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Symmetry01:26

Symmetry

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The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...
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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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Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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Gauss's Law: Spherical Symmetry01:26

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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 has a...
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Gauss's Law: Cylindrical Symmetry01:20

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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,...
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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Symmetry controlled excited state dynamics.

Max D J Waters1, Anders B Skov, Martin A B Larsen

  • 1Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark. theis@chem.ku.dk.

Physical Chemistry Chemical Physics : PCCP
|November 7, 2018
PubMed
Summary
This summary is machine-generated.

Structural symmetry significantly impacts internal conversion dynamics in cyclic amines. N-Methyl morpholine (NMM) preserves quantum coherence, unlike its isomer, due to a conical intersection facilitating non-Fermi-like decay.

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Area of Science:

  • Physical Chemistry
  • Chemical Physics
  • Quantum Dynamics

Background:

  • Internal conversion is a key non-radiative decay process in molecules.
  • Understanding symmetry effects on internal conversion is crucial for controlling molecular dynamics.
  • Femtosecond spectroscopy provides insights into ultrafast electronic processes.

Purpose of the Study:

  • To investigate the influence of structural symmetry on internal conversion dynamics.
  • To explore the role of conical intersections in ultrafast electronic transitions.
  • To elucidate the mechanism of coherence preservation in isomeric cyclic amines.

Main Methods:

  • Femtosecond velocity map imaging (VMI) experiments were performed on isomeric cyclic tertiary aliphatic amines.
  • Analysis of potential energy surfaces and normal modes of vibration.
  • Comparison of dynamics between N-Methyl morpholine (NMM) and its isomer.

Main Results:

  • Preserved quantum coherence was observed in NMM, attributed to symmetry-allowed pathways.
  • Repositioning an atom (oxygen) in the ring disrupted coherence, leading to faster internal conversion.
  • A conical intersection between 3p and 3s Rydberg states in NMM facilitates non-Fermi-like decay dynamics.

Conclusions:

  • Molecular symmetry profoundly affects the preservation of quantum coherence during internal conversion.
  • Atom substitution can dramatically alter ultrafast dynamics by modifying potential energy surfaces and conical intersection geometries.
  • The findings highlight the importance of symmetry in controlling energy dissipation pathways in molecules.