Nonempirical Construction of Current-Density Functionals from Conventional Density-Functional Approximations

Density-functional approximations for the exchange-correlation energy Exc[n] of a many-electron ground state are highly developed and widely useful. When a paramagnetic current jp(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=Delta x (jp/n):Exc[n, jp]=Exc[n, jp=0] + DeltaE(VR)(xc)[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, jp];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.