Belyaev Andrey K, Lasser Caroline, Trigila Giulio
Department of Theoretical Physics, Herzen University, St. Petersburg 191186, Russia.
Zentrum Mathematik, Technische Universität München, Munich, Germany.
J Chem Phys. 2014 Jun 14;140(22):224108. doi: 10.1063/1.4882073.
A class of surface hopping algorithms is studied comparing two recent Landau-Zener (LZ) formulas for the probability of nonadiabatic transitions. One of the formulas requires a diabatic representation of the potential matrix while the other one depends only on the adiabatic potential energy surfaces. For each classical trajectory, the nonadiabatic transitions take place only when the surface gap attains a local minimum. Numerical experiments are performed with deterministically branching trajectories and with probabilistic surface hopping. The deterministic and the probabilistic approach confirm the affinity of both the LZ probabilities, as well as the good approximation of the reference solution computed by solving the Schrödinger equation via a grid based pseudo-spectral method. Visualizations of position expectations and superimposed surface hopping trajectories with reference position densities illustrate the effective dynamics of the investigated algorithms.
研究了一类表面跳跃算法，比较了两个最近的用于非绝热跃迁概率的朗道 - 齐纳（LZ）公式。其中一个公式需要势能矩阵的 diabatic 表示，而另一个仅依赖于绝热势能面。对于每个经典轨迹，非绝热跃迁仅在表面间隙达到局部最小值时发生。使用确定性分支轨迹和概率性表面跳跃进行了数值实验。确定性和概率性方法都证实了两个 LZ 概率的相似性，以及通过基于网格的伪谱方法求解薛定谔方程计算得到的参考解的良好近似。位置期望值的可视化以及叠加的具有参考位置密度的表面跳跃轨迹说明了所研究算法的有效动力学。
