The effective atomic number concept

The concept of the effective atomic number applies particularly well to carbonyl and nitrosyl compounds of the d-block elements. For example, the composition of mononuclear nickel(O) and iron(0) carbonyl complexes may be rationalized in terms of effective atomic number. To attain the krypton configuration, nickel (28 electrons) and iron (26 electrons) need to accept four and five electron pairs, respectively. Thus, [Ni(CO)4] and [FefCOls] are the predicted compositions, linear nitrosyls are three-electron donors and so binding of a [Co(CO)3l fragment (33 electrons) to a single NO ligand to form [Co(NO)(CO)3] would result in the krypton electron configuration. 

The noble gases in each of the three long periods have eighteen valence electrons (i.e. (n-l)s2, (n-Dp, nd O) and extension of the effective atomic number concept, therefore, suggests that many stable coordination compounds will similarly possess 18 valence electrons. 

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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. 

The effective atomic number is a convenient parameter for defining the X-rays attenuation properties of a complex medium as a biological tissue, and particularly for the calculation of dose in radiography. The concept of the effective atomic number is based on a proportional relation of the elemental cross-section per atom to Z where m depends on the process considered. For a specific interaction the atomic cross-section of an element is generally expressed as... 

For nearly a century, the Lewis valence theory [1] and the subsequent development of the effective atomic number (BAN) rule [2, 3] as well as the valence bond theory [4] have constituted the fundamental basis concepts used for rationalizing the structure and bonding in a tremendously large area of covalent chemistry [5]. However, there are families of compounds, which have been, at least in part, reluctant to stick to this conventional two-center/two-electron approach, in particular those in which hypervalency and/or hypercoordination are present. This is the case, of... 

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. 

When Max Planck wrote his remarkable paper of 1901, and introduced what Stehle (1994) calls his time bomb of an equation, e = / v , it took a number of years before anyone seriously paid attention to the revolutionary concept of the quantisation of energy the response was as sluggish as that, a few years later, whieh greeted X-ray diffraction from crystals. It was not until Einstein, in 1905, used Planck s concepts to interpret the photoelectric effect (the work for which Einstein was actually awarded his Nobel Prize) that physicists began to sit up and take notice. Niels Bohr s thesis of 1911 which introduced the concept of the quantisation of electronic energy levels in the free atom, though in a purely empirical manner, did not consider the behaviour of atoms assembled in solids. 

The naive concept that a fixed set of valence AOs suffices for all charge states and bonding environments is equivalent to the use of a minimum basis set (e.g., STO-3G), which is known to be quite inadequate for quantitative purposes. Nevertheless, if the AOs are properly allowed to adjust dynamically in the molecular environment, one recovers a minimal-basis description that is surprisingly accurate the natural minimal basis. In the NBO framework the effective natural atomic orbitals are continually optimized in the molecular environment, and the number of important NAOs therefore remains close to minimal, greatly simplifying the description of bonding. 

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