The valences of Cu and bond covalencies in ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+y}$ have been investigated using complex chemical bond theory. This theory is the generalization of Phillips, Van Vechten, Levine, and Tanaka’s scheme. The results indicate that the valences of Cu(1) and Cu(2) in our calculation agree well with those obtained by the bond valence sum method. The valences of Cu(1) and Cu(2) in our calculation also suggest that the holes introduced by Ca substitution only reside in ${\mathrm{CuO}}_2$ planes and there is a competing mechanism for the hole density in ${\mathrm{CuO}}_2$ planes between Ca doping and oxygen depletion. These conclusions are in satisfactory agreement with experiments. The calculated ordering of covalencies is $\mathrm{Cu}\left(1\right)-\mathrm{O}\left(4\right)>\mathrm{Cu}\left(1\right)-\mathrm{O}\left(1\right)\mathrm{}$ $>\mathrm{Cu}\left(2\right)-\mathrm{O}(2,3)>\mathrm{Cu}\left(2\right)-\mathrm{O}\left(1\right)>\mathrm{C}\mathrm{a}-\mathrm{O}>\mathrm{Y}-\mathrm{O}\mathrm{\sim }\mathrm{B}\mathrm{a}-\mathrm{O},$ regardless of the Ca doping level and oxygen content.

• Received 2 February 1998

DOI:https://doi.org/10.1103/PhysRevB.58.958