Abstract
Non-linear Hartree-Fock (HF) equations are usually solved using a self-consistent (SC) method. However, its convergence is not a priori guaranteed and problems arise in e.g. system with strong electron correlation.
There are two reasons for a nonconvergence of a HF solution: non-existence of the studied system itself and existence of nearby-lying solution of lower symmetry. Implementation of the perturbative method allows us to find a symmetry-adapted HF solution even in the cases when the SC method fails and, in addition, the region of (non)-existence of the system can be determined from analysis of perturbative energy series.
The existence of a solution of lower symmetry that lies below the symmetry-adapted one can be determined by constructing a so-called matrix of stability. In the case that the found symmetry-adapted solution is unstable, we report on how one can obtain a solution of lower symmetry.