General theory of exchange-broadened nmr line shapes II. Exploitation of invariance properties

Abstract

In this paper we examine the feasibility of applying group-theoretical and commutation principles to the general quantum-mechanical theory of exchangebroadened high-resolution NMR line shapes, presented in paper I of this series. For exchanging spin systems exhibiting certain permutation symmetry properties the unsaturated steady-state equation of the nuclear spin density vector in a composite Liouville representation may be projected onto smaller Liouville subspaces without loss of information, thus materially simplifying the practical computation of line shapes. Three special cases are treated explicitly: (1) mutual-exchange factorization, (2) magnetic-equivalence factorization, and (3) symmetry factorization for the permutation symmetry group of order 2. A procedure is also described for taking advantage of mutual-exchange factorization simultaneously with magnetic equivalence or symmetry factorization. Applications of the computer program DNMR3, which is based on the formalism of the present paper, are illustrated by several sample calculations.