Linnett model

To be technologically useful, bonding models must reliably predict the existence, structure, and properties of the compounds (molecular or solid) of particular elements using atomic characteristics. They should be so simple that neither supercomputers nor dedicated specialists are required for their use. None of the existing models given below meets these requirements but each of them is successful for a selected class of compounds or for certain aspects. Thus the molecular orbital (MO) model is good for most of the features noted but needs computers and is weak in properties. The Linnett model predicts structure well in a simple way but is qualitative. The Miedema modeP is restricted to metals and ignores structure and many properties, the Pearson scheme is best for molecules, and the Johnson model is for metals only and is also qualitative. However, all of them are useful in one sphere or another, and they can be combined in one model that meets... 

This qualitative model for the chemical bond describes molecular structure with localized valence electrons. Valence electrons repel each other strongly when they are close to each other in the same shell on one atom and have the same spin. The Linnett model for the bond is based on the recognition that electron correlation exists, which means that the position or the path of a valence electron strongly depends on the positions of the other valence electrons. 

The Linnett model assumes that localized valence electrons form bonds for the usual reason lowering of energy. Linnett electrons behave as follows ... 

Figure 2.23. Arrangement of the valence electrons in a few molecules according to the Linnett model. The boron and nitrogen atoms in the centers of the tetrahedra form a ring the hydrogen atoms are at the sites of the electron pairs. Electrons of both spins are indicated with filled and open circles. Reprinted with permission from the Journal of Chemical Education, Vol. 44,1967, pp. 206-212 copyright 1967, Division of Chemical Education, Inc.

The Linnett model is not parameterized as the Pearson and Miedema models are and bond enthalpies cannot be calculated from atomic data. However, it is strong on molecular structures and provides a simple (but qualitative) explanation for them without the need for much resonance and configuration interaction. 

Linnett used the concept that an octet of valence shell electrons consists of two sets of four opposite-spin electrons to show that in diatomic and other linear molecules the two tetrahedra are not in general formed into four pairs as we have discussed for F2 and the CC triple bond in C2H2. This idea is the basis of the double-quartet model, which Linnett applied to describe the bonding in a variety of molecules. It is particularly useful for the description of the bonding in radicals, including in particular the oxygen molecule, which has two unpaired electrons and is therefore paramagnetic This unusual property is not explained by the Lewis structure... 

Fig. 32 shows on the left a conventional, localized domain model of the electronic environment of an atom that satisfies the Octet Rule. Each domain is occupied by two electrons. It is well known, however, that the assumption of two electrons per orbital is unnecessarily restrictive 27>122>. Better energies are obtained in quantum mechanical calculations if different orbitals are used for electrons of different spins, a fact first demonstrated in quantitative calculations on helium by Hylleraas 123> and Eckart 124>. Later, this "split-orbital method was applied to 71-electron systems 27,125) Its general application to chemical systems has been developed by Linnett 126>. 

Linnett s procedure may be viewed as a refinement of classical structural theory In Linnett s theory, the van t Hoff-Lewis tetrahedral model is applied twice, once to each set of spins, with the assumption that, owing to coulombic repulsions between electrons of opposite spin, there may be, in some instances, a relatively large degree of spatial anticoincidence between a system s two spin-sets. 

Fig. 32. Electron-domain representation of (left) strong-field and (right) weak-field models of an octet, after Linnett 12 6>...

In the Linnett, weak-field model of an octet, the spin-densities off opposite comers of the octet are of opposite signs, Fig. 32. This suggests that two, identical magnetic ions coordinated colinearly by an oxide ion might be coupled antiferromagnetically, Fig. 33, as, in fact, has been... 

A further observation of Linnett et al. [511], which has also since become of interest in connection with kinetic modelling of the system, is that afterglows following explosions occurred in the alumina coated vessel, lasting sometimes as long as twenty seconds. 

Bonding. —In the valence-bond description of XeF2, Coulson has emphasized the dominance of the canonical forms (F-Xe)+F and F (Xe-F) in the resonance hybrid. This representation accounts well for the polarity FXe F , indicated by nmr, Moss-bauer, ESCA, and thermodynamic data. It is particularly impressive that the enthalpy of sublimina-tion derived for the XeFy case, by Rice and his co-workers in 1963, on the basis of the charge distribution "FXe+F , is 13.3 kcal mol , whereas the experimental value reported in 1968 is 13.2 kcal mol . It should be recognized that the Coulson valence-bond model is not, in the final analysis, significantly different from the Rundle and Pimentel three-center molecular orbital description or the Bilham and Linnett one-electron-bond description, but it does provide for a more straightforward estimation of thermodynamic stabilities of compounds than the other approaches do. 

This latter interpretation follows a model developed by J.W. Linnett in 1964 (ref. 107) in which the orbital concept is largely ignored in favour of spin correlation which is a consequence of the antisymmetrization of the total wavefunction demanded by the Pauli principle. In such a model, what matters are the most likely relative positions of the electrons. It can be shown that, with an antisymmetric wavefunction, electrons having parallel spins tend to be as far apart as possible around the nucleus of an atom. Let us take the carbon atom as an example. For its excited valence configuration 2s, 2p, the four electrons have preferably parallel spins (extension of Hund s rule to excited configurations) and, among the infinity of spatial arrangements, the most likely ones are those in which the four electrons define the vertices of a tetrahedron centred at the nucleus. In particular, for... 

Based upon Linnett s model, Gillespie begins by associating each unpaired electron with a region or domain in the atom, and then defines electron pair domains as regions of the atom in which there is a high probability of finding a pair of electrons of opposite spin, for example... 

Using a simplified representation of centroid of charge distributions, one obtains the pictures collected in Table V, for a series of model free radicals. When two centroids of different types (a and /3) are near one to the other, we adopt the Linnett notation, i.e., a line, but we do not distinguish between spatial and nonspatial pairs. Moreover, centroids of the CH, NH, or OH bond are not always indicated. 

The extent to which individual electron pairs are localized in distinct spatial regions has been carefully analyzed by Bader and Stephens (1975) using the minimum fluctuation criterion. These authors arrive at the conclusion that the model of spatially localized pairs is appropriate for LiH, BeH2, BH3, and BH-r, it is borderline for CH4, but in NHj, OH2, FH, Ne, N2, and F2, the motions of the valence electrons are so strongly inter-correlated, the localized pair model ceases to afford a suitable description. Moreover, their results provide no physical basis for the view that there are two separately localized pairs of nonbonded electrons in H20. This clearly shows the limit of the Lewis electron pair concept which otherwise has practically disappeared in Linnett s theory. 

Another approach to the problem of molecular stability in terms of the valence bond picture was introduced by Linnett [8] (also see reference [3]). According to Linnett s model, valence electrons occupy tetrahedrally oriented spatial configurations. Six possible resonance structures can be drawn for this model, as shown below for the NJ, CNO", and NCO ions. (A full line indicates a pair of electrons of opposite spin in the same spatial orbital a dotted line indicates a pair of electrons of opposite spin in different spatial orbitals, and o andx represent single electrons of different spin.)... 

The views of Green and Linnett were subjected to criticism by R. D. Brown and llarcourt [113]. The latter pointed out that Green and Linnett had overlooked the significant effect of a-electron delocalization upon N —N and N —C bonds. Brown and Harcourt proposed a new electronic structure with o + n model. 

The basis common to the Pearson, Miedema, Linnett, and Johnson models that have been described in Sections 2.6 to 2.9 can be summarized as follows ... 

Explain the structure of some complexes and covalent inorganic molecules in terms of Linnett s localized electron model. 

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