  Monoclinic crystal structure of the undoped BaBiO3 can be described as a
cubic perovskite distorted by a frozen breathing and tilting phonon modes of
BiO6 octahedra. The phonon mode softening is experimentally observed [M. Braden
et al., Europhysics Letters (EPL) 34, 531 (1996)] in Ba1-xKxBiO3 through
potassium doping followed by a transition into an ideal cubic perovskite
structure at x = 0.37 close to the appearance of superconductivity. In our
previous paper [D. Korotin et al., Journal of Physics: Condensed Matter 24,
415603 (2012)] we demonstrated that it is necessary to take into account
correlation effects by DFT+U method in Wannier functions basis to obtain a good
agreement between the calculated and experimental values of crystal structure
distortion and energy gap in BaBiO3. In the present work with the same method
we calculated the breathing mode phonon frequencies as a function of potassium
doping level in Ba1-xKxBiO3. Obtained frequencies are in a good agreement with
experimental values and the breathing mode softening with doping effect is
reproduced while calculations without consideration of correlation effects
failed to do so. We shown 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.
