Ab initio study of the density dependence of the Gr\"{u}neisen parameter at pressures up to 360 GPa

Ab initio calculations based on the Density Functional Theory are used to show that the Debye frequency is a linear function of density to a high accuracy for several elemental solids at pressures (at least) up to 360 GPa. This implies that the ratio of density over the (Debye-frequency-based) vibrational Gr\"{u}neisen parameter is a linear function of density in this region. Numerical data from first principles calculations for several systems at temperatures up to 2000K suggest that this is also true for the thermal Gr\"{u}neisen parameter in the same range of pressure. Our analytical form of the vibrational Gr\"{u}neisen parameter is applied to an implementation of the Lindemann's melting criterion to obtain a simple extrapolation formula for the melting temperatures of materials at higher densities. This prediction is tested against available experimental and numerical data for several elemental solids.