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

Abstract

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.