties.