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相关概念视频

Relative Motion Analysis using Rotating Axes-Problem Solving01:29

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Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
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直接Givens旋转方法基于错误反向传播算法,用于自相一致的场域解决方案.

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  • 1Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan.

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这项研究引入了一种新的直接能量最小化算法,使用顺序的Givens旋转来解决自相一致的场计算. 这种方法确保了轨道直角性,并避免了电子结构计算中的变化崩.

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科学领域:

  • 计算化学是一种计算化学.
  • 量子化学是一种量子化学.
  • 电子结构理论 电子结构理论

背景情况:

  • 自相一致的场 (SCF) 程序对于Hartree-Fock和Kohn-Sham密度函数理论 (DFT) 的计算至关重要.
  • 标准SCF方法的趋同在理论上并未得到保证,因此需要采用替代方法.
  • 直接最小化方法,如增强拉格朗的方法 (ALM) 和二级SCF (SOSCF) 提供基于梯度的解决方案,但有局限性.

研究的目的:

  • 为SCF计算提出一种新的直接能量最小化算法.
  • 为了确保轨道直角性,并防止SCF优化期间的变化崩.
  • 为现有的SCF算法提供一种替代方案,具有潜在改进的融合特性.

主要方法:

  • 开发了一个新的SCF算法,该算法基于最小化ALM拉格朗数.
  • 在单位转换中,在被占用和虚拟轨道之间使用了顺序的Givens旋转.
  • 利用错误反向传播方法计算Givens旋转的复杂梯度.
  • 将开发的Direct Givens Rotation (DGR) 方法的性能与已建立的算法进行比较.

主要成果:

  • 拟议的DGR方法通过直接最小化能源有效地获得SCF解决方案.
  • 顺序的Givens旋转成功地保持了轨道直角性,并防止了变化崩.
  • 插图应用展示了该方法的特点,并将其性能与代子空间的直接倒置 (DIIS),SOSCF和ALM进行了比较.

结论:

  • 在电子结构计算中,DGR方法为实现SCF解决方案提供了可行的和强大的替代方案.
  • 使用顺序的Givens旋转提供了一种可靠的方式来处理单元变换,并保持轨道的正规性.
  • 需要对DGR方法在各种量子化学系统中的效率和适用性进行进一步的研究.