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Molecular Orbital Theory I02:35

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An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
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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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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.
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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轨道功能的严格正式化.

Neil Qiang Su1

  • 1Center for Theoretical and Computational Chemistry, Frontiers Science Center for New Organic Matter, State Key Laboratory of Advanced Chemical Power Sources, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Department of Chemistry, <a href="https://ror.org/01y1kjr75">Nankai University</a>, Tianjin 300071, China.

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概括
此摘要是机器生成的。

这项研究使用克利福德代数严格地正式化了轨道和职位函数,为复杂的电子系统提供了传统密度函数理论方法的优越替代方案.

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科学领域:

  • 量子化学是一种量子化学.
  • 理论物理学的理论物理.
  • 计算材料科学 计算材料科学

背景情况:

  • 传统的密度函数理论 (DFT) 方法面临着电子密度不映射到非相互作用引用的系统的局限性.
  • 现有的轨道依赖函数需要严格的数学正式化,以获得更广泛的应用.

研究的目的:

  • 严格正式化取决于被占用,未被占用或分数轨道的函数.
  • 为轨道和职业优化建立一个变量原理.
  • 将轨道函数作为DFT的严格替代品呈现出一个新的视角.

主要方法:

  • 使用克利福德代数的正式化.
  • 为优化建立一个变量原理.
  • 发展轨道 (和职业) 优化作为一个正式的实施方法.

主要成果:

  • 对于轨道和职业函数的严格数学框架.
  • 一个变化原理,使得直接轨道和职业优化.
  • 一种方法的演示,可以绕过标准Kohn-Sham DFT的局限性.

结论:

  • 通过克利福德代数形式化的轨道和职业函数,为传统的DFT提供了严格且优越的替代方案.
  • 这些先进的功能克服了描述非标准电子密度映射系统的局限性.
  • 已确定的变量原则有助于实际实施和优化.