Abstract
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 nonperturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 au (∼235 kT) in strength. CDFT functionals based on the TPSS and B98 forms are investigated, and their performance is assessed by comparison with accurate coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) data. In the weak field regime, magnetic properties such as magnetizabilities and nuclear magnetic resonance shielding constants show modest but systematic improvements over generalized gradient approximations (GGA). However, in the 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 that the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations.
Highlights
The foundations of current density-functional theory (CDFT) and its Kohn–Sham (KS) implementation were established in the late 1980s with the seminal works of Vignale, Rasolt and Geldart,[1,2,3] where it was recognized that the exchange–correlation functionals must depend on the electronic density, ρ, and the paramagnetic current density jp in the presence of an electromagnetic field
It is worth emphasizing that in the course of our investigation we found that the implementation of the meta generalized gradient approximation (mGGA) functionals including a generalized kinetic energy density was straightforward
The modified mGGA functionals cB98, cTPSS and cTPSS(h) show a level of accuracy in predicting weak field magnetic properties that is competitive with existing generalized gradient approximations (GGA) functionals without any additional fitting
Summary
The foundations of current density-functional theory (CDFT) and its Kohn–Sham (KS) implementation were established in the late 1980s with the seminal works of Vignale, Rasolt and Geldart,[1,2,3] where it was recognized that the exchange–correlation functionals must depend on the electronic density, ρ, and the paramagnetic current density jp in the presence of an electromagnetic field.
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