Spin conversion recombination

The theory of geminate recombination experienced a similar evolution from primitive exponential model and contact approximation [19,20], to distant recombination carried out by backward electron transfer [21], However, all these theories have an arbitrary parameter initial separation of reactants in a pair, / o. This uncertainty was eliminated by unified theory (UT) proposed in two articles published almost simultaneously [22,23], UT considers jointly the forward bimolecular electron transfer and subsequent geminate recombination of charged products carried out by backward electron or proton transfer. The forward transfer creates the initial condition for the backward one. This is the distribution of initial separations in the geminate ion pair/(ro), closely analyzed theoretically [24,25] and inspected experimentally [26,27], It was used to specify the geminate recombination kinetics accompanied by spin conversion and exciplex formation [28-31], These and other applications of UT have been covered in a review published in 2000 [32],... 

The border between the irreversible and reversible ionization lies at a AG, value where the rate of the backward transfer to the ground state equals the rate of reverse transfer to the excited state kb(AG°) = kc(AG°). As a rule AG° is negative and not small, so that the border (indicated by the dashed line in Fig. 3.47) is far below the resonance reached at AG, = 0. To shift it up another channel of charge, recombination should be opened and its rate must be faster than kc. This ionic reaction may be parallel to that included in scheme (3.90) or recombination through the triplet channel proposed in Refs. 107 and 150. The latter is discussed in Section XI among other reactions affected by the spin conversion. 

Here we will confine ourselves mainly to the incoherent (rate) description of spin conversion, which provides the simplest way to account for spin-forbidden recombination of RIPs in complex photochemical reactions. Since ks from Eq. (3.557) depends on H through co-(H), the charge separation yield is also affected by the magnetic field. Therefore, the ratio... 

From now on the recombination efficiency Z depends not only on the starting point ro and encounter diffusion coefficient D but also on the spin conversion rate ks. 

If there is no spin conversion (x ks 0), the recombination is entirely absent Z = 0 and cp = 1. Otherwise we have the following for the slow and fast spin conversions ... 

The only difference from the single-channel EM outlined above (Section V.A) is the substitution of k et by the sum of the spin-allowed and spin-forbidden transfer rates k et + k c, to the ground and triplet states, respectively. Like k-eh the intersystem crossing rate kKC does not depend on viscosity. Moreover, EM does not separate the two different steps of the forbidden transition spin conversion to the triplet RIP and subsequent allowed electron transfer into the triplet product [212-216]. However, as has been shown in Section XI.A, even in the case of a single channel but spin-forbidden reaction (I), one should discriminate between the spin conversion and subsequent recombination through electron transfer. The qualitative difference between the spin-allowed and... 

In the opposite limit of infinitely fast spin conversion the recombination through the singlet channel is 4 times slower because of the full equilibration of the spin state populations of RIPs. 

A similar result was expected in Ref. 221 for cps(c>) = 1 — cp(cr), but the obtained difference between the recombination rates in the opposite limits was half as much kc for the slowest conversion and kj2 for the fastest one. This is because the isotropic Ag mechanism determining the spin conversion in Ref. 221 mixes the singlet with the 7b) sublevel only. In the rate approximation one can easily get the same, assuming that the spin transitions between the singlet and triplet RIPs occurs with equal rates in the forward and backward directions as in Eq. (3.585b). However, the transition from the slow to the fast conversion limit resulting from the rate approximation differs somehow from that obtained with the Hamiltonian approach in Ref. 221. 

With the constraint (3.601) at any spin conversion (p(r) is exactly the same as in the equation of the spinless theory, (3.211). This is because the transitions between the singlet and triplet RIPs do not modulate their recombination rates, leaving z = kc/4na as well as product yields, 1 [Pg.318]

Figure 3.76. The effect of spin conversion on /E (a) and

Even more straightforward evidence in favor of recombination to the triplet state was obtained by heavy-atom substitution into the fluorescence quencher, which also enhances the rate of spin conversion. By measuring the transient absorption of both ion radicals and the triplet products of their recombination, it was demonstrated that the quantum yield of triplets increases when the charge separation yield 9(0) decreases as a result of heavy-atom substitution [225]. As was shown in Figure 3.76, triplet state is faster than to the singlet state, while the quantum yield of triplets produced from the singlet precursor only increases with ks. Hence these data also indicate that the triplet channel of recombination is the most efficient. 

As a result of spin conversion, the initial singlet state of this pair changes to a triplet one and thus opens the way for the electron transfer to a triplet product as well. This becomes possible in parallel with the allowed RIP recombination through a singlet channel, to either the excited or ground states, M- or M- as in Section XI.C ... 

It is instructive to note that neither of these quantities depends on x if k r = kt. In this particular case the spin conversion does not modulate the rate of recombination so that cp = (1 + ksr/kD) l as in the spinless theory and w j is the weight of the singlet in the uncorrelated pairs composed in the bulk. 

As has been shown, the fitting of the linear viscosity dependence of chemiluminescence is completely different if the geminate recombination is considered alone or accompanied by the bulk reaction. In the former case the faster the spin conversion, the better, while in the latter case it can be set to zero provided the rate of electron transfer through the triplet channel is high enough. A similar alternative will be presented in the next section. There the combination of geminate and bulk reaction appears more preferable, especially because the spin conversion carried out by the hyperfine interaction is usually weak. 

The shape of the kernels (3.651) is rather obvious from the physical point of view. The kernels R and R are exactly the same as in Eq. (3.369) of the spinless theory. When spin conversion during encounter is negligible, the backward electron transfer to the ground state remains the single channel of geminate ion recombination. Therefore, the kernel R is 4 times smaller than... 

The first two represent the reversible ionization of the triplet excitations and accumulation of triplet RIPs. In the absence of the spin conversion, since there is no geminate recombination of triplet RIPs to the ground state these kernels are equal. R describes the recombination of triplet RIPs to the triplet excited states. The last kernel represents the recombination of ions to either the triplet or ground state, in proportion to the equilibrium weights of competing channels. 

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