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-d
ensity functional theory (CDFT); The properties of the exact exchange-corre
lation functional are not well known in CDFT and the approximate current-de
nsity functional due to Vignale, Rasolt, and Geldart is the only functional
valid for perturbing fields in routine use. Recent studies using this func
tional 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-c
orrelation scaler potentials from densities for systems in the absence of a
ny applied fields. By extending this technique, we have derived a quadratic
ally convergent procedure to deliver numerical exchange-correlation scalar
and vector potentials from densities and current densities at finite magnet
ic-field strengths. We demonstrate this technique by calculating exchange v
ector potentials for a number of small molecules from Hartree-Fock densitie
s and current densities. We examine the relationship between the computed a
nd true Kohn-Sham exchange-correlation potentials. [S1050-2947(99)03901-3].