We consider a model where the most exciting features of the hole centers Cu
O45- in doped cuprates are in their unusually complicated ground state as a
result of electronic quasi-degeneracy accompanied by the (pseudo-)Jahn-Tel
ler effect. An additional hole, doped to the basic CuO46- cluster with the
b(1g) hole can occupy both the same hybrid Cu3d-O2p orbital state resulting
in a Zhang-Rice singlet (1)A(1g) and the purely oxygen e(u) molecular orbi
tal resulting in the singlet or triplet term with close energies. We presen
t a detailed analysis of the (pseudo-)Jahn-Teller effect and local structur
e distortions driven by the near-degeneracy within the ((1)A(1g), E-1,3(u))
manifold.