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

• 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. ωI = ωQ). 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) τRωI ≥ 1, where τR is the rotational correlation time and ωI 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 T1Q and a spin-spin relaxation time T2Q that become equal in the zero field limit. In the slow tumbling limit, the quadrupole spin relaxation times, T1Q, T2Q, are equal to (3/2)τR.

Nyckelord

quadrupole enhanced proton spin relaxation

quadrupole dip

stochastic Liouville equation

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