It was well known that pressure can have profound effects on the structural, magnetic, and electronic properties of transition metal oxides. However, it is a challenge both experimentally and theoretically to determine the exact structural and magnetic order of a complicated oxide system under pressure. To this end, we develop a global optimization approach based on the genetic algorithm by taking into account explicitly both structural and magnetic degrees of freedom. With this approach, we investigate the effect of pressure on the structure, magnetism, and charge ordering of the recently synthesized perovskite oxide $\mathrm{PbCo}{\mathrm{O}}_{3}$, which is an interesting system since both Pb and Co sites can change the valence states. At low pressure, we predict that $\mathrm{PbCo}{\mathrm{O}}_{3}$ can order in two multiferroic phases (i.e., $R3c$ and $Pna{2}_{1}$). Both phases are ferroelectric with a large electric polarization due to unusual coupling between the ferroelectric mode and other antipolar modes. Both phases display weak ferromagnetism. The ferroelectric polarization and weak ferromagnetism in these two phases are coupled to each other, suggesting that they may be used to realize the electric field control of magnetism. At higher pressure, the valence transition takes place from $\mathrm{P}{\mathrm{b}}^{4+}\mathrm{C}{\mathrm{o}}^{2+}{\mathrm{O}}_{3}$ to the $A$-site and $B$-site charge-ordering state $\mathrm{P}{\mathrm{b}}^{2+}{\mathrm{Pb}}_{3}^{4+}{\mathrm{Co}}_{2}^{2+}{\mathrm{Co}}_{2}^{3+}{\mathrm{O}}_{12}$ accompanied with an unusual enhancement of the band gap. In this work, we not only provide a general powerful method to determine the spin-orbital-charge ordering of intriguing correlated systems, but also predict that $\mathrm{PbCo}{\mathrm{O}}_{3}$ may be a multiferroic material under low pressure.
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