Calculation of NMR Chemical Shifts

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Abstract
A condition in the application of the total orbital angular momentum operator to generate a trial function for a variational calculation of chemical shifts is derived from the equation of continuity in a rotating coordinate system. Group‐theoretical arguments are used to show that the origin for the angular momentum operator should be chosen at a center of symmetry or along an axis of symmetry if no center of symmetry is present. The method is applied to a hydrogen atom in an electric field and the results are compared to the exact solution. For multicenter problems, the trial function must be modified as required by invariance of the Schrödinger equation under translations. A modified function is proposed and an explicit formula for the chemical shift is derived, which is invariant to choice of origin. Application is made to the calculation of the chemical shifts of nuclei of ions in crystalline fields. Relationships of the variational method with perturbation methods are discussed.

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