Perturbed radiative lifetime

Time dependent perturbation theory provides an expression for the radiative lifetime of an excited electronic state, given by Tr ... 

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. 

If one adopts the correct point of view that the complete wave function of any state of a diatomic molecule has contributions from all other states of that molecule, one can understand that all degrees of perturbation and hence probabilities of crossover may be met in practice. If the perturbation by the repulsive or dissociating state is very small, the mean life of the excited molecule before dissociation may be sufficiently long to permit the absorption spectrum to be truly discrete. Dissociation may nevertheless occur before the mean radiative lifetime has been reached so that fluorescence will not be observed. Predissociation spectra may therefore show all gradations from continua through those with remnants of vibrational transitions to discrete spectra difficult to distinguish from those with no predissociation. In a certain sense photochemical data may contribute markedly to the interpretation of spectra. 

In an actual experiment, it is frequently not possible to work under conditions where there are no relaxation effects. The usual reason for this is that the intensity of the fluorescence becomes too weak to observe as the concentration of excited molecules is reduced. The lowest pressures which can be used are defined by a number of parameters the strength of the transition, the power of the laser and the detection efficiency of the system are among the most important. It therefore follows that, in interpreting the results of lifetime measurements, one must consider carefully the possible effects of rotational and vibrational redistribution in the excited state. In a regular unperturbed state where there is little or no change in radiative lifetime with changes in rotational and vibrational level, the effects of relaxation are not observable so long as the fluorescence is still detected with the same efficiency. However, if the excited state is perturbed, for example by predissociation, then the effects of redistribution must be carefully studied. 

Two of the four investigated naphthyridines (1,8- and 2,7-naphthyridine with C%v symmetry) have one spin sublevel that is radiatively forbidden, the other two have all spin sub-levels active. Phosphorescent emission have been observed for all naphthyridines, but the radiative lifetimes are not available. The measured lifetime of 1,5-naphthyridine (0.02 s) is much shorter, than our radiative value. This again indicates that vibronic coupling (leading to non-radiative or radiative decay) is a strong contributor to the lifetimes of the triplet states of azanaphthalenes, in a perturbative sense thus stronger than the action of dipole and spin-orbit coupling. 

As the potential curves suggest, the A 2I1 and B 2S+ can mix considerably above about B 2S+(u = 5), and since the B 2S+ state has a shorter radiative lifetime, the 2 +-Y 2+ system predominates in the tail bands. The relative intensities of the perturbed lines at low pressure indicated that A 2I1 (t> = 10) was populated in CH2C12 flames about 30 times more rapidly than B 2S+(u = 0), and that A 11 (u = 7) was formed 4 times faster than X2X+ v = 11). 

The emission lifetimes of the bipy and phen complexes of ruthenlum(II) at 77°K are generally in the range t = 0.5-10 ps. (Table 7). Since these values are intermediate to those generally observed for the fluorescence and phosphorescence of organic compounds, the radiative transition in the ruthenium complexes was suggested to be a heavy-atom perturbed spin-forbidden process (168,169). From a determination of the absolute quantum yields as well as lifetimes of a series of ruthenium(II) and osmium(II) complexes, the associated radiative lifetimes were calculated (170). The variations in these inherent lifetimes within the series could be rationalized with a semi-emipirical spin-orbit coupling model thus affording further evidence that the radiative transitions are formally spin forbidden in these systems. 

From the emission lifetime (1 /is) and the luminescence quantum yield (< 10-4) at room temperature, the radiative lifetime is estimated to be > l0 Js, a figure expected for a perturbed 3LC emission and inconsistent with a 3MLCT emission for Rh(bpy)3+ [86] and Pt(tpy)2(CH2Cl)Cl, which are bona fide 3LC emitters, the radiative lifetime is 5xl0-3s-1, whereas for Ru(bpy) + [87] and Pt(tpy)2 (Section III.E.l), which are 3MLCT emitters, the radiative lifetime is -lx 10-5 s-1. 

Perturbations by States with Infinite Radiative Lifetime Simple Intensity Borrowing... 

The Nj ion, which is isoelectronic with CN, has similar B2E+ A2II perturbations. Dufayard, et al., (1974) have measured radiative lifetimes for individual... 

Figure 6.4 Mixing fractions in 30Si32S A1 II (o = 5). The deperturbation model fits all observed lines, main and extra, perturbed and unperturbed, in the spectrum without systematic residuals. Mixing coefficients computed from such a deperturbation model should be more accurate than from measurements of radiative lifetimes [Prom Harris, et al. (1982).]...

When one remote perturber, j), dominates the radiative lifetime of state z), where the j —> X transition is allowed, the lifetime of the t) state, Tj, can be easily estimated using experimental data, by the formula ... 

Radford (1961, 1962) and Radford and Broida (1962) presented a complete theory of the Zeeman effect for diatomic molecules that included perturbation effects. This led to a series of detailed investigations of the CN B2E+ (v — 0) A2II (v = 10) perturbation in which many of the techniques of modern high-resolution molecular spectroscopy and analysis were first demonstrated anticrossing spectroscopy (Radford and Broida, 1962, 1963), microwave optical double resonance (Evenson, et at, 1964), excited-state hyperfine structure with perturbations (Radford, 1964), effect of perturbations on radiative lifetimes and on inter-electronic-state collisional energy transfer (Radford and Broida, 1963). A similarly complete treatment of the effect of a magnetic field on the CO a,3E+ A1 perturbation complex is reported by Sykora and Vidal (1998). The AS = 0 selection rule for the Zeeman Hamiltonian leads to important differences between the CN B2E+ A2II and CO a/3E+ A1 perturbation plus Zeeman examples, primarily in the absence in the latter case of interference effects between the Zeeman and intramolecular perturbation terms. 

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