The effect of oxygen-deficiency on the charge distributions and orbital energies for small copper oxide clusters representing the superconducting materials $YBa_2Cu_3O_x (6{leq}x{leq}7)$ were investigated by the extended Huckel molecular orbital (EHMO) method with the tight-binding model. Our calculations show +3 oxidation state of Cu(1) in the $CuO_3$ chain and +2 or +1 of Cu(2) in the $CuO_2$ layers for $YBa_2Cu_3O_7$ with the nominal charge of $Cu_3$ = +7 (or +5), while for $YBa_2Cu_3O_6$ +1 oxidation state of Cu(1) and +3 (or +2) of Cu(2) in the $CuO_2$ layers with the nominal charge of $Cu_3$ = +7 (or +5). For $Cu_3O_{12}$ cluster representing $YBa_2Cu_3O_7$ with the nominal charge of $Cu_3$ = +7 the Cu(2) $d_{{x^2}-{y^2}}$ orbitals in the $CuO_2$ layers is a typical Jahn-Teller $d^9$ system with the partial hole and the Cu(1) $d_{{_z2}-{_y2}}$ orbital in the $CuO_3$ chain contains hole occupancy. For $Cu_3O_{10}$ cluster representing $YBa_2Cu_3O_6$ with the nominal charge of Cu = +5 the orbital character of the highest partially occupied MO (HPOMO) and the lowest completely unoccupied MO (LCUMO) of $Cu_3O_{12}$ representing $YBa_2Cu_3O_7$ with the nominal charge of $Cu_3$ = +7 is reversed, and the character of Cu(1) $d{{x^2}-{y^2}}$ orbital of LCUMO of the $Cu_3O_{12} $cluster is vanished. It is suggested that the local crystal field environment of Cu(1) by the oxygens in the Cu(1) chain may play a vital role in conductivity and superconductivity, either alone or through cooperative electronic coupling with the Cu(2) layers in $YBa_2Cu_3O_7.$