The Effective Atomic Number EAN Rule

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. 

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. 

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. 

A variation on the 18-electron rule, often called the effective atomic number (EAN) rule, is based on electron counts relative to the total number of electrons in noble gases. The EAN rule gives the same results as the 18-electton rale and will not be considered further in this text. 

Also called the effective atomic number (EAN) rule. 

In addition to the 18- and 16-electron rules, there is also the Effective Atomic Number (EAN) rule, which looks to the periodic table for verification of what can be calculated using the 18-electron rule. To put this rule simply, it says that an organometallic complex (as a system) binds as many ligands as possible to reach the number of electrons of the next noble gas configuration. 

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. 

Table 2.9. Application of the effective atomic numbers (EAN) or 18-electron rule to metal clusters...

In Chapter 2, a series of concepts and models for describing bonding in borane and metal cluster were analyzed. The most versatile of such descriptions appears to be those rules related with the Effective Atomic Number (EAN) and with the Skeleton Electron Pairs (SEP). As assumed in some of the rules described in Table 2.16, frequently main group element fragments are actually involved in cluster bonding so that they obey the same electron counting rules. 

Just as organic compounds follow the octet or eight valence electron rule, typical organometallic compounds tend to follow the 18e rule. This is also known as the noble-gas or effective atomic number (EAN) rule because the metals in an 18e complex achieve the noble-gas configuration— for example, in the Werner complexes, the cobalt has the same EAN as Kr, meaning it has the same number of electrons as the rare gas. We first discuss the covalent model that is the most appropriate one for counting compounds with predominant covalency, such as most organometallics. 

The starting point for most molybdenum-based carbonyl chemistry is the white crystalline air stable hexacarbonyl [Mo(CO)6], which is commercially available. Low valent compounds that are derived from this starting material tend to give products that obey the Effective Atomic Number Rule (EAN Rule). Since Mo° has a d configuration, six two-electron ligands are required to obey the EAN rule. 

It should be noted that zirconium and hafnium usually form electron deficient complexes (see Electron Deficient Compound), which do not obey the Effective Atomic Number Rule (EAN mle) (see Effective Atomic Number Rule) and have a maximum of only 16 electrons. Monomers MX4 with monodentate ligands are rather strong Lewis acids and readily yield adducts with two, three, or four donor ligands. In MX4 monomers with tt-donor ligands X (see n-Base), there is a noticeable shortening of the M X distances in comparison with the sum of the covalent radii (0.26 A for X = F 0.15 A for X = Cl, NMe2), thus pointing to some multiple bond character in these compounds. 

Table 1 Examples of simple molecules adhering to the effective atomic number rule (EAN)...

Since we always deal with electron counts that are >18, it is more convenient in cluster chemistry to use the alternative name of the 18e rule, the effective atomic number, or EAN rule. The closed-shell configuration resem-... 

Like the octet rule for the first-row elements, there is an 18-electron rule for the transition metals. The rationale behind this rule is simply that the metal ion at the most can use nine atomic orbitals, five d orbitals, three p orbitals, and one s orbital, for bond formations and housing 18 electrons in its valence shell. Methane, water, and so on, are stable molecules, as they have eight electrons around the central atom that uses one s and three p orbitals. Similarly, many organometallic complexes that have 18 electrons in the valence shell of the metal are stable complexes. This rule is often referred to as the 18-electron rule, or the rule of effective atomic number (EAN). 

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. 

Uncharged mononuclear and polynnclear metal carbonyls are known for the group 5 to group 10 metals. The EAN rule see Effective Atomic Number Rule) is normally obeyed, so elements with an even atomic number form mononuclear compounds, for example, Cr(CO)6, Fe(CO)5, and Ni(CO)4, while elements with an odd atomic number form dinuclear compounds, for example, Mn2(CO)io and Co2(CO)g, containing metal-metal bonds. 

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