Non-linearity of the Hartree-Fock equations. Multiple Hartree-Fock solutions.

We determined multiple closed-shell Hartree-Fock-Roothaan solutions for the systems: BH, FH, LiH, and OH-, considering double and triple zeta bases. To calculate them, we used the self-consistent field method and the algebraic method. The Hartree-Fock solutions obtained were classified with respect to the kind of extreme. All these extremes generate the same configuration interaction space. Our key objective in this work is to illustrate that it is possible to obtain a wide variety of Hartree-Fock solutions for any molecular system.