Effective nuclear charge rules

Based upon Slater s rules, we have found that the effective nuclear charge increases sharply between periods one and three and then stays at 2.20 for the rest of the alkali metal group. You may recall that the ionization energy for an element can be calculated by using the equation ... 

In these equations the p term is the product of the effective nuclear charge, derived by the application of Slater s rules (see Box 4.2), and the distance apart of the two nuclei, R, in atomic units, i.e. Ze(fRJ2aQ. The two functions are plotted against p in Figure 4.3, which shows that n overlap becomes more and more efficient as... 

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. 

The shielding rules of Clementi and Raimondi explicitly account for penetration of outer orbital electrons. They are thus more realistic than Slater s rules, at the expense, however, of more complex computation with a larger number of parameters. If accuracy greater than Uiat afforded by Slater s rules is necessary, it would appear tliat direct application Of the effective nuclear charges from the SCF wave functions is not only simple but also accurate. Such values arc listed in Table 22. Witli the accurate values of Table 22 available, the chief justification of "rules , whetlier Slater s or those of Clementi and Raimondi, is the insiglit tliey provide inlo tlie phenomenon of shielding. 

Slater " formulated a set of simple rules that serve as a rough guide to this effect. He defined the effective nuclear charge Z as a measure of the nuclear attraction for an electron. Z can be calculated from Z = Z - S, where Z is the nuclear charge and S is the shielding constant. The rules for determining S for a specific electron are as follows ... 

Ionization energies should depend on the effective nuclear charge that holds the electrons in the atom. Calculate Z (Slater s rules) for N, P, and As. Do their ionization energies seem to match these effective nuclear charges If not, what other factors influence the ionization energies ... 

A set of empirical rules (Slater s rules) for estimating the effective nuclear charges experienced by electrons in different atomic orbitals is described in Box 1.6. 

Effective nuclear charges, Z ff, experienced by electrons in different atomic orbitals may be estimated using Slater s rules. These rules are based on experimental data for electron promotion and ionization energies, and Z ff is determined from the equation ... 

Applying Slater s rules, the effective nuclear charge experienced by the 4 electron for the configuration 1 2 2/3/3/45 is ... 

Slater s rules have been used to estimate ionization energies, ionic radii and electronegativities. More accurate effective nuclear charges have been calculated by Clement and Raimondi by using self-consistent field (SCF) methods, and indicate much higher eff values for the d electrons. However, the simplicity of Slater s approach makes this an attractive method for back-of-the-envelope estimations of Zeff. 

Allred and Rochow chose as a measure of electronegativity of an atom the electrostatic force exerted by the effective nuclear charge eff (estimated from Slater s rules, see Box 1.6) on the valence electrons. The latter are assumed to reside at a distance from the nucleus equal to the covalent radius, r y, of the atom. Equation 1.36 gives the method of calculating values of the Allred-Rochow electronegativity, X... 

Next, using rules developed by Slater to estimate how much the various electrons in the ls22s22p6 configuration shield the outer electrons from the nuclear charge, we obtain 4.15 for the shielding parameter. The effective nuclear charges, Z, felt by the outer electrons are then, for Na+ with Z = 11 ... 

In the expression for the radial part of an STO (equation 3-18), A is a normalizing factor, n is the principal quantum number, aH is the Bohr radius (0.529 A) and p is a function of the effective nuclear charge for an electron in the orbital concerned. Slater proposed rules for adjusting the value of... 

---