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Title: On the NP-completeness of the Hartree-Fock method for translationally invariant systems

The self-consistent field method utilized for solving the Hartree-Fock (HF) problem and the closely related Kohn-Sham problem is typically thought of as one of the cheapest methods available to quantum chemists. This intuition has been developed from the numerous applications of the self-consistent field method to a large variety of molecular systems. However, as characterized by its worst-case behavior, the HF problem is NP-complete. In this work, we map out boundaries of the NP-completeness by investigating restricted instances of HF. We have constructed two new NP-complete variants of the problem. The first is a set of Hamiltonians whose translationally invariant Hartree-Fock solutions are trivial, but whose broken symmetry solutions are NP-complete. Second, we demonstrate how to embed instances of spin glasses into translationally invariant Hartree-Fock instances and provide a numerical example. These findings are the first steps towards understanding in which cases the self-consistent field method is computationally feasible and when it is not.
Authors:
 [1] ;  [2] ;  [3]
  1. Vienna Center for Quantum Science and Technology, Department of Physics, University of Vienna, Boltzmanngasse 5, Vienna (Austria)
  2. Department of Computer Science, University College London, Gower Street, WC1E 6BT London (United Kingdom)
  3. (Spain)
Publication Date:
OSTI Identifier:
22413321
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 23; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; HAMILTONIANS; HARTREE-FOCK METHOD; SELF-CONSISTENT FIELD; SOLUTIONS; SPIN GLASS STATE