Calibration of STUD+ Parameters to Achieve Optimally Efficient Broadband Adiabatic Decoupling in a Single Transient

Abstract

To provide the most efficient conditions for spin decoupling with least RF power, master calibration curves are provided for the maximum centerband amplitude, and the minimum amplitude for the largest cycling sideband, resulting from STUD+ adiabatic decoupling applied during a single free induction decay. The principal curve is defined as a function of the four most critical experimental input parameters: the maximum amplitude of the RF field,RFmax, the length of the sech/tanh pulse,Tp, the extent of the frequency sweep,bwdth,and the coupling constant,Jo. Less critical parameters, the effective (or actual) decoupled bandwidth,bweff, and the sech/tanh truncation factor, β, which become more important asbwdthis decreased, are calibrated in separate curves. The relative importance of nine additional factors in determining optimal decoupling performance in a single transient are considered. Specific parameters for efficient adiabatic decoupling can be determined via a set of four equations which will be most useful for13C decoupling, covering the range of one-bond13C1H coupling constants from 125 to 225 Hz, and decoupled bandwidths of 7 to 100 kHz, with a bandwidth of 100 kHz being the requirement for a 2 GHz spectrometer. The four equations are derived from a recent vector model of adiabatic decoupling, and experiment, supported by computer simulations. The vector model predicts an inverse linear relation between the centerband and maximum sideband amplitudes, and it predicts a simple parabolic relationship between maximum sideband amplitude and the productJoTp. The ratiobwdth/(RFmax)2can be viewed as a characteristic time scale, τc, affecting sideband levels, with τc≈Tpgiving the most efficient STUD+ decoupling, as suggested by the adiabatic condition. Functional relationships betweenbwdthand less critical parameters,bweffand β, for efficient decoupling can be derived from Bloch-equation calculations of the inversion profile for a single sech/tanh pulse. Residual splitting of the centerband, normally associated with incomplete or inefficient decoupling, is not seen in sech/tanh decoupling and therefore cannot be used as a measure of adiabatic decoupling efficiency. The calibrated experimental performance levels achieved in this study are within 20% of theoretical performance levels derived previously for ideal sech/tanh decoupling at high power, indicating a small scope for further improvement at practical RF power levels. The optimization procedures employed here will be generally applicable to any good combination of adiabatic inversion pulse and phase cycle.