Quantum-mechanical modeling of minerals at high pressures. The role of the Hamiltonian in a case study: the beryl (Al4Be6Si12O36)

Ab initio calculations of the beryl structure at room and higher pressures, and of its equation of state, have been performed both at the Hartree–Fock (HF) and density functional (DFT) level. In the latter case, three different hybrid HF/DFT Hamiltonians have been employed, in which the exact non-local exchange contribution increases from 20% (B3LYP Hamiltonian, indicated with the symbol F20) to 50% (F50) and 60% (F60). Within the DFT series, the equilibrium volume (V 0) increases as the HF exchange contribution decreases; with respect to the experimental datum, F20 overestimates V 0 by 2.9%, whereas F60 underestimates it by 0.9%; F50 (and HF) volume is very close to the experimental datum (error less than −0.1%). All four Hamiltonians overestimate the bulk modulus (K 0); with respect to the experimental datum (obtained in the present work) [K 0=179(1) GPa], the F20 Hamiltonian leads to the smallest error (+2.7%); the corresponding errors for the F50, F60 and HF Hamiltonians are +13.2, +16.2 and +16.3%, respectively. In the case of F20, in spite of the small error in K 0, the relatively large error in V 0 leads to an incorrect P(V) equation of state, which significantly overestimates the pressure at a given volume, compared to the experimental one at the same volume; the maximum error in the pressure range investigated is at the largest pressure (P max=26.4 GPa) and amounts to +34.8%. The corresponding errors for the F50, F60 and HF Hamiltonians are +12.9, +5.7 and +15.5%.