  While the phase diagrams of the one- and multi-orbital Hubbard model have
been well studied, the physics of real Mott insulators is often much richer,
material dependent, and poorly understood. In the prototype Mott insulator
V$_{2}$O$_{3}$, chemical pressure was initially believed to explain why the
paramagnetic-metal to antiferromagnetic-insulator transition temperature is
lowered by Ti doping while Cr doping strengthens correlations, eventually
rendering the high-temperature phase paramagnetic insulating. However, this
scenario has been recently shown both experimentally and theoretically to be
untenable. Based on full structural optimization, we demonstrate via the charge
self-consistent combination of density functional theory and dynamical
mean-field theory that changes in the V$_{2}$O$_{3}$ phase diagram are driven
by defect-induced local symmetry breakings resulting from dramatically
different couplings of Cr and Ti dopants to the host system. This finding
emphasizes the high sensitivity of the Mott metal-insulator transition to the
local environment and the importance of accurately accounting for the
one-electron Hamiltonian, since correlations crucially respond to it.
