1 First draft of the final paper published : Computational Materials Science Volume 42, Issue 1, March 2008, Pages 156–160 DFT evaluation of thermomechanical properties of scheelite type MLiF 4 (M=La, Ce, Pr, Nd, Pm, Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu) Benoit Minisini, Patrick Bonnaud, Qiuping A. Wang, and François Tsobnang. Institut Supérieur des Matériaux et Mécaniques Avancés du Mans, 44 Av. Bartholdi, 72000 Le Mans, France Abstract : Rare earth fluoroscheelites lattice parameters have been investigated using the Vienna Ab initio Simulation Package within the generalized gradient approximation. Elastic constants were evaluated by stress-strain method as implemented in MedeA interface for all the compounds. In all the calculations the f electrons were kept frozen in the core. The calculated bulk moduli are in good agreement with the three available experimental data. Consequently we can think in a reliable prediction of the ten others values. From energies of formation and mechanical stability criteria all the structures are supposed to be stable even though cationic repulsion is important in compounds from La to Sm. PACS: 62.20-x; 1. Introduction Because of their interest as laser host materials, a large number of doped or pure Rare Earth Fluoroscheelites (REF) have been synthesized during the last centuries[1][2]. Due to their field of application, most of the studies were focused on magnetic[1]-[5] or optical properties[6]-[8]. However, the determination of mechanical properties is also of