Towards a unified first-principles-based description of VO$_2$ using DFT+DMFT with bond-centered orbitals

We present a combined density-functional theory and dynamical mean-field theory (DFT+DMFT) study of the full structural phase space of rutile-based vanadium dioxide (VO$_2$), including also the less studied M2 and T phases, using an unconventional bond-centered orbital basis. The use of bond-centered orbitals allows us to treat all main phases of VO$_2$, and the structural transitions between them, using one consistent approach with moderate computational cost and without pre-pattering of the structure into dimerized and undimerized V--V pairs. We obtain two distinct insulating states on the two different types of vanadium chains in the M2 phase, a singlet-insulator on the dimerized chains and a Mott-insulator on the zigzag-distorted chains, which, however, are strongly coupled in the M2 phase and thus the metal-insulator transition always occurs concomitantly for both types of sites. We also demonstrate that the M2 phase corresponds to a local energy minimum in the structural phase space of VO$_2$, the stability of which, apart from the internal structural distortion, depends crucially on the unit cell strain relative to the undistorted rutile phase. Our calculations further indicate that the symmetry-distinct triclinic T phase corresponds electronically to either an M1 or an M2-type insulator with an abrupt transition as a function of distortion. Finally, we disentangle the effect of the dimerization and zigzag distortions by constructing hypothetical structures that contain only one site type, finding that the zigzag distortion strongly favors emergence of the Mott-insulating state, both as function of distortion and on-site interaction.