Solutions to quasi-relativistic multi-configurative HartreeFock equations in quantum chemistry

We establish the existence of infinitely many distinct solutions to the multi-configurative HartreeFock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy -α- ²Δ^xn+α-⁴-α-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 ^Zc. The proofs are based on a new application of the LionsFangGhoussoub critical point approach to nonminimal solutions on a complete analytic HilbertRiemann manifold, in combination with density operator techniques.