Excited Singlet-state Radiative Lifetime

The excited singlet-state radiative lifetime, o, of Si is the lifetime of Si in the absence of any radiationless transitions that is, the only 

Since is greater than kf, the observed excited singlet-state lifetime is less than the excited singlet-state radiative lifetime. h only approaches ho as intersystem crossing and internal conversion from Si become much slower processes than fluorescence. 

the fluorescence quantum yield, ( )f, is the fraction of excited molecules that fluoresce. This is given by the rate of fluorescence, Jf, divided by the rate of absorption, Jabs  

Under conditions of steady illumination, a steady state will be reached, where the rate of formation of excited molecules, R, is equal to the rate of deactivation by the intramolecular processes  

An order-of-magnitude estimate of the radiative lifetime of Si is given 

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The primary photophysical processes occuring in a conjugated molecule can be represented most easily in the Jablonski diagram (Fig. 1). Absorption of a photon by the singlet state So produces an excited singlet state S . In condensed media a very fast relaxation occurs and within several picoseconds the first excited singlet state Si is reached, having a thermal population of its vibrational levels. The radiative lifetime of Si is in the order of nanoseconds. Three main routes are open for deactivation ... 

In the previous sections we have shown that all existing theories qualitatively indicate that the probability for internal conversion decreases as the energy separation increases. Because of this, and the fact that excited singlet states have rather short radiative lifetimes we feel that internal conversion from the first excited singlet to the ground state, as discussed in these theories, would not be competitive with the radiative process. 

Upper excited states are extremely short-lived. When the molecule is promoted to an excited singlet state beyond S1 the non-radiative deactivation by internal conversion is much faster than the spin-forbidden intersystem crossing to any triplet state. Therefore, the first excited singlet state is formed with near unit quantum yield. If an upper triplet state could be reached, it would also deactivate very rapidly to T1 and no singlet excited state would be formed. The extremely short lifetime of all upper excited states Sb(m>1) and Tb(w>1) means that luminescence emission and chemical reaction are, as a rule, not observed from such states. There are some exceptions to this rule, but there are many more mistaken reports of chemical reactions from short-lived upper excited states. Any such report... 

The energies of the planar ground and excited states are taken from the review of Saltiel et al. (1) and are summarized in Table 1. Isomerization of It and lc is presumed to occur via a common twisted intermediate Ip without intersystem crossing to the triplet manifold. The minimum is ascribed to either an avoided or allowed crossing of the first ( Bu ) and second (lAg ) excited singlet states (13). The fluorescent It state has a radiative lifetime of 1.7- 2.7 ns. A barrier of... 

The well known anomalous fluorescence from S2 has been interpreted in terms of a much slower radiationless transition out of S2 than Si, such that for Si the fluorescence lifetime is severely shortened relative to the radiative lifetime. The anomaly is related to the unusual energy disposition of the two lowest excited singlet states. Hochstrasser and Li wished to ascertain whether the spectral linewidths were consistent with this interpretation and also whether the Si linewidths of azulene-ds were narrowed in comparison, as theoretically predicted. Their results are listed in Table 1. The spectral resolution was claimed to be <0.15 cm-1 as linewidths in the S2 system corresponding to the observed fluorescence lifetime are of the order of 10-4 cm-1, the linewidths of 0.50 cm-1 measured must be considered crystal-imposed. It is assumed that the maximum crystal inhomogeneity contribution to the Si linewidth is similarly 0.50 cm-1. This leads to a line broadening due to rapid nonradiative electronic relaxation of 1.61 (-hs) and 1.27 (-da) cm-1 as compared to 0.64 cm-1 (-hs) determined by Rentzepis 50> from lifetime studies of azulene in benzene solution at 300 K. 

Fluorescence lifetimes of the first excited singlet states of HSO and DSO. Analytical expression used to compute vibrational energy dependence of non-radiative rates Dye-laser excitation spectrum of A A (004) — X A (000) band of HSO... 

The lifetimes of molecules in the lowest excited singlet state are typically of the order of 10 "-10 7 s. Typical rates of proton transfer reactions are 10" s 1 or less. Consequently, excited-state proton transfer may be much slower, much faster, or competitive with radiative deactivation of the excited molecules. 

Eq. 20 is only valid if 0a 0, cind fx - 0. This implies that radiationless processes occur from the triplet state only, and furthermore that the radiationless processes occur only from the Ty and T sublevels. The Tx sublevel decays predominantly by radiative processes at 1.2 °K. This little calculation assumes, of course, that the sublevel decay constants measured at 1.2 K may be applied to quantum yield data at 77 K. As we will discuss in more detail in a later section, the low temperature decay constants predict a somewhat longer triplet lifetime than is observed experimentally at 77 °K which indicates the presence of thermally-activated radiationless quenching of the tryptophan triplet even at liquid nitrogen temperature. This effect is rather small, however, and should not affect the general conclusions reached above concerning the energy d radation pattern of the tryptophan excited singlet state. The decay pattern of the triplet sublevels of tryptophan is shown in Fig. 8. 

Considerable information is available on electronic states of NO and 2 and their lifetimes. Because tandem experiments have an intrinsic time delay of tens of microseconds between ion formation and reaction, excited singlet states will undergo radiative decay to the ground state, either directly or via cascade processes, before the reactant ions reach the... 

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