Electron covalent models

Simple metals like alkalis, or ones with only s and p valence electrons, can often be described by a free electron gas model, whereas transition metals and rare earth metals which have d and f valence electrons camiot. Transition metal and rare earth metals do not have energy band structures which resemble free electron models. The fonned bonds from d and f states often have some strong covalent character. This character strongly modulates the free-electron-like bands. 

The covalent, or shared electron pair, model of chemical bonding was first suggested by G N Lewis of the University of California m 1916 Lewis proposed that a sharing of two electrons by two hydrogen atoms permits each one to have a stable closed shell electron configuration analogous to helium... 

Vanadium(n) Complexes.—Dehydration of VSO. THjO has been shown to proceed via the formation of VS04,mH20 (where n = 6, 4, or 1) and V(OH)-(SO4), which were characterized by X-ray studies. The polarographic behaviour and the oxidation potential of the V -l,2-cyclohexanediamine-tetra-acetic acid complex, at pH 6—12, have been determined.Formation constants and electronic spectra have been reported for the [Vlphen),] " and [V20(phen)] complexes. The absorption spectrum of V ions doped in cadmium telluride has been presented and interpreted on a crystal-field model. The unpaired spin density in fluorine 2pit-orbitals of [VF ] , arising from covalent transfer and overlap with vanadium orbitals, has been determined by ENDOR spectroscopy and interpreted using a covalent model. " ... 

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 are halides for which it is impossible to construct a strictly covalent model with all atoms in octet configuration, because they contain too many halogen atoms, e.g. PF5, SF6, IF7, PC15, SC14, SeCl4 and IC13. If, in PF5, five P F bonds are accepted, ten electrons would belong to each P atom the S atom in SF6 would have 12 electrons, and the I atom in IF7 14 electrons. 

The qualitative interpretation of these results in terms of conduction —> covalent electronic transformation model is based on the following principles (1) covalent electrons are localized and therefore are identifiable with a group of ions, whereas conduction ( free ) electrons are delocalized and are simultaneously shared by all ions. (2) thus, covalent electrons having no Fermi surface whereas conduction electrons (because of the Pauli exclusion principle) having well defined Fermi surface, and (3) electrons are needed in forming covalent bonds, (i.e., under no circumstances can holes be substituted for electrons in forming bonds) in sharp contrast, holes behave in much the same way as electrons in band structure. 

The reduction of the free-ion parameters has been ascribed to different mechanisms, where in general two types of models can be distinguished. On the one hand, one has the most often used wavefunction renormalisation or covalency models, which consider an expansion of the open-shell orbitals in the crystal (Jprgcnscn and Reisfeld, 1977). This expansion follows either from a covalent admixture with ligand orbitals (symmetry-restricted covalency mechanism) or from a modification of the effective nuclear charge Z, due to the penetration of the ligand electron clouds into the metal ion (central-field covalency mechanism). 

A striking analogy exists between localized molecular orbital, electron-domain models of organic and other covalently bonded molecules (Figs. 3—8) and ion-packing models of inorganic compounds 47). 

Estimation of Interatomic Distances. The notion of transferable interference radii — that, e.g., a hydrogen atom is approximately the same size whether it is attached to a phenyl ring (Fig. 1) or to a cyclohexane ring (Fig. 2) or that a sodium ion is approximately the same size whether it is surrounded by chloride ions in NaCl or by, say, bromide ions in NaBr — has found wide application in the estimation of distances between (i) adjacent atoms in adjacent molecules in molecular solids and (ii) adjacent atoms in ionic solids. Extension of these results to the estimation of interatomic distances within covalent molecules through use of the localized electron-domain model and one, new, two-parameter relation (but no new empirical radii) is illustrated in Fig. 28. 

Cp2Zr(CH3)(THF)]+ The zirconium oxidation state is 4+ and each Cp ligand donates six electrons. The ligand CTC donates two electrons. The solvent molecule, THF, also donates two electrons, and the total electron count is 12 + 0 + 2 + 2=16. With the covalent model zirconium is in the zero oxidation state and has four electrons Ad2,5s2) in the valence shell. Both Cp and CH3 are considered as radicals and therefore donate five and one electron, respectively. The valence electron count is therefore 4 + 2x5 + 1+ 2-1 = 16. Notice that because of the positive charge, we subtract one electron. 

Co(CO)4 Since there is a net negative charge and CO is a neutral ligand, the formal oxidation state of cobalt is 1 —. The electron count is therefore 10 + 4X2=18. According to the covalent model, the electron count is also 9 + 4X2 + 1 = 18, but cobalt is assumed to be in a zero oxidation state, and one electron is added for the negative charge. 

The shared-electron pair model introduced by G.N. Lewis showed how chemical bonds could form in the absence of electrostatic attraction between oppositely-charged ions. As such, it has become the most popular and generally useful model of bonding in all substances other than metals. A chemical bond forms when electrons are simultaneously attracted to two nuclei, thus acting to bind them together in an energetically -stable arrangement. The covalent bond is formed when two atoms are able to share a... 

We overview our valence bond (VB) approach to the ir-electron Pariser-Parr-Pople (PPP) model Hamiltonians referred to sis the PPP-VB method. It is based on the concept of overlap enhanced atomic orbitals (OEAOs) that characterizes modern ab initio VB methods and employs the techniques afforded by the Clifford algebra unitary group approach (CAUGA) to carry out actual computations. We present a sample of previous results, sis well sis some new ones, to illustrate the ability of the PPP-VB method to provide a highly correlated description of the ir-electron PPP model systems, while relying on conceptusilly very simple wave functions that involve only a few covalent structures. 

In Table 4 we see some of the common ligands and their electron counts on the ionic and covalent models. In the former, we dissect an M-X bond into M+ and X and in the latter... 

The description of bonding within these compounds has been treated by several different approaches that come to the same conclusion. The (8 — N) rule that is generahzed by Mooser and Pearson uses a covalent model with collective counting of electrons. The generahzed 8 — N rule can be easily defined for simple binary compounds of the general formula, as 8x electrons are required in order... 

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