Comparative studies of density-functional approximations for light atoms in strong magnetic fields

Abstract

For a wide range of magnetic fields, 0 B 2000 a.u., we present a systematic comparative study of the performance of different types of density-functional approximations in light atoms (2 Z 6). Local, generalized-gradient approximation (GGA; semilocal), and meta-GGA ground-state exchange-correlation (xc) functionals are compared on an equal footing with exact-exchange, Hartree-Fock (HF), and current-densityfunctional-theory (CDFT) approximations. Comparison also is made with published quantum Monte Carlo data. Though all approximations give qualitatively reasonable results, the exchange energies from local and GGA functionals are too negative for large B. Results from the Perdew-Burke-Ernzerhof ground-state GGA and Tao-Perdew-Staroverov-Scuseria (TPSS) ground-state meta-GGA functionals are very close. Because of confinement, self-interaction error in such functionals is more severe at large B than at B = 0, hence selfinteraction correction is crucial. Exact exchange combined with the TPSS correlation functional results in a self-interaction-free (xc) functional, from which we obtain atomic energies of comparable accuracy to those from correlated wave-function methods. Specifically for the B and C atoms, we provide beyond-HF energies in a wide range of B fields. Fully self-consistent CDFT calculations were done with the Vignale-Rasolt-Geldart (VRG) functional in conjunction with the PW92 xc functional. Current effects turn out to be small, and the vorticity variable in the VRG functional diverges in some low-density regions. This part of the study suggests that nonlocal, self-interaction-free functionals may be better than local approximations as a starting point for CDFT functional construction and that some basic variable other than the vorticity could be helpful in making CDFT calculations practical.

Current Density Functional Theory Using Meta-Generalized Gradient Exchange-Correlation Functionals

“…Higuchi and Higuchi 33 (HH) have also presented a vorticity dependent form, derived to obey known exact relations for the CDFT exchange-correlation functional. Whilst the vorticity is a theoretically convenient choice to ensure the gauge invariance of the exchange-correlation energy it has been observed that in practical self-consistent calculations it can lead to significant numerical stability issues 16,17 . How severe these issues are depends on the exact parameterization of the the functional form, however, in all cases some degree of numerical regularization is required to ensure that the self-consistent field solution of the Kohn-Sham equations can be obtained.…”

“…The KS orbitals are defined to minimize the non-interacting kinetic energy and yield the physical electronic density via Eq. (16). They also have appealing properties; for example the highest occupied MO energy is minus the first ionization potential (IP) 49,50 and the remaining orbital energies can be interpreted as Koopman's type approximations to higher IPs 51 .…”

Coupled-cluster theory for atoms and molecules in strong magnetic fields

“…Additionally, there is a great interest to formulate a density-functional theory (DFT) that properly takes into account the interaction with magnetic fields. [14][15][16][17][18][19][20] For these approaches, it is mandatory to have benchmark values to assess the quality of the results and help to construct improved functionals.…”

Density-functional theory for internal magnetic fields

“…Finally, practical experience with available approximate paramagnetic CDFT functionals has shown that vorticity is a numerically difficult quantity to work with [44][45][46]. A formulation in terms of physical currents is therefore an interesting alternative avenue to explore in the construction of practical density-functional approximations.…”