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La doped SrFeO$_{3}$, La$_{1/3}$Sr$_{2/3}$FeO$_{3}$, exhibits ametal-to-insulator transition accompanied by both antiferromagnetic and chargeordering states along with the Fe-O bond disproportionation below a criticaltemperature near 200K. Unconventionally slow charge dynamics measured in thismaterial near the critical temperature shows that its excited charge orderingstates can exhibit novel electronic structures with nontrivial energy profiles.Here, we reveal possible metastable states of charge ordering structures inLa$_{1/3}$Sr$_{2/3}$FeO$_{3}$ using the first-principle and climbing imagenudged elastic band methods. In the strong correlation regime,La$_{1/3}$Sr$_{2/3}$FeO$_{3}$ is an antiferromagnetic insulator with a chargeordering state of the big-small-big pattern, consistent with the experimentalmeasurement of this material at the low temperature. As the correlation effectbecomes weak, we find at least two possible metastable charge ordering stateswith the distinct Fe-O bond disproportionation. Remarkably, a ferroelectricmetallic state emerges with the small energy barrier of $\sim$7 meV, driven bya metastable CO state of the small-medium-big pattern. The electronicstructures of these metastable charge ordering states are noticeably differentfrom those of the ground-state. Our results can provide an insightfulexplanation to multiple metastable charge ordering states and the slow chargedynamics of this and related oxide materials.

First-principle Study of Multiple Metastable Charge Ordering States in La$_{1/3}$Sr$_{2/3}$FeO$_{3}$