- provides estimates of the Effective nuclear charges, Zeff, experienced by electrons in different atomic orbitals.
- based on experimental ionization energies
Zeff = Z - S
  S = screening (or shielding) constant
Values of S may be estimated as follows:
1. Write out the electronic configuration of the
element in the following order and groupings:
 
2. Electrons in any group higher  in this sequence than
the electron under consideration contribute
nothing to S.
3. Consider a particular electron in an ns or np orbital:
(i) Each of the other electrons in the (ns, np)
group contributes S = 0.35.
(ii) Each of the electrons in the (n - 1) shell
contributes S = 0.85.
(iii) Each of the electrons in the (n - 2) or lower 
shells
 
4. Consider a particular electron in an nd or nf  orbital:
(i) Each of the other electrons in the (nd, nf ) group
contributes S = 0.35.
(ii) Each of the electrons in a lower group than the
one being considered contributes S = 1.00.
Application of Slater’s rules
Confirm that the experimentally observed electronic
configuration of K, 1s2 2s2 2p6 3s2 3p6 4s1, is
energetically more stable than the configuration 1s2
2s2 2p6 3s2 3p6 3d1.
 
The effective nuclear charge experienced by the 4s
electron for the configuration 1s2 2s2 2p6 3s2 3p6 4s1 is:
Zeff = Z - S
= 2.20
For the configuration 1s2 2s2 2p6 3s2 3p6 3d1 is:
Zeff = Z - S
= 1.00
 
Electronic Configurations of Transition Metals, including Lanthanides and Actinides
Solid lines surrounding elements designate filled or half-filled d or f subshells.  
Dashed lines surrounding elements designate irregularities in orbital filling.  
 
Schematic Energy Levels for Transition Elements (TE)
a) Schematic interpretation of electronic configurations for  TE in terms of interorbital repulsion and trend in subshell energies.
b) A similar diagram for ions
The diagram shows that s electrons are removed before d electrons.
The electrons with highest n are always removed first in the formation of ions from the transition elements.
Ex. Sc+: 4s1 3d1 not 4s2
Ex. Cr: 4s1 3d5 not 4s2 3d4
 
Exercises:
1. Use Slater’s rules to estimate values of Zeff for (a) a 4s and (b) a 3d electron in a V atom.
2. Based on Zeff  values, which is the possible valence configuration of the ground state of a V+  ion, 3d3 4s1 or 3d2
4s2.
 
Ionization energies, IE
The first ionization energy, IE1, of an atom is the internal energy change at 0 K, !U(0 K), associated with the removal of the first
valence electron in the gas phase.
X(g) "  X+(g) + e-
The second ionization energy, IE2 is based on the equation
X+(g) "  X+2(g) + e-
Apparent repeating patterns and some features of IEs:
- the high values of IE1 associated with the noble gases
- the very low values of IE1 associated with the group 1 elements
 
- the discontinuity in values of IE1 on going from an element in group 15 to its neighbour in group 16
- the decrease in values of IE1 on going from an element in group 2 or 12 to its neighbour in group 3 or 13
- the rather similar values of IE1 for a given row of d-block  elements.
m i n o r  c h a n g e 
      m      a         j       o
 
The break in the trend at B  is attributed to occupation of new p orbital that has most of its electron density farther away from the nucleus than the other electrons.
At the fourth p electron, at O, a similar drop in ionization energy occurs.
The new (8th) electron shares an orbital with one of the previous 2p electrons.
The pairing energy, or repulsion between two electrons in the same region of space, reduces the ionization energy.
 
Filled and half-filled shells are often referred to as possessing a ‘special stability’.
The key is actually the exchange energy, K!
Consider two electrons in different orbitals.
The repulsion between the electrons if they have anti parallel spins is greater than if they have parallel spins
e.g. for a p2 configuration:
versus
 
 
Electron affinities
The first electron affinity (EA1) is minus  the internal energy change (EA = -!U) for the gain of an electron by a gaseous
atom.
Y(g) + e " Y-(g)
The second electron affinity of atom Y is defined for process
Y-(g) + e "  Y-2(g)
 
The attachment of an electron to an atom is usually exothermic.
 
The pattern of electron affinities with changing Z is similar to that of the IEs, but with smaller absolute numbers.
The noble gases have smallest EAs.
 
Covalent and Ionic Radii (Size)
As the nuclear charge increases, the electrons are pulled in toward the center of the atom, and the size of any particular  orbital (thus the size of atom) decreases.
On the other hand, as the nuclear charge increases, more electrons are added to the atom and their mutual repulsion keeps the outer orbitals large.
Opposing factors:
 
Anions are generally larger than cations with similar numbers of electrons (F -
and Na+ differ only in nuclear charge, but the radius of fluoride is 37% larger)
126
170
O2-
S2-
8
16
 
The radius decreases as nuclear  charge increases for ions with the same electronic structure, such as O2-, F-, Na+, and Mg+2, with a much larger change for  the cations.
Within a family, the ionic radius increases as Z increases because of the larger number of electrons in the ions and, for the same element, the radius decreases with increasing charge on the cation.
861012Mg2+
1161011Na+
119109F-
126108O2-
Crystal Radius and Total Number of Electrons
Crystal Radius and Ionic Charge
2075452Te2-
1843634Se2-
1701816S2-
126108O2-