Slater's rules
In quantum chemistry, Slater's rules provide numerical values for the effective nuclear charge concept. In a many-electron atom, each electron is said to experience less than the actual nuclear charge owing to shielding or screening by the other electrons. For each electron in an atom, Slater's rules provide a value for the screening constant, denoted by s, S, or σ, which relates the effective and actual nuclear charges as
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 et al in the 1960s.
Firstly, the electrons are arranged into a sequence of groups in order of increasing principal quantum number n, and for equal n in order of increasing azimuthal quantum number l, except that s- and p- orbitals are kept together.
Each group is given a different shielding constant which depends upon the number and types of electrons in those groups preceding it.
The shielding constant for each group is formed as the sum of the following contributions:
In tabular form, the rules are summarized as:
An example provided in Slater's original paper is for the iron atom which has nuclear charge 26 and electronic configuration 1s22s22p63s23p63d64s2. The screening constant, and subsequently the shielded (or effective) nuclear charge for each electron is deduced as:
Note that the effective nuclear charge is calculated by subtracting the screening constant from the atomic number, 26.
The rules were developed by John C. Slater in an attempt to construct simple analytic expressions for the atomic orbital of any electron in an atom. Specifically, for each electron in an atom, Slater wished to determine shielding constants (s) and "effective" quantum numbers (n*) such that
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