Abstract: The features and functions of both the empty atom-spheres and atomic empty d-states in linearized muffin tin orbital (LMTO) band structure calculations for sp³-semiconductors are investigated. A new approach, in which the states associated with atomic empty d states and empty-sphere p and d states are only incorprated in the evaluation of matrix elements is suggested. The method is spplied to study the band struture of gaAs as a test case. It is shown that the convantional secular determinant with a size of 36×36 can be reduced to a much smaller one with a aize of 10×10 and the results are still quite reasonable.