Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland.
J Chem Phys. 2012 Mar 7;136(9):094106. doi: 10.1063/1.3690458.
We propose to measure nonadiabaticity of molecular quantum dynamics rigorously with the quantum fidelity between the Born-Oppenheimer and fully nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies in situations where other criteria, such as the energy gap criterion or the extent of population transfer, fail. We further propose to estimate this quantum fidelity efficiently with a generalization of the dephasing representation to multiple surfaces. Two variants of the multiple-surface dephasing representation (MSDR) are introduced, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics (LMFD). The LMFD can be interpreted as the Ehrenfest dynamics of an ensemble of nuclear trajectories, and has been used previously in the nonadiabatic semiclassical initial value representation. In addition to propagating an ensemble of classical trajectories, the MSDR requires evaluating nonadiabatic couplings and solving the Schrödinger (or more generally, the quantum Liouville-von Neumann) equation for a single discrete degree of freedom. The MSDR can be also used in the diabatic basis to measure the importance of the diabatic couplings. The method is tested on three model problems introduced by Tully and on a two-surface model of dissociation of NaI.
我们提出用玻恩-奥本海默和完全非绝热动力学之间的量子保真度来严格地测量分子量子动力学的非绝热性。结果表明，这种非绝热性的度量适用于其他标准（如能隙准则或种群转移程度）失效的情况。我们进一步提出通过将退相位表示推广到多个表面来有效地估计这种量子保真度。引入了两种多表面退相位表示（MSDR）变体，其中核的传播要么使用最少切换的表面跳跃，要么使用局部平均场动力学（LMFD）。LMFD 可以被解释为核轨迹的集合的 Ehrenfest 动力学，并且以前已经在非绝热半经典初始值表示中使用过。除了传播经典轨迹的集合外，MSDR 还需要评估非绝热耦合，并为单个离散自由度求解薛定谔（或更一般的量子刘维尔-冯·诺依曼）方程。MSDR 也可以在绝热基中用于测量绝热耦合的重要性。该方法在 Tully 引入的三个模型问题和 NaI 离解的双表面模型上进行了测试。
