Existence of Hartree-Fock excited states for atoms and molecules
Lewin, Mathieu (2017), Existence of Hartree-Fock excited states for atoms and molecules, Letters in Mathematical Physics, online first, p. 22. 10.1007/s11005-017-1019-y
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01570624
Journal nameLetters in Mathematical Physics
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree-Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This is the equivalent, in Hartree-Fock theory, of the famous Zhislin-Sigalov theorem which states the existence of infinitely many eigenvalues below the bottom of the essential spectrum of the N-particle linear Schrödinger operator. Our result improves a theorem of Lions in 1987 who already constructed infinitely many Hartree-Fock critical points, but with much higher energy. Our main contribution is the proof that the Hartree-Fock functional satisfies the Palais-Smale property below the first energy threshold. We then use minimax methods in the N-particle space, instead of working in the one-particle space.
Subjects / KeywordsHartree-Fock theory; Excited states; Palais-Smale property; Min-max methods; Atoms and molecules; HVZ theorem
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