EAN Rule & Applications

CHELigands & Stability

The Effective Atomic Number (EAN) rule, equivalent to the 18-electron rule, says many stable complexes (especially metal carbonyls) have a metal that attains the electron count of the next noble gas. The subtopic also covers biologically and industrially important complexes such as EDTA, haemoglobin and chlorophyll.

Effective Atomic Number

\text{EAN} = Z - (\text{oxidation state}) + 2\times(\text{coordination number})

Z

= atomic number of the metal; each

\sigma

-donor contributes a lone pair (2 electrons)

18-electron count

N = (\text{metal valence }d\text{-electrons}) + 2\times(\text{number of }\sigma\text{-donor ligands})

N = 18

signals special stability

Worked EAN values

[Fe(CO)_5]\!:\,26-0+10=36\qquad [Ni(CO)_4]\!:\,28-0+8=36

both reach the krypton count (36)

EAN $=$ (atomic number of the metal) $-$ (oxidation state) $+ 2 \times$ (number of ligands donating a lone pair, i.e. the coordination number). A stable complex usually has EAN equal to that of the nearest noble gas.
The equivalent 18-electron rule counts the metal valence $d$ -electrons plus 2 from each $\sigma$ -donor ligand; an 18-electron count signals stability.
$[Fe(CO)_5]$ : $Fe$ (26) $- 0 + 2\times5 = 36$ (Kr) $\rightarrow$ obeys EAN. $[Ni(CO)_4]$ : $Ni$ (28) $- 0 + 2\times4 = 36$ (Kr) $\rightarrow$ obeys EAN.
$[MnBr(CO)_5]$ : oxidation state of Mn $= +1$ ; EAN $= 25 - 1 + 2\times6 = 36$ (Kr), and the 18-electron count $= 7 + 1 + 5\times2 = 18$ (Mn 7, Br 1, five CO 2 each) $\rightarrow$ obeys the rule.
EDTA is a hexadentate chelating ligand (2 N + 4 O donors) forming very stable 1:1 complexes; used in complexometric (EDTA) titrations to estimate $Ca^{2+}$ and $Mg^{2+}$ (water hardness) and to soften water by sequestering these ions.
Biologically important complexes: haemoglobin (Fe(II) in a porphyrin, carries $O_2$ ); chlorophyll (Mg(II) in a porphyrin, drives photosynthesis); vitamin $B_{12}$ (Co in a corrin ring).
The EAN/18-electron rule works best for low-oxidation-state, $\pi$ -acceptor (carbonyl, nitrosyl, phosphine) complexes where back-bonding stabilises a filled valence shell.
Many stable complexes do NOT obey EAN — e.g. $[Fe(CN)_6]^{3-}$ has EAN 35, and many simple Werner complexes deviate; the rule is a useful guideline, not a law.
$Co_2(CO)_8$ and $Mn_2(CO)_{10}$ achieve 18 electrons per metal by forming a metal–metal bond (the M–M bond contributes one electron to each metal), illustrating how dinuclear carbonyls satisfy the rule.
$NO$ is a 3-electron donor when bonded linearly (counts as donating like $NO^+$ plus one extra electron), which must be remembered when applying the 18-electron count to nitrosyl complexes.
EDTA's high stability is a textbook chelate effect: one hexadentate ligand replacing six monodentate waters increases entropy, giving an exceptionally large formation constant.
In haemoglobin the Fe(II)–porphyrin reversibly binds $O_2$ ; CO binds far more strongly to the same site, blocking $O_2$ transport — the basis of carbon-monoxide poisoning.

Where the marks go

Forgetting to subtract the oxidation state in the EAN formula (e.g. computing EAN for $[MnBr(CO)_5]$ without the $-1$ for $Mn^{+1}$ ).
Multiplying by the number of ligands instead of the number of donor atoms (the coordination number) — chelating/polydentate ligands contribute more than one pair.
Assuming every stable complex must obey EAN — many ( $[Fe(CN)_6]^{3-}$ , most Werner complexes) do not; the rule is most reliable for carbonyls.
Counting $NO$ as a 2-electron donor in the 18-electron count when it is linear — it donates 3 electrons.
Mixing up the central metals: haemoglobin and chlorophyll are commonly swapped — haemoglobin is Fe, chlorophyll is Mg, vitamin $B_{12}$ is Co.

How the board asks it

Numericalthe ean formula for zero-oxidation-state carbonyls
Calculate the Effective Atomic Number (EAN) of the central metal in $[Fe(CO)_5]$ and in $[Ni(CO)_4]$ , and state whether each obeys the EAN rule. ( $Z$ of $Fe = 26$ , $Z$ of $Ni = 28$ )
Numericaloxidation-state subtraction in a mixed-ligand carbonyl
Find the Effective Atomic Number of manganese in $[MnBr(CO)_5]$ , clearly showing the oxidation state of $Mn$ used in your calculation. ( $Z$ of $Mn = 25$ )
Define / statestatement of the ean rule and its expression
State the EAN rule and write the expression used to calculate the Effective Atomic Number of the central metal atom in a complex.
Give reasonsexceptions to the ean rule
Account for the fact that $[Fe(CN)_6]^{3-}$ is a stable complex even though its central metal does not attain the Effective Atomic Number of the nearest noble gas.
Give reasonsmetal-metal bonding in dinuclear carbonyls
Explain how each manganese atom in $Mn_2(CO)_{10}$ attains an 18-electron (EAN) configuration, with reference to the role of the metal-metal bond.
Define / statebiologically important coordination compounds
Name the central metal ion present in haemoglobin, chlorophyll and vitamin $B_{12}$ , and state the biological role of each complex.

Practise this topic

PreviousAmbidentate Ligands & Chelate Effect NextIsomerism

Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.