Abstract: The self-consistent Linear Muffin Tin Orbital (LMTO) energy band method is applied to the case of the open structures:Sn(Diamond) and CdTe (Zinc blende). Empty spheres are inserted into the most open parts of the structure and each sphere is assigned a spherically symmetric potential.Using Orthogonal Experimental Design(OED)method for determining the radii of the overlapping atom spheres and empty spheres, the resulting band structure are presented. Good agreement with band results of pseudopoten-tial methods as well as with experiment is found.