A theory of the metal-insulator transition in vanadium dioxide from the high- temperature rutile to the low- temperature monoclinic phase is proposed on the basis of cluster dynamical mean-field theory, in conjunction with the density functional scheme. The interplay of strong electronic Coulomb interactions and structural distortions, in particular, the dimerization of vanadium atoms in the low-temperature phase, plays a crucial role. We find that ${\mathrm{V}\mathrm{O}}_2$ is not a conventional Mott insulator, but that the formation of dynamical V-V singlet pairs due to strong Coulomb correlations is necessary to trigger the opening of a Peierls gap.

Using $t_{2g}$ Wannier functions, a low-energy Hamiltonian is derived for orthorhombic $3d^1$ transition-metal oxides. Electronic correlations are treated with a new implementation of dynamical mean-field theory for noncubic systems. Good agreement with photoemission data is obtained. The interplay of correlation effects and cation covalency (${\mathrm{GdFeO}}_3$-type distortions) is found to suppress orbital fluctuations in ${\mathrm{LaTiO}}_3$ and even more in ${\mathrm{YTiO}}_3$, and to favor the transition to the insulating state.

A versatile method for combining density functional theory in the local density approximation with dynamical mean-field theory (DMFT) is presented. Starting from a general basis-independent formulation, we use Wannier functions as an interface between the two theories. These functions are used for the physical purpose of identifying the correlated orbitals in a specific material, and also for the more technical purpose of interfacing DMFT with different kinds of band-structure methods (with three different techniques being used in the present work). We explore and compare two distinct Wannier schemes, namely the maximally localized Wannier function and the $N\text{th}$ order muffin-tin-orbital methods. Two correlated materials with different degrees of structural and electronic complexity, $\mathrm{Sr}\mathrm{V}{\mathrm{O}}_3$ and $\mathrm{Ba}\mathrm{V}{\mathrm{S}}_3$, are investigated as case studies. $\mathrm{Sr}\mathrm{V}{\mathrm{O}}_3$ belongs to the canonical class of correlated transition-metal oxides, and is chosen here as a test case in view of its simple structure and physical properties. In contrast, the sulfide $\mathrm{Ba}\mathrm{V}{\mathrm{S}}_3$ is known for its rich and complex physics, associated with strong correlation effects and low-dimensional characteristics. Insights into the physics associated with the metal-insulator transition of this compound are provided, particularly regarding correlation-induced modifications of its Fermi surface. Additionally, the necessary formalism for implementing self-consistency over the electronic charge density in a Wannier basis is discussed.

We present a study of the paramagnetic metallic and insulating phases of vanadium sesquioxide by means of the $N\mathrm{th}$ order muffin-tin orbital implementation of density functional theory combined with dynamical mean-field theory. The transition is shown to be driven by a correlation-induced enhancement of the crystal-field splitting within the $t_{2g}$ manifold, which results in a suppression of the hybridization between the $a_{1g}$ and $e_g^{\pi }$ bands. We discuss the changes in the effective quasiparticle band structure caused by the correlations and the corresponding self-energies. At temperatures of about $400\mathrm{K}$, we find the $a_{1g}$ orbital displays coherent quasiparticle behavior, while a large imaginary part of the self-energy and broad features in the spectral function indicate that the $e_g^{\pi }$ orbitals are still far above their coherence temperature. The local spectral functions are in excellent agreement with recent bulk sensitive photoemission data. Finally, we also make a prediction for angle-resolved photoemission experiments by calculating momentum-resolved spectral functions.