Chemical Shift Scales on an Absolute Basis

Nuclear magnetic shielding is a second-order molecular electronic property which provides a severe test of the accuracy of molecular quantum mechanical calculations. While electric dipole polarizability and hyperpolarizabilities provide tests of the wavefunction at the outer regions, nuclear shielding is very sensitive, especially to contributions from high angular momentum functions, in the regions close to a particular nucleus. Precise measurements of differences in shielding are easy to carry out. In most NMR studies the resonance frequencies are measured and a chemical shift is defined as δ = (νi − νref)/νref. From the relationship between the resonance frequency νi, the external magnetic field B0, the magnetogyric ratio γ , and the nuclear shielding σ i, i.e. νi = (γ /2π)(1 − σ i) B0, we can write the chemical shifts in terms of the nuclear shielding as δ = (σ ref − σ i)/(1 − σ ref). Reasonably accurate calculations are now available for nuclei in the first row of the Periodic Table in molecules with a small number of first row atoms and for hydrides of the second row, as may be seen in the articles on IGLO, LORG and SOLO and GIAO shielding calculations described by Kutzelnigg, Hansen and Pulay in this Encyclopedia (Shielding Calculations: LORG and SOLO Approaches, Shielding Calculations: IGLO Method, Shielding Theory: GIAO Method). In making a comparison of theoretical ab initio values at the equilibrium molecular geometries with experimental chemical shifts, it is necessary to have absolute quantities (absolute shielding values) to compare with rather than shielding differences or chemical shift values. Accurate chemical shift measurements can be carried out by simultaneous measurement of two frequencies in the same physical sample in the field. If we know the absolute shielding value corresponding to the first frequency, then the accurate chemical shift between the two provides the absolute shielding of the second, or indeed of any number of systems whose chemical shifts can be related to the absolute shielding of any one system. But how do we establish the absolute shielding value of the very first one?