Humeniuk Alexander, Mitrić Roland
Institut für Physikalische und Theoretische Chemie, Julius-Maximilians Universität Würzburg, Emil-Fischer-Straße 42, 97074 Würzburg, Germany.
J Chem Phys. 2016 Jun 21;144(23):234108. doi: 10.1063/1.4954189.
A surface-hopping extension of the coupled coherent states-method [D. Shalashilin and M. Child, Chem. Phys. 304, 103-120 (2004)] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schrödinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully's fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronic wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both interference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [A. Ferretti, J. Chem. Phys. 104, 5517 (1996)], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and interferes with itself. These interference effects are absent in classical trajectory-based molecular dynamics but can be fully incorpo rated if trajectories are replaced by surface hopping coupled coherent states.
提出了耦合相干态方法[D. Shalashilin和M. Child，《化学物理》304，103 - 120(2004)]的表面跳跃扩展，用于模拟具有原子核量子效应的非绝热动力学。原子核运动的含时薛定谔方程在一个移动基组中求解。该基组由经典轨迹引导，经典轨迹可以在不同的电子势能面之间随机跳跃。非绝热跃迁由Tully最少开关算法的一个改进版本建模。轨迹由原子核相空间中的高斯函数(相干态)与电子波函数的振幅组合而成。不同相干态之间的含时矩阵元决定了总多态波函数中每条轨迹的振幅；对角矩阵元决定了跳跃概率和梯度。通过这种方式，干涉效应和非绝热跃迁都可以以一种非常紧凑的方式描述，如果在轨迹数量上实现收敛并且全局已知势能面，就会得到精确解。该方法在一个锥形交叉的二维模型上进行了测试[A. Ferretti，《化学物理杂志》104，5517(1996)]，其中一个核波包环绕两个势能面之间的简并点并与自身发生干涉。这些干涉效应在基于经典轨迹的分子动力学中不存在，但如果用表面跳跃耦合相干态代替轨迹，就可以完全纳入。
