Correlation-assisted phonon softening and the orbital-selective Peierls transition in VO2

To explore the driving mechanisms of the metal-insulator transition (MIT) and the structural transition in VO${}_{2}$, we have investigated phonon dispersions of rutile VO${}_{2}$ ($R$-VO${}_{2}$) in the density functional theory (DFT) and the DFT$+U$ ($U$: Coulomb correlation) band calculations. We have found that the phonon softening instabilities occur in both cases, but the softened phonon mode only in the DFT$+U$ describes properly both the MIT and the structural transition from $R$-VO${}_{2}$ to monoclinic VO${}_{2}$ (M${}_{1}$-VO${}_{2}$). The present ab initio phonon dispersion calculations clearly demonstrate that the Coulomb correlation effect plays an essential role of assisting the Peierls transition in $R$-VO${}_{2}$ and producing the spin-Peierls ground state in M${}_{1}$-VO${}_{2}$.