Coordination Compounds: Bonding, Colour and Applications

Werner's theory correctly predicted the shapes, formulas, and isomers of coordination compounds, but it was entirely silent on three deeper questions. Why do only certain elements, mostly the transition metals, form coordination compounds so readily in the first place? Why do the bonds holding a ligand to a metal have such strongly directional character, producing precise octahedral or tetrahedral or square planar shapes rather than something looser? And why do coordination compounds so often display vivid, characteristic colours and unusual magnetic behaviour, properties that simple ionic or covalent bonding models don't obviously predict? Two theories, developed independently, answer these questions from two different starting points: Valence Bond Theory, which treats metal-ligand bonding as ordinary covalent bonds using specially hybridised orbitals, and Crystal Field Theory, which treats it as a purely electrostatic interaction between a metal ion and its surrounding ligands.

Valence Bond Theory proposes that a central metal atom or ion, under a ligand's influence, hybridises a combination of its (n-1)d, ns, and np orbitals, or its ns, np, and nd orbitals, to produce a set of equivalent orbitals matching the complex's actual geometry. A coordination number of 4 with sp3 hybridisation gives a tetrahedral shape; with dsp2 hybridisation it gives square planar instead. A coordination number of 6 with sp3d2 hybridisation gives octahedral, and so does d2sp3 hybridisation, the difference between the two being exactly which set of d orbitals gets used. Each of these hybrid orbitals then overlaps with a ligand orbital that donates an electron pair for the bond, meaning every single metal-ligand bond in this model is, structurally, an ordinary coordinate covalent bond.

Which specific d orbitals a metal uses in hybridisation has real, measurable consequences. In the diamagnetic complex [Co(NH3)6]3+, cobalt(III) has a 3d6 configuration, and six electron pairs from the six ammonia ligands occupy hybrid orbitals built using the inner 3d orbitals themselves, alongside 4s and 4p, giving d2sp3 hybridisation. Because this uses the metal's own inner d orbitals, [Co(NH3)6]3+ is called an inner orbital, or low spin, or spin-paired complex. Compare this to the paramagnetic [CoF6]3-, which instead uses the outer, empty 4d orbitals in its hybridisation, sp3d2, and is accordingly called an outer orbital, or high spin, or spin-free complex. Exactly the same metal, exactly the same oxidation state, two entirely different hybridisation schemes, purely because of which ligand is attached.

For metal ions with up to three d electrons, hybridisation is straightforward: two d orbitals are always empty and available. But once a metal ion has more than three d electrons, Hund's rule means a vacant pair of d orbitals is only available if some existing electrons pair up first, and whether that pairing actually happens depends entirely on the specific ligand. This produces real, measured anomalies. [Mn(CN)6]3- has a magnetic moment corresponding to two unpaired electrons, while [MnCl6]3-, the same metal ion, has four. [Fe(CN)6]3- shows just one unpaired electron, while [FeF6]3- shows five. [CoF6]3- is paramagnetic with four unpaired electrons, while [Co(C2O4)3]3- is completely diamagnetic. Valence Bond Theory explains every one of these pairs the same way: the strong-field ligand (CN-, oxalate) forces electron pairing and inner orbital hybridisation, while the weak-field ligand (Cl-, F-) does not, leaving the outer orbital hybridisation with more electrons unpaired.

Valence Bond Theory explains a great deal, the formation, structures, and rough magnetic behaviour of coordination compounds, reasonably well. But it has real limits. It rests on a number of assumptions rather than derivations. It cannot give a quantitative prediction of magnetic data, only a qualitative one. It has nothing at all to say about why coordination compounds are so often vividly coloured. It offers no quantitative handle on a complex's thermodynamic or kinetic stability. It cannot cleanly predict, in advance, whether a given four-coordinate complex will turn out tetrahedral or square planar. And it treats every strong-field or weak-field ligand as a special case to be fitted after the fact, rather than explaining, from first principles, why some ligands are strong and others weak. Crystal Field Theory was developed to answer exactly these remaining questions.

