Slater's rules
/ SLAY-터즈 (SLAY-terz) /
If effective nuclear charge is the idea that an electron feels less than the full nuclear pull, Slater's rules are the simple arithmetic recipe for actually putting a number on it. Devised by John Slater in 1930, they let you estimate the screening constant S — how much the other electrons shield a chosen one — using nothing more than the electron configuration and a short list of point values.
The recipe, in plain terms: group the electrons into bins like (1s), (2s,2p), (3s,3p), (3d), (4s,4p) and so on. To find the shielding S felt by one electron, add up contributions: electrons in shells further out count 0 (they do not shield inward). Electrons in the same group contribute 0.35 each (except the 1s group, where the other 1s electron counts 0.30). For an s or p electron, electrons in the shell just inside (n-1) contribute 0.85 each, and electrons two or more shells inside count a full 1.00. For a d or f electron, every electron in any inner group counts a full 1.00. Add the pieces to get S, then Zeff = Z - S.
Slater's rules are a teaching and estimating tool, not a precise theory. They give surprisingly serviceable values for atomic size, ionization-energy trends, and the relative penetration that puts 4s below 3d — and they make the abstract idea of shielding concrete and calculable. But the coefficients (0.35, 0.85, 1.00) are empirical fudge factors fitted to data, the rules ignore the finer structure within a shell, and modern computation does far better. Treat a Slater Zeff as a back-of-envelope estimate that explains a trend, never as the true charge on an electron.
For a 3s/3p electron in chlorine (Z=17): same-shell electrons 6 x 0.35 = 2.10, the (2s,2p) shell 8 x 0.85 = 6.80, the 1s shell 2 x 1.00 = 2.00; S = 10.90, so Zeff = 17 - 10.90 = 6.10.
A pencil-and-paper Zeff for chlorine's valence electron.
The 0.85 and 1.00 coefficients are empirical, fitted to match measured energies — they are not derived from first principles. Slater's rules are a rule of thumb, and they are noticeably rough for d and f electrons.