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Interpolation between Hartree-Fock and Müller functional: Continuity and existence of a minimiser

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The ground state energy of atoms can be bounded from above by the infimum of the Hartree-Fock functional. Also, numerical results suggest that the Müller functional gives a lower bound for the ground state energy. Thus, the so-called Power functional introduced in [1], which interpolates between these functionals, is an important tool to compute the ground state energy of atoms in quantum chemistry. The aim of my Master’s thesis was to prove rigorous statements for the Power functional. In the talk, I will start with the càdlàg property for the ground state energy depending on the interpolation parameter. Then, the existence of a minimiser for infinitely many electron numbers N and any proton number Z>1/2 will be presented. At the end, I will shortly comment on the recent proof of the ionisation conjecture for the Power functional [2].
  1. S. Sharma et al. “Reduced density matrix functional for many-electron systems”. In: Physical Review B 78 .20 (2008), Nr. 201103.
  2. C. Kehle. “The maximal excess charge for a family of density-matrix-functional theories including Hartree-Fock and Müller theories.” arXiv preprint arXiv:1609.06272 (2016).

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