18 Electron Rule Calculator

What the 18 electron rule says

The 18 electron rule is chemistry's version of the octet rule, aimed at transition metals. A main group atom like carbon is happiest with 8 electrons in its outer shell. A transition metal has room for 18, because its outer shell holds five d orbitals, three p orbitals and one s orbital, and each orbital holds 2 electrons. That is 9 orbitals times 2, which gives 18. A metal that reaches 18 has filled every bonding and nonbonding slot in its valence shell, the way a noble gas does.

The rule is a guide, not a law. Thousands of stable complexes hit 18 exactly, especially metal carbonyls and other organometallic compounds with strong accepting ligands. Plenty of others are stable above or below it, the way boron compounds are stable with 6 electrons. Chemists still use the count every day because it predicts behavior: a complex sitting below 18 is usually hungry for another ligand, while one above 18 will often kick a ligand off or carry unusual radical character. The LibreTexts chapter on the 18 electron rule calls the sub 18 case coordinatively unsaturated, which is the formal name for that hunger.

Counting electrons by hand is a two step job: work out how many electrons the metal itself brings, then add what each ligand donates. The calculator above does both steps from four or five inputs. The sections below walk through each input so the numbers on screen stop being a black box.

Counting the metal: groups, oxidation states and d electrons

A transition metal's contribution is called its d electron count, and there is a shortcut that avoids electron configurations entirely. Take the metal's group number in the periodic table, subtract the oxidation state, and the result is the number of d electrons. Iron sits in group 8, so Fe(0) brings 8, Fe(II) brings 6, and Fe(III) brings 5. A higher positive charge strips more electrons away, which is exactly what oxidation means.

Ferrocene shows the whole method. The formula Fe(C5H5)2 hides a split into charged pieces: each C5H5 ring is a Cp anion with a charge of minus 1, so two of them balance iron at plus 2. Iron in group 8 minus 2 gives 6 d electrons. Each Cp ring donates 6 electrons, two rings donate 12, and the total is 6 + 12 = 18. That perfect score is a large part of why ferrocene is famously unreactive and air stable.

Watch what oxidation state does to the answer. Take the same metal with different partners: nickel in group 10 with zero charge brings 10 electrons, and four CO ligands bring 8 more, so Ni(CO)4 counts 10 + 8 = 18. If nickel were somehow in the +2 state with four neutral CO ligands, the count would drop to 16, and such a species would be a cation with a different formula. The lesson is to fix the charges first, because the oxidation state is the input that moves the metal's contribution the most.

What each ligand brings to the count

Ligands donate electrons to the metal, and the donation depends on the ligand type, not on guesses. The table lists the donors that cover most textbook and lab complexes, counted the ionic way, where anionic ligands are treated as closed shell ions.

Three patterns make the table easy to remember. Neutral molecules with a lone pair, like CO or ammonia, donate 2. Anions that bind through one atom, like chloride or methyl, also donate 2, because their lone pair is what they bring. Rings and chains that grip the metal with several carbon atoms at once donate in bigger bites: 4 for an allyl anion, 6 for Cp or a flat arene ring. The hapticity number in front of eta counts the carbons taking part, so an eta5 Cp is a 5 carbon hug worth 6 electrons.

The calculator groups its inputs along these lines rather than by name: type the count of neutral 2 electron donors, anionic 2 electron donors, Cp rings, allyls, arene rings, and then use the extra electrons box for anything unusual, such as a bridging ligand or a metal metal bond, where the convention is 1 electron per bond for each metal.

Four famous counts, worked out

Classics of the organometallic shelf, run through the same arithmetic. Each one takes under a minute by hand and about five seconds in the calculator.

Nickel tetracarbonyl, Ni(CO)4. Nickel is in group 10 with no charge, so 10 d electrons. Four CO ligands at 2 each add 8. The total is 10 + 8 = 18, which is why this toxic liquid is nonetheless a stable, isolable compound.

Iron pentacarbonyl, Fe(CO)5. Iron in group 8 at oxidation state 0 brings 8. Five CO ligands add 10, and 8 + 10 = 18. Every simple mononuclear metal carbonyl that obeys the rule is a small counting puzzle: how many CO ligands does this metal need to reach 18?

