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arXiv · 1708.00287

Existence of Hartree-Fock excited states for atoms and molecules

Mathieu Lewin
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Abstract

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 Schr{ö}dinger 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.

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Mathieu Lewin. 2017-10-18. Existence of Hartree-Fock excited states for atoms and molecules. https://doi.org/10.1007/s11005-017-1019-y

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