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