Hartree–Fock formalism for the calculation of total energies and charge densities of thin films

A formalism has been developed by which the Hartree–Fock self‐consistent equations for thin films and surfaces are solved in an essentially exact way from first principles. The Fourier transform method, which was developed and used very successfully for the calculation of bulk properties, has now been extended to permit the study of the surfaces of crystals of a wide variety of materials. The development is sufficiently general to permit the treatment of any surface of any crystal geometry together with relaxations and reconstructions. A basis set of Slater‐type, layer orbitals is used to compute a self‐consistent density matrix for electrons in the field of bare nuclei in a slab geometry. The basis functions are handled in the Fourier representation which reduced many of the integrals to sums of one‐dimensional ones which are computed in closed form. The use of the Fourier integral representation also permits an analytical treatment of the cancellation of the Coulomb singularities in the classical potential.