The results of first principles electronic structure calculations for the metallic rutile and the insulating monoclinic M1 phase of vanadium dioxide are presented. In addition, the insulating M2 phase is investigated for the first time. The density functional calculations allow for a consistent understanding of all three phases. In the rutile phase metallic conductivity is carried by metal t2g orbitals, which fall into the one-dimensional d band, and the isotropically dispersing e π g bands. Hybridization of both types of bands is weak. In the M1 phase splitting of the d band due to metal-metal dimerization and upshift of the e π g bands due to increased p-d overlap lead to an effective separation of both types of bands. Despite incomplete opening of the optical band gap due to the shortcomings of the local density approximation, the metal-insulator transition can be understood as a Peierls-like instability of the d band in an embedding background of e π g electrons. In the M2 phase, the metal-insulator transition arises as a combined embedded Peierls-like and antiferromagnetic instability. The results for VO2 fit into the general scenario of an instability of the rutile-type transition-metal dioxides at the beginning of the d series towards dimerization or antiferromagnetic ordering within the characteristic metal chains. This scenario was successfully applied before to MoO2 and NbO2. In the d 1 compounds, the d and e π g bands can be completely separated, which leads to the observed metal-insulator transitions.

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The electronic properties of paramagnetic V2O3 are investigated by the computational scheme LDA+DMFT(QMC). This approach merges the local density approximation (LDA) with dynamical mean-field theory (DMFT) and uses quantum Monte Carlo simulations (QMC) to solve the effective Anderson impurity model of DMFT. Starting with the crystal structure of metallic V2O3 and insulating (V0.962Cr0.038)2O3 we find a Mott-Hubbard transition at a Coulomb interaction U approximately 5 eV. The calculated spectrum is in very good agreement with experiment. Furthermore, the orbital occupation and the spin state S = 1 determined by us agree with recent polarization dependent x-ray-absorption experiments.

PACS 71.15.Mb, 71.27.+ a, 71.30.+ h Conventional band structure calculations in the local density approximation (LDA) [1 -3] are highly successful for many materials, but miss important aspects of the physics and energetics of strongly correlated electron systems, such as transition metal oxides and f-electron systems displaying, e.g., Mott insulating and heavy quasiparticle behavior. In this respect, the LDA + DMFT approach which merges LDA with a modern many-body approach, the dynamical mean-field theory (DMFT), has proved to be a breakthrough for the realistic modeling of correlated materials. Depending on the strength of the electronic correlation, a LDA + DMFT calculation yields the weakly correlated LDA results, a strongly correlated metal, or a Mott insulator. In this paper, the basic ideas and the set-up of the LDA + DMFT(X) approach, where X is the method used to solve the DMFT equations, are discussed. Results obtained with X = QMC (quantum Monte Carlo) and X = NCA (non-crossing approximation) are presented and compared, showing that the method X matters quantitatively. We also discuss LDA + DMFT results for two prime examples of correlated materials, i.e., V 2 O 3 and Ce which undergo a Mott -Hubbard metal -insulator and volume collapse transition, respectively.

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