A physical picture of multiple-quantum coherence

Abstract

A pictorial physical model is proposed to describe the characteristic properties of homonuclear multiple-quantum coherence. Double-quantum coherence is prepared by a pulse sequence that aligns two individual spins within a given molecule in a transverse parallel configuration, either ↑↑ or ↓↓. The ensemble average over the entire sample is represented by two pairs of diametrically opposed macroscopic magnetization vectors. For the duration of the evolution interval, spin–spin splitting is suspended, locking these vectors in opposition, thus accounting for the “invisibility” of double-quantum coherence. At the end of the evolution interval, a 90° pulse reinstates the normal spin–spin splitting, allowing differential precession of these vectors and the buildup of a detectable nuclear magnetic resonance response in the receiver. By focusing attention on the evolution of individual spins within a given molecule, we calculate the probability that at the end of the evolution period they are simultaneously aligned parallel or antiparallel to a particular transverse axis, thus obtaining expressions for the modulation of the final observed signal. Fourier transformation as a function of the evolution time t1 gives a spectrum consisting of the multiple-quantum frequencies, determined by sums and differences of chemical shifts. Calculations for weakly coupled homonuclear two-spin and three-spin systems give results in good agreement with those predicted by the product operator treatment. For the heteronuclear multiple-quantum correlation technique, a purely macroscopic vector picture appears to explain the experimental observations. ©1998 John Wiley & Sons, Inc. Concepts Magn Reson 10: 63–84, 1998