Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-12, India.
J Phys Chem B. 2010 Sep 30;114(38):12284-92. doi: 10.1021/jp1014466.
In some bimolecular diffusion-controlled electron transfer (ET) reactions such as ion recombination (IR), both solvent polarization relaxation and the mutual diffusion of the reacting ion pair may determine the rate and even the yield of the reaction. However, a full treatment with these two reaction coordinates is a challenging task and has been left mostly unsolved. In this work, we address this problem by developing a dynamic theory by combining the ideas from ET reaction literature and barrierless chemical reactions. Two-dimensional coupled Smoluchowski equations are employed to compute the time evolution of joint probability distribution for the reactant (P((1))(X,R,t)) and the product (P((2))(X,R,t)), where X, as is usual in ET reactions, describes the solvent polarization coordinate and R is the distance between the reacting ion pair. The reaction is described by a reaction line (sink) which is a function of X and R obtained by imposing a condition of equal energy on the initial and final states of a reacting ion pair. The resulting two-dimensional coupled equations of motion have been solved numerically using an alternate direction implicit (ADI) scheme (Peaceman and Rachford, J. Soc. Ind. Appl. Math. 1955, 3, 28). The results reveal interesting interplay between polarization relaxation and translational dynamics. The following new results have been obtained. (i) For solvents with slow longitudinal polarization relaxation, the escape probability decreases drastically as the polarization relaxation time increases. We attribute this to caging by polarization of the surrounding solvent. As expected, for the solvents having fast polarization relaxation, the escape probability is independent of the polarization relaxation time. (ii) In the slow relaxation limit, there is a significant dependence of escape probability and average rate on the initial solvent polarization, again displaying the effects of polarization caging. Escape probability increases, and the average rate decreases on increasing the initial polarization. Again, in the fast polarization relaxation limit, there is no effect of initial polarization on the escape probability and the average rate of IR. (iii) For normal and barrierless regions the dependence of escape probability and the rate of IR on initial polarization is stronger than in the inverted region. (iv) Because of the involvement of dynamics along R coordinate, the asymmetrical parabolic (that is, non-Marcus) energy gap dependence of the rate is observed.
在某些双分子扩散控制的电子转移（ET）反应中，如离子复合（IR），溶剂极化弛豫和反应离子对的相互扩散都可能决定反应的速率甚至产率。然而，用这两个反应坐标进行全面处理是一项具有挑战性的任务，并且尚未得到完全解决。在这项工作中，我们通过结合 ET 反应文献和无势垒化学反应的思想来发展一种动态理论来解决这个问题。采用二维耦合 Smoluchowski 方程来计算反应物（P((1))(X,R,t))和产物（P((2))(X,R,t))的联合概率分布的时间演化，其中 X 如 ET 反应中通常那样，描述溶剂极化坐标，R 是反应离子对之间的距离。反应由反应线（汇）描述，该反应线是通过对反应离子对的初始和最终状态施加相等能量条件而获得的 X 和 R 的函数。所得的二维耦合运动方程已使用交替方向隐式（ADI）方案（Peaceman 和 Rachford，J. Soc.Ind. Appl. Math.1955，3，28）进行数值求解。结果揭示了极化弛豫和平移动力学之间的有趣相互作用。得到了以下新结果。（i）对于具有缓慢纵向极化弛豫的溶剂，随着极化弛豫时间的增加，逃逸概率急剧下降。我们将此归因于周围溶剂的极化笼效应。正如预期的那样，对于具有快速极化弛豫的溶剂，逃逸概率与极化弛豫时间无关。（ii）在缓慢弛豫极限下，逃逸概率和平均速率对初始溶剂极化的依赖性很大，再次显示出极化笼的影响。随着初始极化的增加，逃逸概率增加，平均速率降低。同样，在快速极化弛豫极限下，初始极化对 IR 的逃逸概率和平均速率没有影响。（iii）对于正常和无势垒区域，逃逸概率和 IR 速率对初始极化的依赖性强于倒置区域。（iv）由于涉及 R 坐标的动力学，观察到非对称抛物线（即非马库斯）能隙对速率的依赖性。
