The use of perturbation-dependent London atomic orbitals, also called gauge including atomic orbitals, has proven efficient for calculations of NMR shielding constants and other magnetic properties in the nonrelativistic framework. In this paper, the theory of London atomic orbitals for NMR shieldings is extended to the four-component relativistic framework and our implementation is described. The relevance of London atomic orbitals in four-component calculations as well as computational aspects are illustrated with test calculations on hydrogen iodide.
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