Covalent and ionic models for

Figure 10 Electron counting on the covalent and ionic models. For (24), note the adjustment to account for the positive ionic charge on the complex as a whole for anions, the net charge is added to the total...

Figure 2. Covalent and ionic models for some 1 and 2 coordinated molecules of...

This is generalized for ligands of L X type in the covalent model, which quite naturally become L X " ligands in the ionic model. The cyclopentadienyl radical (Cp), a neutral species with five n electrons (an L2X ligand, 1-5), is therefore considered in its monoanionic form (Cp with six 7T electrons). Table 1.3 presents the numbers of electrons attributed to the principal ligands that have been considered so far in the covalent and ionic models. 

Assign the oxidation states, d configurations, and electron counts for the two species shown below, which are in equilibrium in solution. Use both the covalent and ionic models. 

Covalent contribution to the bonding is confirmed by analysis of the components of V2p. The average values of 2, and X2, representing the contraction of the density in the directions perpendicular to the bond (chapter 6), are found to be — 9eA"s, compared with —4eA 5 for the independent-atom model (IAM) density and — 6eA"5 for the ionic model. In addition, the density at the bond critical point ph is l.leA"3, higher than 0.85 eA"3 and 0.68 eA"3 calculated for the IAM and ionic models, respectively. Results for the borosilicate danburite CaB2Si208, are similar, with ph(SiO) 0.95 eA-3, and large positive values of V2p for the Si—O bonds (Downs and Swope 1992). 

The usually accepted approach is to adopt an ionic model for the superoxide ion on the surface. In this model, an electron is transferred from the surface to the oxygen to form 02, and there is an electrostatic interaction between the cation at the adsorption site and the superoxide ion. A calculation of the g tensor based on this model (Section 111,A,1) accounts for nearly all the data from adsorbed 02 and is consistent with the evidence that the spin density on both oxygen nuclei is the same (Section III,A,2). However, there are examples of oxygen adsorbed on the surface where the g values do not fit the predictions of the ionic model (Section IV,E) and also a few cases where the spin density on the two oxygen nuclei is found to be different. In these situations it seems likely that a covalent model in which a a bond is formed between the cation and the adsorbed oxygen, is more relevant. 

There can be resonance between covalent and ionic states. In the molecule H H a complete shift of the electron pair to the left would have the effect to make the left-hand H atom a negative ion, leaving the right-hand one as a positive ion. Next to the state H H there will be two others, H H+ and H+H , which closely resemble the electrostatic model for the H2 molecule. Since the three states are resonating, the states H H+ and H+H will make a contribution to the bonding energy, too in this case, however, their contribution will be relatively small, because the energy of the covalent state H H certainly is much lower than that of the ionic states. H H+ and H+H-. 

Explain the difference between constructing a cluster model for covalent and ionic crystals. 

Both components yield the conserved overall bond index Af P) = 1 in the whole range of bond polarizations P e [0,1]. Therefore, this model properly accounts for the competition between the bond covalency and ionicity, while... 

There are at least three types of cluster expansions, perhaps the most conventional simply being based on an ordinary MO-based SCF solution, on a full space entailing both covalent and ionic structures. Though the wave-function has delocalized orbitals, the expansion is profitably made in a localized framework, at least if treating one of the VB models or one of the Hubbard/PPP models near the VB limit -and really such is the point of the so-called Gutzwiller Ansatz [52], The problem of matrix element evaluation for extended systems turns out to be somewhat challenging with many different ideas for their treatment [53], and a neat systematic approach is via Cizek s [54] coupled-cluster technique, which now has been quite successfully used making use [55] of the localized representation for the excitations. 

Althou the short in-plane contact of 2.50 (1) A between the XeF3 ion and the closest F atom (F(2)) of an anion could be represented as an indication of some covalency, the ionic model provides a simple and direct accounting for the observed structural features, if due allowance is made for the polarizing character of the cation. 

As we said above, bonds aren t always purely ionic or purely covalent. The best models for ionic bonds include some electron sharing. And covalent bonds don t always share electrons completely evenly. Any difference in electronegativity between bonding nuclei means that the electrons will be attracted more to one nucleus than the other. However, a bond could be considered purely covalent if it is between two identical nuclei, as in hydrogen gas, H2, or oxygen gas, O2. An extreme example of equality in electron sharing is the metallic bond. In a metal, all the atoms are identical and share electrons so readily that the metal can be thought of as one big molecule. 

Despite these spectacular successes, the molecular structures of the boranes were entirely unknown and basically unknowable at that time. Lacking modem tools such as NMR and single-crystal X-ray diffi-action techniques (5), and with ideas of covalence in that era dominated by Lewis-style electron pair bonding as found in organic compounds. Stock and his contemporaries could only speculate about structure. For lack of a better idea, they assumed that the boron hydrides, notwithstanding an apparent deficiency of electrons, must adopt hydrocarbon-like chain structures such as the examples shown in Chart 1, for which both non-ionic and ionic models were suggested (4). 

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