Valence electrons effective nuclear charge

If core electrons completely shielded valence electrons from nuclear charge (i.e., if each core electron reduced nuclear charge by 1 unit) and if valence electrons did not shield one another from nuclear charge at aU, what would be the effective nuclear charge experienced by the valence electrons of each atom ... 

Electronegativity x is the relative attraction of an atom for the valence electrons in a covalent bond. It is proportional to the effective nuclear charge and inversely proportional to the covalent radius ... 

FIGURE 1.45 The variation ol the effective nuclear charge for the outermost valence electron with atomic number. Notice that the effective nuclear charge increases from left to right across a period but drops when the outer electrons occupy a new shell. (The effective nuclear charge is actually Zc,tfe, hut Zal itself is commonly referred to as the charge.)... 

Sodium is in Group 1 of the periodic table and can be expected to form a +1 ion. However, the valence electron is tightly held by the effective nuclear charge—... 

All the elements in a main group have in common a characteristic valence electron configuration. The electron configuration controls the valence of the element (the number of bonds that it can form) and affects its chemical and physical properties. Five atomic properties are principally responsible for the characteristic properties of each element atomic radius, ionization energy, electron affinity, electronegativity, and polarizability. All five properties are related to trends in the effective nuclear charge experienced by the valence electrons and their distance from the nucleus. 

Polarizability decreases from left to right in any row of the periodic table. As the effective nuclear charge (Zgff) increases, the nucleus holds the valence electrons more tightly. 

In this equation, Z is the effective nuclear charge, which takes into account the fact that an outer electron is screened from experiencing the effect of the actual nuclear charge by the electrons that are closer to the nucleus (see Section 2.4). In principle, the Allred-Rochow electronegativity scale is based on the electrostatic interaction between valence shell electrons and the nucleus. 

Each CGTO can be considered as an approximation to a single Slater-type orbital (STO) with effective nuclear charge f (zeta). The composition of the basis set can therefore be described in terms of the number of such effective zeta values (or STOs) for each electron. A double-zeta (DZ) basis includes twice as many effective STOs per electron as a single-zeta minimal basis (MB) set, a triple-zeta (TZ) basis three times as many, and so forth. A popular choice, of so-called split-valence type, is to describe core electrons with a minimal set and valence electrons with a more flexible DZ (or higher) set. 

Within a given series, the principal quantum number does not change. [Even in the long series in which the filling may be in the order ns, (n - l)d, up, the outermost electrons are always in the nth level.] The effective nuclear charge increases steadily, however, since electrons added to the valence shell shield each other very ineffectively. For the second series ... 

Covalent radii typically decrease from left to right across a period. The reason is the same as for atomic radii (Section 1.15) the increasing effective nuclear charge draws in the electrons and makes the atom more compact. Like atomic radii, covalent radii increase down a group because, in successive periods, the valence electrons occupy shells that are more distant from the nucleus and are better shielded by the inner core of electrons. Such fatter atoms cannot approach their neighbors very closely hence they form long, weak bonds. 

The same effects felt by the group 1A elements when a single electron is lost are felt by the group 2A elements when two electrons are lost. For example, loss of two valence-shell electrons from an Mg atom (Is2 2s2 2p6 3s2) gives the Mg2+ cation (Is2 2s2 2p6). The smaller valence shell of the Mg2+ cation and the increase in effective nuclear charge combine to cause a dramatic shrinkage. In the same way, a similar shrinkage is encountered whenever any of the metal atoms on the left-hand two-thirds of the periodic table is converted into a cation. 

The expansion that occurs when a group 7A atom gains an electron to yield an anion can t be accounted for by a change in the quantum number of the valence shell, because the added electron simply completes an already occupied p subshell [Ne] 3s2 3p5 for a Cl atom becomes [Ne] 3s2 3p6 for a Cl- anion, for example. Thus, the expansion is due entirely to the decrease in effective nuclear charge and the increase in electron-electron repulsions that occurs when an extra electron is added. 

Why does the octet rule work What factors determine whether an atom is likely to gain or to lose electrons Clearly, electrons are most likely to be lost if they are held loosely in the first place—that is, if they feel a relatively low effective nuclear charge, Zeff, and therefore have small ionization energies. Valence-shell electrons in the group 1A, 2A, and 3A metals, for example, are shielded from the nucleus by core electrons. They feel a low Zeff, and they are therefore lost relatively easily. Once the next lower noble gas configuration is reached, though, loss of an additional electron is much more difficult because it must come from an inner shell where it feels a high Zeff. 

In contrast, the valence d and f orbitals in heavy atoms are expanded and destabilized by the relativistic effects. This is because the contraction of the s orbitals increases the shielding effect, which gives rise to a smaller effective nuclear charge for the d and f electrons. This is known as the indirect relativistic orbital expansion and destabilization. In addition, if a filled d or f subshell lies just inside a valence orbital, that orbital will experience a larger effective nuclear charge which will lead to orbital contraction and stabilization. This is because the d and f orbitals have been expanded and their shielding effect accordingly lowered. 

---