Crystal Field Theory takes an entirely different starting assumption: that the metal-ligand bond is purely ionic, arising only from electrostatic attraction, with ligands modelled as simple point charges (for anions) or point dipoles (for neutral molecules like NH3 or H2O). In an isolated metal atom or ion, all five d orbitals are degenerate, identical in energy. A perfectly spherical field of negative charge would keep them that way, but real ligands surround the metal from specific directions, not uniformly, and that asymmetry lifts the degeneracy. In an octahedral complex, the dx2-y2 and dz2 orbitals point directly along the same axes the six ligands approach from, so electrons in those orbitals experience more repulsion and are pushed up in energy, the eg set. The dxy, dyz, and dxz orbitals point between the ligands instead, experience less repulsion, and drop in energy, the t2g set. This splitting between the two sets is called the crystal field splitting energy, given the symbol Δo, and the eg set sits 3/5 Δo above, while t2g sits 2/5 Δo below, the original unsplit energy level.

How large Δo turns out to be depends on the specific ligand, and decades of absorption-spectrum measurements let chemists rank ligands into a spectrochemical series, running from weak field to strong field: I- < Br- < SCN- < Cl- < S2- < F- < OH- < C2O42- < H2O < NCS- < edta4- < NH3 < en < CN- < CO. For metal ions with a d4, d5, d6, or d7 configuration, this ranking decides everything about how electrons fill the split orbitals. If Δo is smaller than the pairing energy P, the required energy to force two electrons into one orbital, the next electron simply occupies the higher eg level rather than pairing up, giving a high spin complex with a weak field ligand. If Δo is larger than P, pairing up in the lower t2g level costs less energy than jumping to eg, giving a low spin complex with a strong field ligand instead. The entire earlier puzzle, why [Mn(CN)6]3- and [MnCl6]3- behave so differently, comes down to exactly this comparison: CN- sits at the strong end of the spectrochemical series and forces pairing, while Cl- sits at the weak end and doesn't.

Crystal field splitting doesn't just explain magnetism, it explains colour too. White light passing through a coloured complex has part of its visible spectrum absorbed, and the colour that reaches your eye is the complementary colour to whatever was absorbed; a complex that absorbs green light appears red. Take [Ti(H2O)6]3+, a violet octahedral complex where titanium's single d electron (Ti3+ is d1) sits in the lower t2g level in the ground state. Absorbing a photon in the blue-green region of the spectrum provides exactly enough energy to excite that electron from t2g up to the empty eg level, and the light that isn't absorbed reaches your eye as violet. Crucially, this only works because ligands are present to split the d orbitals in the first place: heat water off [Ti(H2O)6]Cl3 and the resulting anhydrous compound, with no ligands left to split anything, turns completely colourless. The same logic explains why anhydrous CuSO4 is white while CuSO4.5H2O is blue, and gives ruby its red and emerald its green, both really just Cr3+ ions sitting in a slightly different crystal environment, absorbing slightly different wavelengths as a result.

Homoleptic metal carbonyls, compounds where every ligand is carbon monoxide, form well-defined, predictable shapes: tetracarbonylnickel(0) is tetrahedral, pentacarbonyliron(0) is trigonal bipyramidal, hexacarbonylchromium(0) is octahedral. The metal-carbon bond inside them has a genuinely unusual, cooperative character. A sigma bond forms first, an ordinary donation of carbon monoxide's own lone pair into an empty orbital on the metal. But a second, pi-type bond forms alongside it, running the opposite direction: a filled d orbital on the metal donates a pair of electrons into carbon monoxide's own empty antibonding pi* orbital. Each of these two bonds reinforces the other, more sigma donation from CO makes the metal more willing to donate pi electrons back, and more pi back-donation makes CO an even better sigma donor in turn, a mutually strengthening arrangement called synergic bonding.

Coordination compounds turn up doing real, practical work across an enormous range of fields. Chlorophyll is a coordination compound of magnesium; haemoglobin, the oxygen-carrying pigment in blood, is one of iron; vitamin B12 is one of cobalt. EDTA, a hexadentate chelating ligand, is used to titrate and measure water hardness by binding the calcium and magnesium ions responsible for it, and the very same chelating ability is used medically to treat lead poisoning, by binding and removing toxic lead ions from the body. Gold and silver are extracted from ore as cyanide complexes, [Au(CN)2]- and [Ag(CN)2]-, then displaced back to pure metal using zinc, and impure nickel is purified by converting it to volatile [Ni(CO)4], which decomposes cleanly back to pure metal on heating. Wilkinson's catalyst, a rhodium complex, hydrogenates alkenes industrially. Photographic film is fixed by dissolving away undeveloped silver bromide as a silver-thiosulphate complex. And certain platinum coordination compounds, cisplatin among them, are used directly as cancer chemotherapy drugs, effectively inhibiting tumour growth.