A general approach to the realistic electronic structure calculations of non-local correlated systems, which combines the Local Density Approximation with the cluster Dynamical Mean-Field Theory (LDA+CDMFT) is discussed. We present a quantum theory of the Mott transition in Ti2O3 [1] and VO2 [2]. Strong competition between the local Coulomb interaction and chemical bonding in a metal-metal pair results in a small insulating gap of low temperature phase. The cluster LDA+DMFT scheme successfully describe the non-local spin and orbital fluctuation effects and Mott transition in these compounds. The interplay of strong electronic Coulomb interactions and structural distortions, in particular the dimerization of metal atoms in the low temperature phase, plays a crucial role. We find these oxides are not a conventional Mott insulator, but that the formation of dynamical meta-metal singlet pairs due to strong Coulomb correlations is necessary to trigger the opening of a Peierls gap. The possibilities to includes the general interaction vertex in the cluster DMFT calculations within the continuous time QMC-scheme[3] as well as k-dependence of self-energy [4] will be discussed.

[1] A. Poteryaev, A. Lichtenstein, and G. Kotliar "Nonlocal Coulomb Interactions and Metal-Insulator Transition in Ti2O3: A Cluster LDA + DMFT Approach ", Phys. Rev. Lett. 93, 086401 (2004).
[2] S. Biermann, A. Poteryaev, A. I. Lichtenstein, and A. Georges "Dynamical Singlets and Correlation-Assisted Peierls Transition in VO2", Phys. Rev. Lett. 94, 026404 (2005).
[3] V. Savkin, A. Rubtsov, M. Katsnelson, and A. Lichtenstein "Correlated Adatom Trimer on a Metal Surface: A Continuous-Time Quantum Monte Carlo Study", Phys. Rev. Lett. 94, 026402 (2005).
[4] A.N. Rubtsov, M.I. Katsnelson and A.I. Lichtenstein, "Dual fermion approach to nonlocal correlations in the Hubbard model", cond-mat/0612196.