Current Density-Functional Theory using meta-Generalized Gradient Exchange--Correlation Functionals

TL;DR

This paper introduces a self-consistent implementation of current-dependent meta-GGA density functionals in Kohn-Sham CDFT, enabling exploration of magnetic fields up to 1 a.u. and improving descriptions of magnetic properties and paramagnetic bonding.

Contribution

The paper develops a non-perturbative, stable implementation of current-dependent mGGA functionals in CDFT, extending the applicability to high magnetic fields and improving accuracy over previous functionals.

Findings

Modest improvements in magnetic properties in weak fields.

Significant accuracy gains in strong magnetic fields for paramagnetic bonding.

Stable numerical performance of the new functionals at high magnetic fields.

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 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.