  We present the self-consistent implementation of current-dependent (hybrid)
meta generalized gradient approximation (mGGA) density functionals using London
atomic orbitals. A previously proposed generalized kinetic energy density is
utilized to implement mGGAs in the framework of Kohn--Sham current
density-functional theory (KS-CDFT). A unique feature of the non-perturbative
implementation of these functionals is the ability to seamlessly explore a wide
range of magnetic fields up to 1 a.u. ($\sim 235000$T) in strength. CDFT
functionals based on the TPSS and B98 forms are investigated and their
performance is assessed by comparison with accurate CCSD(T) data. In the weak
field regime magnetic properties such as magnetizabilities and NMR shielding
constants show modest but systematic improvements over GGA functionals.
However, in strong field regime the mGGA based forms lead to a significantly
improved description of the recently proposed perpendicular paramagnetic
bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals
based on the vorticity these forms are found to be numerically stable and their
accuracy at high field suggests the extension of mGGAs to CDFT via the
generalized kinetic energy density should provide a useful starting point for
further development of CDFT approximations.
