The performance of hybrid density functionals in solid state chemistry: the case of BaTiO₃

Abstract

The performance of hybrid exchange functionals is investigated within the framework of Density Functional Theory (DFT), in describing the properties of cubic and tetragonal ferroelectric phases of BaTiO₃. A variable fraction ξ of non-local HF exchange is mixed with Becke's GGA formulation, and coupled with the LYP correlation functional. Standard DFT functionals (LDA, PW, B3LYP) and uncorrelated HF are also added for comparison. Inclusion of the non-local HF exchange has a noticeable effect on the calculated electronic density, and several observables show clear trends as a function of the mixing parameter ξ; these include not only the band gap, but also lattice parameter and bulk modulus, structural distortions, relative ionic sizes, electronic polarizability and polarization of the tetragonal phase. In this context, it is shown that hybrid functionals yield results that are generally in better agreement with experiment than local (LDA and GGA) DFT formulations. A higher fraction of HF exchange than the 20% optimized in the B3LYP functional for molecular systems is required in the solid state. This is due to the localization effect played by the Madelung field on the electronic distribution; in this situation, the self-interaction error in local DFT functionals is more pronounced, and is empirically corrected by a high fraction of exact HF exchange component in the hybrid functional.

Acknowledgements

I would like to thank the CRYSTAL groups in Torino and Daresbury, for their help and assistance throughout the years; the contributions made by Vic Saunders for the efficiency and accuracy of the algorithms have always proven as invaluable as his scientific advice. I also thank EPSRC for an advanced research fellowship.

Notes

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Additional information

Notes on contributors

Furio Corà *

Email: [email protected]