Born-Haber-Fajans Cycle Generalized: Linear Energy Relation between Molecules, Crystals, and Metals
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Classical procedures to calculate ion-based lattice potential energies (UPOT) assume formal integral charges on the structural units; consequently, poor results are anticipated when significant covalency is present. To generalize the procedures beyond strictly ionic solids, a method is needed for calculating (i) physically reasonable partial charges, , and (ii) well-defined and consistent asymptotic reference energies corresponding to the separated structural components. The problem is here treated for groups 1 and 11 monohalides and monohydrides, and for the alkali metal elements (with their metallic bonds), by using the valence-state atoms-in-molecules (VSAM) model of von Szentply et al. (J. Phys. Chem. A 2001, 105, 9467). In this model, the Born-Haber-Fajans reference energy, UPOT, of free ions, M+ and Y-, is replaced by the energy of charged dissociation products, M+ and Y-, of equalized electronegativity. The partial atomic charge is obtained via the iso-electronegativity principle, and the asymptotic energy reference of separated free ions is lowered by the "ion demotion energy", IDE = -1/2(1 - VS)(IVS,M - AVS,Y), where VS is the valence-state partial charge and (IVS,M - AVS,Y) is the difference between the valence-state ionization potential and electron affinity of the M and Y atoms producing the charged species. A very close linear relation (R = 0.994) is found between the molecular valence-state dissociation energy, DVS, of the VSAM model, and our valence-state-based lattice potential energy, UVS = UPOT - 1/2(1 - VS)(IVS,M - AVS,Y) = 1.230DVS + 86.4 kJ mol-1. Predictions are given for the lattice energy of AuF, the coinage metal monohydrides, and the molecular dissociation energy, De, of AuI. The coinage metals (Cu, Ag, and Au) do not fit into this linear regression because d orbitals are strongly involved in their metallic bonding, while s orbitals dominate their homonuclear molecular bonding.
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