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π Electron Effects on Chemical Shift: Overview01:27

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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.
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A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
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Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
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Enhanced stark effect in Dirac materials.

Thomas Garm Pedersen1, Horia D Cornean2

  • 1Department of Materials and Production, Aalborg University, DK-9220 Aalborg Øst, Denmark.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|August 16, 2022
PubMed
Summary
This summary is machine-generated.

The Stark effect in nanostructures is more sensitive to boundary conditions than previously thought. Using the Dirac equation, we show a significant enhancement in polarizability for honeycomb nanoribbons.

Keywords:
Dirac materialsPerturbation theoryStark effect

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Materials science

Background:

  • The Stark effect, the shifting of spectral lines under an electric field, is sensitive to boundary conditions in confined systems.
  • Infinite-barrier models (Schrödinger equation) predict weak polarizability due to vanishing wave functions at boundaries.
  • Dirac equation models offer less restrictive boundary conditions, potentially altering polarizability.

Purpose of the Study:

  • To investigate the Stark effect in nanostructures using the Dirac equation.
  • To quantify the polarizability enhancement in honeycomb-lattice armchair nanoribbons compared to Schrödinger-based models.
  • To derive exact analytical expressions for Dirac polarizability.

Main Methods:

  • Analytical derivation of exact Dirac polarizability for armchair nanoribbons.
  • Investigation of polarizability dependence on mass, momentum, and ribbon width.
  • Derivation of frequency-dependent dynamic polarizability.
  • Validation of analytical results using numerical atomistic models.

Main Results:

  • Demonstrated an order-of-magnitude enhancement in polarizability for nanoribbons described by the Dirac equation.
  • Obtained an exact Dirac polarizability formula applicable to arbitrary parameters.
  • Derived an exact expression for frequency-dependent dynamic polarizability.
  • Analytical and numerical results showed excellent agreement.

Conclusions:

  • The Dirac equation provides a more accurate description of the Stark effect in certain nanostructures, revealing significantly enhanced polarizability.
  • Boundary conditions play a crucial role, and the Dirac equation's less restrictive conditions lead to stronger electric field responses.
  • The derived analytical formulas offer valuable tools for predicting and designing nanodevices with tailored electronic properties.