Frontiers of Physics

, 14:23604 | Cite as

A two-density approach to the general many-body problem and a proof of principle for small atoms and molecules

  • Thomas PopeEmail author
  • Werner Hofer
Research Article


An extended electron model fully recovers many of the experimental results of quantum mechanics while it avoids many of the pitfalls and remains generally free of paradoxes. The formulation of the many-body electronic problem here resembles the Kohn–Sham formulation of standard density functional theory. However, rather than referring electronic properties to a large set of single electron orbitals, the extended electron model uses only mass density and field components, leading to a substantial increase in computational efficiency. To date, the Hohenberg–Kohn theorems have not been proved for a model of this type, nor has a universal energy functional been presented. In this paper, we address these problems and show that the Hohenberg–Kohn theorems do also hold for a density model of this type. We then present a proof-of-concept practical implementation of this method and show that it reproduces the accuracy of more widely used methods on a test-set of small atomic systems, thus paving the way for the development of fast, efficient and accurate codes on this basis.


many-body condensed matter Hartree–Fock density functional theory extended electrons 



The authors acknowledge EPSRC funding for the UKCP consortium (Grant No. EP/K013610/1). This work was also supported by the North East Centre for Energy Materials (NECEM). Finally, this research made use of the Rocket High-Performance Computing service at Newcastle University.

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Natural and Environmental SciencesNewcastle UniversityNewcastleUK
  2. 2.Institute of Physics & University of Chinese Academy of SciencesChinese Academy of SciencesBeijingChina

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