Structure and Energetics Calcium Oxide

As indicated before, the ab initio electronic-structure theory of solid-state materials has largely profited from density-functional theory (DFT), and the performance of DFT has turned out well even when the one of its molecular quantum-chemical competitors - Hartree-Fock theory - has been weakest, namely for metallic materials. For these, and also for covalent materials, DFT is a very reasonable choice. On the other hand, ionic compounds (with both metals and nonmetals present) are often discussed using only the ionic model, on which most of Section 1.2 was based, and the quantum-mechanical approach is not considered at all, at least in introductory textbooks. Nonetheless, let us see, as a first instructive example, how a t5q)ical ionic material can be described and understood by the ionic and the quantum-chemical (DFT and HF) approaches, and let us also analyze the strengths and weaknesses. 

Calcium oxide, CaO, or simply lime is a white, caustic, alkaline chemical which has found applications in a number of fields. CaO can be made by heating calcium carbonate, CaCOj, to several hundred degrees Celsius, and CaO 

In order to predict which structure type is actually found, one often reads (see Section 1.1) that the quotient of the cation and anion radii, Tc/ra, needs to be calculated, and the critical value is 0.732 for the change from [CsCl] to [NaCl] and 0.414 from [NaCl] to [ZnS]. Indeed, rdra is found to be 0.714 for the [NaCl] type but only if the values for six-fold coordination of Ca + and C are used. Taking, for example, the radii, the ratio is 0.789, a self-fulfilling prophecy in favor of the [CsCl] type with eight-fold coordination. Clearly, this classical criterion is unfortunately unreliable. 

We may derive another prediction for the lattice parameters of CaO in the three different crystal structures, simply by considering the volume increments of Ca (6.5 cm /mol) and 0 (11 cm /mol), and the total 17.5 cm /-mol which corresponds to 29.06 A per ion pair. Given that the unit cells of the [ZnS]/[NaCl] and [CsCl] structures contain four and one formula unit per cell, respectively, the lattice parameters of CaO are predicted to be 4.88 A for 

There is yet another classical method used to predict these lattice parameters namely by the bond-valence method. In the [ZnS] type, the +2 bond-valence sum of Ca + results from four Ca +-0 bonds of bond valence 2/4 = 0.5. For the [NaCl] and [CsCl] types, there are six/eight corresponding bonds with bond valences of 2/6 = 0.3333 and of 2/8 = 0.125. Together with the bond-valence parameter of 1.967 A from Table 1.3 and using Equation (1.15), the interionic Ca +-0 distances are 2.22, 2.37, and 2.48 A which corresponds to (see above conversion) lattice parameters of 5.14, 4.75, and 2.86 A for the [ZnS], [NaCl], and [CsCl] types. 

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