Triplet spin-lattice relaxation time

CIDEP Initial Polarization. The establishment and the development of the photoexcited triplet mechanism in CIDEP of transient radicals in solution had been rather controversial, if not as turbulent and exciting as the photoexcitation process itself. The early objections centered around two very important questions. The first one concerns the uncertainty of whether the spin polarization in the molecular frame can be effectively transferred to the laboratory frame for triplet systems in liquid solution. The second related question involves the fact that the polarized triplet molecules are rotating rapidly with respect to the laboratory axes and the triplet spin lattice relaxation time T x (normally between 10 and lO-- - s) would be too short for the polarization to be retained in the radical pair. The earlier photoexcited triplet mechanism developed by Wong et al. (136,137) is based on a "static model" with the excited triplet molecules being randomly oriented. Such a static model cannot deal satisfac-... 

A technique for measuring triplet spin-lattice relaxation times in fluid solution, based on the observation of chemically induced electron spin polarization, in the presence of a triplet quencher, has been applied to duroquinone with triethylamine as the triplet quencher.237 E.s.r. studies of the triplet states of 9-aza-bicyclo-... 

Interestingly, the spin-lattice relaxation time according to the direct process involving the triplet substates II and I remains unchanged within fimits of experimental error. For Pt(2-thpy-hg)2 and for Pt(2-thpy-dg)2 the sir times at T = 1.3 K are r jj. (720 10) ns and (710 10) ns, respectively (see Sect. 4.2.7.2 and Ref. [23]). Obviously, perdeuteration of the chromophore does not strongly influence the sir at low temperatures. Moreover, it is indicated that the matrix cages of the two compounds in n-octane are similar. Otherwise one would expect to observe distinctly different sir times as has been shown for Pt(phpy)2 (compare Fig. 1) in n-octane [64]. 

Fig. 26. Energy level diagram for the triplet sublevels of (a) perprotonated, (b) partially deu-terated, and (c) perdeuterated Pt(2-thpy)2 dissolved in an n-octane matrix (Shpol skii matrix). Emission decay times and spin-lattice relaxation times are given for T= 1.3 K. Several vibrational satellites are specified, HT = Herzberg-Teller active vibration, FC = Franck-Condon active vibration. The emission spectrum of the partially deuterated compound (b) exhibits vibrational satellites of the two different ligands. (Compare Fig. 27b.) The data given for Pt(2-thpy-hg)(2-thpy-d6) (b) refer to the lower lying site A. (Compare Ref. [23])...

Table 11. Energies of electronic states [cm emission decay and spin-lattice relaxation times of triplet sublevels (I, II, and III) at T< 3 K. The compounds are arranged according to an increasing value of the total zero-field splitting AEjnj...

Since singlet-triplet mixing can be induced by the application of a static field, the spin dynamics can be investigated using the time-resolved magnetic field effect (TR MEE) on fluorescence. This method has been exploited to give measurements of spin-lattice relaxation times [8, 9]. It has been well documented in the literature that the experimentally observed fluorescence intensity I (t) can be expressed by the relation ... 

With temperature increase from T = 1.2 K to T > 5 K, the decay behavior changes drastically. At T = 5 K, the decay is already monoexponential with a decay time of r(5 K) = (230 10) ps (Plot (b) of Fig. 6). Within limits of experimental error this value is constant at least up to T = 40 K [57]. Obviously, temperature increase induces an efficient spin-lattice relaxation between the three triplet substates. This leads to a fast thermalization. The observed monoexponential decay demonstrates that the sir is much faster than the shortest emission decay component. 

The results discussed above have shown that time-resolved emission spectroscopy can provide detailed insight into vibronic deactivation paths of triplet substates, even when the zero-field splitting is one order of magnitude smaller than the obtainable spectral resolution (= 2 cm ). This is possible at low temperature (1.3 K), because the triplet sublevels emit independently. They are not in a thermal equilibrium due to the very small rates of spin-lattice relaxation between these substates. In the next section, we return to this interesting property by applying the complementary methods of ODMR and PMDR spectroscopy to the same set of triplet substates. 

Figure 11 shows that deuteration of the matrix material has an interesting and not anticipated effect on the temperature dependence of the emission decay of Pd(2-thpy)2. At r = 1.3 K, one observes the three individual decay components of the three triplet substates I, II, and III, as discussed in Sect. 3.1.3. Within limits of experimental error, deuteration of the n-octane matrix does not alter this decay behavior. (Compare Fig. 11a to Fig. 6 a.) With temperature increase, the emission decay times are reduced in both matrices due to effects of thermaliza-tion between the three triplet sublevels, i.e. due to the growing in of spin-lattice relaxation (e.g. see Sects. 3.1.3 and 4.2.6). These processes are particularly important for the long-Hved components. For example, already at T = 2.0 K this component is reduced to 950 ps and 840 ps for the deuterated and the protonated matrix, respectively (decay curves not reproduced). This trend continues, as is shown in Fig. 11b. At T = 3.0 K, the long-decaying components are determined to 460 ps and 320 ps, respectively. Finally, near T=5 K, thermal equilibration between the three substates is reached for both matrices, and the decays become monoexponential. (Fig. 11c, compare also Sect. 3.1.3.) At this temperature, the emission decay of Pd(2-thpy)2 is again almost equal in n-octane-hig and n-octane-dig.

