Quadrupole-enhanced proton spin relaxation for a slow reorienting spin pair: (I)–(S). A stochastic Liouville approach

Abstract

The field dependence of the proton (I) spin–lattice relaxation rate is calculated for a dipole–dipole coupled spin pair, (I = 1/2) − (S = 1), where the quadrupole nucleus (S) is ²H or ¹⁴N with asymmetry parameter η = 0. The observed relaxation profile shows a marked enhancement for equal proton Larmor and quadrupole spin frequencies (i.e. ω _I = ω_Q). This phenomenon is referred to as the quadrupole dip, and has been observed, for instance, in ¹⁴N−¹H amide 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 re-orientational motion. A characteristic low field dispersion is observed when (3/2) τ_Rω _I ≥ 1, where τ_R is the rotational correlation time and ω _I is the proton Larmor frequency. At higher fields, the relaxation peak exhibits a Lorentzian-like line shape, , 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 that become equal in the zero field limit. In the slow tumbling limit, the quadrupole spin relaxation times, T _1Q, T _2Q, are equal to (3/2)τ_R.