An Empirical Proton NMR Shielding Equation for Alkenes Based on Ab Initio Calculations

Nuclei of hydrogen atoms located over a carbon-carbon double bond in the presence of a strong magnetic field experience a perturbed magnetic field caused primarily by the magnetic anisotropy of the π bond. However, the commonly used theoretical model for predicting the shielding effect of an alkene double bond on hydrogen nuclei is sometimes inconsistent with the observed proton NMR chemical shifts in structures that have covalently bonded hydrogens located over a carbon-carbon double bond. We have used the ab initio gauge including atomic orbital (GIAO) method to calculate isotropic shielding values and to determine the proton NMR shielding increments for a simple model system: methane held at various positions over ethene. These shielding increments calculated for one proton of methane have been mapped as a function of their position in Cartesian coordinates relative to the center of ethene. A mathematical function has been fit to this three-dimensional shielding increment surface at each of four distances from the face of the ethene molecule. Additionally, a single mathematical equation has been developed for predicting the shielding caused by the carbon-carbon double bond in ethene. In contrast to the traditionally employed shielding model, our results predict deshielding for protons within 3 Å above the center of a carbon-carbon double bond, consistent with experimental observations in several molecular systems. The NMR shielding increments predicted by this equation are compared to observed shielding increments in some test alkenes.