Analysis of collective modes in some A_MX_N systems

Abstract

The behavior of spin½ AX₃ and A₂X₂ systems evolving under cross-polarization (CP) and isotropic mixing (IM) is analyzed in detail by computing the time development of the density operator by commutator algebra. The two mixing processes are compared in these cases with respect to their coherence-transfer frequencies, efficiency, and the resulting multiplet patterns. The effect of two types of purge on the density operator is evaluated for the heteronuclear situation. spin½ AX_N systems (N = 1, 2,.., 6) evolving under isotropic mixing are also analyzed employing zero-quantum-frame techniques. Several general properties of isotropic mixing are derived which contrast with the corresponding cross-polarization results. Explicit expressions are given for the X-coupled and gX-decoupled A signal as a function of the isotropic mixing period. The effect of two different purge procedures is evaluated for the heteronuclear case, and general conclusions are drawn about the intensity and time development of the multiplet components in CP and IM. The IM results, except for the discussion of purging, are directly applicable to experiments involving homonuclear spin-locking as well.