Quasi-harmonic thermoelasticity of palladium, platinum, copper, and gold from first principles

We calculate the temperature-dependent elastic constants of palladium, platinum, copper and gold within quasi-harmonic approximation using a first-principles approach evaluating numerically second derivatives Helmholtz free-energy with respect to strain at minimum itself. find an overall good agreement experimental data although anomalies palladium platinum reported room temperature are not reproduced. The contribution electronic excitations is also investigated: we that it non-negligible for $C_{44}$ while irrelevant in other cases. Its effect sufficient explain details found by experiments, even when, case take into account electron-phonon interaction. Lastly, exchange correlation functional addressed important T=0 K, all functionals give similar dependencies.