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Polarization-operator formalism was used to describe the behavior of spin- 1 2 homonuclear off-resonance spin-lock effects occurring in the ROESY experiment. The weak-collision case was assumed. Direct- and cross-relaxation rate constants representing Toff1ρ- and Toff2ρ-relaxation processes were evaluated. Off-resonance effects associated with the ROESY experiment were accommodated in the formalism by the inclusion of Toff1ρ relaxation. ROE contributions dominate the cross-relaxation rate when the tilt angle (β) of the effective field (relative to the static B0 field) in the rotating frame approaches 90°, whereas when β becomes small, NOE contributions predominate. Consequently, a continuous change in the tilt angle of the effective field from 90° to 0° results in a smooth spectral change characteristic of a ROESY to NOESY transition and may be implemented experimentally by the O-ROESY pulse sequence [K. Kuwata and T. Schleich, J. Magn. Reson. A111, 43 (1994)]. Applications of the formalism include the analysis of off-resonance spin-lock effects arising in the O-ROESY experiment, namely, the dependence of cross-peak intensity on RF offset frequency, thereby enabling assessment of macromolecular motional parameters and internuclear separation distance from the cross-peak intensity dispersion behavior. Simplified expressions for the cross- and direct-relaxation rate constants in the rotating frame were derived from the exact formalism using the approximation ωeτc ⪡ 1, which provided virtually identical numerical results to those of the exact formalism. For the case of interacting spin- 1 2 nuclei with similar chemical-shift values, the formalism demonstrates, in accordance with other studies, that particular tilt angles of the effective field may be selected to enable suppression of cross relaxation (β = 35.3°) for slowly reorienting macromolecules, or the constraining of the direct- to cross-relaxation-rate-constant ratio to 0.5 at all values of ωeτc (β = 54.7°). However, at relatively large values of the chemical-shift difference between the interacting spins, these rules do not rigorously apply. Analogous behavior was observed for simulations of the normalized cross-peak intensity vs off-resonance irradiation frequency. |
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