Electronic Structure and the Properties of Metals. I. Formulation

A method is formulated for the calculation from first principles of a variety of electronic and atomic properties of metals. The method depends upon three approximations: (1) the self-consistent-field approximation; (2) the assumption that the core states are the same as in the free atom; and (3) a perturbation solution, carried to second order, of the Hamiltonian matrix based upon orthogonalized plane waves. Only the last approximation distinguishes the method from more traditional band calculations; it is regarded as appropriate for the treatment of most polyvalent metals. The only experimental parameters which enter for a given metal are the atomic number and the atomic volume.It is found that many electronic properties, including the Fermi surface and scattering by defects or phonons, may be calculated as for free electrons with an effective perturbing potential. The matrix elements of this potential may be written as the product of a structure factor, depending only on the ion positions, and a form factor depending only on the Hartree-Fock field of the ion and upon the atomic volume. The form factor is found to be a function only of the magnitude of the change in wave number.It is found that for a given ion density the energy of the system may be written in terms of a central-force, two-body interaction between ions or in terms of a sum over wave number space of the Fourier transform of this interaction (the energy-wave number characteristic). The procedure for computing these functions from the Hartree-Fock field of the corresponding ion is given.