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Related Concept Videos

π Electron Effects on Chemical Shift: Overview01:27

π Electron Effects on Chemical Shift: Overview

An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0, resulting in...
π Electron Effects on Chemical Shift: Aromatic and Antiaromatic Compounds01:14

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In aromatic compounds, such as benzene, the circulation of (4n + 2) π-electrons sets up a diamagnetic or diatropic ring current around the perimeter of the molecule. This current induces a magnetic field that opposes the external field inside the ring and reinforces it on the outside. The protons in benzene are deshielded and exhibit high chemical shifts in the range 6.5–8.5 ppm. The shielding effect at the center of the ring is evident in complex aromatic molecules, such as annulenes. In...
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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
Molecular Spectroscopy: Absorption and Emission01:14

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Molecules possess discrete energy levels called quantum states. Unlike atoms, which have simpler energy levels, molecules possess additional rotational and vibrational energy levels. Each energy level is separated by an energy gap, with the gaps between adjacent electronic, vibrational, and rotational levels varying significantly. The three types of energy levels in a diatomic molecule are shown in Figure 1.

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Related Experiment Video

Updated: Jun 24, 2026

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots
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Size-dependent two-photon absorption in circular graphene quantum dots.

Xiaobo Feng, Xin Li, Zhisong Li

    Optics Express
    |February 25, 2016
    PubMed
    Summary
    This summary is machine-generated.

    We theoretically investigated size-dependent two-photon absorption (TPA) in circular graphene quantum dots (GQDs). Intraband transitions significantly contribute to TPA, and TPA peaks are tunable by GQD size.

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    Area of Science:

    • Condensed matter physics
    • Quantum mechanics
    • Materials science

    Background:

    • Graphene quantum dots (GQDs) exhibit unique electronic and optical properties.
    • Two-photon absorption (TPA) is a crucial nonlinear optical process with applications in various fields.
    • Understanding the size-dependence of TPA in GQDs is essential for their technological applications.

    Purpose of the Study:

    • To theoretically investigate the size-dependence of two-photon absorption (TPA) in circular graphene quantum dots (GQDs).
    • To derive analytical expressions for the TPA coefficient and transition selection rules.
    • To analyze the contribution of intraband and interband transitions to TPA.

    Main Methods:

    • Solving the Dirac-Weyl equation analytically under the infinite-mass boundary condition to obtain electronic energy states.
    • Deriving analytical expressions for the TPA coefficient considering arbitrary size-distributions.
    • Analyzing the transition selection rules for TPA in GQDs.

    Main Results:

    • Intraband transitions within the conduction and valence bands contribute significantly more to TPA than interband transitions.
    • The energy spectrum and TPA peak positions are tunable by altering the size of the GQDs.
    • Analytical expressions for TPA coefficient and selection rules were successfully derived.

    Conclusions:

    • The size of circular graphene quantum dots plays a critical role in tuning their two-photon absorption properties.
    • Intraband transitions are dominant contributors to TPA in GQDs, offering potential for optical applications.
    • Theoretical insights provide a foundation for designing GQD-based optoelectronic devices.