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相关概念视频

Density00:56

Density

14.8K
Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its cgs unit is g/cm3. The density of an object helps in identifying its composition, and also reveals information about the phase of the matter and its substructure. The densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. However, gases have much lower densities than liquids and...
14.8K
Gauss's Law01:07

Gauss's Law

7.3K
If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
7.3K
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

7.5K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
7.5K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

7.6K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
7.6K
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

6.9K
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...
6.9K
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

5.1K
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.
Newton's first law tells us about...
5.1K

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相关实验视频

Updated: Jul 6, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

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密度函数理论的普遍概括 静态相关性理论.

Daniel Gibney1, Jan-Niklas Boyn1, David A Mazziotti1

  • 1Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA.

Physical review letters
|January 5, 2024
PubMed
概括

密度函数理论 (DFT) 与静态相关性作斗争. 这种新方法将减少密度矩阵 (RDM) 理论与DFT结合起来,以准确捕捉静态相关性,改善分子性质的预测.

科学领域:

  • 量子化学 是一个量子化学.
  • 计算材料科学科学 计算材料科学

背景情况:

  • 密度函数理论 (DFT) 在准确描述静态相关性方面存在局限性.
  • 这种缺陷导致预测分子电荷,带间隙,范德瓦尔斯力和反应障碍的错误.

研究的目的:

  • 开发一种通用密度函数理论 (DFT),有效地结合静态相关性.
  • 创建一个计算效率高的方法,可以保持DFT的速度,同时提高对挑战量子分子现象的准确性.

主要方法:

  • 结合一个和两个电子的低密度矩阵 (1-和2-RDM) 理论与DFT.
  • 利用累积的2-RDM的最小单元不变量来制定一个1-RDM的功能理论.
  • 开发了DFT函数的校正,以解决分数轨道职位中的静态相关性.

主要成果:

  • 在静态相关性中实现了DFT的通用O(N3) 概括.
  • 该方法通过纠正功能凸度来准确捕捉静态相关性.
  • 通过揭示校正强度对两电子排斥矩阵痕迹的依赖,证明了预测能力.
  • 成功应用于乙烯旋转障碍物,素和分子解离基准.

结论:

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  • 这种新理论增强了DFT处理静态相关性的能力.
  • 它提供了一种计算效率高的方法来预测量子分子效应.
  • 为准确的分子性质预测和解释开辟了新的途径.