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The Raman spectrum of diopside has been calculated by using three purely Density Functional Theory (DFT) Hamiltonians (PBE, WCPBE, LDA), the Hartree-Fock Hamiltonian (HF) and three hybrid HF/DFT ones (B3LYP, WC1LYP, PBE0). A comparison has been done between the calculated frequencies with those measured by Raman spectroscopy on a natural sample, along with several different orientations and beam polarizations, or retrieved from literature; such a comparison demonstrated the excellent performances of the hybrid Hamiltonians in reproducing the vibrational spectrum of the mineral, in line with what it is generally observed in literature concerning other mineral phases. In particular, the mean average absolute discrepancies of the calculated frequencies with respect to the experimental data were: 3.2 (WC1LYP), 4.7 (B3LYP), 6.5 (PBE0), 18.0 (PBE), 9.7 (WCPBE), 7.3 (LDA) and 40.6 cm -1 (HF). The very good quality of the WC1LYP results, allowed for a reliable assignment of all of the experimentally observed Raman signals, and the corresponding assignments to specific patterns of atomic vibrational motion (normal modes).

The identification of syngenetic inclusions in diamond (i.e. inclusions of minerals that crystallized at the same time and by the same genesis as their host) has long been of paramount importance in diamond studies. However, the widespread assumption that many or most inclusions in diamonds are syngenetic is based on qualitative morphological criteria and few direct measurements. In order to provide statistically significant information on inclusion–host genetic relations for at least one kimberlite, we have determined the crystallographic orientations of 43 olivine inclusions with diamond-imposed morphology, a feature generally interpreted to indicate syngenesis, in 20 diamonds from the Udachnaya kimberlite (Siberia). Our unprecedented large data set indicates no overall preferred orientation of these olivines in diamond. However, multiple inclusions within a single diamond frequently exhibit similar orientations, implying that they were derived from original single monocrystals. Therefore, regardless of the possible chemical re-equilibration during diamond-forming processes, at least some of the olivines may have existed prior to the diamond (i.e. they are protogenetic). Our results imply that a diamond-imposed morphology alone cannot be considered as unequivocal proof of syngenicity of mineral inclusions in diamonds

Ab initio calculations of thermo-elastic properties of beryl (Al 4 Be 6 Si 12 O 36 ) have been carried out at the hybrid HF/DFT level, by using the B3LYP and WC1LYP Hamiltonians. Static geometries and vibrational frequencies were calculated at different values of the unit cell volume, to get static pressure and mode-γ Grüneisen's parameters. Zero point and thermal pressures were calculated by following a standard statistical-thermodynamic approach, within the limit of the quasiharmonic approximation, and added to the static pressure at each volume, to get the total pressure (P) as a function of both temperature (T) and cell volume (V). The resulting P(V,T) curves were fitted by appropriate EoS', to get bulk modulus (K 0 ) and its derivative (K'), at different temperatures. The calculation successfully reproduced the available experimental data concerning compressibility at room temperature (the WC1LYP Hamiltonian provided K 0 and K' values of 180.2Gpa and 4.0, respectively), and the low values observed for the thermal expansion coefficient. A zone-centre soft mode 𝑃6 𝑚𝑐𝑐 ⁄ → 𝑃1 ̅ phase transition was predicted to occur at a pressure of about 14 GPa; the reduction of the frequency of the soft vibrational mode, as the pressure is increased, and the similar behaviour of the majority of the low frequency modes, provided an explanation of the thermal behaviour of the crystal, which is consistent with the RUM model (Rigid Unit Model;Dove et al., 1995), where the negative contribution to thermal expansion is ascribed to a geometric effect connected to the tilting of rigid polyhedra in framework silicates.