A PHYSICAL PICTURE OF MULTIPLE-QUANTUM COHERENCE

A pictorial physical model is proposed to describe the characteristic properties of homonuclear multiple-quantum coherence. Double-quantum c oherence is prepared by a pulse sequence that aligns two individual sp ins within a given molecule in a transverse parallel configuration, ei ther up arrow up arrow or down arrow down arrow The ensemble average o ver the entire sample is represented by two pairs of diametrically opp osed macroscopic magnetization vectors. For the duration of the evolut ion interval, spin-spin splitting is suspended, locking these vectors in opposition, thus accounting for the ''invisibility'' of double-quan tum coherence. At the end of the evolution interval, a 90 degrees puls e reinstates the normal spin-spin splitting, allowing differential pre cession of these vectors and the buildup of a detectable nuclear magne tic resonance response in the receiver. By Focusing attention on the e volution of individual spins within a given molecule, we calculate the probability that at the end of the evolution period they are simultan eously aligned parallel or antiparallel to a particular transverse axi s, thus obtaining expressions for the modulation of the final observed signal. Fourier transformation as a function of the evolution time t( 1) gives a spectrum consisting of the multiple-quantum frequencies, de termined by sums and differences of chemical shifts. Calculations for weakly coupled homonuclear two-spin and three-spin systems give result s in good agreement with those predicted by the product operator treat ment. For the heteronuclear multiple-quantum correlation technique, a purely macroscopic vector picture appears to explain the experimental observations. (C) 1998 John Wiley & Sons, Inc.