Fig. 21. Temperature dependence of the rate k and time ijir of spin-lattice relaxation of state II of Pt(2-thpy)2 dissolved in n-octane. The experimental data (points) result from the emission decay times of state II, but they are corrected according to Eq. (21). The solid line represents a fit according to Eq. (22), while the broken and dotted lines give the contributions of the respective processes. The inset shows the triplet sublevels and depicts schematically the three different processes of spin-lattice relaxation. (Compare Ref. [24])...

In conclusion, it is possible for Pt(2-thpy)2, to separate the emission spectra that are super-imposed in time-integrated spectra by time-resolved emission spectroscopy. It is important that one also obtains a low-temperature (1.3 K) emission spectrum from a higher lying state with the corresponding high spectral resolution. This possibility is a consequence of the relatively slow spin-lattice relaxation. Or vice versa, since the monitored time-resolved emission spectra are clearly assignable to different triplet substates, these results nicely support the concept of a slow spin-lattice relaxation as developed above. Moreover, the results presented reveal even more distinctly a triplet substate selectivity with... 

Fig. 24. Triplet substates I, II, and III of Pt(2-thpy)2 dissolved in an n-octane matrix, T=1.3 K. The vibrational levels of the excited states are given as examples. They refer to the substates II and III, respectively. By use of the new method of time-resolved excitation spectroscopy (Sect. 4.2.9), it is demonstrated that an inter-substate crossing does not occur via excited vibrational states, but it takes place after a fast relaxation to the zero-point vibrational level of the respective triplet substate by relatively slow processes of spin-lattice relaxation [60]. The rates kj[j [24,60,62,64,65] and k%j [65] are determined in the references given (see also text). The intra-state relaxation rate of k ,- = 10 s has been estimated for Pd(2-thpy)2 (Sect. 3.1.2.5). Several vibrational levels of the ground state are also given. PC and HT, respectively, refer to Franck-Condon and Herzberg-Teller activity in the respective radiative deactivations. (Compare Sect. 4.2.4)...

In conclusion, time-resolved excitation spectroscopy or, more correctly, excitation spectroscopy with time-resolved detection of emission, opens access to studies of intra- and inter-system crossing paths, i.e. of relaxation paths within or between hypersurfaces of different triplet substate systems. This method -applied for the first time in our investigation [60] for transition metal complexes - complements other measurements of pico-/subpico-second time resolution. In particular, it is shown that after an excitation of a vibrational state of an excited electronic triplet substate, the relaxation proceeds within the same triplet substate system downwards to the zero-point vibrational level. Subsequently, an inter-system crossing to a different sublevel system occurs in a relatively slow process by spin-lattice relaxation. This result fits well to the concept that a spin-flip is usually slower than the process of intra-state relaxation. 

Finally, we discuss briefly the emission decay behavior. At T = 1.3 K, the emission decay time is mainly determined by radiative and non-radiative processes of state I. For Pt(2-thpy-hg)(2-thpy-dg) one finds a value of (120 3) ps, which thus lies between (110 3) ps and (140 3) ps of the perprotonated and per-deuterated compounds, respectively (see also Fig. 26). Apart from the effects of spin-lattice relaxation occurring in the first microseconds, the decay is strictly monoexponential, at least over five lifetimes. It is important that the decay is exactly equal, when measured on a vibrational satellite, which is related to the protonated part of the molecule (e.g. 713 cm satellite) and to the deuterated part (e. g. 685 cm satellite), respectively. (Fig. 27b) This result also strongly supports the assignment to a delocalized excited state. A similar behavior has also been observed for [Oslbpylj], for which the lowest triplet states are also delocalized [47]. 

Due to the slow processes of spin-lattice relaxation, an emission of a higher lying triplet substate cannot be frozen out even at very low temperature. Thus, emissions of different substates are often superimposed in the usually monitored time-integrated spectra. This fact can strongly complicate an interpretation. However, by use of the method of time-resolved emission spectroscopy, separated triplet sublevel spectra are obtained for Pd(2-thpy)2 (Fig. 8) and for Pt(2-thpy)2 (Fig. 22). Thus, a more reliable assignment of the spectra, particularly in the regions of the vibrational satellites is achieved [58,60]. 

By monitoring excitation spectra with a time-resolved detection of the emission, briefly called time-resolved excitation spectroscopy , it is possible, to identify specific relaxation paths. Although, these occur on a ps time scale, only measurements with a ps time resolution are required. It is shown that the relaxation from an excited vibrational state of an individual triplet sublevel takes place by a fast process of intra-system relaxation (on the order of 1 ps) within the same potential surface to its zero-point vibrational level. Only subsequently, a relatively slow crossing to a different sublevel is possible. This latter process is determined by the slow spin-lattice relaxation. A crossing at the energy of an excited vibrational/phonon level from this potential hypersurface to the one of a different substate does not occur (Fig. 24, Ref. [60]). This method of time-resolved excitation spectroscopy, applied for the first time to transition metal complexes, can also be utilized to resolve spectrally overlapping excited state vibrational satellites and to assign these to their triplet substates. 

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