Linnett theory

In conclusion, the Boys localization procedure may be considered as the mathematification of the qualitative Lewis and Linnett theories. As pointed out, in this perspective a formal signification of the symbols used by these authors can be proposed these represent not localized electrons but centroids of charge of localized orbitals. Within this interpretation, the former theories agree much better with the ideas of quantum mechanics such as the wave character of electrons that prevents their localization. Moreover, the results obtained by the Boys procedure allow us to predict the Lewis and (or) Linnett structures of many chemical species without performing explicit calculations. For example, linear and bent 1,3-dipoles are described by the following general formulas ... 

Our LMO approach to the electronic structure and reactivity of chemical species allowed us not only to generalize the (Lewis and Linnett) theory of valence but also to determine the mechanism of a wide variety of organic reactions. 

Firestone, on the contrary, on the basis of experimental results and theoretical considerations supported by the Linnett theory, has suggested that both types of 1,3 dipole should follow a two-step mechanism, where one first step, leading to a diradical in a cis or trans conformation, and in a second step this diradical would close to the final five-membered ring, according to Scheme XVII ... 

There are other methods. For a discussion of the free-electron method, see Streitwieser Jr., A. Molecular Orbital Theory for Organic Chemists Wiley NY, 1961, p. 27. For the nonpairing method, in which benzene is represented as having three electrons between adjacent carbons, see Hirst, D.M. Linnett, J.W. J. Chem. Soc., 1962,1035 Firestone, R.A. J. Org. Chem., 1969, 34, 2621. 

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. 

We believe J.W. Linnett, in his Methuen Monograph, Wave Mechanics and Valency Theory, 1956, was the first to use elliptical projections to display the phases of the spherical harmonics on the unit sphere. We adopt a projection in which both 0 and (f) coordinates are plotted on linear scales on the minor and major axes of a 30° ellipse of eccentricity a/3/2. This cartographic device is the one proposed by Apianus in 1524, and known as the Apianus II projection. In our early work on the Spherical Shell method we called this a modified Mollweide projection, reversing the historical sequence. 

Thus, Linnett s theory replaces the Lewis octet, corresponding to four pairs of electrons of opposite spins, by the double quartet, corresponding to two sets of four electrons having the same spin within a given set. 

The results provided by Linnett s approach are more detailed than those of Lewis theory. Moreover, particularly in the case of unpaired electron species, they are in better agreement with spectroscopic and structural experimental data. 

On the whole, Linnett s theory is very useful for rationalizing the structure, the stability, and even the reactivity of compounds containing up to four atoms. However, it may not be easily extended to larger molecules. Indeed, for those systems, its use becomes generally very intuitive and its results as ambiguous as those of resonance theory. 

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. 

It seems now that both Samuel and Wheland held the widespread opinion that valence-bond structures for diamagnetic molecules must only have electron-pair bonds. Samuel and Wheland had attempted to transform the molecular orbital configurations for N2 and NO so that they would obtain electron-pair bonds for N2O. But neither worker used the correct procedure to obtain valence-bond stractures from diatomic molecular orbital configurations with one or more singly-occupied anti-bonding molecular orbitals. The technique that should be used was developed by Linnett in 1956 , and then by Green and Liimett in 1960 °, and it has formed the primary Pauling 3-electron bond basis for the increased-valence theory we use in this book. When this theory is applied to the excited Nj and NO... 

---