A general procedure for calculating N.M.R. bandshapes of spin-89 nuclei in spin systems containing quadrupolar nuclei is discussed. A computer programme, QUADREDOCOS, which utilizes this procedure, is described. Some results for the ~A*B~X system are presented. Calculations for the [~A~X]~ system of cis-N~F~ produced spectra comparable to those published ; the effects of J~N', T~N and the correlation of relaxation at the two nitrogen nuclei are discussed. It is probable that 1JNz~. and 3JFF' have opposite signs.
INTRODUCTIONThe analysis, using a time-independent spin hamiltonian, of liquid state highresolution nuclear magnetic resonance (N.M.R.) spectra to obtain the Larmor frequency differences and scalar couplings between pairs of nuclei is now a standard procedure. However, it has been known since the earliest days of high-resolution N.M.R.[1] that this approach is not, in general, adequate to describe the spectra given by molecules containing nuclei of spin > 89 because such nuclei can be efficiently relaxed by the interaction of their quadrupole moments with the random electric field gradients resulting from molecular reorientation. Not only are the resonances of the quadrupolar nuclei themselves broadened, but also those given by spin-89 nuclei in the same molecule are often either broadened or else contain no fine structure arising from scalar couplings between the two kinds of nuclei.The problem of calculating the bandshape given by a spin-89 nucleus weakly scalar-coupled to a second nucleus was first treated in a rigorous manner in the classic relaxation paper [2] of Bloch, who showed that rapid relaxation of the second spin destroyed all fine structure in the resonance of the first (spin-89 nucleus. Subsequently, however, a conceptually different treatment of the problem of bandshape phenomena in systems containing quadrupolar nuclei was given [3]. This consists of assuming that the spin wavefunctions of the individual molecules are eigenfunctions of the time-independent spin hamiltonian ; the resulting problem is then treated by the method introduced by Sack [4] for chemically exchanging systems. This treatment has been frequently used since it was first presented, but it has been pointed out recently [5] that the method cannot be regarded as satisfactory because the assumption made concerning the Downloaded by [University of California, San Diego] at