Theoretical calculations of carbon-13 NMR chemical shifts via the Xα-scattered wave method

The Xα-SW molecular-orbital method is applied to the calculation of carbon-13 NMR nuclear shielding constants in a series of small organic molecules. The application of perturbation theory within the Xα 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 analytic-numerical method of integration in calculating the necessary matrix elements of 1/r, L/r3, and L. 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 atomic-sphere radius, and the origins of this dependence are discussed in terms of discontinuities in the muffin–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.