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The Quantum-Mechanical Model of an Atom02:45

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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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The word "gas" comes from the Flemish word meaning "chaos," first used to describe vapors by the chemist J. B. van Helmont. Consider a container filled with gas, with a continuous and random motion of molecules. During collisions, the velocity component parallel to the wall is unchanged, and the component perpendicular to the wall reverses direction but does not change in magnitude. If the molecule’s velocity changes in the x-direction, then its momentum is changed.
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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.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...
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In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
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灵感来自物理学的进化机器学习方法:从施罗丁格方程到轨道自由DFT动能功能的动能.

Juan I Rodríguez1, Ulises A Vergara-Beltrán2

  • 1Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada, Unidad Querétaro, Instituto Politécnico Nacional, Cerro Blanco 141 Col. Colinas del Cimatario, Querétaro C.P. 76090, México.

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一种新的机器学习 (ML) 方法,ML-Ω,从数据中推导出基本的物理方程. 它成功地重新发现了施罗丁格方程和托马斯-费米函数,并开发了一种高级无轨道密度函数理论 (DFT),用于电子结构计算.

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科学领域:

  • 计算物理和化学计算物理和化学
  • 机器学习在科学发现中的作用
  • 量子力学和电子结构理论

背景情况:

  • 从观测数据中推导出基本的物理定律是一个长期存在的科学挑战.
  • 传统方法通常依赖于人类的直觉和预定义的理论框架.
  • 机器学习为科学发现提供了新的范式,但将其与既定的物理原理相结合仍然是一个活跃的研究领域.

研究的目的:

  • 引入一种新的机器学习 (ML) 监督的进化方法,ML-Ω,灵感来自物理学的变化原理.
  • 为了证明ML-Ω能够直接从数据中导出底层微分方程和函数的能力.
  • 应用ML-Ω来开发密度函数理论 (DFT) 中的高级函数.

主要方法:

  • 开发了ML-Ω,一种从数据中学习模型函数 (函数) 的假设进化方法.
  • 用最小的数据集训练ML-Ω:三个类似的原子能量重新发现施罗丁格方程和功能.
  • 用托马斯-费米 (TF) 能量训练ML-Ω,以获得确切的TF函数.
  • 应用ML-Ω来得出一个局部无轨道 (OF) 动能函数 (Ts) 使用五个原子的能量.

主要成果:

  • ML-Ω成功地从有限的原子能数据中推导出了施罗丁格的确切函数和方程.
  • 该方法准确地复制了确切的托马斯-费米函数.
  • 一个ML-Ω衍生的局部OF-DFT函数 (γTFλvW(0.964,1/4)) 的性能优于现有的OF-DFT函数.
  • 与LDA和一些GGA函数相比,新的函数改善了二原子分子中拉伸键的描述.

结论:

  • ML-Ω进化方法为从数据中发现基本方程和函数提供了一个强大的框架.
  • 这种方法成功地将机器学习与自然科学相结合,使得复杂的物理定律能够得到推导.
  • 通过生成准确和高效的理论模型,ML-Ω显示了推进电子结构计算和其他科学领域的巨大潜力.