Josh and Feizhi have recently published a paper on the stability of generalized Hartree-Fock (GHF) wave functions. During the solution of a variational problem it is possible to converge to a higher energy minima instead of the global minima. Whenever possible, the stability of the wave function should be confirmed. If the wave function is unstable, the orbitals should then be rotated and the wave function reoptimized to find the global minima.
In contrast to restricted (RHF) and unrestricted (UHF) wave functions, GHF wave functions lack spin and time-reversal symmetry. When these symmetry constraints are removed, it becomes even more likely that you will converge to a solution other than the global minima. This work makes it possible to check the stability of the GHF wave function and rotate the molecular orbitals toward the true global minima. Their implementation was tested for some spin frustrated systems and is published in The Journal of Chemical Physics, “Stability of the Complex Generalized Hartree-Fock Equations“.