Nuclear Magnetic Double Resonance in Chemically Exchanging Systems

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Abstract
A density matrix description of nuclear magnetic double resonance on chemically exchanging systems is developed using a double resonance basis set. The chemical exchange coefficients have many properties analogous to the relaxation coefficients. This allows the density matrix computation to be expressed in terms of a symmetric array. The solutions can then be obtained in terms of an eigenvalue procedure. This procedure is more efficient than standard Gauss–Jordan reduction and automatically takes into account the constraints introduced by the summation properties of the relaxation and chemical exchange coefficients and by the symmetry of the spin system. The formalism is illustrated by self-exchange in the AB2 system, 2,2,2-trichloroethanol. Comparison of theoretical and experimental double resonance spectra allow the determination of the chemical exchange lifetime and the relaxation parameters even when the exchange rates are slow compared with the experimental linewidths.