Calculation of Mode Grüneisen Parameters Made Simple

A novel method to calculate mode Grüneisen parameters of a material from first principles is presented. This method overcomes the difficulties and limitations of existing approaches, based on the calculation of either third-order force constants or phonon frequencies at different volumes. Our method requires the calculation of phonon frequencies of a material at only the volume of interest, it is based on the second-order differentiation of a corrected stress tensor with respect to normal mode coordinates, and it yields simultaneously all the components of the mode Grüneisen parameters tensor. In this work, after discussing conceptual and technical aspects, the method is applied to silicon, aluminum, scandium fluoride, and a metallic alloy. These calculations show that our method is straightforward and it is suited to be applied to the broad class of materials prone to exhibit structural instabilities, or presenting anisotropy, or chemical and/or structural disorder.