Screening of nuclear charges

So far the nodal structure of the valence s- and p-orbitals themselves has been in our focus, allowing us to explain the special role of the 2p-elements compared to their heavier homologues. The further modulations of chemical and physical properties as we descend to a given group from period 3 on are often summarized under the term secondary periodicity [65, 66]. The main influences here are incomplete screening of nuclear charge by fllled core or semi-core shells and the effects of special relativity. The former reflect shell structure of the atom as a whole and are already important for differences and similarities of the homologous third and fourth period elements, whereas the latter become crucial mainly for the chemistry of the sixth period elements. These aspects have been discussed in detail in various review articles (see, e.g.. Refs [16, 28, 67]), and we, thus, touch them only briefly. 

Further important influences on the periodic trends arise from partial screening of nuclear charge (including lanthanide/actinide contraction, scandide contraction, and even a 2p-contraction) and from the effects of special relativity. Various aspects of main-group bonding are covered in more detail elsewhere in this book. 

One may think that it is quite possible that logistically the electronic stiucture, especially the shell structure, and the physical process of screening of nuclear charge of atom are intimately linked to the origin of and development of the ionization energy, hardness, electronegativity and electrophilicity indices of atoms and molecules. 

Deviations from Rutherford cross-sections are also found for heavy projectiles at lower impact energies, when the projectile can bind inner shell electrons which screen the nuclear charge. These deviations are usually small and can easily be taken into account by use of a theoretical correction [3.160]. 

For an ion of nuclear charge Ze, the size-screening constant for a given electron is... 

According to Slater, this is because electrons in the same quantum shell (here, the 3p orbitals) screen one another s view of the nuclear charge by only 0.35 unit. Thus, going from A1 to Si, the nuclear charge increases by +1.00, but the added electron screens only +0.35 of this. Electrons in lower shells screen the nuclear charge by essentially +1.00 unit, as seen by the outermost electrons. This same effect explains the lanthanide contraction— the steady shrinking of lanthanide(III) ion radii from 103 to 86 pm as we fill the 4/ quantum shell from La3+ (4/°) to Lu3+ (4/14). 

As far as optical spectra are concerned, Jorgensen (19, 20, 22) has rationalized a large body of experimental data in terms of the parameters 10 Dq and B. Two different origins of the nephelauxetic effect have been advanced (19) (i) the central-field covalency is due to screening the nuclear charge of the central ion by electrons of the ligands (ii) the symmetry-restricted covalency is caused by delocalization of metal d electrons onto the ligands (the delocalization is symmetry dependent eg electrons for... 

The d and f series are exceptions to the rule that the elements become progressively smaller through a period. The reason is that the new electron already belongs to an inner shell and the screening almost compensates the increase of nuclear charge. 

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