Slaters Screening Rules Size of Atoms

The core electrons screen the positive charge of the atomic nucleus in its action on the valence electrons. It is possible to define an effective charge of the nucleus, Z ff, which is smaller than the actual charge, Z. This effective nuclear charge, Z, substitutes Z in the time-independent SE for the electron  

We assume that a part of each occupied AO contributes to a screening factor S of the nucleus. According to electrostatics, charges inside the radius of the test charge contribute to S. If we know S, Z ff may be calculated as 

The orbitals obtained from Equation 2.23 decrease more slowly than the hydrogenlike ones. The number of nodes and the angular dependence remain the same. 

The screening factor S gets its contributions from the inner electronic shells and the shell where the electron belongs to. Nothing comes from shells with higher principal quantum number n than the orbital of the electron. According to Slater s rules, S should be calculated in the following ways  

Contribution to S from the same shell 0.35 from every other electron 

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