Gauge-invariant basis sets for magnetic property calculations

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Abstract
The use of augmented basis sets of the form, {χ, r t χ, r tr u χ, ...} (r t , r u =x, y, z), is proposed for calculating magnetic properties which are almost gauge‐origin independent. It is derived from Epstein’s theorem which states the sufficient condition for unitary invariance. Test calculations using the coupled‐Hartree–Fock/finite perturbation method show that the augmented sets correctly reduce the origin dependence of magnetic shielding constants, and that the results agree well with the experiment. Through systematic modifications of the basis set, a practical procedure in choosing basis functions to be added is suggested.