Isoorbital indicators for current density functional theory

Abstract

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 , where is the von Weizsäcker kinetic energy density and is 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 does and 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 for have 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 density and paramagnetic current density to reproduce the value of in 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.

Keywords:

• isoorbital indicators
• current density functional theory
• meta-generalised gradient approximation
• meta-GGA
• DFT

Acknowledgements

Espen Sagvolden acknowledges useful discussions with John P. Perdew and Simen Kvaal. This work was supported by the Norwegian Research Council through the CoE Centre for Theoretical and Computational Chemistry (CTCC) Grant No. 179568/V30 and Grant No. 171185/V30 and by the European Research Council under the European Union Seventh Framework Programme through the Advanced Grant ABACUS, ERC Grant Agreement No. 267683.