  Distortions of the oxygen octahedra influence the fundamental electronic
structure of perovskite oxides, such as their bandwidth and exchange
interactions. Utilizing a fully ab-initio methodology based on density
functional theory plus dynamical mean field theory (DFT+DMFT), we accurately
predict the crystal and magnetic structure of SrMoO$_3$. Comparing our results
with DFT+$U$ performed on the same footing, we find that DFT+$U$ overestimates
octahedral rotations leading to a different ground state structure. This
demonstrates that structural distortions can be highly sensitive to electronic
correlation effects, even in a moderately correlated metal such as SrMoO$_3$.
Moreover, by comparing different downfolding schemes, we demonstrate the
robustness of the DFT+DMFT method for obtaining structural properties,
highlighting its versatility for applications to a broad range of materials.
