哪个算法最好地传播迈耶-米勒-股票-投映射汉密尔顿对非代数动力学的算法?
Lauren E Cook1, Johan E Runeson2, Jeremy O Richardson2
1Department of Chemistry, University College London, Christopher Ingold Building, London WC1H 0AJ, U.K.
Journal of chemical theory and computation
|September 13, 2023
概括
这项研究比较了使用迈耶-米勒-斯托克-托斯 (MMST) 哈密尔顿式模拟量子-经典动态的三个算法. 动量积分 (MInt) 算法是严格的简单的,而分割-Liouvillian (SL) 则以更低的成本提供可比的准确性.
科学领域:
- 量子化学 是一个量子化学.
- 计算化学计算化学
- 化学物理 化学物理
背景情况:
- 混合量子-经典动力学模拟对于理解化学过程至关重要.
- 迈耶-米勒-股票-托斯 (MMST) 哈密尔顿式和旋转映射方法是这些模拟的常见方法.
- 需要有效和准确的数值算法来整合运动方程.
研究的目的:
- 为了比较MMST哈密尔顿式的三个时间传播算法的性能:动量积分 (MInt),分割-Liouvillian (SL) 和退化自身值 (DE).
- 为了分析准确性,节能性,简易性,Liouville定理的坚持性和计算成本.
- 为在未来的映射变量模拟中选择合适的算法提供指导.
主要方法:
- 实施和比较MInt,SL和DE算法用于MMST哈密尔顿式.
- 评估个别轨迹准确性和相关函数.
- 对保存量 (能量,简易性,Liouville定理) 和计算费用的评估.
主要成果:
- 在那些经过测试的算法中,MInt算法是唯一严格的simplectic方法.
- SL算法实现了与MInt相似的准确性,但计算成本降低.
- 由于其固有的近似性,DE算法表现出很差的能量保存,即使在小时间步骤中也是如此.
结论:
- 算法的选择显著影响混合量子-经典模拟的准确性,保存性质和效率.
- SL算法提供了准确性和计算成本的有利平衡.
- 由于DE算法在节能方面的局限性,因此在应用中需要谨慎.
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