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Related Concept Videos

Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

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Crystal Field Theory
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.
CFT focuses on...
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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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Valence Bond Theory

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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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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.
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Molecular Orbital Energy Diagrams
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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Updated: Dec 15, 2025

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
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Two-dimensional optomechanical crystal cavity with high quantum cooperativity.

Hengjiang Ren1,2,3, Matthew H Matheny1,2,3, Gregory S MacCabe1,2,3

  • 1Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA, 91125, USA.

Nature Communications
|July 8, 2020
PubMed
Summary
This summary is machine-generated.

We developed a novel 2D optomechanical crystal resonator for quantum applications. This device overcomes challenges in operating nanoscale systems at ultralow temperatures, enabling quantum cooperativity greater than 1.

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Related Experiment Videos

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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Area of Science:

  • Quantum Information Science
  • Solid-State Physics
  • Nanotechnology

Background:

  • Optomechanical systems are crucial for quantum information processing and sensing.
  • Operating nanoscale devices at millikelvin temperatures is challenging due to thermal and optical limitations.

Purpose of the Study:

  • To present a two-dimensional optomechanical crystal resonator for quantum applications.
  • To achieve high quantum cooperativity at ultralow temperatures.

Main Methods:

  • Utilized a two-dimensional phononic bandgap structure to host the optomechanical cavity.
  • Isolated the acoustic mode within the bandgap while enabling heat removal via external phonon modes.

Main Results:

  • Achieved large cooperativity (C) and low effective bath occupancy (nb).
  • Demonstrated quantum cooperativity (Ceff) greater than 1 under continuous-wave optical driving.
  • Successfully operated nanoscale optomechanical devices at ultralow temperatures.

Conclusions:

  • The developed resonator overcomes thermal challenges for millikelvin operation.
  • This work enables quantum-coherent optomechanical interactions for quantum transducers.
  • Paves the way for interfacing superconducting circuits with optical photons.