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.

This paper is one of a series exploring simple approaches for the estimation of lattice energy of ionic materials, avoiding elaborate computation. The readily accessible, frequently reported, and easily measurable (requiring only small quantities of inorganic material) property of density, rho(m), is related, as a rectilinear function of the form (rho(m)/M(m))(1/3), to the lattice energy U(POT) of ionic materials, where M(m) is the chemical formula mass. Dependence on the cube root is particularly advantageous because this considerably lowers the effects of any experimental errors in the density measurement used. The relationship that is developed arises from the dependence (previously reported in Jenkins, H. D. B.; Roobottom, H. K.; Passmore, J.; Glasser, L. Inorg. Chem. 1999, 38, 3609) of lattice energy on the inverse cube root of the molar volume. These latest equations have the form U(POT)/kJ mol(-1) = gamma(rho(m)/M(m))(1/3) + delta, where for the simpler salts (i.e., U(POT)/kJ mol(-1) < 5000 kJ mol(-1)), gamma and delta are coefficients dependent upon the stoichiometry of the inorganic material, and for materials for which U(POT)/kJ mol(-1) > 5000, gamma/kJ mol(-1) cm = 10(-7) AI(2IN(A))(1/3) and delta/kJ mol(-1) = 0 where A is the general electrostatic conversion factor (A = 121.4 kJ mol(-1)), I is the ionic strength = 1/2 the sum of n(i)z(i)(2), and N(A) is Avogadro's constant.

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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.

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