The electronic band structure, charge density, and optical properties of diamond have been calculated using the discrete variational method in an ab initio approach with an LCAO Bloch basis set. This technique avoids most of the difficulties encountered with evaluation of the matrix elements of the Hamiltonian, and allows inclusion of the nonspherical terms in the potential. A comparative study of the relative effects of muffin-tin averaging and scaling the ${\rho }^{\frac{1}{3}}$ statistical exchange reveals the large sensitivity of the energy bands to spherical averaging of the potential. For example, in diamond we find that neglect of the nonspherical potential terms shifts the indirect band gap by 5 times the change produced by scaling the exchange between Kohn-Sham and full Slater values. This demonstrates the inadequacy of the muffin-tin approximation for use in quantitative ab initio calculations. A comparison of the energy and location in the Brillouin zone of the indirect transition threshold indicates excellent agreement with experiment for an exchange scaling close to that determined by the $X_{\alpha }$ method. The conventional energy-level ordering is found, as opposed to that obtained in recent pseudopotential calculations. An analysis of the interband density of states reveals that this approach gives good agreement with the available optical data for diamond.

• Received 26 April 1971

DOI:https://doi.org/10.1103/PhysRevB.4.3610