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Hybridization of Atomic Orbitals II03:35

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sp3d and sp3d 2 Hybridization
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Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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Valence Bond Theory and Hybridized Orbitals02:38

Valence Bond Theory and Hybridized Orbitals

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According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...
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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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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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Molecular Orbital Theory II03:51

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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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Updated: Jan 18, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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双混合密度功能理论与基于密度的基数组校正.

Aurore Znaïda1, Julien Toulouse1

  • 1Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France.

The Journal of chemical physics
|September 8, 2025
PubMed
概括
此摘要是机器生成的。

我们提出了一个理论,用于加快双混合近似的基础收,使用基于密度的基础集校正 (DBBSC) 方法. 我们的研究结果表明,DBBSC有效地提高了分子计算的准确性.

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科学领域:

  • 量子化学 是一个量子化学.
  • 计算化学的计算化学
  • 理论化学 理论化学

背景情况:

  • 双混合近似在量子化学中广泛用于准确的分子性质预测.
  • 基础集合的收,即独立于所选基础集合的结果的过程,对于可靠的计算至关重要.
  • 加快双杂交方法的基础集融合是一个持续的挑战.

研究的目的:

  • 开发用于将基于密度的基数组校正 (DBBSC) 方法应用于双杂交近似的理论框架.
  • 调查统一坐标缩放对DBBSC在双混合计算中的准确性的影响.
  • 为了证明DBBSC在加速基础上的效率,为双杂交方法设置了融合.

主要方法:

  • 开发用于一参数双杂交的DBBSC的理论理由.
  • 对基准调整函数与合常量参数 (λ) 的确切依赖性的分析.
  • 将密度和基础函数的统一坐标缩放以1/λ的因数包括在内.

主要成果:

  • 精确的理论揭示了统一的坐标缩放是双杂交的DBBSC函数的组成部分.
  • 对分子原子化能量和反应屏障高度的测试计算证实了DBBSC的有效性.
  • 在DBBSC中忽略双杂交的统一坐标缩放被发现在实践中是一个合理的近似.

结论:

  • DBBSC 方法显著加速了双混合近似的基准集合收.
  • 开发的理论为应用DBBSC提供了坚实的基础,以提高计算效率和准确性.
  • 这项研究证实了DBBSC的实际实用性,即使对坐标缩放进行了简化假设.