Resonance condition spin Hamiltonian

Our task is now to write out the spin Hamiltonian Hs, to calculate all the energy-matrix elements in Equation 7.11 using the spin wavefunctions of Equation 7.14 and the definitions in Equations 7.15-7.17, and to diagonalize the complete E matrix to get the energies and the intensities of the transitions. We will now look at a few examples of increasing complexity to obtain energies and resonance conditions, and we defer a look at intensities to the next chapter. 

In this chapter we continue our journey into the quantum mechanics of paramagnetic molecules, while increasing our focus on aspects of relevance to biological systems. For each and every system of whatever complexity and symmetry (or the lack of it) we can, in principle, write out the appropriate spin Hamiltonian and the associated (simple or compounded) spin wavefunctions. Subsequently, we can always deduce the full energy matrix, and we can numerically diagonalize this matrix to obtain the stable energy levels of the system (and therefore all the resonance conditions), and also the coefficients of the new basis set (linear combinations of the original spin wavefunctions), which in turn can be used to calculate the transition probability, and thus the EPR amplitude of all transitions. 

Polarization-transfer experiments which are based on a resonance condition, i.e. where a variable quantity in the experiment is matched to a parameter of the investigated spin system, can be carried out as a transient experiment or as an adiabatic experiment Figure 11.5 illustrates the differences between these two types of experiments. In a transient or sudden" experiment, the density operator is prepared in a state orthogonal to the effective polarization-transfer Hamiltonian (Fig. 11.5a). When the polarization-transfer Hamiltonian is switched on, the density operator starts precessing around the effective Hamiltonian, and usually maximum polarization transfer is reached after a 180° rotation. Since often the size of the effective Hamiltonian at the matching condition depends on... 

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