A first-principles investigation of hydrous defect and IR frequencies in forsterite: The case for Si vacancies

We investigate charge-balanced hydrous magnesium and silicon defects ((2H)$^{X}$$_{Mg}$, (4H)$^{X}$$_{Si}$) by first principles. Here we propose two new lowest-energy hydrogen configurations for (4H)$^{X}$$_{Si}$. With these new configurations, the distribution of OH-stretching phonon frequencies in Group I ($>$ 3450 cm-1) are better reproduced. Substitution of silicon with 4 hydrogens gives rise to significant elongation of distances between oxygen ions at the tetrahedron of the silicon vacancy. Our calculations indicate that the correlation between O-O distances and O-H-stretching phonon frequencies, which has been well established for hydrous minerals, does not apply directly to nominally anhydrous minerals and should not be used to determine the identity of the hydrous defects responsible for infrared absorption peaks.