Parameters, Calculation of Nuclear Magnetic Resonance

Abstract

AbstractThe fundamental parameters that reproduce a nuclear magnetic resonance (NMR) spectrum in gases, liquids, and solids are the four tensor quantities: the NMR chemical shift of the nucleus, the indirect nuclear spin–spin coupling, the nuclear electric quadrupole coupling, and the direct dipolar coupling tensors. The first three are intimately related to the local electronic structure at the nucleus and the chemical bonds connecting the nuclei. On the other hand, the direct nuclear spin dipole–dipole interaction depends directly and entirely on the third power of the inverse of the direct through‐space distance between two nuclei, whether bonded or otherwise. In gases and in liquids where free tumbling of the molecules bearing the nuclear spins leads to isotropic averaging of these quantities, only the isotropic average values, the average of three components along the principal axes of the chemical shift and the indirect spin–spin coupling tensors determine the observed frequencies in the NMR spectrum. In the solid state, restricted motion permits the tensors to manifest all the components, whether the sample is a polycrystalline powder, an amorphous solid, or a single crystal. Theoretical calculations of the NMR chemical shift, indirect spin–spin coupling, and nuclear quadrupole coupling parameters, using quantum mechanical methods, permit the prediction of NMR spectra and provide the physical basis for the relationship between the parameters and molecular electronic structure, which may include local electronic structure (electronic distribution in the immediate vicinity of the nucleus and neighboring bonds), local molecular geometry, bond connectivities, stereochemical structure, as well as subtleeffects of the chemical environment, such as contributions from remote parts of the molecule, tertiary and secondary structure, crystal packing, solvent effects, and isotopic substitution.