Microscopic Theory of the Phase Transformation and Lattice Dynamics of Si

An ab initio calculation for the solid-solid phase transformation, static structural properties, and the lattice dynamics of Si is presented. A density-functional pseudopotential scheme is used with the atomic number as the only input. The detailed properties of the diamond to $\beta$-tin transition are accurately reproduced. The phonon frequencies and mode-Grüneisen parameters at $\Gamma$ and $X$, along with the lattice constant, bulk modulus, and cohesive energy, are calculated and found to be in excellent agreement with experiment.