Radical Pair Interactions

RP reactions have been found to be well described by the application of a spin Hamiltonian, a common approach used in the field of magnetic resonance, which reduces the full Hamiltonian to one that contains only spin-dependent terms. The interactions capable of influencing spin-state mixing processes in RPs are concisely introduced in the expression for the spin Hamiltonian of a RP, which can be written as a sum of interradical, intraradical, and external interactions. 

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Thurnauer M C and Norris J R 1980 An electron spin echo phase shift observed in photosynthetic algae. Possible evidence for dynamic radical pair interactions Chem. Phys. Lett. 76 557-61... 

In the limit, complete charge transfer leads to an ionic bond in a simple ion-radical pair interaction. In the solid state, the simple pair interaction may not be limited to two molecules but may extend further in a crystal. The ground state is thus partly ionic and may be described by a wave-function DA ... 

Fremy s Salt and Derivatives. Two free radicals were identified by e.s.r. spectroscopy when single crystals of potassium hydroxylamine disulphonate were irradiated with y-rays at 77 K. The identity of the predominant paramagnetic centre remains in doubt, but it appears to be a precursor to Fremy s radical, [0N(S03)2-], which is also present in small concentrations.156 Gangwer has carried out similar investigations but using X-ir-radiation. It was concluded that room-temperature near-neighbour proton and low-temperature radical pair interactions occur in the crystals.157... 

Step 1 Computation of all unique radical-radical pair interactions in the crystal. 

The above discussions may be summarized as follows when the acceptor side of the reaction center is oxidized, i.e., it is in the [Pd] QA-state, light activation produces the P -state, i.e., the [P" -r]-Q -state, where I is the transient intermediary electron acceptor, namely a BO molecule. When the reaction center is pre-reduced to the [Pdj QA -state, light activation produces the P -state, i.e., the [ P-l]-Q -state with a lifetime of 10 ns. Most of the radical pairs recombine to reform the original [P-I] state, but some form the triplet state of P. In the initial excited singlet state [P 4 ], the spins on and r are antiparallel. During the 10-n lifetime of the excited singlet state, the spins of the unpaired electrons on the radical pair interact with nuclear spins on the two molecules, or with the electron spins on or the nonheme iron atom, but in any case there is a rephasing of these two unpaired spins. Recombination of these radical pairs, now with a predominantly triplet character, leads to the formation of the triplet state of P, i.e., theP -state [P -r] QA" [P -H-Qa" -> Pdl-QA. ... 

JL McCracken and K Sauer (1983) Orientation dependence of radical pair interactions in spinach chloroplasts. Biochim Biophys Acta 724 83-93... 

It should be understood that we are not considering here a case in which some P Q radical pairs interact while others do not. In order to include this case we would calculate both the non-interacting radical pair spectrum (CIDEP) and the interacting radical pair spectrum (CRPP). We could then assign a fraction of the ensemble as interacting, with all others non-interacting. 

Figures 8 and 9 show the spin-polarized EPR spectra obtained from 2-TAPD -ZP-2-NQ and 2-TAPD -ZP-l-NQ, respectively, along with simulations of these spectra. The differences in both radical pair distance and orientation between these two molecules is reflected in changes in the EPR spectra of their radical pairs. Thus, the radical pair interactions are a sensitive probe of structure.

The first temi describes the electronic Zeeman energy, which is the interaction of the magnetic field with the two electrons of the radical pair with the magnetic field, Bq. The two electron spins are represented by spin... 

Figure Bl.16.5. An example of the CIDNP net effect for a radical pair with one hyperfme interaction. Initial conditions g > g2, negative and the RP is initially singlet. Polarized nuclear spin states and schematic NMR spectra are shown for the recombination and scavenging products in the boxes.

Figure Bl.16.8. Example of CIDNP multiplet effect for a syimnetric radical pair with two hyperfme interactions on each radical. Part A is the radical pair. Part B shows the spin levels with relative Q values indicated on each level. Part C shows the spm levels with relative populations indicated by the thickness of each level and the schematic NMR spectrum of the recombination product.

