Generalized 8 - N rule

The octet principle can be expressed as a formula by the generalized 8—N rule according to E. Mooser W. B. Pearson. We restrict our considerations to binary compounds, and presuppose the following ... 

Links between atoms serve to compensate for the lack of the electrons which are necessary to attain the electron configuration of the next noble gas in the periodic table. With a common electron pair between two atoms each of them gains one electron in its valence shell. As the two electrons link two centers , this is called a two-center two-electron bond or, for short, 2c2e bond. If, for an element, the number of available partner atoms of a different element is not sufficient to fill the valence shell, atoms of the same element combine with each other, as is the case for polyanionic compounds and for the numerous organic compounds. For the majority of polyanionic compounds a sufficient number of electrons is available to satisfy the demand for electrons with the aid of 2c2e bonds. Therefore, the generalized 8 —N rule is usually fulfilled for polyanionic compounds. 

Because of the apparent success frequently achieved by applying the simple octet rule, we took this rule as our starting point. However, the plain formulation of the octet rule is somewhat cumbersome and is conveniently substituted by the generalized (8-N) rule (77—28). The generalized rule has received considerable attention in recent years as a powerful tool for predicting compound semiconductors. 

Most current versions of the generalized (8-N) rule differ in notation or in their treatment of non-bonding electrons. Although the lack of a consistent notation causes some confusion, formal problems of this type will not be considered here. Any one scheme of notation seems just as good as the others but, for convenience, that previously used by one of the present authors (22) is adopted with some necessary modifications. 

The most common formulation of the generalized (8-N) rule states that virtually all compound semiconductors... 

However, for the purpose of testing or predicting the properties of specific compounds by way of Eqn. 11.18, such improvements of the generalized (8-N) rule are somewhat artificial. Clearly, since no assumptions regarding the nature of Q and T are needed to establish Eqn. 11.18, attempts to reverse the picture with the object of extracting decisive information about these parameters are ill-advised. Moreover, as... 

Before we close this MO/LCAO discussion of the generalized (8-N) rule, we note that a derivation of Eqn. II. 1 has been reported by Hulliger and Mooser (23) on a similar basis. However, a careful analysis of their treatment reveals that, in addition to features of general MO/LCAO theory (Thms. II. 1—II.3) and necessary assumptions (equivalents of Hyps. II.1—II.3), they also introduce some superfluous assumptions and specializations. This not only obscures the treatment, it also introduces new aspects which it may be instructive to dwell on in some detail. In order to keep the number of notational symbols to a minimum, the definitions already invoked in the preceding discussion will be utilized as far as possible. However, the disposition and layout of their paper differ significantly from ours since, moreover, many of Hulliger and Mooser s assumptions are to be classified as being only partly superfluous, some quotations are inescapable. 

It is evident from the above that the requirement for semiconductivity should also be added to the list of superfluous assumptions. However, the association of the generalized (8-N) rule with the question of semiconductivity is not in itself irrelevant. It is also worth noting that R (Def. 11.19) does not enter into Hulliger and Mooser s treatment. The reason for this is hidden in Stms. II.3 and II.4, according to which R =0. Surprisingly enough, Hulliger and Mooser do not draw this conclusion explicitly. 

The counting procedure represented by Eqn. IV.9 is termed the neutral-bonded formalism, and may (like Eqn. IV.7) be regarded as a set of equations supplementary to those presented in Eqn. IV.3 for the generalized (8-N) rule formalism. 

The grouping of three or more components of a given compound into only two categories is in itself an oversimplification, and a more natural classification operates with one class for each kind of atom that can be chemically and structurally distinguished. As a consequence, the asymmetric treatments of valence and number of valence electrons per atom disappear. Within this framework, the generalized (8-N) rule formalism gives rise to a set of equations, one for each kind of atom. 

Equation (13.5) represents the generalized 8-N rule. Compared to the simple 8-N rule (p. 62), it is enlarged by the term [6(MM) + ], and VEC(X) has taken the place of the main group number N. The following specialized cases are of importance ... 

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 generalized by Mooser and Pearson uses a covalent model with collective counting of electrons. The generalized 8 — N rule can be easily defined for simple binary compounds of the general formula, as 8x electrons are required in order... 

ABSTRACT. For compounds with tetrahedral structure or anionic tetrahedron complex two valence electron concentration rules can be formulated which correlate the number of available valence electrons with particular features of the crystal structure. These two rules are known as the tetrahedral structure equation where the total valence electron concentration, VEC, is used as parameter and the generalized 8 - N rule where the parameter of interest is the partial valence electron concentration in respect to the anion, VEC. From the tetrahedral structure equation one can calculate the average number of non-bonding orbitals per atom and, in the case of non-cyclic molecular tetrahedral structures, the number of atoms In the molecule. An application of the generalized 8 - N rule allows the derivation of the average number of anion -anion bonds per anion or the number of valence electrons which remain with the cation to be used for cation - cation bonds and/or lone electron pairs. These rules have been used not only to predict probable structural features of unknown compounds but also to point out possible errors in composition or structure of known compounds. 

The tetrahedron linkage described by (I) can be calculated from the composition of the compound, to be exact, from the anion to central atom ratio (n/m ). The linkage type (II), (III) and the formation of a psi-tetrahedron (IV) can be derived from a modified generalized 8 - N rule, I. e. one needs to calculate the VEC value of the compound. The anion sharing according to (I) is independent of the VEC value and can occur in addition to case (II), (III) and/or (IV). 

The modified generalized 8-N rule. The generalized 8 - N rule shall be used in the modified form... 

---