Dhole Kajal, Modak Brindaban, Samanta Alok, Ghosh Swapan K
Research Reactor Services Division, Bhabha Atomic Research Centre, Mumbai, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jul;82(1 Pt 2):016110. doi: 10.1103/PhysRevE.82.016110. Epub 2010 Jul 20.
We have derived an exact analytical expression for the average forward rate of a reversible electron transfer reaction, modeled through a reaction coordinate undergoing diffusive motion in arbitrary potential wells of the reactant and the product in presence of a localized sink of arbitrary location and strength. The dynamics of diffusive motion is described by employing two coupled generalized diffusion reaction (Smoluchowski) equations with coordinate dependent diffusivity and delta sink. The average forward electron transfer rate constant obtained here for the system, with equilibrium or nonequilibrium distributions as initial condition, is determined by the forward and backward rate constants calculated based on the transition state theory and the weighted average rate for the well dynamics. We also discuss various limiting cases for the rate of electron transfer reactions corresponding to the different experimental situations. As an illustrative example, we have considered back electron transfer (ET) reaction and shown that the present theory can explain the non-Marcus free energy gap dependence of the rate of ET reactions. More importantly, the approach presented here can easily be extended to systems describing the dynamics of diffusive motion in coupled multipotential surfaces associated with electron transfer reactions.
我们推导出了可逆电子转移反应平均正向速率的精确解析表达式，该反应通过反应坐标进行建模，在反应物和产物的任意势阱中进行扩散运动，存在任意位置和强度的局部汇。扩散运动的动力学通过使用两个耦合的广义扩散反应（斯莫卢霍夫斯基）方程来描述，该方程具有坐标依赖的扩散系数和δ汇。在此处获得的系统平均正向电子转移速率常数，以平衡或非平衡分布作为初始条件，由基于过渡态理论计算的正向和反向速率常数以及阱动力学的加权平均速率确定。我们还讨论了对应于不同实验情况的电子转移反应速率的各种极限情况。作为一个说明性示例，我们考虑了反向电子转移（ET）反应，并表明当前理论可以解释ET反应速率的非马库斯自由能隙依赖性。更重要的是，这里提出的方法可以很容易地扩展到描述与电子转移反应相关的耦合多势面中扩散运动动力学的系统。
