Effective Nuclear charge and slater’s RULE

Effective Nuclear charge and Slater's RULE

In quantum Chemistry, Slater’s Rules Provide numerical values for the effective nuclear charge. The rules were devised semi-empirically by John C.Slater and published in 1930. Revised values of screening constants based on computations of atomic structure by the Hartree-Fock method were obtained by Enrico Clementi and co-workers in the 1960s. For each electron in an atom, Slater’s rule provide a value for the screening constant, denoted by s, which related the effective and actual nuclear charge as:

 Z_eff – Z – s

Here, Z is the Actual Nuclear Charge and Z_eff  is the Effective Nuclear Charge.

Firstly, the electron are arrange into a sequence of group in order of increasing principle quantum number n, and for equal of increasing azimuthal quantum number l, except that p-orbitals are kept together.

[1s] [2s, 2p] [3s,3p] [3d] [4s,4p] [4d] [4f] [5s, 5p] [5d] etc.

Each group is given a different sheilding constant which depend upon the number and type of electrons in those group preceding it. The shielding constant for each group is formed as the sum of following contributions;

1.     As amount of 0.35 from each other electron within the same group except for the [1s] group, where the other electron contributes onty 0.30.

2.     If the group is the [s,p] type, an amount of 0.85 from each electron with principal quantum number (n) one less and an amoun of 1.00 for each electron with aneven smallerproincipal quantum number.

3.     If the group is of the [d] or [f]. type, an amount of 1.00 for each electron inside it. This includes,(i) Electron with a smaller principal quantum number n and (ii) Electrons with an equal principal quantum number a smaller azimuthal quantum number(l).

An example is provided below in which iron atom is considered.The screening constant and subsequently the effective nuclear charge for each electron is deduced for iron atom. Iron has a nuclear charge 26 and electronic configuration , 1s², 2s², 2p⁶, 3s², 3p⁶, 3d⁶  4s². The calculation to find out screening constants are show here:

Note:  That the effective nuclear charge is calculation by subtracting the screening constant from the corresponding atomic number.