TY - BOOK
T1 - Universality of Born-Oppenheimer curves
AU - Samojlow, Anton
PY - 2018
Y1 - 2018
N2 - In this thesis, the Born-Oppenheimer curves for diatomic molecules are investigated in the Hartree-Fock model excluding the exchange term. It is exhibited that the curves have a universal behaviour at small internuclear distances which can be understood from the simpler Thomas-Fermi theory. Notably, we show that the atomic screenings in these two theories are comparable up to a distance from the nuclei which is independent of the atomic number. This is proven iteratively, by relating to suitable Thomas-Fermi models at dierent length scales. We in particular study solutions to the Thomas-Fermi partial dierential equation with two singularities and demonstrate that their asymptotic behaviour is universal. This thesis also contains a numerical investigation of the homonuclear Born-Oppenheimer curve in Thomas-Fermi theory which supports the analytic result.
AB - In this thesis, the Born-Oppenheimer curves for diatomic molecules are investigated in the Hartree-Fock model excluding the exchange term. It is exhibited that the curves have a universal behaviour at small internuclear distances which can be understood from the simpler Thomas-Fermi theory. Notably, we show that the atomic screenings in these two theories are comparable up to a distance from the nuclei which is independent of the atomic number. This is proven iteratively, by relating to suitable Thomas-Fermi models at dierent length scales. We in particular study solutions to the Thomas-Fermi partial dierential equation with two singularities and demonstrate that their asymptotic behaviour is universal. This thesis also contains a numerical investigation of the homonuclear Born-Oppenheimer curve in Thomas-Fermi theory which supports the analytic result.
UR - https://rex.kb.dk/primo-explore/fulldisplay?docid=KGL01011929195&context=L&vid=NUI&search_scope=KGL&tab=default_tab&lang=da_DK
M3 - Ph.D. thesis
BT - Universality of Born-Oppenheimer curves
PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen
ER -