Abstract
We have carried out an extended Huckel calculation to rationalize the role of $CuO_3$ chains and the size effect of the charged model clusters for the following charged model culsters : ${{Cu_6}{O_{21}}^{28-},\;{{Cu_6}{O_{22}}^{30-}\;,{{Cu_9}{O_{30}}^{39-}\;,{{Cu_9}{O_{32}}^{43-}\;,{{Cu_{12}{O_{38}}^{48-}\;,{{Cu_{15}{O_{50}}^{65-}\;,{{Cu_{18}{O_{54}}^{66-}\;,{{Cu_{18}{O_{55}}^{68-}\;,{{Cu_{24}{O_{70}}^{84-}\;and\;{{Cu_{27}{O_{78}}^{93-}$ for high-$T_c$ superconductor $YBa_2Cu_3O_7$: ${{Cu_6}{O_{18}}^{22-}\;,{{Cu_9}{O_{26}}^{31-}}\;,{{Cu_{12}{O_{32}}^{36-}\;,{{Cu_{15}{O_{42}}^{49-}\;,{{Cu_{18}{O_{46}}^{50-}\;,{{Cu_{24}{O_{60}}^{64-}\;and\;{{Cu_{27}{O_{66}}^{69-}$ for insulator $YBa_2Cu_3O_6$. The results show that the electronic structures and properties of the charged model clusters relating to high-$T_c$ superconductor are very sensitive to the size change of the clusters with various environmental effects, wherease those of the charged model clusters for insulator $YBa_2Cu_3O_6$ are monotonous to the size change. The $CuO_3$ chains along the b-direction may yield cooperative electronic coupling with the $CuO_2$ layers in determining both conducting and superconducting properties of $YBa_2Cu_3O_{7-x}$ system.
