  Strontium niobate has triggered a lot of interest as a transparent conductor
and as a possible realization of a correlated Dirac semi-metal. Using the
lattice parameters as a tunable knob, the energy landscape of octahedral
tilting was mapped using density functional theory calculations. We find that
biaxial compressive strain induces tilting around the out-of-plane axis, while
tensile strain induces tilting around the two in-plane axes. The two competing
distorted structures for compressive strain show semi-Dirac dispersions above
the Fermi level in their electronic structure. Our density functional theory
calculations combined with dynamical mean field theory (DFT+DMFT) reveals that
dynamical correlations downshift these semi-Dirac like cones towards the Fermi
energy. More generally, our study reveals that the competition between the
in-phase and out-of-phase tilting in SrNbO$_3$ provides a new degree of freedom
which allows for tuning the thermoelectric and optical properties. We show how
the tilt angle and mode is reflected in the behavior of the Seebeck coefficient
and the plasma frequency, due to changes in the band structure.
