A new technique for solving the one-electron Schrödinger equation of crystals using a linear combination of atomic orbitals (LCAO) basis set is presented. The main feature is the use of a Fourier transform, to write all the quantities of interest in terms of the form factors of the atomic orbitals. This leads to a formulation quite similar to the orthogonalized-plane-wave (OPW) method. An obvious advantage is to avoid the calculation of many-center integrals. Another point is that summations are now truncated in reciprocal space. This procedure is found to be more convergent than the usual truncations in real space. Application to diamond in a full self-consistent Hartree-Fock treatment leads to excellent agreement with previously reported results. The optimized atomic orbitals have their exponent increased by 30% with respect to their free-atom value, leading to a good value for the $F_{222}$ x-ray scattering factor. The conduction band is also calculated within an improved OPW approximation, where the plane waves are orthogonalized not only to the core functions but also to the valence-band states. The convergence is found to be quite good (only 15 plane waves are necessary) and the results significantly better for the higher conduction-band states than when using a LCAO basis.

• Received 6 January 1976

DOI:https://doi.org/10.1103/PhysRevB.15.2324