ENERGY GAP LAW FOR RADIATIONLESS TRANSITIONS IN LARGE MOLECULES
ENERGY GAP LAW FOR RADIATIONLESS TRANSITIONS IN LARGE MOLECULES
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DOI：
10.1080/00268977000100171
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发表时间：
1970-01-01
影响因子：
1.7
通讯作者：
JORTNER, J
中科院分区：
文献类型：
--
作者：
ENGLMAN, R;JORTNER, J
在本文中，我们提出了大分子中非辐射衰变过程的统一处理，其中涉及两个电子态之间的电子弛豫或激发电子态中的单分子重排反应。当前的处理类似于先前应用于核反冲和固体光谱中的线形状问题的形式主义。我们能够推导出非辐射衰变概率的理论表达式，以便可以将任意数量的不同分子振动纳入振动重叠因子中。这里得到的一般表达式可以简化为两种极限情况的解析形式，我们称之为强耦合情况（对应于两个电子态势能面的较大水平位移）和弱耦合极限（此时两个势能面的相对水平位移很小）。提供了这两个耦合限制的适用性的定量标准。在强耦合极限下，跃迁概率由能量参数 (ΔE-EM) 的高斯函数决定，其中 ΔE 是两个电子态原点之间的能隙，2EM 是斯托克斯位移。该极限表现出广义的阿累尼乌斯型温度行为，其中跃迁概率以指数方式取决于两个势表面相交的能垒。在低温下，跃迁概率由平均振动频率决定，因此预计仅揭示中等弱的氘同位素效应。弱耦合极限揭示了跃迁概率对能隙 ΔE 的指数（或更确切地说是超指数）依赖性。在此限制下，跃迁概率由最高振动频率（例如 C-H 或 C-D 振动）主导，因此将显示出明显的同位素效应。当提供指前因子的半经验估计时，发现弱耦合极限的近似理论表达式与大有机分子中电子弛豫的可用实验数据一致。
In this paper we present a unified treatment of non-radiative decay processes in large molecules which involve either electronic relaxation between two electronic states or unimolecular rearrangement reactions in excited electronic states. The present treatment is analogous to the formalism previously applied for the line shape problem in nuclear recoil and in the optical spectra of solids. We were able to derive theoretical expressions for the non-radiative decay probability so that an arbitrary number of different molecular vibrations can be incorporated in the vibrational overlap factors. The general expressions obtained herein can be reduced to analytical form for two limiting cases, which we call the strong coupling case (which corresponds to a substantial horizontal displacement of the potential energy surfaces of the two electronic states) and the weak coupling limit (whereupon the relative horizontal displacement of the two potential energy surfaces is small). Quantitative criteria for the applicability of these two coupling limits are provided. In the strong coupling limit the transition probability is determined by a gaussian function of the energy parameter (ΔE-EM), where ΔEis the energy gap between the origins of the two electronic states and 2EMis the Stokes shift. This limit exhibits a generalized Arrhenius type temperature behaviour whereupon the transition probability depends exponentially on the energy barrier for the intersection of the two potential surfaces. At low temperatures the transition probability is determined by the mean vibrational frequency and is thus expected to reveal only a moderately weak deuterium isotope effect. The weak coupling limit reveals an exponential (or rather superexponential) dependence of the transition probability on the energy gap ΔE. In this limit the transition probability is dominated by the highest vibrational frequency (e.g. the C-H or C-D vibrations) and thus will reveal a marked isotope effect. When semi-empirical estimates of the pre-exponential factors are provided, the approximate theoretical expression for the weak coupling limit is found to be consistent with the available experimental data on electronic relaxation in large organic molecules.