Near-Hartree–Fock wave functions for solids: The case of crystalline silicon

Silicon is taken as a test system for assessing present-day feasibility of calculations for crystalline solids of near-Hartree–Fock quality. The calculations have been performed using CRYSTAL, an ab initio Hartree–Fock crystalline-orbital lcao program for periodic systems. The influence of the computational parameters that control the truncation of infinite sums on the results has been investigated; it is shown that a reasonable accuracy (numerical errors on total energy per atom below 10−3 a.u.) can be obtained while keeping the computational burden within manageable limits. The effect on the results of basis-set size and quality is discussed. A number of basis sets have been tested, from minimal to relatively extended sets (28 atomic orbitals per atom). The quality of the wave function has been checked using variational criteria and also through a comparison with experimental data, such as equilibrium geometry, bulk modulus, electron charge density, and electron momentum distribution. For the latter quantities, which are a measure of the accuracy of the one-electron density matrix, the best basis sets provide agreement with experiment that is almost within the experimental error. The correlation energy has been estimated using nonlocal density functionals, based on the one-electron density matrix: After this correction, the atomization energy agrees with experiment to within 2%. The generalization of the above analysis to other crystals is briefly discussed.