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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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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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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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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Updated: Dec 19, 2025

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Anharmonicity and Doping Melt the Charge Density Wave in Single-Layer TiSe2.

Jianqiang Sky Zhou1, Lorenzo Monacelli2, Raffaello Bianco3

  • 1Sorbonne Université, CNRS, Institut des Nanosciences de Paris, UMR7588, F-75252, Paris, France.

Nano Letters
|June 5, 2020
PubMed
Summary

In single-layer TiSe2, electron-hole interactions are weaker than expected, challenging theories of excitonic insulators. Anharmonicity and doping were found to melt the charge density wave, explaining experimental observations.

Keywords:
AnharmonicityCharge density wavesDensity functional theoryDichalcogenides

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • 2D Materials

Background:

  • Low-dimensional systems with vanishing band gaps are theoretically prone to exciton formation.
  • Excitonic insulators are predicted to be more stable in 2D than 3D due to increased exciton binding energy.

Purpose of the Study:

  • Investigate the role of electron-hole interaction and anharmonicity in single-layer TiSe2.
  • Re-evaluate the stability of excitonic insulators in 2D systems.
  • Explain the experimentally observed charge density wave behavior in single-layer TiSe2.

Main Methods:

  • Stochastic self-consistent harmonic approximation to calculate anharmonic phonon spectra.
  • Theoretical modeling of electron-hole interactions in 2D vs. 3D systems.
  • Analysis of doping effects on charge density wave stability.

Main Results:

  • Electron-hole exchange interaction in 2D TiSe2 is significantly smaller than in 3D.
  • Weak influence of electron-hole interaction on phonon spectra in single-layer TiSe2.
  • Calculated charge density wave transition temperatures (TCDW) of ~440 K (undoped) and ~364 K (doped).

Conclusions:

  • Anharmonicity and electron doping are key factors in melting the charge density wave in single-layer TiSe2.
  • Findings challenge conventional understanding of excitonic insulator stability in 2D.
  • The theoretical TCDW values align with experimental observations for supported single-layer TiSe2 samples.