  Using the polarizability of a free electron gas in a magnetic field and the
Current-Density Functional Theory (CDFT) developed by Vignale and Rasolt, we
derive the gradient and current corrections for the energy functional of a
non-uniform electronic system in a strong magnetic field.
  First, we find the Tomishima-Shinjo functional by neglecting the current
variation. Taking into account the current variation leads to new gradient
terms which change contraction effects in the direction perpendicular to the
magnetic field.
