  We investigate the cyclic polyenes (annulenes) C_{M}H_{M}, described by the
Pariser--Parr--Pople (PPP) model, by means of the approximate coupled-pair
theories (ACP, ACPQ). For the systems with the spectroscopic value of the PPP
resonance integral beta=2.5 eV, the ACP method breaks down for M >= 446, and
the ACPQ method--for M>194. In the ACPQ method, for M>170, two close lying
solutions have been observed that become quasi-degenerate for M >= 198. The
results indicate that the ACP and ACPQ methods cannot be applied to the
one-dimensional metallic case.
