Madelung part of lattice energy

Kubaschewski (1972) collected and compared the enthalpies of formation of complex oxides from binary oxides. He did not offer any systematic correlation of these enthalpies with structural properties. Hoppe (1966,1970a, b, 1975) developed the MAPLE concept (Madelung part of lattice energy) as a tool to guide the structural interpretation of bonding in complex oxides and halides. It requires as input parameters the unit cell of a compound and positions of all atoms, and it treats the crystal as an ionic array of point charges. If crystal structure determinations have been properly done, MAPLE calculations for a complex compound are within 2% (sometimes larger, sometimes smaller) of the MAPLE values of the binary (parent) compounds. Therefore, purely ionic-model calculations are not suflftciently sensitive to correlate quantitatively with the relatively small enthalpies of solid-state complexation. 

For nonmolecular solids, called coordinated polymers, he substitutes the Madelung part of the lattice energy... 

The electrostatic (Madelung) part of the lattice energy (MAPLE) has been employed to define Madelung potentials of ions in crystals (Hoppe, 1975). MAPLE of an ionic solid is regarded as a sum of contributions of cations and anions the Madelung constant. A, of a crystal would then be the sum of partial Madelung constants of cation and anion subarrays. Thus,... 

For the Madelung part of the lattice energy, in the case of a salt for which the structure is accurately known, we employed the method of E. F. Bertaut as modified by D. H. Templeton, and evaluated other terms as set out in Ref. 82. When applied to salts that dissociate easily into gaseous molecules, this provided us, via the vant Hofi relationship (see Refs. 80, 82, and 105) with evaluation of the enthalpies of ionization, AH gg [EFa (g) (EFi i)+(g) -I- F (g)] for a variety of F donor molecules, and the fluoride-ion affinities for well known F acceptors, e.g. Ap(BF3) = — AH29g [BF3(g) + F (g) BF4 (g)]. Such evaluations help to provide a more quantitative evaluation of possible reaction chemistry. The intercalation of graphite by one-electron oxidizers and by fluoride-ion acceptors, as covered in Chap. 10, provides examples. Such evaluations are also useful in assessing the likelihood of the existence of salts not yet known, such as [ArFJ fMFg] (see Ref. 92). 

Hoppe, R., 1975, The Madelung part of the lattice energy, MAPLE, as a guide in crystal chemistry, irt Crystal Stnrctirre and Chemical Bonding in Inorganic Chemistry, eds C.J.M. Rooymarrs and A. Rabenau (North-Holland, Amsterdam) pp. 127-161. 

The neutral-ionic transition (NIT) at t = 0 occurs abruptly[94] when the Madelung energy M of the ionic lattice exceeds the energy I — A to transfer an electron form D to A. Long-range Coulomb interactions are treated self-consistently as part of A in the modified Hubbard model[95],... 

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