Nonempirical construction of current-density functionals from conventional density-functional approximations

Density-functional approximations for the exchange-correlation energy E-xc[n] of a many-electron ground state are highly developed and widely useful. When a paramagnetic current j(p)(r) is present, Vignale and Rasolt have extended the Kohn-Sham theorems and presented an additive correction valid to second order in the gauge-invariant vorticity nu=del x(j(p)/n): E-xc[n,j(p)]=E-xc[n,j(p)=0]+Delta E-xc(VR)[n,nu]. Apart from spin-polarization effects, their correction is unambiguous for a generalized gradient approximation (GGA). But for a meta-GGA (MGGA), one needs to know how to go back from the orbital kinetic energy density tau([n,j(p)];r) to tau([n,0];r); we show how to do this here. Numerical tests on the degeneracies for open-shell atoms show that current-density corrections reduce the error of GGA from 2 to 1 kcal/mol, and of MGGA from 5 to 2 kcal/mol.