Quantum 2025 – scientific programme

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FRI: Friday Contributed Sessions

FRI 2: Many-Body Quantum Dynamics III

FRI 2.4: Talk

Friday, September 12, 2025, 11:30–11:45, ZHG002

Fully numerical Hartree-Fock calculations for atoms and small molecules with quantics tensor trains — •Paul Haubenwallner and Matthias Heller — Fraunhofer Institut für Graphische Datenverarbeitung IGD, Darmstadt, Deutschland

We present a fully numerical framework for the optimization of molecule-specific quantum chemical basis functions within the quantics tensor train format using a finite-difference scheme. The optimization is driven by solving the Hartree*Fock equations (HF) with the density-matrix renormalization group algorithm on Cartesian grids that are iteratively refined. In contrast to the standard way of tackling the mean-field problem by expressing the molecular orbitals as linear combinations of atomic orbitals (LCAO) our method only requires as much basis functions as there are electrons within the system. Benchmark calculations for atoms and molecules with up to ten electrons show excellent agreement with LCAO calculations with large basis sets supporting the validity of the tensor network approach. Our work therefore offers a promising alternative to well-established HF-solvers and could pave the way to define highly accurate, fully numerical, molecule-adaptive basis sets, which, in the future, could lead to benefits for post-HF calculations.

Keywords: Hartree-Fock Method; Tensor Networks; Mean-Field Theory; Quantum Chemistry