EAN rule

This mode of calculation has been called the EAN rule (effective atomic number rule). It is valid for arbitrary metal clusters (closo and others) if the number of electrons is sufficient to assign one electron pair for every M-M connecting line between adjacent atoms, and if the octet rule or the 18-electron rule is fulfilled for main group elements or for transition group elements, respectively. The number of bonds b calculated in this way is a limiting value the number of polyhedron edges in the cluster can be greater than or equal to b, but never smaller. If it is equal, the cluster is electron precise. 

The effective atomic number rule (the 18-electron rule) was described briefly in Chapter 16, but we will consider it again here because it is so useful when discussing carbonyl and olefin complexes. The composition of stable binary metal carbonyls is largely predictable by the effective atomic number (EAN) rule, or the "18-electron rule" as it is also known. Stated in the simplest terms, the EAN rule predicts that a metal in the zero or other low oxidation state will gain electrons from a sufficient number of ligands so that the metal will achieve the electron configuration of the next noble gas. For the first-row transition metals, this means the krypton configuration with a total of 36 electrons. 

The Mn atom has 25 electrons. Adding five carbonyl groups would raise the number to 35, leaving the atom one electron short of the krypton configuration. If the single unpaired electron on one manganese atom is then allowed to pair up with an unpaired electron on another to form a metal-metal bond, we have the formula (CO)5Mn-Mn(CO)5 or [Mn(CO)5]2, which is the formula for a manganese carbonyl that obeys the EAN rule. 

The first attempts to interpret Werner s views on an electronic basis were made in 1923 by Nevil Vincent Sidgwick (1873—1952) and Thomas Martin Lowry (1874—1936).103 Sidgwick s initial concern was to explain Werner s coordination number in terms of the sizes of the sub-groups of electrons in the Bohr atom.104 He soon developed the attempt to systematize coordination numbers into his concept of the effective atomic number (EAN).105 He considered ligands to be Lewis bases which donated electrons (usually one pair per ligand) to the metal ion, which thus behaves as a Lewis acid. Ions tend to add electrons by this process until the EAN (the sum of the electrons on the metal ion plus the electrons donated by the ligand) of the next noble gas is achieved. Today the EAN rule is of little theoretical importance. Although a number of elements obey it, there are many important stable exceptions. Nevertheless, it is extremely useful as a predictive rule in one area of coordination chemistry, that of metal carbonyls and nitrosyls. 

Average values two independent molecules in the unit cell no metal-metal bond according to the EAN Rule. 

With regard to the valence electron count, this number determines whether the transition metal ion is using its full complement of valence shell orbitals— i.e., the five nd s, the (n + l)s, and the three (n + l)p s. If the valence electron count is eighteen, all of the orbitals are fully utilized in bond formation and electron pair storage, the effective atomic number (EAN) rule is fulfilled and the metal ion is said to be saturated. If it is seventeen, the metal ion is covalently unsaturated, and if it is sixteen or less, the metal ion possesses at least one vacant coordination site and is said to be coordinatively unsaturated. The importance of the valence electron count in homogeneously catalyzed reactions has been discussed by Tolman (7). 

A large number of stable carbonyls obey the 18-electron rule [sometimes known as the effective atomic number (EAN) rule]. To use this rule one first counts the number of valence electrons in the neutral atom, equal to the group number (thus both s and d electrons are included then adds two electrons for the lone-pair of each attached CO. For example, in Fe(CO)5, the group number of Fe is eight five COs make 18. 

Reactions with halogens. Carbonyl halide complexes are formed by the replacement of CO with a halogen to give products that usually obey the EAN rule. For example,... 

It is interesting to note that the products of these reactions obey the EAN rule. For example, in Co(CO)3NO the Co has 27 electrons, and it gains three from NO and six from the three CO ligands. 

The effective atomic number (EAN) rule is useful for interpreting how ligands with more than one double bond are attached to the metal. Essentially, each double bond that is coordinated to the metal functions as an electron pair donor. Among the most interesting olefin complexes are those that also contain CO as ligands. Metal olefin complexes are frequently prepared from metal carbonyls that undergo substitution reactions. 

In the other complexes, six electrons also come from the three CO molecules. Because iron needs to gain a total of 10 electrons to obey the EAN rule, the cht will coordinate using two double bonds. In the case of the chromium complex, cht will be coordinated to all three double bonds in order to give a total of 36 electrons around Cr. Structures of these complexes are shown in Figure 21.12. 

We have considered compounds of C5H5 as though the ligand is a donor of six electrons, but benzene can also function as a six-electron donor. Therefore, for a metal that has 24 electrons, the addition of two benzene molecules would raise the total to 36, which is exactly the case if the metal is Cr°. Thus, Cr(C6H6)2 obeys the EAN rule, and its structure is... 

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