The stability conditions which ensure that the Brueckner (maximum-overlap) solution maximizes locally the overlap with the exact wave function are derived. These stability conditions are then specified for the closed-shell electronic systems with a spin-independent Hamiltonian yielding the singlet and nonsinglet ("triplet") stability conditions in complete analogy with the Hartree-Fock stability problem. The stability conditions are then applied to the $\pi$-electronic model of benzene. Critical coupling constants are determined for both singlet and nonsinglet instabilities and an example of space-symmetry-broken Brueckner solution is given. The main characteristics of the pure singlet, broken-symmetry Hartree-Fock, and Brueckner solutions are briefly outlined.

• Received 13 February 1973

DOI:https://doi.org/10.1103/PhysRevA.8.640