## 1 Introduction
Moreover, band structure calculations [20] suggest that the monoclinic structure results from an embedded Peierls-like instability, which mediates the metal-metal overlap along chains parallel to the rutile \(c\)-axis embedded in a background of the dispersing \(xz,yz\) states. This scenario has been used to analyze Fermi surface topology and band dispersion of MoO\({}_{2}\) probed, respectively, in de Haas-van Alphen and angle-resolved photoemission spectroscopy (ARPES) experiments [19]. A closer inspection of experiments reveals several exotic properties in MoO\({}_{2}\) which are fundamentally different from simple metals, implying that many-particle correlation effects beyond the local density approximation (LDA) need to be considered. Experimental observations supporting this view are: ARPES [19] and angle-integrated PES [20] measurements show signatures of pseudogap like low-energy features close to the Fermi energy, implying substantial correlation effects. An optical conductivity study reveal a Drude part at low energies followed by a broad bump around 0.8 eV and high-energy features centered above 4 eV [22]. Noteworthy, the first bump was taken as an evidence that normal metallic conduction is not occurring in MoO\({}_{2}\). Noticeable carrier mass enhancement \(m^{\star}/m\approx 5\), a value close to that found for VO\({}_{2}\)[4], reinforces the relevance of dynamical electronic interactions. Finally, resistivity data of Ref. [11] display Fermi liquid (FL) behavior (\(\rho(T)=\rho_{0}+AT^{2}\)), however, in several other cases it deviates significantly [13; 18; 23] from this canonical \(T^{2}\)-dependence of good FL metals. In fact, MoO\({}_{2}\) appears to be a poor-metal at low-\(T\), with a sample dependent resistivity upturn below \(T^{\star}\approx 100\) K [13; 23], implying substantial correlation effects in the Mo \(4d\)-subshell crossing \(E_{F}\). How might scattering processes involving charge and orbital fluctuations produce the observed correlated metal? How robust is the bare bonding-antibonding splitting against sizable electron-electron interactions? Which are the electronic fingerprints of a reconstructed orbital bonding-antibonding state [5] in monoclinic MoO\({}_{2}\)? In this work we address these questions by modeling the correlated electronic structure of monoclinic MoO\({}_{2}\) on the basis of LDA band structure calculations combined with dynamical mean-field theory (DMFT) [8]. Likewise for VO\({}_{2}\), we clearly find an orbital-selective (OS) metallic behavior which results from sizable MO electron-electron interactions in the Mo \(4d\) subshell near \(E_{F}\). Our results are important for understanding the competition between itinerancy and local, MO Hubbard interactions in MoO\({}_{2}\). In particular, low-energy pseudogap-like features probed in photoemission experiments are shown to be driven by a correlation-assisted orbital reconstruction, reflecting incoherent charge localization due to the formation of dynamical metal-metal ion bonds. Our scenario suggests the essential role played by (local) MO Coulomb repulsion acting as the emerging dynamical interaction for the many-fold metal-pair reconstruction in materials with monoclinic distortions. To date, the relevance of local correlations on the electronic structure has been studied within density-functional-theory plus U (DFT+U), for example in molybdenum oxides [24] or other anodic dichalcogenide battery materials like MoS\({}_{2}\)[25]. While DFT+U calculations yield the correct spin and orbital orders, by construction this is a ground state theory and therefore cannot describe dynamical many-particle effects. Here, we extend ab initio density-functional calculations to incorporate these effects within the LDA+DMFT method [8]. Interestingly, this method has been applied to elucidate the electronic structure of SrMoO\({}_{3}\)[26], supporting the hypothesis of multi-orbital dynamical interactions in Mo-base materials in general.