4 2 0 GLYPH<s80>GLYPH<s77>  DMFT DOS $_{1g}$  CI (total) GLYPH<s66> GLYPH<s65> 4 2 0 GLYPH<s80>GLYPH<s73>  CI (e$_{g}$e$_{g}$)  CI (e$_{g}$a$_{1g}$) GLYPH<s65> GLYPH<s66> E-E$_{F }$(eV) E-E$_{F }$(eV) Intensity (arb. units) FIG. 2: (Color online) Incoherent LDA+DMFT and CI cal- culations in the pre-edge region; E$_{F}$ is the Fermi energy. Note the similarity in the main spectral features when crossing the MIT. Also shown are the different contributions of the CI spectrum labeled accordingly to their initial state: the contribution of the ( e π $_{g}$, a$_{1}$$_{g}$ ) → ( e π $_{g}$, e π $_{g}$, a$_{1}$$_{g}$ ) transitions to the peak A(B) is approximately 60%(55%) in the PM phase and 20%(15%) in the PI phase. Considerable insight can be gained by comparing CI and LDA+DMFT calculations. Our LDA+DMFT cal- culations, performed using N $^{th}$-order muffin-tin orbital (NMTO) downfolded Hamiltonian for the 1.1% Cr-doped V$_{2}$O$_{3}$ and Hirsch-Fye Quantum Monte Carlo as impurity solver, confirm the above mentioned tendency (we obtain a mixing of 50:50 and 35:65 for the ( e π $_{g}$, a$_{1}$$_{g}$ ):( e π $_{g}$, e π $_{g}$) oc- cupation in the PM and PI phases). For LDA+DMFT we have chosen the same interaction parameter U = 4 . 2 eV for the PI phase as in Ref. [9] and followed their sug- gestion to slightly decrease its value in the PM phase (we assume U = 4 . 0 eV)[23]. Remarkably the simple struc- ture of the core hole potential in the K -edge spectroscopy allows us to associate the pre-edge spectrum with the k − integrated spectral function above the Fermi energy calculated by LDA+DMFT. The electron–addition part of the spectral function shows three main features in PM phase: a coherent excitation at the Fermi level and a double peak associated to the incoherent electronic ex- citations i.e. the upper Hubbard band (UHB), similarly to the undoped compound. In the PI phase obviously, only the latter survives. Comparison with the experi- mental spectra clearly shows that the pre-edge features have to be related to the “incoherent” part of the spectral function only. The physical reason is that the core hole potential localizes the electrons destroying the coher- ent quasiparticle excitations and making the XAS spec- trum atomic-like. All the “incoherent” LDA+DMFT, CI, and experimental spectra shown in Fig. 2 agree in many aspects, especially as for the splitting of the first two peaks by ≈ 2.0 eV ( ≈ 1.8 eV in experiment) which originates in LDA+DMFT from the Hund’s exchange J in the Kanamori Hamiltonian. This further validates the choice of J = 0 . 7 eV used in our calculations con- trasting with larger values assumed in previous stud- ies [8, 10, 23], and also clarifies the mismatch between XAS and LDA+DMFT spectra reported in the undoped V$_{2}$O$_{3}$ compound [8]. Moreover, the ratio between A and B peak displays the same trend in the PM-PI transition as the CI (or experimental) data. The quantitative dif- ference between the two calculations is attributed to the lack of matrix elements in LDA+DMFT. The intensity ratio of the first two incoherent excita- tions peaks A and B (associated to the quartet and dou- blet states in the oversimplified picture) thus appears as the key spectral parameter to understand the differences between PM and PI. Even in a powder sample, this ratio is still sensitive to the a$_{1}$$_{g}$ orbital occupation of the initial state. Indeed, due to the trigonal distortion a consider- able spectral weight transfer from the peak B to higher energies (corresponding to final states with two a$_{1}$$_{g}$ elec- trons in the limit of large Δ$_{trig}$) can take place for the ( e π $_{g}$, a$_{1}$$_{g}$ ) but not for the ( e π $_{g}$, e π $_{g}$) initial state. Therefore, the K pre-edge XAS can serve as a direct probe of the a$_{1}$$_{g}$ orbital occupation in the ground-state. As a rule of thumb, the larger the ratio between the SW of A and B, the larger the a$_{1}$$_{g}$ orbital occupation. Hard X-ray absorption also provides a unique way to explore the “pressure” pathway across the MIT, from which relevant information can be extracted by applying our interpretation scheme. Fig. 3(a) shows the XAS pow- der spectra of the P-induced MIT with the corresponding spectra for the T- and doping-driven transition (cf. the loci in the phase diagram, Fig. 3). To ease the com- parison, the pressure dataset (P) obtained in transmis- sion mode has been deconvolved from the 1 s Lorentzian lifetime broadening (1 eV FWHM) using the GNXAS code [24] to match the improved resolution of datasets ( x ) and (T) measured by PFY-XAS. Together with the PM − PI differences in Fig. 3(b), Fig. 3(a) clearly evi- dences that, besides a rigid shift of the first two peaks of ∼ +0.13 eV and contrary to the doping- or T-driven tran- sition, very small changes in spectral shapes and weights are observed in the P-driven MIT. In the light of the arguments discussed above, our finding proves that the metallic state reached by applying pressure is character- ized by a much lower occupation of the a$_{1}$$_{g}$ orbitals com- pared to the metallic state reached just by changing tem- perature or doping. Importantly, the spectra measured through the doping induced MIT are identical within the experimental uncertainty to those measured through the T-driven transition. The temperature-doping equiv- alence is confirmed by our photoemission data displayed in Fig. 3(c,d) [15] and is consistent with the very similar lattice parameter changes across the transition [25]. The x and T equivalence is also borne out by the observa- tion from XAS at the L -edges in doped V$_{2}$O$_{3}$ [16] that the a$_{1}$$_{g}$ occupation within both the PM or PI phases is mostly independent of the doping level. Hence, the local incoherent excitations probed by XAS at the V L edge or K pre-edge are not directly affected by disorder [26]. 3