Molecular Geometry & Bonding
what the shape decides
Concept

Back-donation — where it appears

Density given from a filled metal orbital into an empty antibonding orbital on a ligand. It strengthens the metal–ligand bond and weakens the ligand's own, which is why a carbonyl's stretching frequency falls when it binds.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

Donation strengthens the C–O bond, back-donation weakens it. Two interactions computed as two-level problems: 0.39 of an electron donated out of the ligand's σ orbital, worth 0.06 on the C–O bond order, and 0.5 donated back into π*, worth -0.4. Beside them, six measured stretching frequencies: five isoelectronic species differing only in charge, and free CO.

Back-bonding is two interactions

A carbon monoxide molecule bound to a metal donates from an orbital that is slightly antibonding and accepts into one that is strongly antibonding, so the two halves of the bonding move its stretching frequency in opposite directions. Five isoelectronic complexes differing only in charge settle which wins — and one of them stretches above free CO.

applied · Electron count What orders the spectrochemical series, and what does not. Nine ligands' measured octahedral splittings, plotted against charge and against the π parameter that says whether the ligand donates or accepts π density. Charge puts 3 of 20 mixed-charge pairs in the order it predicts; the π parameter puts 35 of 35 in order.

The spectrochemical series is not electrostatics

Ligands can be put in order by how hard they split a d shell, and the order is highly reproducible. It is not the order of charge — three of twenty mixed-charge pairs come out the way a point-charge model predicts, which is worse than tossing a coin — and the two ligands at the strong end are electrically neutral.

wrong · Ligand field The metal's charge is a coordinate, and the count is not. The metal's charge in an octahedral d6 complex, against how much of each shared pair the ligand is given. Half each is Mulliken's rule and the whole to the ligand is the assumption an oxidation state makes; the answer runs over 2.06 electrons between them. The oxidation state itself is 0, which is off the end of the range, and the electron count is the same number at every point on it.

An integer nobody measured

The oxidation state of chromium in the hexacarbonyl is zero. Its charge, computed from the same wavefunction, is anywhere between −3.04 and −0.98 depending on how the shared electrons are divided — and the integer sits outside that whole range. The electron count, meanwhile, is eighteen at every point on it.

applied · Electron count What the second channel buys, and what it cannot. Five measured splittings against three models. Adding the π overlap takes the error from 1747 to 1402 cm⁻¹, and telling the model which ligand is an acceptor takes it to 961 — so the fact about occupation is worth more than twice the integral. The two halides are the pair that fixes which model is which, and no single one of the three gets both them and cyanide right.

The integral that cannot count electrons

Adding the π channel to a ligand-field splitting means one more overlap integral over the same two orbitals at the same distance. It removes a fifth of the error. Telling the model which ligand is a π acceptor — one word per ligand, quoted rather than computed — removes forty-five per cent, because an overlap cannot know whether the orbital it reaches is full or empty.

applied · Ligand field

Named alongside it

The objects these essays reach for when they reach for this one.

Ligand fieldPi acceptord orbitalsAngular overlapCoordination complexElectron countModel limitOverlap integralPi-donorSpectrochemical seriesAntibondingBond order

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