Relativistic corrections in the multiple-scattering method

We show how to introduce the Foldy-Wouthuysen relativistic corrections in the multiple-scattering method, for the determination of the electronic energy levels of molecules. The present derivation begins from a variational expression where the Foldy-Wouthuysen hamiltonian is inserted, instead of the Schrödinger hamiltonian. The resulting secular equation becomes identical with the standard multiple-scattering secular equation, if one neglects the relativistic correction terms.