Nuclear spin sorting

Second, there is usually no escape channel because the two radical termini cannot separate completely. This usually causes a fundamental difference between CIDNP from radical pairs and CIDNP from biradicals Being nuclear spin sorting as described above, intersystem crossing between IS) and ITq) crucially relies on both exit channels leading to different products, whereas intersystem crossing between IS) and IT i) occurs by simultaneous electron-nuclear spin flips, and so creates net nuclear polarizations without the need of different exit channels. 

Nuclear-spin selective intersystem crossing of the spin correlated pairs ("nuclear spin sorting")... 

The theory of CIDNP depends on the nuclear spin dependence of intersystem crossing in a radical (ion) pair, and the electron spin dependence of radical pair reaction rates. These principles cause a sorting of nuclear spin states into different products, resulting in characteristic nonequilibrium populations in the nuclear spin levels of geminate (in cage) reaction products, and complementary populations in free radical (escape) products. The effects are optimal for radical parrs with nanosecond lifetimes. 

The importance of different exit channels can hardly be overstressed. If both exit channels lead to the same product, the spin sorting is undone, and no S-Tq-t)q)e CIDNP results. However, a difference of reaction probabilities suffices for some CIDNP to remain. Another important factor avoiding a cancellation that would otherwise be perfect is nuclear spin relaxation in longer-lived paramagnetic intermediates, free radicals or triplet molecules. Even if there is a complete cancellation of the polarizations at long times but an imbalance of reaction rates, CIDNP occurs as a transient effect and can be detected in a time-resolved experiment. 

The different operating principle of generating nuclear spin polarizations, by electron-nuclear flip-flop transitions instead of by spin sorting, reduces the mechanism to a two-step scheme. 

Development of nuclear polarizations in the spin-correlated pairs or biradicals Because Equation (6) couples the nuclear spin motion and the electron-spin motion, not only the electron-spin state of each pair oscillates but also the nuclear spin state. Over the ensemble, however, the oscillation is not symmetrical because flip-flop fransifions are only possible for one-half of the pairs. Consider, for example, an ensemble of biradicals with one proton, and let the biradicals be bom in state F i). Taking into accoimt also the nuclear spin, one-half of fhe biradicals are fhus born in state T ia) and the other half in state T ijS). The latter cannot undergo flip-flop transitions to the singlet state, so have to remain in the state they were bom. The others oscillate between T ia) and I SjS). If a fracfion n of fhem has reached the singlet state, the total number of biradicals wifh nuclear spin a) is l-n)/2, and the total number of biradicals wifh spin jS) is n/2+1/2. The difference between the number of molecules wifh nuclear spin a) and jS) is fhus -n, in other words the system oscillates between zero polarization (n = 0) and complete polarization of one sort n = -1,... 

This is basically the mechanism described for the dyads of Section 6.6. Spin sorting occurs in the usual way but would be undone by the fact that singlet and triplet exit channels lead to the same product. If, however, the triplet is long lived (e.g. some lOOgs in reaction centres of Rhodobacter sphaeroides P26), a part of its nuclear spin polarizations is destroyed by relaxation, so the cancellation is not perfect, and CIDNP of the singlet exit channel dominates. 

Nuclear spins with different electronic environments may be brought into resonance by either one of two techniques. In the frequency-sweep method, the spectrum is recorded by sweeping the applied radiation frequency. In the transient-response method, the transient signal for its component frequencies is sorted/transformed after an induction (by pulse(s) of an applied field in terms of angles, e.g. 90° or 180°) of transient response in the system. The transient signal is changed into a normal spectrum by Fourier transformation in the transient-response method, which is used by most modem NMR spectrometers. There are four parameters that define the NMR spectrum ... 

The role of nuclear spins in chemical reactions does not seem to have been noted before the advent of CIDNP. It is easy to see, however, how (i) and (ii) can lead to a sorting mechanism for nuclear spins and therefore to strong polarizations in radical pair products. This is demonstrated in Figure 1, which shows a typical photo-induced radical reaction. 

Recalling the spin-sorting nature of the radical pair mechanism, we can anticipate that in the absence of nuclear spin relaxation, random recombination will eventually lead to exact cancellation of the + polarization when the + polarization in A is transferred to A (making the usual assumption that chemical reaction preserves nuclear spin orientation). In such a situation, polarization in A could only be observed in a time-resolved experiment before all the radicals had recombined. Relaxation of the nuclei A , however, allows some of the escape polarization to "leak away preventing complete cancellation (II). Thus, unless the radical lifetime is very much smaller than the nuclear... 

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