CONDITIONAL BOUNDS ON POLARIZATION TRANSFER

The implications of constraints on unitary transformations of spin ope rators with respect to the accessible regions of Liouville space are a nalyzed. Specifically, the effects of spin-permutation symmetry on the unitary propagators are investigated. The influence of S-2 and S-3 pr opagator symmetry on two-dimensional bounds for F-z = Sigma(i=1)(N) 1( iz) <-> G(z) = Sigma(j=1)(M) S-jz polarization transfer in IS and I2S spin-1/2 systems is examined in detail. One result 2 is that the maxim um achievable F-z <-> G(z) polarization transfer is not reduced by per mutation symmetry among the spins. For I2S spin systems, S-3 symmetry in the unitary propagator is shown to significantly reduce the accessi ble region in the 2D F-z-S-z Liouville subspace compared to the case r estricted by unitarity alone. That result is compared with transformat ions under symmetric dipolar and scalar J coupling as well as shift an d RF interactions. An important practical implication is that the refi ned spin thermodynamic theory of Levitt, Suter, and Ernst (J. Chem. Ph ys. 84, 4243, 1986) for cross polarization in solid-state NMR does not predict experimental outcomes incompatible with constraints of unitar ity and spin-permutation symmetry. (C) 1995 Academic Press, Inc.