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Based on temperature-dependent EXAFS studies of Ba1−xKxBiO3 superconducting oxide, a model of the relationship between the local crystal and the local electronic structures has been proposed. Oxygen ions were found to vibrate in a double-well potential and their vibrations are correlated with the local electron pair transfer due to the dynamical exchange BiO6 ↔ Bi\underline{{\rm{L}}}2O6, where \underline{{\rm{L}}}2 denotes the hole pair in the antibonding Bi 6s O2pσ* orbital of the octahedral complex. The similarity of the EXAFS spectra features of Ba1−xKxBiO3 and La2−xSrxCuO4 allowed us to propose a similar model for Cu-based superconducting oxides. The model, in a common approach, explains the antiferromagnetic state, metal–insulator phase transition and the appearance of superconductivity at Sr2+ doping of La2CuO4, and eliminates discrepancy between the neutron-scattering and EXAFS data.

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