| The carbon-13 multiplet spin-lattice relaxation for the {dollar}sp{lcub}13{rcub}{dollar}CH{dollar}sb2{dollar} spin system is studied outside of the limits of extreme narrowing. Various novel pulse sequences are used to perturb the spin system away from thermal equilibrium and create initial conditions for the relaxation. The relaxation of the spin system is simulated by applying the Redfield formalism to relaxation of each element of the density matrix. This approach simulates not only the spin-lattice relaxation that occurs following the perturbing pulse sequence, but also the transverse relaxation that occurs during the dephasing delays inserted into the pulse sequence. Since relaxation simulation is not limited to spin-lattice relaxation, the relaxation matrix contains oscillating terms that complicate solution of the Redfield differential equation. A novel transformation of variables removes these oscillating terms and permits straightforward solution of the differential equation.; Outside of the limits of extreme narrowing, the spectral lines broaden to a sufficient extent that the individual lines of the multiplet cannot be completely resolved. For this reason the computer simulation of the relaxation generates a theoretical spectrum that is fit to the experimental spectrum via nonlinear least squares without considering individual spectral lines. The fitting procedure uses the Favro diffusion model to obtain molecular rotational diffusion coefficients describing the rate of rotation of the molecule in a liquid. This technique has been utilized to probe the tumbling motion of a peptide in aqueous solution. |
