The fractal geometry of Hartree-Fock

Theel, Friethjof; Karamatskou, Antonia; Santra, Robin

doi:10.1063/1.5001681

Journal Article

PUBDB-2017-12959

The fractal geometry of Hartree-Fock

Theel, F. ; Karamatskou, A.CFEL*Extern* ; Santra, R. (Corresponding author)CFEL*DESY*

2017
American Institute of Physics Woodbury, NY

Chaos 27(12), 123103 (2017) [10.1063/1.5001681]

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Please use a persistent id in citations: doi:10.1063/1.5001681 doi:10.3204/PUBDB-2017-12959

Abstract: The Hartree-Fock method is an important approximation for the ground-state electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The Hartree-Fock method is an iterative procedure in which the electronic wave functions of the occupied orbitals are determined. The set of functions found in one step builds the basis for the next iteration step. In this work, we interpret the Hartree-Fock method as a dynamical system since dynamical systems are iterations where iteration steps represent the time development of the system, as encountered in the theory of fractals. The focus is put on the convergence behavior of the dynamical system as a function of a suitable control parameter. In our case, a complex parameter λ controls the strength of the electron-electron interaction. An investigation of the convergence behavior depending on the parameter λ is performed for helium, neon, and argon. We observe fractal structures in the complex λ-plane, which resemble the well-known Mandelbrot set, determine their fractal dimension, and find that with increasing nuclear charge, the fragmentation increases as well.

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