Isoorbital indicators for current density functional theory.

Exchange-correlation density functionals at the meta-generalised gradient approximation level typically use the Kohn–Sham orbitals as an ingredient to create the isoorbital indicator, whereis the von Weizsäcker kinetic energy density andis the kinetic energy density of the Kohn–Sham orbitals. When a magnetic field is included in the treatment, the Kohn–Sham orbitals vary with the vector-potential gauge, as doesand implicitly the exchange-correlation energy. However, it is a known result in current density functional theory that the exact exchange-correlation energy is gauge independent. Three different gauge-independent replacements forhave been proposed by other authors. Only one of these is, however, known to stay between 0 and 1. We modify one of the others, the Maximoff–Scuseria isoorbital indicator, so that it also stays between 0 and 1. We investigate the ability of the isoorbital indicators evaluated in a system with densityand paramagnetic current densityto reproduce the value ofin a system having no paramagnetic current, but the same density. We provide the first example known to us where the Tao–Perdew isoorbital indicator goes outside of the interval from 0 to 1. [ABSTRACT FROM AUTHOR]