[en] The correlation between the structure and thermodynamic properties of minerals has long been considered fundamental. Besides the first-law functions, it is possible to calculate entropy and free energy for a pure ideal crystal if the vibrational properties are taken into account. These calculations imply the precise evaluation of spectroscopic data (Raman, IR, phonon dispersion curves) and allow good estimates of elastic properties and atomic displacement parameters. Whereas the improvement in computer design strongly favors development in this field, there are still several difficulties with respect to general application of these calculations. There is, however, evidence that the difficulties may be overcome, provided adequate simplification in computing techniques is considered. In this chapter, we show that close relationships can be observed between a Raphson Newton process of energy minimization and the calculation of vibration frequencies; based on these techniques, it is possible to check the nature of a minimum and its physical significance. Thus, we can come much closer to a prediction of the entropy and free energy of a crystalline substance. Crystallographic information (including optical data) has long been considered a collection of the open-quotes essentialclose quotes physical properties of a certain mineral. This happens especially because of the well-known traditional connections between crystallography and mineralogy: For a great majority of minerals, there are accurate measurements of unit-cell parameters and X-ray powder diffraction data, together with the values of the refractive indices and the orientation of the indicatrix. For the most important species, these properties (including atomic coordinates, displacement parameters, and other information obtained from careful crystal-structure determination and refinement) have been investigated in a substantial number of specimens by different authors