Vaska's complex, IrCl(CO)(PPh3)2. The chloride anion pulls iridium to the +1 state, and iridium sits in group 9, so the metal brings 8 d electrons. Chloride, CO and two phosphines donate 2 each, for 8 ligand electrons. The total is 8 + 8 = 16. Two electrons short, and that vacancy is the property that made Vaska's complex famous: it binds oxygen and other small molecules at the open site.

Manganese carbonyl dimer, Mn2(CO)10. A single Mn(CO)5 unit counts 7 + 10 = 17, one electron short, which is an odd number and an unhappy one. Two such units join through a metal metal bond, and each manganese claims 1 electron from that bond, landing both at 18. This is the origin of the dimer, and it shows the rule working in reverse: the formula exists because of the count. The history of the rule at the University of Cincinnati traces how these carbonyls led to the rule in the first place.

When the rule bends

Treating 18 as a hard wall will mislead you about whole families of complexes. The best known exception is the square planar d8 group: palladium(II), platinum(II), rhodium(I) and iridium(I) complexes commonly sit at 16 electrons and are perfectly stable. Vaska's complex from the previous section is the running example. These metals leave one orbital nonbonding instead of filling it, and forcing a fifth ligand on them is usually harder, not easier.

Early transition metals bend the rule from the other side. Metals in groups 3 and 4, like titanium and zirconium, have few d electrons to begin with, and their complexes often count 12 to 16 electrons. Titanocene dichloride, Cp2TiCl2, makes the point in numbers: titanium(IV) sits in group 4, so it carries 0 d electrons, and the count is 0 + 12 + 4 = 16, with the 12 from the two Cp rings and the 4 from the two chlorides. It is a stable commercial catalyst precursor at 16 electrons, and group 3 and 4 chemistry is full of such low counts. The LibreTexts text notes that groups 3, 4 and 10 deviate from the rule most often.

Odd electron species are the third family. Cobaltocene, Cp2Co, counts 7 d electrons from Co(II) plus 12 from the rings, for 19 electrons. That one extra electron makes cobaltocene a strong reducing agent, eager to give the electron away, which is exactly how chemists use it. Seventeen electron radicals show the mirror image hunger. Finally, big metal clusters break the rule because their bonding is shared across many metal centers, so per metal counting stops being meaningful. A count far from 18 is not an error in your arithmetic; it is often the most interesting fact about the compound.

Reading the total: what each number tells you

A count is a starting hypothesis about a compound, not a verdict. The table sums up the readings that come up most often in coursework and in the lab, with one familiar example for each total.

Two habits keep the reading honest. First, check the geometry before you trust the exception: a 16 electron count means one thing in a square planar d8 complex and something else entirely in a tetrahedral one, where the metal may have no room for another ligand. Second, remember that the ligand set sets the ceiling. A metal surrounded by sigma donors that cannot accept electron density back will often stop short of 18 and stay perfectly happy there, while a metal loaded with CO or phosphines has every incentive to reach the full count.

The formula also does useful work before any experiment. If a proposed structure counts 20, one ligand too many is the likely story. If it counts 14 with an open coordination site, a ligand addition or an agostic interaction is worth checking. None of this replaces a real structure determination, but it narrows the guesses quickly, which is why the count survives in textbooks long after the theory behind it became more complicated.

Two counting methods, one answer

Textbooks teach two ways to count, and beginners often panic when the two books on their shelf appear to disagree. They never do, if both are done correctly. The ionic method, used throughout this page, pretends the complex fell apart into ions: ligands like hydride, chloride and Cp get their full negative charge, the metal takes the balancing positive charge, and the metal contributes its group number minus that charge. The neutral or covalent method instead pretends every ligand is a neutral radical fragment: hydride counts as neutral H worth 1 electron, chloride as neutral Cl worth 1, and the metal contributes its full group number.

Ferrocene is the example that makes the difference visible: the ionic method takes 2 electrons from iron and gives each ring 6, while the neutral method leaves iron at 8 and gives each ring 5. Two electrons moved from the metal to the ligands, and the total never budged. This is the general rule: whatever the method takes from the metal it hands to the ligands, so both methods must land on the same number. Pick the one your course or lab uses, stay consistent, and use the other as a cross check when a strange ligand makes you unsure. The calculator follows the ionic method because oxidation states are usually the first thing a chemist assigns anyway, but the total it prints is method independent.