  One of the most exciting features of the hole centers CuO_{4}^{5-} in doped
cuprates is an unusually complicated ground state which is the result of the
electronic quasi-degeneracy. An additional hole, doped to the basic
CuO_{4}^{6-} cluster with the b_{1g} hole can occupy both the same hybrid
Cu3d-O2p orbital state resulting in a Zhang-Rice singlet ^1A_{1g} and the
purely oxygen e_u molecular orbital resulting in a singlet or triplet ^{1,3}E_u
term with the close energies. We present detailed analysis of the
(pseudo)-Jahn-Teller effect driven by the near-degeneracy within the
(^1A_{1g},^{1,3}E_u)-manifold.
