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Density functionals in the presence of magnetic field
Author(s) -
Laestadius Andre
Publication year - 2014
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.24707
Subject(s) - hamiltonian (control theory) , wave function , density functional theory , coulomb , paramagnetism , regular polygon , physics , quantum mechanics , mathematics , electron , geometry , mathematical optimization
In this article, density functionals for Coulomb systems subjected to electric and magnetic fields are developed. The density functionals depend on the particle density ρ and paramagnetic current density j p . This approach is motivated by an adapted version of the Vignale and Rasolt formulation of current density functional theory, which establishes a one‐to‐one correspondence between the nondegenerate ground‐state and the particle and paramagnetic current density. Definition of N ‐representable density pairs ( ρ , j p ) is given and it is proven that the set of v ‐representable densities constitutes a proper subset of the set of N ‐representable densities. For a Levy–Lieb‐type functional Q ( ρ , j p ), it is demonstrated that (i) it is a proper extension of the universal Hohenberg–Kohn functionalF H K ( ρ , j p ) to N ‐representable densities, (ii) there exists a wavefunction ψ 0 such that Q ( ρ , j p ) = ( ψ 0 , H 0 ψ 0 )L 2, where H 0 is the Hamiltonian without external potential terms, and (iii) it is not convex. Furthermore, a convex and universal functional F ( ρ , j p ) is studied and proven to be equal the convex envelope of Q ( ρ , j p ). For both Q and F , we give upper and lower bounds. © 2014 Wiley Periodicals, Inc.