Quantum mechanics can be applied to successfully calculate the total en-ergy of a system of nuclei and electrons: atoms, molecules, clusters, and solids. Many properties of these systems are related to the total energy or to total energy differences between configurations. For instance, the cell parameters of a crystal are those that minimize the total energy of the structure. If this structure is also determined by internal parameters, these parameters minimize the energy of the structure and the forces on the atoms. Furthermore, quantum mechanics techniques allow the calculation not only of the optimized geometry of a system, but also of other properties related to the

total energy such as bulk modulus, elastic constants, phonon spectra, phase transition pressures between different structures, etc.