We construct a density-functional formalism adapted to uniform external magnetic fields that is intermediate between conventional density functional theory and Current-Density Functional Theory (CDFT). In the intermediate theory, which we term linear vector potential-DFT (LDFT), the basic variables are the density, the canonical momentum, and the paramagnetic contribution to the magnetic moment. Both a constrained-search formulation and a convex formulation in terms of Legendre–Fenchel transformations are constructed. Many theoretical issues in CDFT find simplified analogs in LDFT. We prove results concerning N-representability, Hohenberg–Kohn-like mappings, existence of minimizers in the constrained-search expression, and a restricted analog to gauge invariance. The issue of additivity of the energy over non-interacting subsystems, which is qualitatively different in LDFT and CDFT, is also discussed.
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14 January 2018
Research Article|
January 08 2018
Uniform magnetic fields in density-functional theory
Erik I. Tellgren
;
Erik I. Tellgren
a)
1
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo
, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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Andre Laestadius;
Andre Laestadius
1
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo
, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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Trygve Helgaker
;
Trygve Helgaker
1
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo
, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
2
Centre for Advanced Study at the Norwegian Academy of Science and Letters
, Drammensveien 78, N-0271 Oslo, Norway
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Simen Kvaal;
Simen Kvaal
1
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo
, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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Andrew M. Teale
Andrew M. Teale
1
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo
, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
2
Centre for Advanced Study at the Norwegian Academy of Science and Letters
, Drammensveien 78, N-0271 Oslo, Norway
3
School of Chemistry, University of Nottingham
, University Park, Nottingham NG7 2RD, United Kingdom
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J. Chem. Phys. 148, 024101 (2018)
Article history
Received:
October 02 2017
Accepted:
December 06 2017
Citation
Erik I. Tellgren, Andre Laestadius, Trygve Helgaker, Simen Kvaal, Andrew M. Teale; Uniform magnetic fields in density-functional theory. J. Chem. Phys. 14 January 2018; 148 (2): 024101. https://doi.org/10.1063/1.5007300
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