Two-dimensional spin-echo NMR spectroscopy: a general method for calculation of spectra

A general method of computation of two-dimensional (2D) spin-echo spectra is presented. Both selective and nonselective excitation by the 180° pulse within coupled spin systems as well as selective excitation of unconnected transitions in weakly coupled spin systems are considered. It is found that in the case of strongly coupled spin systems one can obtain, in the 21) spectrum, transitions with positive as well as negative intensities, the frequencies and intensities of which are sensitive to the spectral parameters. Furthermore, the 2D spin-echo spectra are found to be symmetric for nonselective excitation of all coupled spins. Two-dimensional spin-echo spectra have been calculated for AX, AB, A2X, AMX, and ABX spin systems and analytical expressions for the frequencies and intensities have been obtained for various experimental schemes. Both proton and carbon-13 2D spin-echo spectra are described. An analysis of errors in the 180° pulse reveals additional subspectra in the 2D spin-echo spectrum. These additional subspectra arise from cross-terms between the transformation matrices associated with excitation of various spins with an imperfect pulse