  We use a combination of density functional theory (DFT) and dynamical
mean-field theory (DMFT) to investigate the potential emergence of a
charge-disproportionated insulating phase in SrCrO$_{3}$, whereby the Cr
cations disproportionate according to $3\text{Cr}^{4+} \rightarrow
2\text{Cr}^{3+} + \text{Cr}^{6+}$ and arrange in ordered planes perpendicular
to the cubic [111] direction. We show that the charge disproportionation
couples to a structural distortion where the oxygen octahedra around the
nominal Cr$^{6+}$ sites contract, while the octahedra surrounding the Cr$^{3+}$
sites expand and distort. Our results indicate that the
charge-disproportionated phase can be stabilized for realistic values of the
Hubbard $U$ and Hund's $J$ parameters, but this requires a scaling of the
DFT+DMFT double counting correction by at least 35%. The disproportionated
state can also be stabilized in DFT+U calculations for a specific magnetic
configuration with antiparallel magnetic moments on adjacent Cr$^{3+}$ sites
and no magnetic moment on the Cr$^{6+}$ sites. While this phase is higher in
energy than other magnetic states that can arise in SrCrO$_{3}$, the presence
of an energy minimum suggests that the charge disproportionated state
represents a metastable state of SrCrO$_{3}$.
