ANALYTICAL SOLUTIONS FOR MULTIPLE-QUANTUM-COHERENCE DYNAMICS AMONG 2 OR 3 DIPOLAR-COUPLED, SPIN-1 2 NUCLEI/

Analytical solutions for multiple-quantum (MQ) dynamics in solids are presented for dipolar-coupled networks of two or three spin-1/2 nuclei . The solutions, which are not restricted to specific geometries, calc ulate MQ evolution according to the Liouville equation and use direct- product states (e.g., alpha alpha, beta beta) as the Zeeman basis for the MQ Hamiltonian H-yx. Employing direct-product states in the calcul ation directly reveals the effects of distance and geometry on the for mation and propagation of MQ coherences. Solutions are presented for b oth single orientations and powder distributions, Development of MQ co herences can be viewed in terms of the fundamental underlying steps br ought about by individual pairwise couplings. The amplitudes of specif ic MQ coherences depend on individual dipolar-coupling constants. Meas urements of such amplitudes would elucidate distance information in so lids. However, the overall MQ evolution for a three-spin network depen ds on root-mean-square dipolar coupling and thus is independent of geo metry. This remarkably simple aspect of the solutions suggests possibl e extension to larger numbers of spins. The analytical solution for th ree spins is compared to variable-temperature F-19 MQ experiments on i solated ammonium trifluoromethanesulfonate salts dispersed in polystyr ene. (C) 1996 Academic Press, Inc.