All-electron GW calculation of vanadium dioxide

We present the results of the GW calculation of metallic and insulating vanadium dioxide using a full-potential LMTO basis set. Our calculations show that it is crucial to take into account both the frequency dependence and the off-diagonal elements of the self-energy. We find that the usual 1-shot GW scheme, where the frequency expansion of the self-energy is truncated in the first-order, yields a large error ($>0.1$eV) in quasiparticle energies due to the unsmoothness of the self- energy. In both phases, the dynamical correlation effect within RPA leads to a plasmon satellite above the Fermi level, but not below. This difference can be attributed to matrix element effects. Our 1-shot GW calculation does not reproduce insulating VO$_{2}$ due to the mixing of conduction and valence bands in the LDA calculation, and we reconstruct G and W by updating the quasiparticle wavefunctions and energies to obtain the band gap. The result indicates the importance of self-consistency in GW calculations. Our results are more in line with the Peierls picture of gap opening due to the lattice distortion, rather than the Motto-Hubbard picture of strong correlations.