Stability Conditions for the Solutions of the Hartree-Fock Equations for Atomic and Molecular Systems. VI. Singlet-Type Instabilities and Charge-Density-Wave Hartree-Fock Solutions for Cyclic Polyenes

The singlet-stability conditions of the symmetry-adapted Hartree-Fock (HF) ground state of cyclic polyenes (linear metal with Born-Karman cyclic boundary conditions) are studied, using the Pariser-Parr-Pople Hamiltonian and three different parametrization schemes. It is shown that the HF ground states are singlet-unstable for large enough cycles, so that the diamagnetic (pure singlet) symmetry-nonadapted HF solutions (broken-symmetry HF solutions), having lower energy than the symmetry-adapted HF solutions, must exist. In fact a number of broken-symmetry diamagnetic HF solutions, displaying the charge density waves (CDW' s), exist for large enough cyclic polyenes.. The most important ones, corresponding to the maximum quasi-momentum transfer and having lowest energy, are studied. The HF equations for these symmetry-nonadapted solutions are given In the BCS-Bogoliubov form, and their solutions are found numerically for cycles containing up to 170 atomic sites. It is shown that these new HF solutions display different types of CDW' s, which may be conveniently classified as diagonal and off-diagonal CDW' s. Finally, it is shown that the diagonal CDW HF solutions not only have generally higher energy than the off-diagonal HF solutions, but are, moreover, singlet-unstable, while the off-diagonal CDW solutions are singlet-stable. The implications of the existence of singlet instabilities for the occurrence of the energy-gap and bond-length alternation (sublattice formation), as well as for the applicability of some many-body techniques to these systems, are briefly discussed.