Ab initio thermodynamics of metals: Pt and Ru

We present ab initio calculation of thermodynamic properties of platinum and ruthenium. We show that the method based on quasiharmonic approximation and density-functional perturbation theory can be used to predict precisely thermodynamic properties of metals, from cubic metal Pt to hexagonal metal Ru. The former is so heavy that the spin–orbital coupling should be considered; the latter has anisotropic thermal expansion. Our results for the properties such as thermal expansion and heat capacities are in good agreement with available experimental data in a wide range of temperature.