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Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry
Dublin Institute of Technology.
2012 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 75, no 1, 384-404 p.Article in journal (Refereed) Published
Abstract [en]

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 root-alpha(-2)Delta(xn) + alpha(-4) - alpha(-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 Z(tot) of K nuclei is greater than N - 1 and that Z(tot) is smaller than a critical charge Z(c). 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. (C) 2011 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
2012. Vol. 75, no 1, 384-404 p.
National Category
Mathematics
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URN: urn:nbn:se:uu:diva-174107DOI: 10.1016/j.na.2011.08.038ISI: 000296490000035OAI: oai:DiVA.org:uu-174107DiVA: diva2:526492
Available from: 2012-05-13 Created: 2012-05-13 Last updated: 2017-12-07

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Melgaard, M.

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