The linear generalized equation described in this paper provides a further dimension to the prediction of lattice potential energies/enthalpies of ionic solids. First, it offers an alternative (and often more direct) approach to the well-established Kapustinskii equation (whose capabilities have also recently been extended by our recent provision of an extended set of thermochemical radii). Second, it makes possible the acquisition of lattice energy estimates for salts which, up until now, except for simple 1:1 salts, could not be considered because of lack of crystal structure data. We have generalized Bartlett's correlation for MX (1:1) salts, between the lattice enthalpy and the inverse cube root of the molecular (formula unit) volume, such as to render it applicable across an extended range of ionic salts for the estimation of lattice potential energies. When new salts are synthesized, acquisition of full crystal structure data is not always possible and powder data provides only minimal structural information-unit cell parameters and the number of molecules per cell. In such cases, lack of information about cation-anion distances prevents use of the Kapustinskii equation to predict the lattice energy of the salt. However, our new equation can be employed even when the latter information is not available. As is demonstrated, the approach can be utilized to predict and rationalize the thermochemistry in topical areas of synthetic inorganic chemistry as well as in emerging areas. This is illustrated by accounting for the failure to prepare diiodinetetrachloroaluminum(III), [I(2)(+)][AlCl(4)(-)] and the instability of triiodinetetrafluoroarsenic(III), [I(3)(+)][AsF(6)(-)]. A series of effective close-packing volumes for a range of ions, which will be of interest to chemists, as measures of relative ionic size and which are of use in making our estimates of lattice energies, is generated from our approach.

Thermochemical radii (1-3) can be used in the Kapustinskii equation (1) for binary salts or in the more recent Glasser generalization of this equation (4 ) for more complex salts, to predict lattice potential energies and stabilities of new inorganic materials (see, for example, refs 5, 6 ). They also provide parameters of molecular size to correlate with other ion properties (see, for example, ref 7).Our previous "reappraisal" (3) of these magnitudes is widely cited in the literature and is quoted in inorganic textbooks (8-11) and many others. Our present work offers the largest self-consistent set of thermochemical radii yet produced. These tables include (i) ions previously not considered, (ii) estimates for complex ions of recent and evolving topical interest, and (iii) estimates to update the values of the radii for the more conventional ions where necessary. Estimation of Thermochemical RadiiBartlett et al. (12) demonstrated a linear correlation of lattice enthalpy against the inverse cubic root of the volume per molecule, V, for simple MX salts. We have generalized this correlation and have studied crystals containing complex anions partnered with alkali-metal counter ions of known radius, and have extended the correlation (13) to include complex salts of the type M p X q . Thus for a crystal M p X q containing pM q+ ions and q complex anions X p ᎑ whose thermochemical radius is to be assigned, we use the unit cell parameters (a, b, c, α, β, and γ) derived from the crystal-structure data for the salts to calculate the volume per molecule, V : V = abc 1 -cos 2 α -cos 2 β-cos 2 γ + 2cos α cos β cos γ z where z is the number of molecules per unit cell.

The attempt to prepare hitherto unknown homopolyatomic cations of sulfur by the reaction of elemental sulfur with blue S8(AsF6)2 in liquid SO2/SO2ClF, led to red (in transmitted light) crystals identified crystallographically as S8(AsF6)2. The X-ray structure of this salt was redetermined with improved resolution and corrected for librational motion: monoclinic, space group P2(1)/c (No. 14), Z = 8, a = 14.986(2) A, b = 13.396(2) A, c = 16.351(2) A, beta = 108.12(1) degrees. The gas phase structures of E8(2+) and neutral E8 (E = S, Se) were examined by ab initio methods (B3PW91, MPW1PW91) leading to delta fH theta[S8(2+), g] = 2151 kJ/mol and delta fH theta[Se8(2+), g] = 2071 kJ/mol. The observed solid state structures of S8(2+) and Se8(2+) with the unusually long transannular bonds of 2.8-2.9 A were reproduced computationally for the first time, and the E8(2+) dications were shown to be unstable toward all stoichiometrically possible dissociation products En+ and/or E4(2+) [n = 2-7, exothermic by 21-207 kJ/mol (E = S), 6-151 kJ/mol (E = Se)]. Lattice potential energies of the hexafluoroarsenate salts of the latter cations were estimated showing that S8(AsF6)2 [Se8(AsF6)2] is lattice stabilized in the solid state relative to the corresponding AsF6- salts of the stoichiometrically possible dissociation products by at least 116 [204] kJ/mol. The fluoride ion affinity of AsF5(g) was calculated to be 430.5 +/- 5.5 kJ/mol [average B3PW91 and MPW1PW91 with the 6-311 + G(3df) basis set]. The experimental and calculated FT-Raman spectra of E8(AsF6)2 are in good agreement and show the presence of a cross ring vibration with an experimental (calculated, scaled) stretching frequency of 282 (292) cm-1 for S8(2+) and 130 (133) cm-1 for Se8(2+). An atoms in molecules analysis (AIM) of E8(2+) (E = S, Se) gave eight bond critical points between ring atoms and a ninth transannular (E3-E7) bond critical point, as well as three ring and one cage critical points. The cage bonding was supported by a natural bond orbital (NBO) analysis which showed, in addition to the E8 sigma-bonded framework, weak pi bonding around the ring as well as numerous other weak interactions, the strongest of which is the weak transannular E3-E7 [2.86 A (S8(2+), 2.91 A (Se8(2+)] bond. The positive charge is delocalized over all atoms, decreasing the Coulombic repulsion between positively charged atoms relative to that in the less stable S8-like exo-exo E8(2+) isomer. The overall geometry was accounted for by the Wade-Mingos rules, further supporting the case for cage bonding. The bonding in Te8(2+) is similar, but with a stronger transannular E3-E7 (E = Te) bonding. The bonding in E8(2+) (E = S, Se, Te) can also be understood in terms of a sigma-bonded E8 framework with additional bonding and charge delocalization occurring by a combination of transannular n pi *-n pi * (n = 3, 4, 5), and np2-->n sigma * bonding. The classically bonded S8(2+) (Se8(2+) dication containing a short transannular S(+)-S+ (Se(+)-Se+) bond of 2.20 (2.57) A is 29 (6) kJ/mol higher i...