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Molecular Orbital Theory I02:35

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The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
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The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
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According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
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Photonic Molecule Approach to Multiorbital Topology.

Maxim Mazanov1, Diego Román-Cortés2, Gabriel Cáceres-Aravena2,3

  • 1School of Physics and Engineering, ITMO University, Saint Petersburg 197101, Russia.

Nano Letters
|April 4, 2024
PubMed
Summary

Engineered photonic systems exhibit novel topological states protected by a Z3 invariant. This research demonstrates control over topological transitions in coupled waveguide arrays, paving the way for new photonic topological phases.

Keywords:
femtosecond laser writinginterorbital couplingphotonic orbitalstopological edge statestopological photonics

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Area of Science:

  • Photonics
  • Condensed Matter Physics
  • Topology

Background:

  • Topology offers powerful methods for controlling wave propagation and localization.
  • Engineered photonic degeneracies mimic electron spin states, enabling novel condensed matter-like phenomena.
  • Photonic molecules, clusters of coupled waveguides, are promising platforms for exploring topological physics.

Purpose of the Study:

  • To engineer and investigate topological states in optical waveguide arrays.
  • To explore the role of engineered degeneracies and photonic molecules in creating topological phenomena.
  • To understand topological transitions driven by lattice geometry and excitation wavelength.

Main Methods:

  • Utilizing femtosecond laser-written waveguide arrays in the optical range.
  • Implementing the photonic molecule concept for strong waveguide coupling.
  • Analyzing topological modes protected by a Z3 invariant.

Main Results:

  • Observation of unconventional topological modes protected by a Z3 invariant.
  • Demonstration of topological transitions influenced by interorbital coupling and geometric dimerization.
  • Tracking of multiple topological transitions by varying lattice spacings and excitation wavelength.

Conclusions:

  • Engineered photonic degeneracies provide a route to novel topological phases.
  • The Z3 invariant governs unique topological properties in coupled waveguide systems.
  • This work opens new avenues for designing advanced photonic topological states and devices.