Quantum treatment of the effects of dipole–dipole interactions in liquid nuclear magnetic resonance

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Abstract
Experimental observation of anomalous intermolecular cross‐peaks in two‐dimensional solution NMR spectra have attracted significant recent attention. Extremely simple pulse sequences on extremely simple samples with large equilibrium magnetization give resonances in the indirectly detected dimension which are simply impossible in the conventional density matrix framework of NMR. Here we extend a recently proposed density matrix treatment [Science 262, 2005 (1993)] to calculate the exact time evolution for a variety of pulse sequences. This density matrix treatment explicitly removes two fundamental assumptions of the standard theory—it includes the dipolar interaction between spins in solution (which is only partially averaged away by diffusion) and completely removes the high temperature approximation to the equilibrium density matrix [exp(−βH)≊1−βH]. We compare this quantum mechanical treatment to a corrected classical model, which modifies the dipolar demagnetizing field formulation to account for the effects of residual magnetization, and show that the quantum picture can be reduced to this corrected classical model when certain assumptions about the retained dipolar couplings are valid. The combination of quantum and classical pictures provides enormously better predictive power and computational convenience than either technique alone.