Wliile the earliest TR-CIDNP work focused on radical pairs, biradicals soon became a focus of study. Biradicals are of interest because the exchange interaction between the unpaired electrons is present tliroiighoiit the biradical lifetime and, consequently, the spin physics and chemical reactivity of biradicals are markedly different from radical pairs. Work by Morozova et al [28] on polymethylene biradicals is a fiirther example of how this method can be used to separate net and multiplet effects based on time scale [28]. Figure Bl.16.11 shows how the cyclic precursor, 2,12-dihydroxy-2,12-dimethylcyclododecanone, cleaves upon 308 mn irradiation to fonn an acyl-ketyl biradical, which will be referred to as the primary biradical since it is fonned directly from the cyclic precursor. The acyl-ketyl primary biradical decarbonylates rapidly k Q > 5 x... 

Closs G L and Trifunac A D 1970 Theory of chemically Induced nuclear spin polarization. III. Effect of Isotropic g shifts In the components of radical pairs with one hyperfine Interaction J. Am. Chem. Soc. 92 2183-4... 

Closs G L, Forbes M D E and Norris J R 1987 Spin-polarized electron paramagnetic resonance spectra of radical pairs in micelles. Observation of electron spin-spin interactions J. Phys. Chem. 91 3592-9... 

Norris J R, Morris A L, Thurnauer M C and Tang J 1990 A general model of electron spin polarization arising from the interactions within radical pairs J. Chem. Phys. 92 4239—49... 

The origin of postulate (iii) lies in the electron-nuclear hyperfine interaction. If the energy separation between the T and S states of the radical pair is of the same order of magnitude as then the hyperfine interaction can represent a driving force for T-S mixing and this depends on the nuclear spin state. Only a relatively small preference for one spin-state compared with the other is necessary in the T-S mixing process in order to overcome the Boltzmann polarization (1 in 10 ). The effect is to make n.m.r. spectroscopy a much more sensitive technique in systems displaying CIDNP than in systems where only Boltzmann distributions of nuclear spin states obtain. More detailed consideration of postulate (iii) is deferred until Section II,D. 

C. The Dynamic Behaviour of Badical Pairs A simple model (Fig. 4) will assist in visualizing the time-dependent variation of the separation and hence the interaction of the components of a radical pair. 

Here and H describe radicals A and B of the radical pair and He the interaction of their electrons. The other terms in equation (15) are H g, the spin orbit coupling term, H g and Hgj, representing the interaction of the externally applied magnetic field with the electron spin and nuclear spin, respectively Hgg is the electron spin-spin interaction and Hgi the electron-nuclear hyperfine interaction. 

OIDEP usually results from Tq-S mixing in radical pairs, although T i-S mixing has also been considered (Atkins et al., 1971, 1973). The time development of electron-spin state populations is a function of the electron Zeeman interaction, the electron-nuclear hyperfine interaction, the electron-electron exchange interaction, together with spin-rotational and orientation dependent terms (Pedersen and Freed, 1972). Electron spin lattice relaxation Ti = 10 to 10 sec) is normally slower than the polarizing process. 

Much stronger donor-acceptor interactions stabUze D+A too much to give rise to the pseudoexcitation. The electron transferred configuration is stable and predominant. Electrons transfer to generate ion radical pairs or salts. Covalent bonds do not form and electron transfer results. 

The existence of closely spaced radical pairs can be identified by spin-spin interactions in organic materials irradiated at low temperature [38] and these coupled spins disappear as the temperature is raised, because of both termination and radical migration. 

The trace of D vanishes when dipole coupling between paramagnetic centers determines the ZFS, since dipole interaction is traceless. A typical example is the ZFS of triplets arising from coupled radical pairs, for which SOC is negligible. For transition metal ions in contrast, SOC is the leading contribution to ZFS and the trace of Zl in general has finite values. 

The use of short (fs) laser pulses allows even highly transient ion-radical pairs with lifetimes of t 10 12 s to be detected, and their subsequent (dark) decay to products is temporally monitored through the sequential spectral changes. As such, time-resolved (ps) spectroscopy provides the technique of choice for establishing the viability of the electron-transfer paradigm. This photochemical (ET) mechanism has been demonstrated for a variety of donor-acceptor interactions, as presented in the foregoing section. 

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