Ab initio Hartree–Fock study and charge density analysis of beryl (Al₄Be₆Si₁₂O₃₆)

Abstract

 An ab initio Hartree–Fock calculation on beryl structure has been performed and the wave function has been used for an analysis of the electron density. The equilibrium geometry, determined by minimizing the energy with respect to cell parameters and fractional coordinates, is in good agreement with structural experimental measurements; small differences in length between the various Si–O bonds of the structure are well reproduced by the calculation. The two non-equivalent oxygen atoms (O1 and O2) of beryl show different electron distributions. In particular, the valence shell charge concentration (VSCC) of O1 (the bridge between two Si ions) has a torus-like shape, showing a bulge on the external side of the Si–O–Si angle and a thinning on the internal side of it; by contrast O2 has two lone pairs which are approximately located on the line for O2, normal to the plane passing, on average, through the atoms O2, Si, Be and Al. The electron density of each oxygen is strongly polarized toward the Si ions and much less polarized towards the other cations. Such features of the VSCC of the oxygens can be recast in terms of the valence bond theory, to explain the observed differences in bond lengths. By calculating the potential inside the channels of the beryl structure, predictions could be made about the positions occupied by alkali cations, which are often found in natural minerals belonging to the beryl group: results agree in general with experimental findings, but foresee a shift of such cations off the central positions located on the six fold symmetry axis. Additionally, calculations of position and orientation of H₂O inside the channel, in the alkali-free beryl, locate the molecule close to the basal plane, with the H⋯H axis parallel to [001] or oriented at 40^∘ from it.