H-2 NMR THEORY OF TRANSITION-METAL DIHYDRIDES - COHERENT AND INCOHERENT QUANTUM DYNAMICS

In this paper a simple phenomenological description of the effects of coherent quantum and incoherent mutual exchange of two deuteron nuclei in solid state transition metal complexes on their H-2 NMR spectra is given. This description is based on the quantum-mechanical density ma trix formalism developed by Alexander and Binsch. Only the nuclear spi n system is treated quantum mechanically. The quantum exchange interac tion in NMR is included in the nuclear spin Hamiltonian, and the inter action with the surrounding bath and incoherent exchange processes are treated as phenomenological rate processes described by rate constant s. The incoherent exchange corresponds formally to 180 degrees rotatio ns or jumps of the D-D vector around an axis perpendicular to this vec tor and averages the different quadrupole splitting of the two deutero ns. In principle the dideuteron pair will exist in several rovibration al states. However, if the interconversion among these states is fast, the dideuteron exchange can be described by an average exchange coupl ing or tunnel frequency X-12 and a single average rate constant kit of the incoherent exchange. It is shown that the incoherent exchange giv es rise to a relaxation of rate -2k(12) between coherences created bet ween states of different symmetry. The H-2 NMR line shape of a dideute ron pair in the solid state as a function of tunnel and incoherent exc hange rate is studied numerically. For single crystals, the effects of coherent and incoherent exchange are strongly different, in particula r if the rate constants are on the order of the quadrupole splitting. The spectra of nonoriented powder samples are more similar to each oth er. Nevertheless, our calculations show that there are still pronounce d differences, which should allow the distinction between coherent and incoherent exchange even in nonoriented samples.