Li Lesheng, Giokas Paul G, Kanai Yosuke, Moran Andrew M
Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA.
J Chem Phys. 2014 Jun 21;140(23):234109. doi: 10.1063/1.4882664.
Kinetic models based on Fermi's Golden Rule are commonly employed to understand photoinduced electron transfer dynamics at molecule-semiconductor interfaces. Implicit in such second-order perturbative descriptions is the assumption that nuclear relaxation of the photoexcited electron donor is fast compared to electron injection into the semiconductor. This approximation breaks down in systems where electron transfer transitions occur on 100-fs time scale. Here, we present a fourth-order perturbative model that captures the interplay between time-coincident electron transfer and nuclear relaxation processes initiated by light absorption. The model consists of a fairly small number of parameters, which can be derived from standard spectroscopic measurements (e.g., linear absorbance, fluorescence) and/or first-principles electronic structure calculations. Insights provided by the model are illustrated for a two-level donor molecule coupled to both (i) a single acceptor level and (ii) a density of states (DOS) calculated for TiO2 using a first-principles electronic structure theory. These numerical calculations show that second-order kinetic theories fail to capture basic physical effects when the DOS exhibits narrow maxima near the energy of the molecular excited state. Overall, we conclude that the present fourth-order rate formula constitutes a rigorous and intuitive framework for understanding photoinduced electron transfer dynamics that occur on the 100-fs time scale.
基于费米黄金规则的动力学模型通常用于理解分子 - 半导体界面处的光致电子转移动力学。在这种二阶微扰描述中隐含的假设是，光激发电子供体的核弛豫比电子注入半导体的速度要快。在电子转移跃迁发生在100飞秒时间尺度的系统中，这种近似就不成立了。在此，我们提出一种四阶微扰模型，该模型能够捕捉由光吸收引发的同时发生的电子转移与核弛豫过程之间的相互作用。该模型由相当少的参数组成，这些参数可以从标准光谱测量（例如，线性吸光度、荧光）和/或第一性原理电子结构计算中得出。对于一个双能级供体分子与（i）单个受体能级以及（ii）使用第一性原理电子结构理论计算得到的TiO₂态密度（DOS）相耦合的情况，展示了该模型所提供的见解。这些数值计算表明，当DOS在分子激发态能量附近呈现出狭窄的最大值时，二阶动力学理论无法捕捉到基本的物理效应。总体而言，我们得出结论，当前的四阶速率公式构成了一个严谨且直观的框架，用于理解发生在100飞秒时间尺度上的光致电子转移动力学。
