Performance of various Hamiltonians in the study of the piezoelectric properties of crystalline compounds: The case of BeO and ZnO

The spontaneous polarization and the piezoelectric constants of ZnO and BeO are evaluated at the ab initio level with the CRYSTAL program that uses a Gaussian-type basis set. The results obtained with four different Hamiltonians, namely, Hartree-Fock (HF), local-density approximation (LDA), Perdew-Burke-Ernzerhof, and Becke's three-parameters exchange functional plus Lee-Yang-Parr correlation functional (B3LYP) are compared. As the same basis set and the same computational conditions have been used, differences in the results reflect genuine different behavior of the four Hamiltonians. LDA always gives the largest absolute value for the e₃₁ and e₃₃ piezoelectric constants, whereas the lowest absolute value is provided either by HF or B3LYP. The range of values of each eᵢⱼ is relatively large $(0.22$ and 0.48C/m² for e₃₁ and e₃₃ for BeO, and $0.15$ and 0.25C/m² for ZnO) and is comparable with the value of the constant itself. The present LDA results have been compared to previous results obtained with a full linearized augmented plane waves [Dal Corso et al., Phys. Rev. B 50, 10 715 (1994)] scheme and plane-waves pseudopotential methods [Bernardini et al., Phys. Rev. B 56, R10 024 (1997); Hill and Waghmare, Phys. Rev. B 62, 8802 (2000)]. A good agreement is observed with the latter and former studies (the largest difference is $0.03$ and 0.18C/m², respectively); differences with respect to Bernardini et al. are larger $(0.28$ and 0.53C/m² for BeO, $0.18$ and 0.43C/m² for ZnO).