Carbon-13 relaxation in multispin systems of the type AXn

Abstract

The equations of time evolution which describe various aspects of longitudinal relaxation in methylene and methyl groups are derived on the basis of the Redfield–Bloch density operator theory of relaxation. It is assumed that the relaxation is dominated by intramolecular dipole–dipole interactions. The (cross-) correlation between the various internuclear vectors is explicitly taken into account; it is not assumed that the various pairwise interactions are additive. Although such correlation effects have long been dismissed, the present calculations demonstrate quite vividly such effects may be much more influential than is commonly thought, especially in the relaxation of carbon. Multiplet relaxation in the four-spin 13CH3 system is discussed in some detail with numerical calculations included to provide some compelling arguments against continued complacency regarding the need to consider multispin correlations. More general applications of the present theory await many inviting experimental studies.