J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic.
J Chem Phys. 2017 Mar 21;146(11):114101. doi: 10.1063/1.4978289.
We present surface hopping dynamics on potential energy surfaces resulting from the spin-orbit splitting, i.e., surfaces corresponding to the eigenstates of the total electronic Hamiltonian including the spin-orbit coupling. In this approach, difficulties arise because of random phases of degenerate eigenvectors and possibility of crossings of the resulting mixed states. Our implementation solves these problems and allows propagation of the coefficients both in the representation of the spin free Hamiltonian and directly in the "diagonal representation" of the mixed states. We also provide a detailed discussion of the state crossing and point out several peculiarities that were not mentioned in the previous literature. We also incorporate the effect of the environment via the quantum mechanics/molecular mechanics approach. As a test case, we apply our methodology to deactivation of thiophene and selenophene in the gas phase, ethanol solution, and bulk liquid phase. First, 100 trajectories without spin-orbit coupling have been calculated for thiophene starting both in S and S states. A subset of 32 initial conditions starting in the S state was then used for gas phase simulations with spin-orbit coupling utilizing the 3-step integrator of SHARC, our implementation of the 3-step propagator in Newton-X and two new "one-step" approaches. Subsequently, we carried out simulations in ethanol solution and bulk liquid phase for both thiophene and selenophene. For both molecules, the deactivation of the S state proceeds via the ring opening pathway. The total population of triplet states reaches around 15% and 40% after 80 fs for thiophene and selenophene, respectively. However, it only begins growing after the ring opening is initiated; hence, the triplet states do not directly contribute to the deactivation mechanism. For thiophene, the resulting deactivation lifetime of the S state was 68 fs in the gas phase, 76 fs in ethanol solution, and 78 fs in the liquid phase, in a good agreement with the experimental value of 80 fs (liquid phase). For selenophene, the obtained S lifetime was 60 fs in the gas phase and 62 fs for both ethanol solution and liquid phase. The higher rate of intersystem crossing to the triplet states in selenophene is likely the reason for the lower fluorescence observed in selenium containing polymer compounds.
我们展示了源于自旋轨道分裂的势能表面上的表面跳跃动力学，即对应于包括自旋轨道耦合在内的总电子哈密顿量本征态的表面。在这种方法中，由于简并本征向量的随机相位和混合态的交叉的可能性，出现了困难。我们的实现解决了这些问题，并允许在无自旋哈密顿量的表示和混合态的“对角表示”中传播系数。我们还详细讨论了状态交叉，并指出了以前文献中未提到的几个特点。我们还通过量子力学/分子力学方法纳入了环境的影响。作为一个测试案例，我们将我们的方法应用于噻吩和硒吩在气相、乙醇溶液和本体液相中的失活。首先，对于噻吩，在没有自旋轨道耦合的情况下，我们计算了 S 和 S 态下各 100 条轨迹。然后，从 S 态开始，选择了 32 个初始条件子集，用于气相模拟，利用 SHARC 的 3 步积分器、我们在 Newton-X 中的 3 步传播子的实现以及两种新的“一步”方法，加入了自旋轨道耦合。随后，我们对噻吩和硒吩在乙醇溶液和本体液相中的进行了模拟。对于这两种分子，S 态的失活都通过环打开途径进行。噻吩和硒吩的三重态的总种群分别在 80 fs 后达到约 15%和 40%。然而，只有在环打开开始后，它才开始增长；因此，三重态不会直接参与失活机制。对于噻吩，在气相中 S 态的失活寿命为 68 fs，在乙醇溶液中为 76 fs，在液相中为 78 fs，与实验值 80 fs（液相）吻合良好。对于硒吩，在气相中获得的 S 寿命为 60 fs，在乙醇溶液和液相中均为 62 fs。硒吩中三重态的系间窜越率较高，可能是含硒聚合物化合物中观察到的荧光较低的原因。
