  In contrast to the previous reports that the divalent perovskite SrCrO$_3$
was believed to be cubic structure and nonmagnetic metal, recent measurements
suggest coexistence of majority tetragonally distorted weak antiferromagnetic
phase and minority nonmagnetic cubic phase. Within the local (spin) density
approximation (L(S)DA) our calculations confirm that a slightly tetragonally
distorted phase indeed is energetically favored. Using the correlated band
theory method (LDA+ Hubbard U) as seems to be justified by the unusual behavior
observed in SrCrO$_3$, above the critical value $U_c$=4 eV only the distorted
phase undergoes an orbital-ordering transition, resulting in $t_{2g}^2 -->
d_{xy}^1$($d_{xz}d_{yz}$)$^1$ corresponding to the filling of the $d_{xy}$
orbital but leaving the other two degenerate. The Fermi surfaces of the cubic
phase are simple with nesting features, although the nesting wavevectors do not
correlate with known data. This is not uncommon in perovskites; the strongly
directional d-d bonding often leads to boxlike Fermi surfaces, and either the
nesting is not strong enough, or the matrix elements are not large enough, to
promote instabilities. Fixed spin moment calculations indicate the cubic
structure is just beyond a ferromagnetic Stoner instability (IN(0)~1.1) in
L(S)DA, and that the energy is unusually weakly dependent on the moment out to
1.5$\mu_B$/Cr (varying only by 11 meV/Cr), reflecting low energy
long-wavelength magnetic fluctuations. We observe that this system shows strong
magneto-phonon coupling (change in Cr local moment is ~7.3 $\mu_B$/\AA) for
breathing phonon modes.
