Abstract
We revisit the problem of the insulating ground state of the monoclinic ${M}_{1}$ phase in vanadium dioxide and argue that essential intersite correlation effects within vanadium dimers can be captured by the static mean-field approximation. We propose the LDA + DMFT +$V$ approach, which combines the density functional theory within the local density approximation (LDA) with the extended Hubbard model. In this approach, the intersite Coulomb interactions beyond the LDA are taken into account by the Hartree-Fock approximation, while the on-site ones are described by the dynamical mean-field theory (DMFT). The proposed approach as well as the cluster extension of the DMFT are used to study the spectral and magnetic properties of the ${M}_{1}$ phase. According to our results, taking into account intersite correlations in vanadium dimers enhances bonding-antibonding splitting with respect to the LDA one, resulting in an insulating ground state, whereas on-site correlations only slightly change the picture, leading to a renormalization of bands. The magnetic properties of the ${M}_{1}$ phase can be attributed to the singlet ground state of vanadium dimers. We conclude that the ${M}_{1}$ phase is a correlated band insulator and the Peierls scenario, enhanced by the intersite correlation effects, is the driving mechanism of the metal-insulator transition in VO${}_{2}$.
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