Use of group theory for calculation of dynamic N.M.R. spectra applications to liquid crystalline solutions

A group theoretical method is developed for calculating dynamic magnetic resonance spectra by the density matrix formalism. The method takes into account the symmetry of the molecules involved in the dynamic process and the nature of the reaction. The application of this method results in the factorization of the lineshape problem and in a very significant simplification of the numerical calculation of the spectra. The method is demonstrated on a number of examples involving molecules dissolved in liquid crystalline solvents. In all cases the solute molecules undergo an intramolecular isomerization reaction and their dynamic proton N.M.R. spectrum is calculated. The following four examples (two of them involving hypothetical reactions) are discussed: (i) the bond shift reaction in cyclobutadiene, (ii) ring inversion in s-trioxane; (iii) bond shift isomerization in cyclohexatriene; (iv) bond-shift isomerization in cyclooctatetraene.