We generalize a previously established ab initio approach—originally developed for hexagonal close-packed (hcp) metals—to accommodate solids with both internal and external degrees of freedom. This extension enables the thermodynamic and thermoelastic characterization of insulators, including those with nonvanishing piezoelectric and pyroelectric tensors. Utilizing Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT) within the quasiharmonic approximation, we derive the pressure and temperature dependence of these properties. Specifically, we investigate internal degrees of freedom using two distinct frameworks: the Zero Static Internal Stress Approximation (ZSISA) and Full Free Energy Minimization (FFEM). We then compare these approximations by computing internal and external thermal expansions, as well as temperature-dependent piezoelectric and pyroelectric tensors. Finally, we demonstrate the generalized formalism by calculating the thermodynamic properties of wurtzite ZnO across a broad range of pressures and temperatures.

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• Elasticity
• Mechanical & acoustical properties
• II-VI semiconductors
• Transition metal oxides
• Density functional theory
• Density functional theory development
• First-principles calculations
• Materials modeling
• Perturbation theory