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We assess the validity of various exchange-correlation functionals forcomputing the structural, vibrational, dielectric, and thermodynamicalproperties of materials in the framework of density-functional perturbationtheory (DFPT). We consider five generalized-gradient approximation (GGA)functionals (PBE, PBEsol, WC, AM05, and HTBS) as well as the local densityapproximation (LDA) functional. We investigate a wide variety of materialsincluding a semiconductor (silicon), a metal (copper), and various insulators(SiO$_2$ $\alpha$-quartz and stishovite, ZrSiO$_4$ zircon, and MgO periclase).For the structural properties, we find that PBEsol and WC are the closest tothe experiments and AM05 performs only slightly worse. All three functionalsactually improve over LDA and PBE in contrast with HTBS, which is shown to faildramatically for $\alpha$-quartz. For the vibrational and thermodynamicalproperties, LDA performs surprisingly very good. In the majority of the testcases, it outperforms PBE significantly and also the WC, PBEsol and AM05functionals though by a smaller margin (and to the detriment of structuralparameters). On the other hand, HTBS performs also poorly for vibrationalquantities. For the dielectric properties, none of the functionals can be putforward. They all (i) fail to reproduce the electronic dielectric constant dueto the well-known band gap problem and (ii) tend to overestimate the oscillatorstrengths (and hence the static dielectric constant).

Accuracy of generalized gradient approximation functionals for density functional perturbation theory calculations