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

We establish the existence of infinitely many distinct solutions to the multi-configurative Hartree–Fock type equations for NN-electron Coulomb systems with quasi-relativistic kinetic energy −α−2Δxn+α−4−α−2 for the nnth 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 KK nuclei is greater than N−1N−1 and that Ztot is smaller than a critical charge Zc. 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.