A relativistic generalization of the augmented-plane-wave (APW) method is presented. The upper components of a Dirac plane wave are joined continuously on the Slater sphere to a linear expansion of centralfield Dirac orbitals. The lower components of the functions in the two regions are discontinuous. A variational expression for the energy which is appropriate for this type of basis function is developed. The matrix elements between these relativistic APW's are derived and compared with the nonrelativistic case.

• Received 10 March 1965

DOI:https://doi.org/10.1103/PhysRev.139.A1333