Scaling in one and two dimensional NMR spectroscopy in liquids

Abstract

The principles of scaling in NMR spectroscopy have been described. We have tried to unify several isolated experiments under the umbrella of 'scaling in NMR spectroscopy'. After a brief description of the mathematical tools, namely 'average Hamiltonian theory' and 'product operator description' of density operator treatments of nuclear spin systems, several one dimensional scaling experiments have been analysed. Extending to two dimensions, the versatility of scaling manipulations in the experimental scheme of 2D NMR spectroscopy has been demonstrated. Specific pulse sequences designed to scale the chemical shifts, coupling constants and line widths in three different categories of 2D NMR spectroscopy, namely J-resolved spectroscopy, correlated spectroscopy and multiple quantum spectroscopy, have been discussed. It has been shown that for optimisation of sensitivity and resolution in 2D spectra, the scaling requirements are different in the three different kinds of experiments. At every stage the merits and demerits of the scaling experiments have been discussed. Apart from the generalised applications in sensitivity and resolution enhancements, specific applications in observation of long range correlations, measurement of coupling constants and measurement of exchange (or cross relaxation) rates have been discussed. We believe that this general exposition should enable the NMR spectroscopists to select a suitable pulse scheme and optimise the scaling factors to derive specific results on the systems of interest.