Ab initio calculations of cohesive properties, elastic constants, and phonon dispersions for ${\mathrm{CoSi}}_2$ were performed by means of the Vienna ab initio molecular-dynamics package (VAMP), which makes use of ultrasoft pseudopotentials. In addition, the all-electron full-potential linearized augmented-plane-wave method was used for the calculation of equilibrium properties as well as elastic constants derived from second derivatives of total energies. For both methods, total energies, their derivatives, and related quantities are fully converged with respect to basis sizes and number of k points. Our results for ${\mathit{C}}_{44}$ prove that atomic positions in the strained crystal have to be fully relaxed in order to get quantitatively useful results. The results of both methods obtained within the same type of local-density approximation are in very good agreement between each other. Because elastic constants are very sensitive quantities for an ab initio method in general, the reproduction of high-quality all-electron data by VAMP demonstrates the power of suitably constructed pseudopotentials even for systems containing transition elements. VAMP was also applied to calculate elastic constants in two other ways, namely, directly from the stress-strain relations (which yielded the same results as obtained from total-energy derivatives) and from acoustic branches of the phonon dispersion. In this case, however, we only succeeded in getting a useful result for ${\mathit{C}}_{44}$ whereas for the remaining two elastic constants prohibitively large supercells would be needed. Finally, VAMP calculations were performed within the framework of the generalized gradient approximation to density-functional theory. From that, data were derived which are in very good agreement with experimental values. © 1996 The American Physical Society.

• Received 8 February 1996

DOI:https://doi.org/10.1103/PhysRevB.54.1729