Knowledge Bank

The stationary part of the Hamiltonian describing a nuclear double resonance experiment on a three spin system, in a coordinate system rotating at the frequency of the strong radio frequency field is given, in the usual notation, by $$H=\Sigma_{i}A_{i}I_{z}(i)+\Sigma_{i,i}I_{}I_{}I_{i}+\Sigma_{i}V_{2i}I_{x}(i)$$ where the summations extend over the three spins. the last term in this expression, which is the essential feature of the double resonance Hamiltonian, connects states with different values of the z component of total spin, and it thus becomes necessary to diagonalize an $8\times 8$ matrix to calculate the transition energies and intensities in a ''frequency sweep'' experiment. A graphical $method2$ is described to obtain the ''field sweep'' double resonance spectra from the frequency sweep calculations. The method of analysis has been applied to the proton-proton double resonance spectrum of 2-amino, 3-methylpyridine. The two radio-frequency fields appropriate for the double resonance experiment were obtained by magnetic field modulation and the sideband resonances were detected by a lock-in $detector.3$ The principal features of the double resonance spectra seem to be adequately described by the method of analysis outlined. The resonances of the 4-proton in 2-amnio, 3-methylpyridine, which appear broad in a single resonance experiment, revealed a doubling when the methyl group is decoupled, showing that the broadening is due to small but significant coupling between the two kinds of protons.]