Numerical and exact density functional studies of light atoms in strong magnetic fields

Details Numerical and exact density functional studies of light atoms in strong magnetic fields Numerical and exact density functional studies of light atoms in strong magnetic fields

Nov 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005phdt.........4z&link_type=abstract

Ph.D dissertation, 2005. Section 0070, Part 0748 174 pages; United States -- Florida: University of Florida; 2005. Publication

Statistics

Computation

13

Light Atoms, Magnetic Fields, Hooke'S Atom

Scientific paper

Although current density functional theory (CDFT) was proposed almost two decades ago, rather little progress has been made in development and application of this theory, in contrast to many successful applications that ordinary density functional theory (DFT) has enjoyed. In parallel with early DFT exploration, we have made extensive studies on atom-like systems in an external magnetic field. The objectives are to advance our comparative understanding of the DFT and CDFT descriptions of such systems. A subsidiary objective is to provide extensive data on light atoms in high fields, notably those of astrophysical interest.
To address the cylindrical symmetry induced by the external field, an efficient, systematic way to construct high quality basis sets within anisotropic Gaussians is provided. Using such basis sets, we did extensive Hartree-Fock and DFT calculations on helium through carbon atoms in a wide range of B fields. The applicability and limitations of modern DFT and CDFT functionals for atomic systems in such fields is analyzed.
An exact soluble two-electron model system, Hooke's atom (HA), is studied in detail. Analogously with known results for zero field, we developed exact analytical solutions for some specific confinement and field strengths. Exact DFT and CDFT quantities for the HA in B fields, specifically exchange and correlation functionals were obtained and compared with results from approximate functionals. Major qualitative differences were identified. A major overall conclusion of the work is that the vorticity variable, introduced in CDFT to ensure gauge invariance, is rather difficult to handle computationally. The difficulty is severe enough to suggest that it might be profitable to seek an alternative gauge-invariance formulation of the current-dependence in DFT.

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