Spin-State Mixing

0 dliaiing magnetic moment perpendiciilar g epplied fteid  

Static magnetic moment In diredton of applied field  

FIGURE 8.3 Vector representation of RP spin states in an applied external magnetic field. The vectors are each in constant precession about the magnetic field axis at the Larmor frequency of the respective radical. 

Critical to the observation of magnetic field effects in solution is the ability of the RP to interconvert between triplet (nonreactive) and singlet (reactive) spin states. Having established the various interactions present in the RP, we can now consider how such a mixing process might take place. 

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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. 

The intraradical interactions provide the mechanism for coherent spin-state mixing and the interradical interactions act contrary to this process. 

Here, spin-state mixing is possible only at distances beyond Rq, and is the separation at which the radicals can recombine. D is the mutual diffusion coefficient for the radicals in the given solvent. 

It is possible to perform more precise calculations that simultaneously account for the coherent quantum mechanical spin-state mixing and the diffusional motion of the RP. These employ the stochastic Liouville equation. Here, the spin density matrix of the RP is transformed into Liouville space and acted on by a Liouville operator (the commutator of the spin Hamiltonian and density matrix), which is then modified by a stochastic superoperator, to account for the random diffusive motion. Application to a RP and inclusion of terms for chemical reaction, W, and relaxation, R, generates the equation in the form that typically employed... 

Here, H is the spin Hamiltoniam of the radical ion pair (RIP), R is the relaxation super operator, and K is the reaction operator. In H, the effect of the Zeeman interaction within the Ru -moiety is most efficient in pair spin state mixing due to the strong anisotropy of the g-... 

Ru -moiety is most efficient in pair spin state mixing due to the strong anisotropy of the g-... 

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