Radiative lifetimes from integrated absorption

Although the direct measurement of fluorescence decay is to be preferred as a method for obtaining radiative lifetimes, they can be calculated from the Einstein B coefficient [99] (see also ref. 98) via an equation first derived by Strickler and Berg [100]. This equation gives good results for a wide variety of molecules when applied within the limits of its validity, i.e. the transition should be optically allowed and the electronic transition moment independent of nuclear configuration. 

The radiative lifetime may be calculated from the Einstein B coefficient as determined from the integrated absorption spectrum. The absolute intensity of electronic transitions is usually determined from the absorption spectrum since for emission it is difficult to determine the number of molecules in the excited state. The parameter measured experimentally is the absorption coefficient, kv, which is defined by the relation 

The direct measurement of the fluorescence lifetime of IC1 (A) by Bradley Moore and co-workers [76] has been discussed above. These authors also calculated the lifetime from the integrated absorption spectrum in the wavelength range 591.4—500.1 nm. Their calculated value for Bnm was (1.08 0.2) x 106 sg 1. The Einstein A coefficient for spontaneous emission is given by 

Species Excited state Ground state Lifetime  

Earlier fluorescence studies erroneously assigned to BO. Now shown [177] to be BO2. 

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The estimations of the radiative lifetime, from integrated absorption intensity, yield values between 0.3 fjsec (Neuberger and Duncan, 1959) and 1.5 isec (Donnelly and Kaufman, 1977), while the observed decay times are... 

The natural radiative lifetime is independent of temperature, but is susceptible to environmental perturbations. Under environmental perturbation, such as collisions with the solvent molecules or any other molecules present in the system, the system may lose its electronic excitation energy by nonradiative processes. Any process which tends to compete with spontaneous emission process reduces the life of an excited state. In an actual system the average lifetime t is less than the natural radiative lifetime as obtained from integrated absorption intensity. In many polyatomic molecules, nonradiative intramolecular dissipation of energy may occur even in the absence of any outside perturbation, lowering the inherent lifetime. 

It is realized that the mechanism just postulated is a greatly simplified version of a very complex situation unless either the fluorescence yield is unity and independent of pressure or there is no crossover to the triplet state. It must be mentioned that l/fc = to is the radiative lifetime of the upper singlet state, i.e., the quantity which in principle may be calculated from integrated absorption coefiScients. The observed lifetime will be l/13fci[M], where is the sum of all of the quantities... 

Since the 4550 cm-1 state is the first excited state of PuF6, its radiative lifetime can be determined to be a reasonable approximation by integrating the optical absorption spectrum of PuF6 over the wavelength range where absorption due to the 4550 cm- state occurs. Some uncertainty arises since optical absorption from the next higher state undoubtedly overlaps that due to the 4550 cm-1 state. 

The natural radiative lifetime gives an upper limit to the lifetime of an excited molecule and can be calculated from the integrated absorption intensity. The quantity to be plotted is e vs v if (3.96) is used and... 

There are established techniques for the determination of and np (Section 10.2). In this expression, kf and kp are reciprocals of the radiative lifetimes of flucrescene and phosphorescence states, respectively, kf can be obtained experimentally from the integrated area under the absorption curve and kp is obtained from the measured decay rates for phosphorescence at 77K in EPA. In Table 5.3 the observed quantities, their symbols, relation to rate constants and sources of studies are summarized. 

Fluorescence from ketene upon absorption of light in the near ultraviolet has not been observed. The quantum yield of fluorescence is less than 10 3. Since the radiative lifetime calculated from the integrated absorption cocflicicnt is 40 //see. the lifetime of the excited state must be less than 0.4 nsec. Since the lifetime of the initially formed excited state is much shorter than the dissociative lifetimes, an excited state responsible for dissociation must be different from the one initially formed at 3340 and 3660 A. 

As with N02, the observed radiative lifetime of the A 1Bl state of S02 (4 x 10"5 sec) is much longer than the value calculated from the integrated absorption coefficient (2 x 10" 7 sec)229. This is again presumably due to strong interaction with the electronic ground state203. 

If, therefore, l/iium is plotted as a function of [M], the ratio of slope to intercept provides a value of kq/A, even if Iium is measured in arbitrary units and Jabs is not determined. Thus, if the Einstein A factor is known, or can be measured, the value of the quenching rate constant can be calculated. The A factor can be calculated from the B factor by use of the v3 relationship presented as Eq. 9 (and B itself can be calculated from the measured integrated extinction coefficient for the absorption band, as implied by Eq. 15). It is also possible, under suitable conditions, to measure A directly by observation of the decay of emission after suddenly extinguishing the illuminating beam. As will be explained at the end of this section, the fluorescence or phosphorescence lifetime may be shorter than the natural radiative lifetime as a result of intermolecular and intramolecular nonradiative energy degradation, so that due care must be taken in the interpretation of emission decay measurements. 

Benzophenone is another example of a molecule showing small-molecule behavior in a specific region of its absorption spectrum 30<31). Here it concerns intersystem crossing between the lowest excited singlet and triplet states, which are separated by about 2800 cm-1. Very fast intersystem crossing is induced by inter molecular interactions 3°). Under isolated-molecule conditions relative to the radiative lifetime as calculated from the integrated oscillator strength, irreversible behavior is not obtained. 

With regard to lifetimes, it is often the case that the experimentally measured lifetime represents the decay of a specific excited state and can thus be equated to the mechanistic lifetime of that state. However, this need not be so. For example, the decay of E-type fluorescence follows the lifetime of the phosphorescing state (14). In principle, the radiative lifetime of an excited state can be determined indirectly from the integrated extinction coefficient of the absorption transition that connects the same two states as the emission. In practice, however, several difficulties are encountered in such a determination (6,8,14). 

In a very new report, Fujino et al. challenge the two-isomerization-mechanism concept on the basis of their time-resolved and time-integrated femtosecond fluorescence measurements of B-azobenzene following excitation of the (7t,7t ) State. They use the extremely weak fluorescence (cf. Figure 1.8) as an indicator for the population of the emitting state. From the ratios of their measured fluorescence lifetimes (S2 0.11 ps Sp 0.5 ps) and the radiative lifetimes deduced from the (absorption-spectra-based) oscillator strengths, they determine the fluorescence quantum yields 2.5310 for the emission and 7.5410" for the Si—>So emission. By comparison... 

In molecules such as the aromatic hydrocarbons for which the most experimental data are available, it was found that the fluorescence lifetimes were much shorter than that which could be deduced from the integrated absorption intensity. The latter provides the oscillator strength f, and a radiative lifetime... 

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