Dynamical matrices and free energies

The calculation of the entire dynamical matrix of a periodic supercell (containing a defect or not) provides several most useful pieces of information. At first, the eigenvalues of this matrix are all the normal mode frequencies of the cell, including the local, pseudolocal, and resonant modes associated with the defect under study. The eigenvalues can also be used to construct phonon densities of state which in turn allow the calculation of (Helmholtz) free energies, vibrational entropies, and specific heats. The eigenvectors of the dynamical matrix can be used to prepare a system in thermal equilibriumat a desired temperature. This allows constant-temperature MD simulations to be peformed without thermalization or thermostat. Applications to the calculation of vibrational lifetimes and decay channels are discussed. Finally, the vibrational, rotational, and charge-carrier contributions to the free energy are described. Configurational entropies are calculated in realistic systems.