Calculating The Effective Nuclear Charge
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
- Z is the number of protons in the nucleus (atomic number), and
- S is the average number of electrons between the nucleus and the electron in question (the number of nonvalence electrons).
S can be found by the systematic application of various rule sets, the simplest of which is known as "Slater's rules" (named after John C. Slater). Douglas Hartree defined the effective Z of a Hartree-Fock orbital to be:
where
H is the mean radius of the orbital for hydrogen, and Z is the mean radius of the orbital for an electron configuration with nuclear charge Z.
Note: Zeff is also often written Z*.
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