Theory of molecular symmetry in dynamic N.M.R. spectra of intramolecularly exchanging spin systems

Abstract

The form of dynamic N.M.R. lineshape equation for intramolecularly exchanging spin systems is derived which contains explicitly the symmetries of the rearranging spcies. The lineshape equation is formulated in the composite Liouville space which comprises only one primitive space for each chemically distinct species. Two types of symmetry invariances, macroscopic and microscopic, are recognized, the former being inherent in all systems of symmetric species undergoing exchange. It is shown formally that, owing to the macroscopic invariance of symmetry, exchange processes do not couple symmetry-allowed with symmetry-forbidden transitions. A construction of a symmetry-adopted operator basis is described in which both the symmetry invariances effect the corresponding factorization of spectral matrices. It is demonstrated, using the example of intramolecular rearrangements in octahedral transition metal complexes, H₄ ML ₄, the extent to which both the macroscopic and microscopic factorizations can simplify the lineshape calculations.