Effective nuclear charge


The effective nuclear charge is the net positive charge experienced by an electron in a polyelectronic atom. The term "effective" is used because the shielding effect of negatively charged electrons prevents higher orbital electrons from experiencing the full nuclear charge of the nucleus due to the repelling effect of inner-layer electrons. The effective nuclear charge experienced by the electron is also called the core charge. It is possible to determine the strength of the nuclear charge by the oxidation number of the atom. Most of the physical and chemical properties of the elements can be explained on the basis of electronic configuration. Consider the behavior of ionization energies in the periodic table. It is known that the magnitude of ionization potential depends upon the following factors:
Size of atom
The nuclear charge
The screening effect of the inner shells
The extent to which the outermost electron penetrates into the charge cloud set up by the inner lying electron.

Calculations

In an atom with one electron, that electron experiences the full charge of the positive nucleus. In this case, the effective nuclear charge can be calculated from Coulomb's law.
However, in an atom with many electrons, the outer electrons are simultaneously attracted to the positive nucleus and repelled by the negatively charged electrons. The effective nuclear charge on such an electron is given by the following equation:
where
S can be found by the systematic application of various rule sets, the simplest of which is known as "Slater's rules". Douglas Hartree defined the effective Z of a Hartree–Fock orbital to be:
where

Values

Updated effective nuclear charge values were provided by Clementi et al. in 1963 and 1967. In their work, screening constants were optimized to produce effective nuclear charge values that agree with SCF calculations. Though useful as a predictive model, the resulting screening constants contain little chemical insight as a qualitative model of atomic structure.

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