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### Incorporating static intersite correlation effects in vanadium dioxide through DFT+V
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Lea Haas, Peter Mlkvik, Nicola A. Spaldin, and Claude Ederer
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#### Abstract:
We analyze the effects on the structural and electronic properties of vanadium dioxide (VO2) of adding an empirical inter-atomic potential within the density-functional theory+V (DFT+V) framework. We use the DFT+V machinery founded on the extended Hubbard model to apply an empirical self-energy correction between nearest-neighbor vanadium atoms in both rutile and monoclinic phases, and for a set of structures interpolating between these two cases. We observe that imposing an explicit intersite interaction V along the vanadium-vanadium chains enhances the characteristic bonding-antibonding splitting of the relevant bands in the monoclinic phase, thus favoring electronic dimerization and the formation of a band gap. We then explore the effect of V on the structural properties and the relative energies of the two phases, finding an insulating global energy minimum for the monoclinic phase, consistent with experimental observations. With increasing V, this minimum becomes deeper relative to the rutile structure, and the transition from the metallic to the insulating state becomes sharper. We also analyze the effect of applying the +V correction either to all or only to selected vanadium-vanadium pairs, and both in the monoclinic as well as in the metallic rutile phase. Our results suggest that  DFT+V can indeed serve as a computationally inexpensive unbiased way of modeling VO2 which is well suited for studies that, e.g., require large system sizes.
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All calculations were performed using the Quantum Espresso code (versions 7.1 and 7.2), using the PBE exchange-correlation functional with the GBRV pseudopotentials (see paper for details).

The main folder contains input files for all calculations presented in the paper, with subfolders indicating which type of calculation the data corresponds to. Each folder is separated into distortion or non-distortion calculations, VO2 phase, V=0 or V=/=0 calculations, where the V is applied, and what the V value is.