Symmetry and isotropic coherence transfer

Abstract

Homonuclear coherence transfer experiments, exemplified by the so-called COSY technique, make up an important class of two-dimensional N.M.R. methods. The COSY experiment is useful because coherence transfers in weakly coupled spin systems are confined to spin pairs that are directly coupled, and this restriction may be exploited as a sequential assignment technique. In practice, sequential assignments by COSY methods alone may be very difficult especially if the spin system is complicated (e.g., biopolymers) and the cross peaks in the corresponding COSY spectrum are poorly resolved. Spectral assignments often may be made by relayed coherence transfers, however, where coherence is transferred between remote spins through an intervening network of weakly coupled spins. Recently, a series of experiments have been proposed to effect coherence transfers between remote spins through the application of trains of pulses during the mixing period of a two-dimensional experiment. In this paper we propose a theory of these isotropic mixing methods based in the superoperator formalism, and treat the effect of pulse imperfections on such experiments for the two-spin case. In a subsequent manuscript a generalization of this theory based upon the Young tableaux formalism is applied to larger spin systems. The Young tableaux have been applied to strong coupling problems in atomic and nuclear spectroscopy, and enable a decomposition of the state space and coherent state space of a multiple-particle system into simultaneous irreducible representations of the rotation and permutation groups.