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Hybridization of Atomic Orbitals II03:35

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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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Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
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一个可重复使用的库,用于使用信任区域方法进行二次轨道优化.

Jonas Greiner1, Ida-Marie Høyvik2, Susi Lehtola3

  • 1DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg. 206, 2800 Kgs. Lyngby, Denmark.

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概括
此摘要是机器生成的。

我们开发了OpenTrustRegion,这是一个新的开源库,用于信任区域优化. 这个强大的软件有效地优化了电子结构理论中的分子轨道,使各种应用受益.

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科学领域:

  • 计算化学是一种计算化学.
  • 电子结构理论 电子结构理论
  • 软件开发 软件开发

背景情况:

  • 分子轨道优化对于准确的电子结构计算至关重要.
  • 现有的方法可能缺乏效率或广泛适用性.
  • 信任区域算法为复杂的优化问题提供了强大的框架.

研究的目的:

  • 介绍OpenTrustRegion,这是一个新的开源库,用于二级信任区域优化.
  • 为通用分子轨道优化提供多功能工具.
  • 为了促进先进的优化技术的集成到电子结构软件.

主要方法:

  • 实施二级信任区域算法.
  • 开发可重复使用和许可许可的OpenTrustRegion软件库.
  • 对自相一致的场计算,轨道定位和对称化任务进行了广泛的基准测试.

主要成果:

  • 已经证明了OpenTrustRegion库的稳定性和效率.
  • 在电子结构理论中成功应用于具有挑战性和病态系统.
  • 在各种计算化学任务中验证图书馆的性能.

结论:

  • OpenTrustRegion为分子轨道优化提供了一个强大而灵活的工具.
  • 该图书馆的开源和允许许可证鼓励广泛采用.
  • 这种实现提高了电子结构软件的功能.