Energy gap law for radiationless transitions

R. Englman and J. Jortner, The Energy Gap Law For Radiationless Transitions in Large Molecules, in Mol. Phys., in press. 

The lifetime of the MLCT excited state of [Ru(bipy)3] has been measured in several solvents and at different temperatures. Among the- conclusions drawn are that k, is only slightly solvent-dependent, that k , agrees quantitatively with predictions of energy gap law for radiationless transitions, and that the solvent dependence of kinetic parameters for MLCT —> d, dctransitions can be considered in the context of electron-transfer theory. These results may have implications for the use of [Ru(bipy)3] as sensitizer. The solvent dependence of the MLCT transitions of [Ru(bipy)3], [Os(bipy)3], [Os(bipy)2(py)2p, and [Os(bipy)2 l,2-(Ph2P)2CsH4 f has been interpreted in... 

Englman R and Jortner J (1970) The energy gap law for radiationless transitions in large molecules. Mol Phys 18 145-164... 

The Sj radiationless transition rate is sensitive to both solvatochromic and substituent-induced shifts of the Sj - Sj energy gap. Figure 1.2 shows that an almost linear dependence of the logarithm of the rate constant of radiationless decay on the Sj - Sj energy gap is observed for a series of 1-and 1,3-fluorine-substituted azulenes in a range of solvents, as expected if the energy gap law of radiationless transition theory applies and internal conversion is the sole Sj decay process. 1,3-Difluoroazulene in ethanol... 

The probability of intramolecular energy transfer between two electronic states is inversely proportional to the energy gap, AE, between the two states. The value of the rate constant for radiationless transitions decreases with the size of the energy gap between the initial and final electronic states involved. This law readily provides us with a simple explanation of Kasha s rule and Vavilov s rule. 

The rate of internal conversion (IC), a radiationless transition between isoenergetic levels of different states of the same multiplicity, may be of the same order of magnitude or even faster than vibrational relaxation. It depends, however, on the energy separation AEqo between the zero-vibrational levels of the electronic states involved (energy gap law, see Section 5.2.1). Similar relations hold for intersystem crossing transitions between states of different multiplicity, which are slower by 4-8 orders of magnitude. 

Studies of radiationless transitions in matrix-isolated molecules represent a nice case of constructive interaction between theory and experiment. Most early experimental studies showed very poor agreement with the theoretical predictions. Thus in NH and OH, neither the expected temperature dependence, nor the energy-gap law predictions were fulfilled. Similarly, no steep temperature dependence of the relaxation rates was found in matrix-isolated CO. The experimental studies, however, permitted to identify the reasons for the failure of the simple theories. This in turn led to development of new models, describing more adequately the experimental results. " ... 

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