Molecular Geometry & Bonding
what the shape decides
Concept

D d transition — where it appears

An excitation of one electron between two d orbitals split by a ligand field. It is weak in a centrosymmetric complex because parity forbids it, and it is behind most of the pale colours of transition metal salts.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

Where the d–d band falls, and where the eye is. Nine ligands' measured splittings as wavelengths, on a logarithmic scale, with the visible range shaded. Three fall inside it; the halides sit in the near infrared and carbon monoxide in the ultraviolet. The splitting decides where the band is and does not decide what is seen.

Where a d–d band falls

A splitting is an energy and an energy is a wavelength, so the ligand field fixes where a complex absorbs. Only three of nine common ligands put that band inside the visible range at all — and the most intensely coloured transition-metal compound in the cupboard has no d electrons to excite.

applied · Ligand field Dipole selection rules in Oh. For every pair of symmetry species, whether an electric dipole transition between them is allowed and along which polarisation. An entry is allowed exactly when the triple product of representations contains the totally symmetric one.

Why a d–d band is weak

In a centrosymmetric complex the transition between the two halves of a split d shell is forbidden — exactly, by parity, with no small quantity anywhere. What makes it visible at all is that the molecule is never quite centrosymmetric, and the computation says which vibrations do the work.

spectra · Representation 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 electrons repel each other less inside the complex. Seven chromium(III) complexes. Δ is the first band; B is solved from the second in closed form; β is B against the free ion's 918 cm⁻¹, which is measured on the gaseous ion. Every β is below one — the electrons in a complex repel each other less than the same electrons in the free ion, because they have more room. The two orderings are different: fluoride splits least and reduces the repulsion least, cyanide does both most, and the middle of the two series is not the same middle.

The electrons repel less inside the complex

Two measured bands determine two parameters in closed form, and one of them is the repulsion between the d electrons — which comes out below the free ion's value for every complex, by between two and forty-seven per cent. The ligands that split most are not the ligands that reduce the repulsion most, so a complex is characterised by two numbers rather than one.

applied · Ligand field

Named alongside it

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

Ligand fieldSpectrochemical seriesSplittingAbsorptiond orbitalsElectron correlationSelection rulesAngular overlapBack-donationCharge transferCoordination complexCovalent bonding

All concepts