Generalized valence bond geometric

This collection of papers ends with the first extension of the valence concept beyond its purely numerical character. In a second example of almost simultaneous publication Jacobus Hen-ricus van t Hoff (1852-1911) and Joseph AchiUe le Bel (1847-1930) developed the relation between optical activity and chemical constitution, a relation not understandable unless valence bonds had directional characteristics in space. Though le Bel framed his hypothesis in more general geometrical terms, both arrived at the proposal that the valence bonds at a carbon atom must be directed to the comers of a tetrahedron.Only in this way can the correct number of isomers be explained for substitution products of methane with the formulas Caab, Ga2bc, Cabed, where a, b, c, d... 

While this definition is arbitrary it is appropriate because it is based on chemical as well as geometric considerations and, like other definitions, it agrees with the conventional assignment in cases where there is no dispute. The definition can be justified for use with the bond valence model since any true bond that is excluded by this definition contributes at most only 4 per cent to the cation bond valence sum, and generally much less given that eqn (3.1) tends to overestimate the valence of weak bonds. 

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