A More Detailed Explanation of Trends Using Slater's Rules

First of all, there a few terms which must be defined and explained:

Shielding - An electron in a many electron atom experiences repulsion from all the other electrons present. The repulsion the electron experiences at a distance r from the nucleus can be modelled by a point negative charge on the nucleus, with the charge magnitude equal to the charge of electrons within a sphere of radius r. The effect of the point negative charge is to lower the full charge of the nucleus from Z to Zeff. It is said that the electron experiences a shielded nuclear charge.

Penetration - Due to their wavefunctions, an electron in an s orbital is more likely to be found close to the nucleus than an electron in a p orbital. More of the s electron is distributed close to the nucleus. It is said that the s electron penetrates closer to the nucleus. An electron which is closer to the nucleus experiences a stronger attraction than one which is further away. This is because it experiences less shielding than an electron which is further away and therefore experiences a larger Zeff.

Effective nuclear charge - This is simply a way of expressing the net outcome of the nuclear attraction and electronic repulsions. The effective nuclear charge can be calculated using the following equation: Zeff = Z - S
S is different for electrons in different orbitals, due to shielding and penetration, and can be calculated for an individual electron using slater's rules.

Slater's Rules - The calculation of S

First place the electrons into groups as follows: [1s] [2s2p] [3s3p] [3d] [4s4p] [4d] [4f] [5s5p] [5d] [5f], etc, then use the rules underneath to calculate S.

  1. Electrons to the right of an [nsnp] group do not contribute to shielding.
  2. Every other electron within an [nsnp] group contributes 0.35 towards S.
  3. Electrons in a [1s] group contribute only 0.3 to S.
  4. Every electron in a group immediately to the left contributes 0.85 towards S.
  5. Every electron 2 groups or more to the left contributes 1.0 to S.
  6. For electrons in [nd] and [nf] groups rules (1) and (2) apply, but all electrons to the left contribute 1.0 to S.


Explaining Trends

For Carbon Z=6, so now we need to calculate S.
The electron arrangment of Carbon is 1s22s22p2.
So using slater's rules, S = 3×0.35 + 2×0.85 = 2.75
Therefore Z = Zeff - S = 6 - 2.75 = 3.25

For Nitrogen Z=7.
The electron arrangement of Nitrogen is 1s22s22p3.
So using slater's rules, S = 4×0.35 + 2×0.85 = 3.1
Therefore Z = Zeff - S = 7 - 3.1 = 3.9

The electron arrangement of Oxygen is 1s22s22p4.
So using slater's rules, S = 5×0.35 + 2×0.85 = 3.45

The electron arrangement of Sulphur is 1s22s22p63s23p4.
So using slater's rules, S = 5×0.35 + 8×0.85 + 2×1.0 = 10.55

Move on to the next page: Electronegativity in molecules

Author: Alex Warren (document modification date - 10 May 2003)

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