Bond Length and Radii Variations in Fluoride and Oxide Molecules and Crystals

Molecular orbital calculations completed on fluoride molecules containing first and second row cations have generated bond lengths, R, that match those observed for coordinated polyhedra in crystals to within ",0.04 A, on average. The calculated bond lengths and those observed for fluoride crystals can be ranked with the expression R = Kp 0.22, where p = sir, s is the Pauling strength of the bond, r is the row number of the cation and K = 1.34. The exponent 0.22 (~ 2/9) is the same as that observed for oxide, nitride and sulfide molecules and crystals. Bonded radii for the fluoride anion, obtained from theoretical electron density maps, increase 'nearly with bond length. Those calculated for the ca.lons as well as for the fluoride anion match calculated promolecule radii to within '" 0.03 A, on average, suggesting that the electron density distributions in the vicinity of the minima along the bond paths possess a significant atomic component despite bond type. Bonded radii for Si and 0 ions provided by experimental electron density maps measured for the oxides coesite, danburite and stishovite match those calculated for a series of monosilicic acid molecules. The resulting radii increase with bond length and coordination number with the radius of the oxide ion increasing at a faster rate than that of the Si cation. The oxide ion within danburite exhibits several distinct radii, ranging between 0.9 and 1.2 A, rather than a single radius with each exhibiting a different radius along each of the nonequivalent bonds with B, Si and Ca. Pro molecule radii calculated for the coordinated polyhedra in danburite match pro crystal radii obtained in a structure analysis to within 0.002 A. The close agreement between these two sets of radii and experimentally determined bonded radii lends credence to Slater's statement that the difference between the electron density distribution observed for a crystal and that calculated for a procrystal (lAM) model of the crystal "would be small and subtle, and very hard to determine by examination of the total charge density. " Introduction In 1982, Gibbs suggested that a molecule might serve as a useful basis for modeling the bond length and angle variations of a silicate mineral. This suggestion was based on the observation that the separations and angles between the Si and 0 atoms in the coordinated polyhedra of a number of siloxane molecules are not unlike those in quartz (Gibbs et al. 1972; Tossell and Gibbs 1978; Newton and Gibbs 1980; Gibbs et al. 1981; Gibbs and Boisen 1986; Gibbs et al. 1987). He also suggested that such models might provide important insight into the forces that govern bond length and angle variations and electron density distributions of the silica polymorphs and silicates in general. The development of such models has since yielded a theoretical basis for the correlation first observed by Smith (1953) between SiO bond length and bond strength sum for melilite and later established for a variety of oxide bond lengths by Baur (1970) and a number of correlations established by Brown and Shannon (1973) between bond strength and bond length (Gibbs et al. 1981; Gibbs et al. 1987). They have also provided a basis for a correlation proposed between SiO bond length and SiOSi angle (Cruickshank 1961; Brown et al. 1969; Newton and Gibbs 1980; Boisen et al. 1990; Boisen and Gibbs 1993). Since that time, molecular orbital (MO) calculations, completed on a variety of molecules with 4and 6-coordinated first and second row metal atoms, have generated bond lengths and angles that match those observed, to within a few percent, for chemically similar oxide, sulfide and nitride molecules and crystals (Geisinger and Gibbs 1981; Julian and Gibbs 1985, 1988; Gibbs and Boisen 1986; Gibbs et al. 1987b; Bartelmehs et al. 1989; Buterakos et al. 1992). The close correspondence between observed and calculated bond length data for chemically similar molecules and crystals suggests that the force field that governs bond length and angle variations in a wide range of insulating materials is short ranged and, in large part, independent of the forces exerted on the coordinated polyhedra by the other atoms Table 1. Observed and theoretical bond lengths, Ro(XF) and R,(XF), and crystal (Shannon 1976), bonded, and pro molecule radii, r (X), rb(X), and rp(X), for first and second row atoms c Hm_nxn+Fm XF Ro (X F) R, (XF) r/X) rb (X) rp(X) H3LiF 4 LiF 1.88 1.81 0.73 0.70 0.72 HsLiF 6 LiF 2.05 1.96 0.90 0.75 0.77 HBeF3 BeF 1.45 1.46 0.30 0.52 0.53 HzBeF 4 BeF 1.56 1.54 0.41 0.54 0.55 H4BeF6 BeF 1.74a 1.73 0.59a 0.60 0.61 BF3 BF 1.30 1.30 0.15 0.44 0.45 HBF4 BF 1.40 1.39 0.25 0.46 0.47 H3BF6 BF 1.56 1.59 0.41 a 0.52 0.57 CF4 CF 1.44b 1.30 0.29b 0.42 0.49 HzCF 6 CF 1.45 e 1.52 0.30e 0.56 0.67 HNF6 NF 1.42 e 1.50 0.27e 0.69 0.72 H3NaF4 NaF 2.28 2.13 1.13 0.99 1.01 H4NaF s NaF 2.29 2.18 1.14 1.00 1.03 HsNaF6 NaF 2.31 2.22 1.16 1.02 1.04 HzMgF 4 MgF 1.86 1.85 0.71 0.83 0.85 H3MgF s MgF 1.95 1.92 0.80 0.86 0.87 H4MgF 6 MgF 2.01 1.96 0.86 0.87 0.89 HAlF4 AlF 1.68 1.68 0.53 0.73 0.75 HzAIFs AlF 1.77 1.75 0.62 0.75 0.77 H3AIF6 AlF 1.82 1.80 0.675 0.77 0.79 SiF4 SiF 1.55 1.56 0.40 0.65 0.68 HzSiF6 SiF 1.69 1.68 0.54 0.69 0.72 PFs PF 1.58 1.55 0.43 0.62 0.65 HPF6 PF 1.67a 1.61 0.52a 0.64 0.68 SF6 SF 1.58 a 1.55 0.43 a 0.60 0.68 a Denotes radii calculated from bond length bond strength curves b Denotes radii from Pauling e Denotes radii from Ahrens