Muffin-tin orbitals of arbitrary order

We have derived orbital basis sets from scattering theory. They are express ed as polynomial approximations to the energy dependence of a set of partia l waves, in quantized form. The corresponding matrices, as well as the Hami ltonian and overlap matrices, are specified by the values on the energy mes h of the screened resolvent and its first energy derivative. These orbitals are a generalization of the third-generation linear muffin-tin orbitals an d should be useful for electronic-structure calculations in general.