THEORY OF DYNAMIC MAGIC-ANGLE-SPINNING NUCLEAR-MAGNETIC-RESONANCE ANDITS APPLICATION TO C-13 IN SOLID BULLVALENE

Carbon-13 magic angle spinning (MAS) spectra of bullvalene, at a spinn ing frequency of about 4 kHz, are presented for the temperature range -30-degrees-C to +85-degrees-C. At low temperatures ( < -10-degrees-C) , separate center peaks are observed for the aliphatic and olefinic ca rbons, as well as spinning sidebands for the latter. Upon heating to r oom temperature and above, the peaks broaden and eventually coalesce t o a single line at the weighted average chemical shift frequency. Thes e results are interpreted in terms of two independent processes-a conc erted Cope rearrangement reorientation and symmetric threefold jumps a bout the molecular C3 axes. In both processes, the high order of the b ullvalene crystals is preserved. A quantitative analysis of the spectr a yields the following kinetic equations for, respectively, the Cope r earrangement reorientation and the threefold jump processes: kc(s-1)=1 .38 x 10(14) exp (-14.5/RT); k(J)(s-1) = 2.53 x 10(19) exp (-21.0/RT), where R is in kcal/mol degree. The analysis of the spectra was perfor med by comparing the experimental results with simulated line shapes, computed using the formalism of Schmidt and Vega, which is based on Sh irley's theory of solving the Schrodinger equation with a time-periodi c Hamiltonian. In a theoretical section, we rederive the line shape eq uation.without, however, making use of Floquet's theorem as formulated by Shirley. In an appendix, the equivalence of both approaches, as we ll as a derivation of Floquet's theorem, are presented.