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

Argaez, Carlos and Melgaard, Michael (2012) Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry. Nonlinear Analysis: Theory, Methods and Applications, 75 (1). pp. 384-404. ISSN 0362-546X

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## Abstract

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.

Item Type: Article Semilinear elliptic equations; Multiple solutions; Abstract critical point theory; Palais–Smale sequences School of Mathematical and Physical Sciences > Mathematics Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems Michael Melgaard 19 Sep 2013 09:58 13 Jul 2017 08:10 http://srodev.sussex.ac.uk/id/eprint/46366