Fully adaptive propagation of the quantum-classical Liouville equation.
Fully adaptive propagation of the quantum-classical Liouville equation.
复制标题
量子经典刘维尔方程的完全自适应传播。
DOI：
10.1063/1.1691015
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
C. Schütte
中科院分区：
文献类型：
--
作者：
I. Horenko;M. Weiser;B. Schmidt;C. Schütte
在混合量子经典分子动力学中，动态系统的很少但重要的自由度是通过量子力学建模的，而其余的自由度则在经典近似内处理。在偏微分方程理论中建立的 Rothe 方法用于基于全局容差准则来控制时间和空间离散化误差。 TRAIL（刘维尔动力学自适应积分梯形法则）方案[I. Horenko 和 M. Weiser，J. Comput。化学。 24, 1921 (2003)] 已扩展到解释量子经典刘维尔方程描述的分子动力学中的非绝热效应。在粒子方法的背景下，相空间分布的空间近似的质量被最大化，而粒子参数的最小二乘问题的数值条件被最小化。由此产生的动力学方案基于相空间中移动粒子（高斯和狄拉克三角洲轨迹）的同时传播，采用完全自适应策略将狄拉克粒子升级为高斯粒子，反之亦然，将高斯粒子降级为狄拉克型轨迹。这允许将基于蒙特卡罗的多维问题中的密度和相干性采样策略与非绝热效应的确定性处理相结合。数值例子证明了该方法在不同维度的自旋玻色子系统中的应用。在非绝热表示中处理圆锥形交叉处发生的非绝热效应。通过降低全局容差，从 TRAIL 方案获得的数值解显示出收敛于精确结果。
In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.