Coherent Spin-State Mixing

The complete spin Hamiltonian for the RP in zero and applied field can be written as follows  

MAGNETIC FIELD EFFECTS ON RADICAL PAIRS IN HOMOGENEOUS SOLUTION 

FIGURE 8.4 The spin Hamiltonian for the simplest RP consisting of one electron and a radical with a single spin-1/2 nucleus on the basis of the high-held S/T states. The coupling between individual RP spin states can be directly obtained from the off-diagonal elements. 

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

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... 

To understand any coherence other than SQC, we need a new and more general definition of coherence. Coherence arises from the quantum mechanical mixing or overlap of spin states ( superposition ). In the two spin system (I, S = ll, 13C) we have four spin states (aa, up, pa, and PP), which are all stable states of defined energy. Let s talk about a single - C pair (one molecule). It is possible for this pair to be in any one of the four energy states, but it is also possible for the pair to be in a mixture or overlap or superposition of two states. This is one of the fundamental tenets of quantum mechanics Sometimes you cannot be sure which energy state a particle is in. Let s say that this particular pair is in a mixture of states aa and pp ... 

In the previous section, we learned how the recombination probability of a radical pair depended on the coherent mixing of the spin states caused by the S-To mixing. On the other hand, it also depends on the incoherent mixing caused by transversal and longitudinal relaxation. In this section, we will show that one can obtain a qualitative understanding of these effects by considering the spin evolution described by the Bloch equations. From textbooks of Quantum Mechanics, any Hermitian operator F has the following property ... 

Second, the mapping approach to nonadiabatic quantum dynamics is reviewed in Sections VI-VII. Based on an exact quantum-mechanical formulation, this approach allows us in several aspects to go beyond the scope of standard mixed quantum-classical methods. In particular, we study the classical phase space of a nonadiabatic system (including the discussion of vibronic periodic orbits) and the semiclassical description of nonadiabatic quantum mechanics via initial-value representations of the semiclassical propagator. The semiclassical spin-coherent state method and its close relation to the mapping approach is discussed in Section IX. Section X summarizes our results and concludes with some general remarks. 

The preparation period consists of the creation of a non-equilibrium state and, possibly, of the frequency labeling in 2D experiments. Usually, the preparation period should be designed in such a way that in the created non-equilibrium state, the population differences or coherences under consideration deviate as much as possible from the equilibrium values. During the relaxation period, the coherences or populations evolve towards an equilibrium (or a steady-state) condition. The behavior of the spin system during this period can be manipulated in order to isolate one specific type of process. The detection period can contain also the mixing period of the 2D experiments. The purpose of the detection period is to create a signal which truthfully reflects the state of the spin system at the end of the relaxation period. As always in NMR, sensitivity is a matter of prime concern. 

In this chapter multiple-pulse sequences for homonudear Hartmann-Hahn transfer are discussed. After a summary of broadband Hartmann-Hahn mixing sequences for total correlation spectroscopy (TOCSY), variants of these experiments that are compensated for crossrelaxation (clean TOCSY) are reviewed. Then, selective and semiselective homonudear Hartmann-Hahn sequences for tailored correlation spectroscopy (TACSY) are discussed. In contrast to TOCSY experiments, where Hartmann-Hahn transfer is allowed between all spins that are part of a coupling network, coherence transfer in TACSY experiments is restricted to selected subsets of spins. Finally, exclusive TACSY (E.TACSY) mixing sequences that not only restrict coherence transfer to a subset of spins, but also leave the polarization state of a second subset of spins untouched, are reviewed. 

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