Frequency dependence of nuclear spin relaxation in paramagnetic transition-metal complexes

Abstract

Proton spin-lattice relaxation times have been determined as a function of magnetic field strength (H₀) for a series of paramagnetic transition-metal complexes chosen so that, for some, the electron spin relaxation times (t_e) fall in the Redfield limit (t_e » t_r) while for others t_e << t_r being the rotational correlation time. When t_e » t_r dominates the nuclear relaxation and the experimental results can be readily explained by Redfield theory. When t_e << t_r current theory predicts the nuclear T₁ values to get longer as H₀ decreases. This is not observed experimentally. This can only be explained by using non-Redfield relaxation theory and by assuming the spacings of the electron-nuclear spin energy levels are not dominated by H₀. It is shown that, although the trace of the zero-field splitting tensor is zero TrD = 0 because TrD is averaged by t_r when t_e < t_r the value of D_zz is important in determining the energy-level spacings. By this approach the frequency dependence can be explained. Experimentally, it is shown that a Phase Alternating Pulse Sequence (PAPS) is required to measure T₁. The problem originates from interference from transverse magnetization. A density matrix theory of the PAPS sequence is presented.