Empirical electronic polarizabilities of iodine (I ⁻ ) and bromine (Br ⁻ , Br ⁷⁺ ) for the prediction of refractive indices

Abstract. Empirical electronic polarizabilities of I−, Br−, and Br7+ were determined to predict refractive indices of iodides, bromides, and perbromates, respectively, at λ=589.3 nm. Polarizabilities of the iodine and bromine ions were derived from the total electronic polarizabilities of compounds containing I or Br by subtracting the polarizabilities of the remaining cations and anions, yielding the contribution of the halogen ions to the total electronic polarizabilities calculated from the mean refractive indices using the Anderson–Eggleton relationship. Refractive indices (RIs) of iodides, bromides, and perbromates are taken from literature data and from our own measurements on potassium iodide (KI), sodium iodide dihydrate (NaI ⋅ 2H2O), potassium bromide (KBr), and sodium perbromate monohydrate (NaBrO4 ⋅ H2O). Powder X-ray diffraction analyses were done for basic characterization and to check the purity. Structure analyses were performed using single-crystal X-ray diffraction data on KI, KBr, NaI ⋅ 2H2O, and NaBrO4 ⋅ H2O. Refractive indices were determined using the immersion method with a micro-refractometer spindle stage at λ=589.3 nm, yielding <n> = 1.671(8) for isotropic KI, nx=1.585(9), ny=1.593(4), and nz=1.615(6), with a mean refractive index of <n> =1.598(6) for NaI ⋅ 2H2O; <n> = 1.560(2) for isotropic KBr; and nx=1.470(2), ny=1.491(2), and nz=1.492(2) with a mean refractive index of <n> = 1.484(2) for an optically biaxial NaBrO4 ⋅ H2O crystal. The anion polarizability parameters α-o and No for I− were determined by least-squares methods from 20 iodide compounds with known refractive indices, combined with data from this study. The electronic polarizability of the anion is described by the equation α-=α-o⋅10-No/Van1.20, yielding α-o (I−) = 8.53(5) Å3 and No(I−) = 0.90 Å3.6. Similarly, for Br−, analysis of 20 bromide compounds with established refractive indices, together with data from this study, resulted in α-o (Br−) = 5.4(3) Å3 and No(Br−) = 1.00 Å3.6. The determination of the refractive indices of NaBrO4 ⋅ H2O with four-coordinated Br7+ yielded an electronic polarizability value of 0.938 Å3 for Br7+. Using this value enables the prediction of refractive indices of perbromates. All values were validated against known halide data and used to predict refractive indices of iodine- and bromine-containing compounds. A total of 120 refractive indices was predicted. The results are compared with refractive indices calculated from Gladstone–Dale constants.