TheXagr;hyphen;SW molecularhyphen;orbital method is applied to the calculation of carbonhyphen;13 NMR nuclear shielding constants in a series of small organic molecules. The application of perturbation theory within theXagr; framework is discussed in order to place the equations used in the calculation of the shielding constants on firm theoretical ground. Use is made of a highly accurate mixed analytichyphen;numerical method of integration in calculating the necessary matrix elements of 1/r,L/r3, andL. The results for both overlapping and nonoverlapping spheres calculations are shown to reproduce trends in experimental shielding constants remarkably well, but not the correct magnitudes. Calculated shielding constants are shown to be strongly dependent upon the carbon atomichyphen;sphere radius, and the origins of this dependence are discussed in terms of discontinuities in the muffinndash;tin potential. An established method of choosing sphere radii based upon an initial approximation to the molecular charge density yields results which correlate well with experiment.
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