Outer-shell occupancy

The chemical reactions of nitrogen and phosphorus are similar because they share the same number of electrons in their outer shell (five). The reactivity of oxygen resembles the reactivity of sulfur because of their shared outer-shell occupancy (six). This outer-shell occupancy of an atom is called its valence. Carbon has a valence of four (with four electrons in its outer shell), and its chemistry shares some similarities with silicon, which also has a valence of four. Silicon, germanium, tin, and lead, which have the same valence, have all been used in various proportions to form semiconductors, interesting and important materials that we will investigate later when we discuss chemical bonding. 

Note that packing contributions are most obvious in the outer shell contribution to Eq. (33) because the indicator function 0 (1 — bj) constrains that term to the case where no occupancy of the defined inner shell is permitted. These excluded volume interactions are the essense of packing contributions. To study those contributions, we consider a fictitious solute that does not interact with the solvent at all e AU/kT = 1. In that case, of course, p7x is zero and we write... 

However, for elements that belong to the same group but different periods these principles are not relevant because it s difficult to qjply these principles to systems with almost the same degree of occupancy in the outer shell. Moreover, the general trend of polarizability is to increase and of hardness is to decrease as the number of shells is increasing due to the screening effects. 

The structure of edges in an absorption spectrum allows a precise determination of inner-shell binding energies (see Section 3.2). Inner-shell energies are mainly determined by the strong nuclear potential, but to some extent they also depend on the electron density in outer shells, which, in turn, depends on the specific chemical state. Interesting cases are the transition and rare-earth elements with partly unfilled 3d and 4/ states, respectively. We discuss some studies of the occupancy of the 4/ valence band. 

I HE PERIODIC TABLE is the most significant tool that chemists use for organizing and remembering chemical facts. As we saw in Chapter 6, the periodic table arises from the periodic patterns in the electron configurations of the elements. Elements in the same column contain the same number of electrons in their outer-shell orbitals, or valence orbitals. For example, O [He]2s 2p ) and S ([NelSs Sp" ) are both members of group 6A the similarity in the occupancies of their valence s and p orbitals leads to similarities in their properties. 

Table 8.4. NAO (natural atomic orbital) electron occupancies In outer-shell orbitals of C and Ag...

Table 8.5. Changes in electron occupancies upon adsorption (AOc) in the outer-shell orbitals of Ag...

The outer-shell electrons of transition metals are separated into two bands. The filling of the narrow d-band corresponds to the occupation of the t/-shell, whereas a broad 5j 7-band is produced by the valence electrons of the free atom, rf-states are comparatively non-dispersive, the electrons being rather localized, whereas 5/ -states are more free-electron like. In real space this means that whereas rf-electrons to a large proportion reside around a certain atomic core or within a certain Wigner-Seitz cell sp-electrons penetrate the entire bulk [5]. Hence a comprehensive theoretical model of a metal surface has to account for delocalized electron states as well as for the discrete atomic character of the adsorbent. 

Fig. 2.2 The approxiinate position of the energy levels of the molecular orbitals in the homonuclear molecule X2 formed from the atomic levels in X. Consider N2 as an example. Since every nitrogen contributes 5 outer shell electrons, the lowest 5 MOs are doubly occupied. It is the occupation of the

The 3(BI)/3bi contributions of the different orbitals are computed through a systematic inspection of the Periodic Table, i.e. by recording the characteristic variation in the bonding indicator when a new outer orbital appears in the atomic electronic configuration. In this way, the s and p contributions are usually assessed. In the transition series , however, the further complication exists that the unsaturated shells across the series may give different contributions to the bonding, i.e. the contribution 9(BI)/3bi depends on the occupancy number Uv,i in the atomic configuration v. 

The most stable state of the lanthanides in their complexes is in all cases the M3+ ion, in which all outer electrons reside in the 4/ shell, in contrast to the uncharged atom M where, in addition to the 4/and 6s electrons, the 5d shell may be partly occupied. The M4+ ions also have all outer electrons in the 4/ shell, but there is partial 5d occupation in some M2+ ions. 

The Mendeleev table represents more than just a grid of information-it is a kind of compass in chemistry. Instead of having a wilderness where all the elements exhibit their unique physical and chemical properties as deus ex machirm, we obtain the understanding that the animals are in a zoo, and ate not unrelated, that there are some families, which follow from similar structures and occupancies of the outer electronic shells. Moreover, it became clear for Mendeleev that there were cages in the zoo waiting for animals yet to be discovered. The animals could have been described in detail before they were actually found by experimentation. This periodicity pertains not only to the chemical and physical properties of elements, but also to all parameters that appear in theory and are related to atoms, molecules, and crystals. 

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