A first-principle procedure is proposed to determine the Gruneisen parameter for a crystal by calculating the external pressure and the vibration spectrum as functions of the volume of a unit cell. In the gradient approximation of the electron density functional theory, on the basis of a linear combination of atomic orbitals, the elastic and the thermodynamic Gruneisen parameters of silver azide, which decrease with volume (with increasing pressure), are calculated with the use of the CRYSTAL09 code. The equilibrium values of the parameter γ 0 for various cold equations of state of crystals and for the thermodynamic models used are, respectively, ~2.3 and 1.6.

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