Institut für Physikalische und Theoretische Chemie, Universität Würzburg, Emil-Fischer-Str. 42, Campus Nord, 97074 Würzburg, Germany.
J Chem Phys. 2017 Aug 14;147(6):064302. doi: 10.1063/1.4989780.
In solving the time-dependent Schrödinger equation for a coupled electron-nuclear system, we study the motion of wave packets in a model which exhibits a conical intersection (CoIn) of adiabatic potential energy surfaces. Three different situations are studied. In the first case, an efficient non-adiabatic transition takes place while the wave packet passes the region of the CoIn. It is demonstrated that during these times, the nuclear probability density retains its Gaussian shape and the electronic density remains approximately constant. Second, dynamics are regarded where non-adiabatic transitions do not take place, and the nuclear dynamics follows a circle around the location of the CoIn. During this motion, the electronic density is shown to rotate. The comparison with the Born-Oppenheimer nuclear dynamics reveals the geometrical phase being associated with the circular motion. This phase is clearly revealed by an analysis of time-dependent autocorrelation functions and spectra obtained from the numerically exact and the Born-Oppenheimer calculation. The intermediate situation with a small non-adiabatic transition probability is characterized by wave-packet splitting into several fractions.
在求解耦合电子-核体系的含时薛定谔方程时，我们研究了在表现出绝热势能面交叉（CoIn）的模型中波包的运动。研究了三种不同的情况。在第一种情况下，波包通过 CoIn 区域时会发生有效的非绝热跃迁。结果表明，在这些时间内，核概率密度保持高斯形状，电子密度近似保持不变。其次，研究了不发生非绝热跃迁的动力学情况，核动力学沿着 CoIn 位置周围的圆运动。在此运动过程中，电子密度被证明会发生旋转。与 Born-Oppenheimer 核动力学的比较揭示了与圆运动相关的几何相位。通过对数值精确和 Born-Oppenheimer 计算得到的时变自相关函数和谱的分析，可以清楚地揭示出这种相位。具有小非绝热跃迁概率的中间情况的特征是波包分裂成几个分数。
