路径积分刘维尔动力学方法的进一步探讨
详细信息 查看官网全文
- 英文论文题名：Further study of path integral Liouville dynamics
- 论文作者：李德彰 ; 刘歆子建 ; 刘剑
- 英文论文作者：Dezhang Li ; Xinzijian Liu ; Jian Liu ; Beijing National Laboratory for Molecular Science ; Institute of Theoretical and Computational Chemistry ; College of Chemistry and Molecular Engineering ; Peking University
- 年：2016
- 作者机构：北京分子科学国家实验室,北京大学化学与分子工程学院;
- 论文关键词：时间关联函数 ; 量子动力学效应 ; 虚时间路径积分 ; 朗之万动力学
- 会议召开时间：2016-07-01
- 会议录名称：中国化学会第30届学术年会摘要集-第十九分会：化学中的量子与经典动力学
- 语种：中文
- 分类号：O413
- 学会代码：ZGHY
- 会议名称：中国化学会第30届学术年会-第十九分会 ; 化学中的量子与经典动力学
- 会议地点：中国辽宁大连
- 主办单位：中国化学会
- 学会名称：中国化学会
- 页数：1
- 文件大小：198k
- 原文格式：D
- 会议级别：全国
摘要
计算分子体系的量子时间关联函数为人们理解预测其动力学过程提供了有力的理论工具。我们立足于魏格纳相空间,回顾了平衡刘维尔动力学、平衡连续性动力学和平衡哈密顿动力学这三种相空间量子动力学方法。它们可以保证平衡系统热力学物理量不随时间变化,并满足任意算符的时间关联函数的经典、高温、或谐振子极限。在速度分布满足全局高斯分布的条件下,它们可以推导出相同的运动方程。利用虚时间路径积分表示该运动方程的有效力,并对路径积分珠子做Staging变换,用分子动力学对路径积分珠子位置空间进行取样,可以推导出路径积分刘维尔动力学。我们分析指出,当路径积分刘维尔动力学和应用白噪声的朗之万动力学控温方法结合,在朗之万摩擦系数和路径积分刘维尔动力学中的绝热频率相等时,自由粒子极限下对路径积分珠子位置空间进行取样的效率最高,因此绝热频率可以作为最优朗之万摩擦系数的建议值。我们还建议了一种更高效的算法来演化路径积分刘维尔动力学的轨线。
Path integral Liouville dynamics(PILD) is a trajectory-based quantum dynamics approach that has the two important properties: conserves the quantum Boltzmann distribution and recovers exact thermal correlation functions(of even nonlinear operators) in the harmonic limit. We show that PILD can be derived from equilibrium continuity dynamics, as well as originally from equilibrium Liouville dynamics or equilibrium Hamiltonian dynamics, when a global Gaussian momentum distribution is presented in the Wigner phase space density distribution function. It has been shown that the Staging transformation of the path integral beads offers a much more efficient sampling approach for evaluating the effective force in the free particle limit. When Langevin dynamics is employed as the thermostatting method in PILD, the optimum Langevin friction coefficient is suggested to be the same as the adiabatic frequency w_(ad). We also propose a more efficient algorithm(than the velocity Verlet) for integrating the PILD equations of motion.
Path integral Liouville dynamics(PILD) is a trajectory-based quantum dynamics approach that has the two important properties: conserves the quantum Boltzmann distribution and recovers exact thermal correlation functions(of even nonlinear operators) in the harmonic limit. We show that PILD can be derived from equilibrium continuity dynamics, as well as originally from equilibrium Liouville dynamics or equilibrium Hamiltonian dynamics, when a global Gaussian momentum distribution is presented in the Wigner phase space density distribution function. It has been shown that the Staging transformation of the path integral beads offers a much more efficient sampling approach for evaluating the effective force in the free particle limit. When Langevin dynamics is employed as the thermostatting method in PILD, the optimum Langevin friction coefficient is suggested to be the same as the adiabatic frequency w_(ad). We also propose a more efficient algorithm(than the velocity Verlet) for integrating the PILD equations of motion.
引文
[1]Liu,J.;Miller,W.J.Chem.Phys.2011,134:104101
[2]Liu,J.;Miller,W.J.Chem.Phys.2011,134:104102
[3]Liu,J.J.Chem.Phys.2011,134:194110
[4]Liu,J.J.Chem.Phys.2014,140:224107
[5]刘剑,李德彰,刘歆子建.中国科学:化学,2016,46(1):27
[6]Liu,J.;Zhang,Z.J.Chem.Phys.2016,144:034307
[2]Liu,J.;Miller,W.J.Chem.Phys.2011,134:104102
[3]Liu,J.J.Chem.Phys.2011,134:194110
[4]Liu,J.J.Chem.Phys.2014,140:224107
[5]刘剑,李德彰,刘歆子建.中国科学:化学,2016,46(1):27
[6]Liu,J.;Zhang,Z.J.Chem.Phys.2016,144:034307