Rowland Brad A, Wyatt Robert E
Institute for Theoretical Chemistry and Department of Chemistry and Biochemistry, The University of Texas at Austin, 1 University Station A5300, Austin, Texas 78712, USA.
J Phys Chem A. 2007 Oct 18;111(41):10234-50. doi: 10.1021/jp072419i. Epub 2007 Jul 24.
In this study, an analysis of the one-dimensional Eckart and Gaussian barrier scattering problems is undertaken using approximate quantum trajectories. Individual quantum trajectories are computed using the derivative propagation method (DPM). Both real-valued and complex-valued DPM quantum trajectories are employed. Of interest are the deep tunneling and the higher energy barrier scattering problems in cases in which the scattering barrier is "thick" by comparison to the width of the initial wave packet. For higher energy scattering problems, it is found that real-valued DPM trajectories very accurately reproduce the transmitted probability densities at low orders when compared to large fixed-grid calculations. However, higher orders must be introduced to obtain good probabilities for deep tunneling problems. Complex-valued DPM is found to accurately reproduce transmitted probability densities at low order for both the deep tunneling and the higher energy scattering problems. Of particular note, complex-classical trajectories are found to very nearly give the exact result for the deep barrier tunneling scattering problem, and the complex DPM converges well at high orders for these thick barrier scattering problems. A variety of analyses are performed to elucidate the dynamics of complex-valued DPM trajectories. The complex-extended barrier potentials are examined in detail, including an analysis of the complex force. Of particular interest are initial conditions for complex-valued DPM trajectories known as isochrones. All trajectories launched from an isochrone arrive on the real axis on the transmitted side of the barrier at the same time. The computation and properties of isochrones as well as the behavior of the initial wave packet in the complex plane are also examined.
在本研究中，使用近似量子轨迹对一维埃卡特（Eckart）势垒和高斯势垒散射问题进行了分析。利用导数传播方法（DPM）计算单个量子轨迹。采用了实值和复值的DPM量子轨迹。研究的兴趣点在于散射势垒相对于初始波包宽度而言“较厚”的情况下的深隧穿和高能势垒散射问题。对于高能散射问题，发现与大型固定网格计算相比，实值DPM轨迹在低阶时能非常精确地重现透射概率密度。然而，对于深隧穿问题，必须引入更高阶才能获得良好的概率。发现复值DPM对于深隧穿和高能散射问题在低阶时都能精确地重现透射概率密度。特别值得注意的是，发现复经典轨迹对于深势垒隧穿散射问题几乎能给出精确结果，并且对于这些厚势垒散射问题，复DPM在高阶时收敛良好。进行了各种分析以阐明复值DPM轨迹的动力学。详细研究了复扩展势垒势，包括对复力的分析。特别感兴趣的是复值DPM轨迹的初始条件，即等时线。从等时线出发的所有轨迹会在同一时间到达势垒透射侧的实轴上。还研究了等时线的计算和性质以及初始波包在复平面中的行为。
