Effective Atomic Number (EAN) Rule

The Effective Atomic Number (EAN) rule was an early attempt, proposed by Sidgwick, to explain why some coordination compounds are especially stable. The EAN of a complex's central metal ion is the TOTAL number of electrons effectively surrounding it once you add in every electron donated by its ligands, calculated as $EAN = Z - X + Y$, where Z is the metal's atomic number, X is the number of electrons the free metal atom lost in forming that particular ion (numerically, its oxidation state), and Y is the total number of electrons donated to the metal by all its ligands combined (each ordinary two-electron donor bond contributes 2 to Y). The rule is said to be OBEYED whenever the calculated EAN exactly equals the total electron count of the next noble gas in the periodic table -- 18 for Ar, 36 for Kr, 54 for Xe, or 86 for Rn -- meaning the metal ion has, in this electron-counting sense, effectively reached a noble-gas-like electron count. Worked through for [Co(NH3)6]3+: cobalt's atomic number Z = 27; the oxidation state (X) is +3; each of the six NH3 ligands donates one electron pair (2 electrons) so Y = 6 x 2 = 12; giving $EAN = 27-3+12 = 36$, matching krypton, so this complex obeys the EAN rule. Cr(CO)6 and Fe(CN)6 are both cited as further examples that o …