Quadrupole Enhanced Proton Spin Relaxation for a Slow Reorienting Spin Pair:(I)--(S). The stochastic Liouville Approach

Per-Olof Westlund (1)

1 Department of Chemistry

The field dependence of the proton (I) spin-lattice relaxation rate is calculated for a dipole-dipole coupled spin pair, (I=$\frac{1}{2}$)--(S=1) where the quadrupole nucleus (S) is $^{2}$H or $^{14}$N with asymmetry parameter $\eta=0$. The observed relaxation profile shows a marked enhancement for equal proton Larmor and quadrupole spin frequencies (i.e. $\omega_I$= $\omega_Q$), This phenomenon is referred to as the quadrupole dip, and has been observed for instance in $^{14}N-^1H$ amid groups of immobilized proteins. In this work an analysis of the observed relaxation enhancement is presented when the dipole-dipole coupling and the quadrupole interaction are modulated by the overall reorientational motion. A characteristic low field dispersion is observed when $\frac{3}{2}\tau_R\omega_I \ge 1$ where $\tau_R$ is the rotational correlation time. At higher fields the relaxation peak exhibits a Lorenzian like lineshape; L(\omega_I)= [(\omega_Q-\omega_I)^2 tau_R^2(\frac{3}{5})^2+1]^{-1} which is centred at the quadrupole frequency. The quadrupole spin system shows a spin-lattice T_{1Q} and a spin-spin relaxation time $ T_{2Q}$ which become equal in the zero field limit. In the slow tumbling limit, the the quadrupole spin relaxation times, $T_{1Q},T_{2Q}$} are equal to 3/2 tau_R.

Mots clés: Physical Sciences

Per-Olof Westlund. Quadrupole Enhanced Proton Spin Relaxation for a Slow Reorienting Spin Pair:(I)--(S). The stochastic Liouville Approach. Molecular Physics, 2009, 107 (20), pp.2141-2148. ⟨10.1080/00268970903185909⟩. ⟨hal-00521566⟩