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First Law: Particles in One-dimensional Equilibrium01:10

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Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
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Every mathematical equation that connects separate distinct physical quantities must be dimensionally consistent, which implies it must abide by two rules. For this reason, the concept of dimension is crucial. The first rule is that an equation's expressions on either side of an equality must have the exact same dimension, i.e., quantities of the same dimension can be added or removed. The second rule stipulates that all popular mathematical functions, such as exponential, logarithmic, and...
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First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
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In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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将概念密度函数理论扩展到第一阶减少密度矩阵:福井矩阵上的开放子系统观点

Guillaume Acke1, Daria Van Hende1, Xeno De Vriendt1

  • 1Department of Chemistry - Ghent Quantum Chemistry Group, Ghent University, Krijgslaan 281 (S3), Ghent B-9000, Belgium.

Journal of chemical theory and computation
|August 2, 2023
PubMed
概括
此摘要是机器生成的。

福井矩阵是概念密度函数理论中福井函数的延伸,只有在具有非局部外部潜力的情况下,它才是定义得很好的. 这项工作揭示了福井职业和自然人如何捕捉分子中的静态相关效应.

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科学领域:

  • 理论化学 理论化学
  • 量子化学 是一个量子化学.
  • 化学反应理论 化学反应理论

背景情况:

  • 福井函数是概念密度函数理论 (CDFT) 中的一个关键反应性描述函数,传统上依赖于基于密度的框架.
  • 福井函数的矩阵扩展已经被提出,以结合电子相关性效应,超出简单的基于密度的方法.
  • 这些矩阵扩展所提供的理论基础和化学见解,特别是它们的自身分解,需要进一步澄清.

研究的目的:

  • 严格研究将福井函数扩展到CDFT内的矩阵表示的理论有效性.
  • 阐明福井矩阵自身分解中编码的化学信息,特别是福井职业和福井自然.
  • 探索这些矩阵描述符与化学系统中的电子相关性效应之间的联系.

主要方法:

  • 通过将外部潜力概括为非局部,引入概念第一阶降密矩阵功能理论 (CFRDMF).
  • 从交互开放子系统的角度解释安德森杂质模型.
  • 对福井职业和福井自然人的分析,以了解它们与静态相关性的关系.

主要成果:

  • 福井函数的矩阵扩展只有当外部潜力被概括为非局部时,才被证明在理论上是合理的.
  • 福井职业和福井自然被证明反映了不断增加的静态相关性的影响.
  • 在这些矩阵描述符中确定了特征模式,提供了对分子相关电子行为的见解.

结论:

  • 本研究建立了在CDFT中使用反应性描述符的矩阵扩展的理论基础.
  • 这项工作为解释福岛职业和自然资源作为电子相关性指标提供了一个框架.
  • 这项研究代表了将CDFT推广到纯粹基于密度的方法之外的重大进展.