University of Sussex
Browse

File(s) not publicly available

Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry

journal contribution
posted on 2023-06-08, 15:50 authored by Carlos Argaez, Michael MelgaardMichael Melgaard
We establish the existence of infinitely many distinct solutions to the multi-configurative Hartree–Fock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy $\sqrt{ -\a^{-2} \D_{x_{n}} + \a^{-4? }} -\a^{-2}$ for the nth electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove the existence of a ground state. The results are valid under the hypotheses that the total charge Ztot of K nuclei is greater than N-1 and that Ztot is smaller than a critical charge Ztot. The proofs are based on a new application of the Lions–Fang–Ghoussoub critical point approach to nonminimal solutions on a complete analytic Hilbert–Riemann manifold, in combination with density operator techniques.

History

Publication status

  • Published

Journal

Nonlinear Analysis: Theory, Methods and Applications

ISSN

0362-546X

Publisher

Elsevier Ltd

Issue

1

Volume

75

Page range

384-404

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2013-09-19

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC