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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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Electronic Structure of Atoms02:28

Electronic Structure of Atoms

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An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
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Hybridization of Atomic Orbitals II03:35

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sp3d and sp3d 2 Hybridization
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The Quantum-Mechanical Model of an Atom

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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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Hybridization of Atomic Orbitals I03:24

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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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相关实验视频

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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通过使用通用机器学习的功能近似来弥合电子和经典的密度函数理论.

Michelle M Kelley1, Joshua Quinton2, Kamron Fazel1

  • 1Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.

The Journal of chemical physics
|October 8, 2024
PubMed
概括
此摘要是机器生成的。

机器学习正在为电子和流体系统中的密度函数理论 (DFT) 计算创建通用非局部函数. 这种方法在各种应用中实现了高精度,统一了不同的研究方法.

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科学领域:

  • 计算物理 计算物理
  • 材料科学 材料科学 材料科学
  • 统计力学 统计力学

背景情况:

  • 密度函数理论 (DFT) 的准确性依赖于非局部函数的近似值 (电子 DFT 中的交换相关性,经典 DFT 中的过量).
  • 当前的近似通常是半局部或有限的非局部形式,尽管确切的函数是高度非局部的.
  • 机器学习 (ML) 在电子和经典DFT中提供了改进非局部功能近似的潜力.

研究的目的:

  • 开发一个通用的机器学习框架来学习非局部密度函数近似.
  • 统一电子和经典DFT研究中使用的不同的ML方法.
  • 创建准确的非本地函数,适用于各种系统.

主要方法:

  • 制定一个通用ML框架,将等价卷积神经网络和加权密度近似结合起来.
  • 开发一种标准化的培训协议,用于学习非局部函数.
  • 在1D和准1D系统上对框架进行原型设计和测试.

主要成果:

  • 在使用相同超参数的多种系统中表现出卓越的准确性.
  • 成功地将ML函数应用于硬棒流体,不均的Ising模型和电子交换能量.
  • 在无轨道的DFT和具有1D不均性的液态水中获得了电子运动能的准确结果.

结论:

  • 开发的通用ML框架为学习非局部函数提供了通用的方法.
  • 这种统一的方法显示出在电子和经典DFT中近似精确的3D函数的显著前景.
  • 为推进多个科学领域的DFT应用奠定了基础.