Ionic limit bond energy

Apart from the difference in the bond energy, other criteria, both direct and indirect, exist between the two different types of bond. Ionic molecules in the solid state form an ionic crystal lattice which r.har ir,teristic lo he particular molecule In such a lattice, ea ion is surrounded by ions of opj site char at equal distances from the central ion and individual molecules cease to exist. The number of ions packed round the central ion is limited by the size of the ions, the attraction and repulsion energies between the ions and other factors. The links of the central ion with its nearest neighbours are all of the same strength and the number of such... 

These successful applications of Equation (3.1) to estimate bond energies are exceptions, rather than the rule. If AA is too large, so that ionic bonds are formed, then size factors will dominate the bonding. We want the bonding to be mainly due to electron transfer in one direction, but limited in extent. The best examples will be those where a coordinate covalent bond is formed. Charge transfer complexes should usually qualify, but only if similar molecules (and orbitals) are compared. 

Favorable thermodynamics (AG° (298K) <0) for obtaining acetylene diolates from M-M bonded complexes occurs when 2(M-0)>(M-M)+ 147 kcal while single metal units require that the M-0 bond energy exceed 78 kcal (Table I, entries u,v). This limiting type of CO coupling is best known for reactions of alkali metals with CO which form solid ionic acetylene diolate compounds.Rhodium macrocycle complexes have Rh-0 bond energies 50-60 kcal and thus are excluded as potential candidates for acetylene diolate formation. 

The problems are not limited to H2. A classic foible is that of F2 in which a molecule with a weak covalent bond is calculated to be unbound by Hartree-Fock theory. While the difference in the calculated energy of the covalent/ionic combination and that of the molecule at equilibrium has occasionally been taken to be the bond energy, the energy difference between that of the neutral separated products and of the molecule is more formally correct. The calculated energy of the F2 molecule at equilibrium is less stable than that of the separated atoms. Calculated results are usually not that wrong. However, problems with dissociation are not limited to homonuclear bonds or even to covalent bonds. For example, in the gas phase, hence in the absence of solvent, the ionic NaCl homolytically dissociates into Na-l-CI and not Na+ - -Cr the electron affinity of Cl is less than the ionization energy of Na. Furthermore, the problem is not merely at infinite separation - even at the equilibrium distance there is an incorrect contribution of the ionic component to the molecular wavefunction. Any dissociation for which the number of unpaired electrons in the molecule and its components differ is problematic. We note the problem... 

Consider now the behaviour of the HF wave function 0 (eq. (4.18)) as the distance between the two nuclei is increased toward infinity. Since the HF wave function is an equal mixture of ionic and covalent terms, the dissociation limit is 50% H+H " and 50% H H. In the gas phase all bonds dissociate homolytically, and the ionic contribution should be 0%. The HF dissociation energy is therefore much too high. This is a general problem of RHF type wave functions, the constraint of doubly occupied MOs is inconsistent with breaking bonds to produce radicals. In order for an RHF wave function to dissociate correctly, an even-electron molecule must break into two even-electron fragments, each being in the lowest electronic state. Furthermore, the orbital symmetries must match. There are only a few covalently bonded systems which obey these requirements (the simplest example is HHe+). The wrong dissociation limit for RHF wave functions has several consequences. 

The dissociation problem is solved in the case of a full Cl wave function. As seen from eq. (4.19), the ionic term can be made to disappear by setting ai = —no- The full Cl wave function generates the lowest possible energy (within the limitations of the chosen basis set) at all distances, with the optimum weights of the HF and doubly excited determinants determined by the variational principle. In the general case of a polyatomic molecule and a large basis set, correct dissociation of all bonds can be achieved if the Cl wave function contains all determinants generated by a full Cl in the valence orbital space. The latter corresponds to a full Cl if a minimum basis is employed, but is much smaller than a full Cl if an extended basis is used. 

The HF wave funetion eontains equal amounts of ionie and eovalent eontributions (Section 4.3), For covalently bonded systems, like H2O, the HF wave funetion is too ionie, and the effect of electron correlation is to increase the covalent contribution. Since the ionic dissociation limit is higher in energy than the covalent, the effect is that the equiUbrium bond length increases when correlation methods are used. For dative bonds, such as metal-ligand compounds, the situation is reversed. In this case the HF wave function dissociates correctly, and bond lengths are normally too long. Inclusion of... 

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