Interspin vector

Four-pulse DEER measurements were performed on a dimer of copper-substituted azurin molecules with a Cu(II)-Cu(II) distance of 26 A.27 Experiments were performed at 10 K with pulse lengths of 16 ns for ji/2 and 32 ns for p pulses and a 75 MHz difference between the frequencies of the pump and observe pulses. Analysis of the dipolar frequencies required consideration of orientation selection in both the pump and observe pulses because only a subset of the Pake pattern is represented in the Fourier transform of the experimental data. For this sample the orientation of the interspin vector relative to the g matrices of the two centres was known from high-field EPR. Dipolar modulation could not be detected for a second dimer with a copper-copper distance of 14.6 A.27... 

The time dependence of the interaction can arise from variations in the interspin vector, r, due to the relative translational motions of the / and 5 spins. It can be shown that if the spins I and S are in different molecules and can be treated as diffusing independently, an expression for the reduced spectral density 7)1 =7d,co/- d,o can be obtained. The result is—... 

Fig. 5. Rectangular and polar coordinates to define interspin vector r.

In a nuclear magnetic resonance measurement in solution, the direct dipolar interaction Xo actually disappears because, due to rapid molecular motion, the interspin (internuclear) vectors are rapidly space-averaged within the time-scale of a measurement. Hence, the terms Xs and Xj are detectable as sharp lines or splittings in a high-resolution spectrum of H or and they can be related to detailed molecular structure or conformation of the substance investigated. In a solid, on the contrary, the directions of the internuclear vectors are stationary even if they are distributed randomly in space. Then, X gives a very wide linewidth to the zeroth-order absorption line and completely masks all lines due to Xs and Xj. 

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