Hellmann-Feynman forces within the DFT + U in Wannier functions basis.

The most general way to describe localized atomic-like electronic states in strongly correlated compounds is to use Wannier functions. In the present paper we continue development of widely-used DFT + U method with the Wannier function basis set and propose a technique to calculate Hubbard contribution to atomic forces. The technique was implemented as a part of plane-waves pseudopotential code Quantum-ESPRESSO and tested on two compounds: charge transfer insulator NiO with cubic crystal structure and correlated metal SrVO3 with perovskite structure.

Correlation effects and phonon modes softening with doping in Ba1-xKxBiO3.

The monoclinic crystal structure of the undoped BaBiO3 can be described as a cubic perovskite which is distorted by the frozen breathing and tilting phonon modes of the BiO6 octahedra. The phonon mode softening is experimentally observed (Braden et al 1996 Europhys. Lett. 34 531) in Ba1-xKxBiO3 through potassium doping followed by a transition into an ideal cubic perovskite structure at x = 0.37, close to the emergence of superconductivity. In our previous paper (Korotin et al 2012 J. Phys.: Condens. Matter 24 415603) we demonstrated that it is necessary to take into account correlation effects using the DFT+U method in Wannier functions as a basis to obtain a good agreement between the calculated and experimental values of crystal structure distortion and the energy gap in BaBiO3. In the present work, using the same method, we calculated the breathing mode phonon frequencies as a function of the potassium doping level in Ba1-xKxBiO3. The obtained frequencies are in good agreement with experimental values and the breathing mode softening with doping is reproduced, contrary to calculations made without consideration of correlation effects. We show that the cubic crystal structure becomes stable at x = 0.30 in agreement with the experimental transition to cubic perovskite at x = 0.37. The possible connections between the correlation effects, phonon mode softening and superconductivity in Ba1-xKxBiO3 are discussed.

Electronic correlations and crystal structure distortions in BaBiO3.

BaBiO3 is a material where Bi4+ ions with half-filled 6s-states form an alternating set of Bi3+ and Bi5+ ions resulting in a charge ordered insulator. The charge ordering is accompanied by breathing distortion of the BiO6 octahedra (extension and contraction of the Bi-O bond lengths). Standard density functional theory (DFT) calculations fail to obtain the crystal structure instability caused by the pure breathing distortions. Combining effects of the breathing distortions and tilting of the BiO6 octahedra allows DFT to reproduce qualitatively an experimentally observed insulator with monoclinic crystal structure but strongly underestimates the breathing distortion parameter and energy gap values. In the present work we reexamine the BaBiO3 problem within the GGA + U method using a Wannier function basis set for the Bi 6s-band. Due to the high oxidation state of bismuth in this material, the Bi 6s-symmetry Wannier function is predominantly extended spatially on surrounding oxygen ions and hence differs strongly from a pure atomic 6s-orbital. That is in sharp contrast to transition metal oxides (with exclusion of high oxidation state compounds) where the major part of the d-band Wannier function is concentrated on the metal ion and a pure atomic d-orbital can serve as a good approximation. The GGA + U calculation results agree well with experimental data, in particular with experimental crystal structure parameters and energy gap values. Moreover, the GGA + U method allows one to reproduce the crystal structure instability due to the pure breathing distortions without octahedra tilting.