Structural properties of tetrahedrally coordinated crystals from first-principles calculations of pressure and total energies

The total-energy and pressure-volume relations are calculated nonrelativistically for Si, Ge, and {α}-Sn within the local-density-functional formalism, with use of first-principles nonlocal pseudopotentials. Ground-state static structural properties (total energy, lattice constant, and bulk modulus and its pressure derivative) are obtained and are in good agreement with experimental values. A prediction of these for {α}-Sn from pressure determinations has not yet been reported. Its bulk modulus from both total-energy and pressure calculations is much smaller than that determined by experimental measurement. This confirms a recent theoretical prediction from other authors casting doubts on the experimental value. An assessment has been made on the advantages and disadvantages of pressure calculations over total-energy calculations and on the influence on the results of the size of all cutoff parameters and perturbative schemes used.