Exchange vector potentials in current-density functional theory

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Abstract
In the presence of a magnetic field, knowledge of both the density and the paramagnetic current density is required to derive a Hohenberg-Kohn theorem. The energy is written as a functional of these two variables in current-density functional theory (CDFT). The properties of the exact exchange-correlation functional are not well known in CDFT and the approximate current-density functional due to Vignale, Rasolt, and Geldart is the only functional valid for perturbing fields in routine use. Recent studies using this functional have shown that it is not a reliable predictor of molecular magnetic properties such as magnetizabilities and nuclear shielding constants. Zhao, Morrison, and Parr have shown that it is possible to construct exchange-correlation scalar potentials from densities for systems in the absence of any applied fields. By extending this technique, we have derived a quadratically convergent procedure to deliver numerical exchange-correlation scalar and vector potentials from densities and current densities at finite magnetic-field strengths. We demonstrate this technique by calculating exchange vector potentials for a number of small molecules from Hartree-Fock densities and current densities. We examine the relationship between the computed and true Kohn-Sham exchange-correlation potentials.