An algorithm for predicting the NMR shielding of protons over substituted benzene rings

In a strong magnetic field, hydrogen nuclei located over an aromatic ring experience a reduced magnetic field as a result of the induced magnetic field associated with circulating pi electrons. We used GIAO-SCF, an ab initio subroutine in Gaussian 94 to calculate isotropic shielding values and to determine the proton nuclear magnetic resonance (NMR) shielding increment for a simple model system: methane held at various positions over a substituted benzene ring. The NMR shielding increments experienced by the proximal protons of methane have been mapped as a function of their position X, Y, and Z relative to the center of aniline and, separately, nitrobenzene. A mathematical function of the same form has been fit to the three-dimensional shielding increment surface at each of five distances from the face of each aromatic ring. In addition, a single mathematical equation has been developed for predicting the shielding caused by either substituted aromatic ring. The chemical shifts predicted by using the results of this equation in conjunction with additive substituent increments are compared to observed values.