Slater Type Orbitals (STO) are an approximation and
do not represent the realistic orbitals. This
oversimplified model is found according to the semi-empirical results.
In the STO, the nuclear charge Z and the principal quantum number n are
replaced by the effective nuclear charge Z*, and the
effective principal quantum number n* respectively;
in order to fit the two following formula for the radial function
and energy of any electron in any atom:
R(r) = Nr rn* - 1
exp {- (Z*/n*) r}
Nr is the normalization constant for different orbitals.
E = - (Z*/n*)2 (13.6 eV)
R(r) = Nr rn*-1
exp {- (Z*/n*) r}
Nr is the normalization constant for different orbitals
E = - (Z*/n*)2 (13.6 eV)
Here are the Slater's rules to calculate an approximate value
for the effective nuclear charge "felt" by an electron in a
particular orbital of an atom.
1 - Write the electronic configuration for the atom using
the following grouping, called Slater electron configuration:
2 - Any electron to the right of the considered electron
of interest do not contribute to shielding,
3 - All other electrons in the same group of the considered electron
shield by 0.35 nuclear charge units each; except for 1s, the screening
is reduced to 0.30,
4 - If the considered electron is an s or p electron in the shell of
principal quantum number n, all electrons with one less value n-1
shield by 0.85 units of nuclear charge each; and all electrons with two
less values n-2 shield by 1.00 units. The n-3, n-4, ... shield by
1.00 units each as well.
5 - If the considered electron is an d or f electron: all electrons
to the left shield by 1.00 units of nuclear charge each.
6 - Sum all the shielding amounts for each group. To obtain the
effective charge for each group, subtract from the nuclear
charge value the corresponding shielding.
7 - For larger principal quantum numbers, n is corrected as
follows:
n = 1, 2, 3, 4, 5, 6
n* = 1, 2, 3, 3.7, 4.0, 4.2
Fundamentals of 