Energy gap law for triplet states

OPTICAL AND PHOTOPHYSICAL PROPERTIES A. Energy Gap Law for Triplet States 

The optical and PL spectroscopies have been undertaken to understand the structure-property correlations of this important family of triplet-emitting polymers. The red shift in the absorption features upon coordination of the metal groups is consistent with there being an increase in conjugation length over the molecule through the metal center. The trade-olf relationship between the phosphorescence parameters (such as emission wavelength, quantum yield, rates of radiative and nonradiative decay) and the optical gap will be formulated. For systems with third-row transition metal chromophores in which the ISC efficiency is close to 100%,76-78 the phosphorescence radiative (kr)y, and nonradiative (/cm)p decay rates are related to the measured lifetime of triplet emission (tp) and the phosphorescence quantum yield ( PP) by equations 1 and 2  

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Detailed studies have been performed on the photophysics of a range of Pt poly-ynes [68, 75-77], and the energy-gap law for triplet states in a series of platinum poly-ynes has been established [78]. Convincing evidence for Jt-conjugation between metal sites in the main chain has been provided by some of the experiments [75]. The photophysics of polymers with fluorene and carbazole spacers has also been investigated in depth, and the studies indicate that the singlet state extends over more than one repeat unit whereas the triplet state is strongly localized [79]. 

The factor that most strongly influences allowedness of a transition is spin. Transitions between states with different spins, such as singlet and triplet, are very inefficient. Direct So to T1 absorption is rarely important, and the reverse emissive process, phosphorescence, occurs quite slowly. The heavy atom effect can relax this selection rule through a spin-orbit effect. As a result, S-T interconversions are much more facile in molecules that contain atoms such as Br or 1. The second major factor that influences the efficiency of transitions is the general spatial overlap of the wavefunctions for the two states. This term favors it,it transitions over ,ir transitions, for reasons discussed above. Another important factor is a general energy gap law. For processes such as intersystem crossing, the smaller the gap between the... 

The lowest triplet states of porphyrins and metallopoiphyrins with typical metal atoms have generally long lifetimes from several hundreds of j.s to several ms even in fluid solution at ambient temperature (Table 2). Nonradiative deactivation from the triplet state of porphyrins was revealed to be well described [19,24,25] by the energy gap law [23]. As typical examples, OEP derivatives with Er larger than that of TPP are shown to have generally a longer triplet lifetime than TPP daivatives (Table 2). For magnesium porphyrins, the nonradiative rate constant of the lowest triplet state was expressed by Eq. (2) [25,26]... 

Experimentally, one thus expects that a triplet paramagnet (5=1) should display Pgff = 2.83pg, a quintet (5 = 2) 4.90 pg, and so on. A mixture of two states of different spin should have a value intermediate between the two values. For two such states in equilibrium, the energy gap can be calculated from the value of % and the Weiss temperature 0 in the Curie-Weiss law (Eq. 5.) ... 

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