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MO Theory and Covalent Bonding02:40

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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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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.
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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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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多态密度函数理论的近似函数.

Alexander Humeniuk1

  • 1Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-Ku, Kyoto 606-8502, Japan.

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|June 21, 2024
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概括
此摘要是机器生成的。

激发状态的新密度函数理论揭示了电子性质的普遍矩阵函数. 这项工作为多态函数提供了第一个近似,对于准确计算电子相互作用至关重要.

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科学领域:

  • 量子化学 是一个量子化学.
  • 计算物理 计算物理
  • 材料科学 材料科学 材料科学

背景情况:

  • 密度函数理论 (DFT) 传统上侧重于基本状态.
  • 在量子化学中,激发状态带来了重要的计算挑战.
  • 精确的电子相互作用建模对于理解化学和物理过程至关重要.

研究的目的:

  • 为激发电子状态开发一种新而严格的密度函数理论 (DFT).
  • 为动力和电子排斥操作员建立矩阵密度的通用函数.
  • 提出多态通用函数的第一个近似.

主要方法:

  • 将动力运算子和电子排斥运算子投射到最低电子状态的子空间.
  • 将托马斯 - 费米 - 迪拉克 - - 韦兹塞克尔模型和同质电子气相对应能量适应为矩阵函数.
  • 确保矩阵函数在基础集合转换下正确转换,并恢复单个状态的基态函数.

主要成果:

  • 开发的多态通用函数独立于电子状态的数量,并且具有分析性.
  • 该近似准确地复制了LiF的电子排斥运算子的矩阵元素,包括代表状态间相互作用的离对角元素.
  • 动能函数显示最大的误差,表明需要改进约束.

结论:

  • 这项研究通过引入矩阵函数介绍了激发状态的DFT的显著进步.
  • 拟议的近似显示了准确计算电子相互作用的前景,甚至是偏斜的哈密尔顿元素.
  • 需要进一步开发,特别是动能函数,以提高精度超出局部密度近似值.