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We describe a method to calculate structural properties of semiconductors from the electron-ion Hamiltonian using density-functional expressions for the total energy. The method is applied to Si using an ionic pseudopotential with a plane-wave basis and considering TO (), TA (X), and C₁₁-C₁₂ lattice distortions. Harmonic and anharmonic forces and Gr\"uneisen coefficients are shown to be in reasonable agreement with experiment except that additional steps toward self-consistency appear to be essential for the very sensitive TA (X) mode. Charge densities for the distorted crystals show the nature of the electronic forces and the relation to phenomenological models.
Wendel et al. (1979) studied this question.