${\mathrm{Ba}}_2{\mathrm{CuO}}_{3+\delta }$ $(\delta \sim 0.2)$ has recently attracted considerable interest as an unconventional cuprate superconductor, yet its precise crystal structure remains theoretically under debate, primarily because its primitive cell may contain hundreds of atoms, which exceeds the size limits of density functional theory (DFT). To address this issue, we combine DFT with Deep-Potential molecular dynamics (DPMD) to explore a wide range of oxygen-deficient configurations. First, we construct a comprehensive training set for $\delta =0.0-1.0$, to train the accurate interatomic potential, and perform large-scale DPMD simulations for ${\mathrm{Ba}}_2{\mathrm{CuO}}_{3+\delta }$. Both DFT and DPMD phonon calculations reveal that the previously reported high-symmetry phase of ${\mathrm{Ba}}_2{\mathrm{CuO}}_3$ hosts soft phonon induced by planar oxygen vibrations leads to a charge ordered phase with alternating long and short Cu-O bonds. This bond disproportionation corresponds to mixed Cu valence states of ${\mathrm{Cu}}^{+}$ $\left(3d^{10}\right)$ and ${\mathrm{Cu}}^{3+}$ $\left(3d^8\right)$. Moreover, for ${\mathrm{Ba}}_2{\mathrm{CuO}}_{3.2}$, DPMD calculations indicate that the ground state adopts a one-dimensional Cu-O chain structure, and total energy and phonon analyses identify several dynamically metastable structures, which complicates the experimental fabrication of superconducting samples. Finally, DPMD simulations demonstrate that external pressure does not alter the ground state of the one-dimensional chain even at 20 GPa. These results provide a robust theoretical foundation for determining the correct crystal structure of ${\mathrm{Ba}}_2{\mathrm{CuO}}_{3+\delta }$ and indicate that its electronic ground state fundamentally deviates from that of ${\mathrm{CuO}}_2$ planes in two-dimensional cuprates. The superconducting pairing mechanism in this system may lie beyond standard electron-phonon coupling or doped Hubbard model.

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• Electron-phonon coupling
• Superconductivity
• Cuprates
• Deep learning
• Deep potential molecular dynamics
• Density functional theory