Stability conditions for the solutions of the hartree‐fock equations. VII. Stability of some closed‐shell nonalternant systems

The instabilities of the solutions to the Hartree‐Fock equations for the nonalternants in the pentalene, heptalene, etc., series and in the azulene, etc., series are examined. The systems are found to have symmetry‐adapted solutions which are unstable for values of the core integral β close to the standard (spectroscopic) value; for example, the pentalene solution is unstable with β equal to 75% of its standard value. The “broken” symmetry solutions although exhibiting only a very slightly lower energy (0.01 eV) may exhibit dramatically different values for other properties, e.g., 30% changes in bond orders. The off‐diagonal charge‐density wave ( CDW ) appearing in the “broken” symmetry solutions at the onset of instability is amplified as the cooperative phenomena dominate, until in the “fully correlated” limit, the linked‐ethylenic (bond alternating) structure is obtained.