Spin-correlated Pairs

3 Spin-correlated Pairs. Spin-correlated radical pairs have been studied for many years now through both transient and pulsed EPR. These have proved to be powerful techniques in analysing the radical pairs that are formed as shortlived intermediates in the primary energy conversion steps of photosynthesis and a general review has appeared recently showing the application of transient EPR to Photosystem I.  

However, in many cases a multi-frequency approach has been found to be most useful, as shown by two recent comprehensive studies on the structure of the Ptoo Ai radical pair intermediate in Photosystem I. These combined multifrequency studies at X- and Q- (and W-) band to determine the main structural parameters and then used W-band studies to work out the orientation of the radical pair with respect to the membrane plane.In one study this was achieved by using magneto-orientation of photosynthetic centres by freezing the sample in the presence of the magnetic field (3.5 T) to get quasi-single crystal spectra. However, in the other study the g tensor of Pyoo was measured directly using single crystals of Photosystem I (which have only recently become available).  

The fact that the singlet-triplet mixing in radical pairs becomes faster at high fields, due to the increase of the Zeeman interaction, can also permit modelling of the sequential electron-transfer process of both the primary and secondary pairs. The importance of protein dynamics on the electron-transfer rate was noted in a 95 GHz study of bacterial photosynthetic reaction centres with slow electron-transfer rates.  

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CIDEP originates in two independent processes, the triplet mechanism and the radical pair mechanism. The last one arises in spin correlated pairs [60]. The final spectrum gives a direct insight in the working mechanism. 

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

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,... 

As has already been mentioned, the spin-correlated pair can oscillate between the singlet and triplet states. The origin of these oscillations is illustrated by the vector diagram for the case when a pair is located in strong magnetic field (Figure 3). The pair bom in the singlet state can convert into the Tq state and vice versa if the Larmor precession fi-equencies of two spins are different. The difference in the fi-equencies can be due to a difference in both g-factors and... 

Formally, a pattern of quantum beats can be characterized by the parameters such as the set of oscillation fi-equencies, oscillation decay time, the phase shift of oscillations, and, finally, their amplitude. Each parameter contains useful information about the processes in radiation spurs. The oscillation frequencies correspond to the splittings in the ESR spectrum of radical ions. The decay of oscillations contains information about spin relaxation times. The phase shift reflects the time delay of pair formation from its precursor. Finally, the amplitude of oscillating component is determined by the fraction of spin correlated pairs. 

Here F(t)is the recombination rate of the ion pair, 9 is the fraction of spin-correlated pairs, which is assumed to be constant but can vary for different chemical systems and pss (t) is the time dependence of the singlet state population of the spin-correlated pair. The second term in Eq. (8.2) includes the contribution of the singlet component of the spin-uncorrelated pairs to the fluorescence intensity. Typically, the results of the TR MFE decay are presented as a ratio of the fluorescence intensity at an applied field (Ib ) and at zero field (7o), which becomes independent of the unknown function Fit). 

Table 8.5 Spin relaxation time as a function of t (fraction of pairs that recombine via crossrecombination) and 9 (fraction of original spin-correlated pairs that recombined)...

Utilizing FT-EPR teclmiques, van Willigen and co-workers have studied the photoinduced electron transfer from zinc tetrakis(4-sulfonatophenyl)porphyrin (ZnTPPS) to duroquinone (DQ) to fonn ZnTPPS and DQ in different micellar solutions [34, 63]. Spin-correlated radical pairs [ZnTPPS. . . DQ ] are fomied initially, and the SCRP lifetime depends upon the solution enviromnent. The ZnTPPS is not observed due to its short T2 relaxation time, but the spectra of DQ allow for the detemiination of the location and stability of reactant and product species in the various micellar solutions. While DQ is always located within the micelle, tire... 

Figure Bl.16.22. Schematic representations of CIDEP spectra for hypothetical radical pair CH + R. Part A shows the A/E and E/A RPM. Part B shows the absorptive and emissive triplet mechanism. Part C shows the spin-correlated RPM for cases where J and J a.. ...

Buckley C D, Hunger D A, Here P J and McLauchlan K A 1987 Electron spin resonance of spin-correlated radical pairs Chem. Phys. Lett. 135 307-12... 

Avdievich N I and Forbes M D E 1995 Dynamic effects in spin-correlated radical pair theory J modulation and a new look at the phenomenon of alternating line widths in the EPR spectra of flexible biradicals J. Phys. Chem. 99 9660-7... 

Forbes M D E, Avdievich N I, Schulz G R and Ball J D 1996 Chain dynamics cause the disappearance of spin-correlated radical pair polarization in flexible biradicals J. Phys. Chem. 100 13 887-91... 

Since the coiTelation between opposite spins has both intra- and inter-orbital contributions, it will be larger than the correlation between electrons having the same spin. The Pauli principle (or equivalently the antisymmetry of the wave function) has the consequence that there is no intraorbital conelation from electron pairs with the same spin. The opposite spin correlation is sometimes called the Coulomb correlation, while the same spin correlation is called the Fermi correlation, i.e. the Coulomb correlation is the largest contribution. Another way of looking at electron correlation is in terms of the electron density. In the immediate vicinity of an electron, here is a reduced probability of finding another electron. For electrons of opposite spin, this is often referred to as the Coulomb hole, the corresponding phenomenon for electrons of the same spin is the Fermi hole. 

Using a variety of transient and CW spectroscopies spanning the time domains from ps to ms, we have identified the dominant intrachain photoexcitations in C )-doped PPV films. These are spin-correlated polaron pairs, which are formed within picoseconds following exciton diffusion and subsequent dissociation at photoinduced PPV+/Cw> defect centers. We found that the higher-energy PA band of polaron pairs is blue-shifted by about 0.4 eV compared to that of isolated polarons in PPV. 

O.G. Poluektov, L.M. Utschig, A.A. Dubinskij and M. Thurnauer, ENDOR of spin-correlated radical pairs in photosynthesis at high magnetic field A tool for mapping electron transfer pathways, J. Am. Chem. Soc., 2004, 126, 1644. 

Thus it is of some interest to know if the Stoll ansatz is correct, especially since several other ansUtze have been developed and used as input to a spin-resolved pair correlation function. For example, Perdew and Wang (PW) [51,52] proposed a scaling relation... 

The discovery that azo compounds undergo singlet sensitized decomposition is particularly relevant to the problem of spin correlation effects in free radical reactions. Any radical pair precursor that gives a difference in products depending upon whether it is produced as a singlet or triplet excited state is said to show a spin correlation effect. 

In one of the earliest spin correlation studies, Hammond and Fox159a produced cyanocyclohexyl radicals by photolysis of azo-l-cyanocyclohexane (40) and its related ketenimine (41) (cf. Fig. 5). The radical pairs that do not... 

In Chap. 6, Sect. 4, the effect of a magnetic field on the probability and the rate of (neutral) radical radical-pair recombination was discussed. Much of this can be extended to the case of ion-pair recombination. There are three means by which spin correlation may be lost [403]. 

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