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相关概念视频

Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
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Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
173
Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

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Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...
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Stability of Equilibrium Configuration01:23

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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
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Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

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The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
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Oscillations about an Equilibrium Position01:04

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Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
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Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
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数字稳定的共振哈特里-福克.

Ericka Roy Miller1, Shane M Parker1

  • 1Department of Chemistry, Case Western Reserve University, 10900 Euclid Ave, Cleveland, Ohio 44106, USA.

The Journal of chemical physics
|March 12, 2025
PubMed
概括
此摘要是机器生成的。

我们介绍了一种稳定的共振哈特里-福克 (ResHF) 方法来模拟激发状态,改善波函数优化. 这种计算效率高的方法对电子结构计算具有前景.

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科学领域:

  • 计算化学计算化学
  • 量子化学 是一个量子化学.
  • 电子结构理论 电子结构理论

背景情况:

  • 高效模拟兴奋状态是电子结构 (ES) 方法的一个重大挑战.
  • 现有的正交ES方法有局限性,对于激发状态的非正交方法,特别是与非正交轨道优化,研究较少.
  • 在处理近直角轨道的方法中,常常会出现数值不稳定.

研究的目的:

  • 为激发状态计算开发共振哈特里-福克 (ResHF) 方法的数值稳定的配方.
  • 在ResHF方法中改进波函数优化过程.
  • 将改进的ResHF方法的性能与完整的活性空间自相一致场 (CASSCF) 等既有方法进行比较.

主要方法:

  • 介绍了共振哈特里-福克 (ResHF) 方法的数值稳定的配方.
  • 利用矩阵附加物来减轻由近直角轨道引起的数值不稳定性.
  • 在各种化学系统中对CASSCF进行基准ResHF比较,包括LiF避免了交叉,乙烯扭转和小分子中的单元-三元能量差距.

主要成果:

  • 由于新配方,在ResHF波函数优化方面取得了显著的改进.
  • ResHF准确地描述了兴奋状态,结合了轨道放松,同时保持了正确的状态交叉.
  • 开源实现,yucca,可用于更广泛的使用.

结论:

  • 稳定ResHF方法为激发状态模拟提供了一个有希望的,计算效率高的方法.
  • 它结合了特定状态 (轨道放松) 和状态平均 (正确状态交叉) 方法的好处.
  • 开发的ResHF实现为电子结构计算提供了有价值的工具.