Abstract: The correlation among the combinative energy, superconductivity, oxygen content, the position of holes in different planes, and the position of holes in the Cu(2)-O plane in LnBa$_2$Cu$_3$O$_{7-x}$ (Ln= Nd, Er, and Sm) has been investigated on the basis of a block model. The results indicate that the combinative energy decreases with increasing $T_{\rm c}$ in all of these compounds. And also, the combinative energies are obviously different with holes at different positions in the Cu(2)-O plane when the oxygen deficiency is low. However, this difference becomes less with increasing the oxygen deficiency. The effect of the holes in different positions on the combinative energy supplies some clue to the understanding of an unresolved problem, i.e. whether the distribution of carriers in the CuO$_2$ plane is uniform or inhomogeneous. The results not only show that the structural characters, the combinative energy between two structural blocks and the superconductivity are closely interrelated in this class of compounds, but also reveal some differences among these systems. The relationship between the combinative energy and the $T_{\rm c}$ value in NdBa$_2$Cu$_3$O$_{7-x}$ shows some features different from the systems containing Er or Sm.

Key words: structure, cohesive energy, superconductivity