Empirical electronic polarizabilities for use in refractive index measurements at 589.3 nm: Hydroxyl polarizabilities

Abstract Refractive indices of minerals and inorganic compounds can be calculated from their chemical compositions using the additivity rule for electronic polarizabilities and converting the sum of polariz-abilities α using the Anderson-Eggleton relationship:αAE=(nD2-1)Vm4π+(4π3-2.26)(nD2-1) with the molar volume Vm solved for the mean refractive index nD at 589.3 nm. Whereas the polariz-ability of cations is a single parameter, the polarizability of anions is described by a two-parameter term α−=α−o10−No/Van1.20 with α– = anion polarizability, Van = anion molar volume, and the two least-squares parameters α−o (corresponding to free-ion polarizability) and No. For hydroxyls, Shannon and Fischer (2016) introduced different parameter sets for non-H-bonded hydroxyls (α−o = 1.79 Å3, No = 1.792 Å3.6) and moderately strong H-bonded hydroxyls (α−o = 1.73 Å3, No = 2.042 Å3.6). In an effort to understand the lower polarizability of the H-bonded hydroxyl ions, we have evaluated observed and calculated polarizabilities, O-H, H∙∙∙O, O∙∙∙O distances, and O-H∙∙∙O angles in 10 minerals with non-hydrogen-bonded hydroxyls (mean <O∙∙∙O> distance 3.143 Å, mean <H∙∙∙O> distance 2.352 Å), in seven minerals with H-bonded-hydroxyls (<O∙∙∙O> = 2.739 Å, <H∙∙∙O> = 1.856 Å), and in 10 minerals with very strongly H-bonded hydroxyls (<O∙∙∙O> = 2.531 Å, <H∙∙∙O> = 1.525 Å). On the basis of quantum chemical cluster calculations using atomic parameters of well determined crystal structures of hydroxyl containing compounds, we found that calculated intrinsic polariz-abilities of OH are correlated with the hydrogen bond lengths H∙∙∙O and O∙∙∙O between donor and acceptor of the H-bond. This is demonstrated for LiOH, brucite [Mg(OH)2], portlandite [Ca(OH)2], clinometaborite (β-HBO2), sassolite (H3BO3), archerite (KH2PO4), kalicinite (KHCO3), metaborite (γ-HBO2), and NaPO2(OH)2. Thus, we find that these summed intrinsic polarizabilities for OH-bonds which are involved in H-bonding are significantly lower than the corresponding summed intrinsic polarizabilities for OH-bonds not involved in H-bonding. We attribute the reduction in polarizability of hydroxyl ions in clinometaborite, sassolite, archerite, kalicinite and metaborite, and the compound NaPO2(OH)2 to the presence of H-bonds and a reduction of Hirshfeld atomic charge on the O atom.