## 2 Results and Discussion
### Correlated Electronic Structure
Appreciable SWT within the \(yz,xz\)-orbitals is also visible in the lower panels of Figure 3. Interestingly, electronic interactions in these orbitals lead to sharp quasiparticle peaks close to \(E_{F}\). These collective Kondo-like resonances move to energies close to 0.1 eV at \(U=5\) eV with concomitant appearance of pseudogaped electronic states in the \(xz,yz\) orbitals. Moreover, given sizable \(U^{\prime}\), interband dynamical proximity effects between \(x^{2}-y^{2}\) and \(yz,xz\) orbitals yield the creation of bonding-antibonding bands in the \(yz,xz\) channels. Correlated electron features in the valence band DOS will lead to local magnetic moments associated with the developing of a prominent LHB in the \(x^{2}-y^{2}\) orbital. Noteworthy, magnetic ordering and unconventional superconductivity (\(T_{c}=7\) K) were observed in potassium-doped MoO\({}_{2}\) samples, K\({}_{x}\)MoO\({}_{2-\delta}\)[37]. In these compounds, X-ray powder-diffraction data suggest that K-atoms increase the lattice parameters of the monoclinic structure with increasing K composition. Taken together these observations with our LDA+DMFT results suggest that under strain, inducing band narrowing due to expansion of the lattice crystal structure, anisotropic excitations would be seen in magnetic susceptibility data of pure MoO\({}_{2}\) at low \(T\). The bottom panel of Figure 4 displays the total LDA and LDA+DMFT spectral function. As a major effect of electron-electron interactions, the bonding-antibonding feature in LDA re-emerges and persists above \(E_{F}\) with increasing \(U\) for all three orbitals. From this result we can now draw the following conclusion: The bonding-antibonding states (reflecting charge localization within Mo-Mo dimers in LDA, see Figure 1) are transferred to energies above \(E_{F}\) by MO dynamical correlations. Figure 4: Bottom panel: Role of electron–electron interactions on the total LDA+DMFT DOS. LDA results are shown for comparison. Notice the formation of a lower Hubbard band at energies close to \(-2\) eV and the evolution of the reconstructed electronic structure above \(E_{F}\). The top panel shows the theory-experiment comparison between LDA+DMFT one-particle spectral functions and the photoemission spectra taken from Ref. [19]. Notice the good theory-experiment agreement at low energies and the correlation induced transfer of spectral weight compared to LDA from low to high binding energies. Interestingly, our LDA+DMFT band splitting is consistent with soft-X-ray absorption spectra [20], showing two main broad features separated by almost 4 eV as in Figure 4. Extant PES and ARPES data can also be interpreted on the basis of our correlated electronic structure. An ARPES study [19] shows a broad maximum around 0.2 eV binding energy which moves towards to \(E_{F}\) with increasing the emission angle and the photon energy. We assign this primary maximum as the small bump found for \(U=5\) eV at \(\omega=-0.28\) eV, as shown in the top panel of Figure 4. Smaller \(U\) values provide a huge peak at low binding energies which is not seen in experiment [19]. Importantly, the LDA+DMFT results for \(U=5\) eV show good agreement with PES data [19] at low energies, implying the suppression of the Landau-FL coherence in the electronic states and unconventional metallicity in pure and doped MoO\({}_{2}\) systems [37]. Moreover, valence band spectra recorded on thin films show an energy band peaked at \(-1.8\) eV, consistent with our LHB centered at energies close to \(-2.2\) eV. It is worth noting that this value coincides with the energy gap in LDA where oxygen \(p\)-bands start. The fact that this bare band gap is not seen in PES experiments [20] is the one-particle fingerprint of dynamical MO correlations, and goes beyond previous ab initio formulations for monoclinic MoO\({}_{2}\). Understanding the modification of anisotropic charge dynamics in MoO\({}_{2}\) promises to shed light upon the precise nature of the reconstructed (by dynamical correlations) orbital state discussed above.