Coordination Chemistry and Bonding Theories

Non-heme metalloproteins

Metalloproteins are classified by how the metal is held. Heme proteins contain an iron–protoporphyrin IX prosthetic group, as in hemoglobin, myoglobin and cytochrome P-450. Non-heme metalloproteins bind the metal directly to amino acid side chains or to inorganic sulfide, without a porphyrin ring. Hemocyanin, the oxygen carrier of many arthropods and molluscs, has a binuclear copper active site and contains no heme, so it is non-heme. Hemerythrin uses a non-heme diiron centre bound by carboxylate and histidine ligands, and carbonic anhydrase is a zinc enzyme, so both are non-heme. Carboxypeptidase is a zinc exopeptidase and is also non-heme. Iron–sulfur proteins contain inorganic sulfide in their clusters, and acid treatment releases that sulfide as H_2S. The number of H_2S equivalents equals the number of inorganic sulfide ions in the cluster. Rubredoxin has one iron bound to four cysteinyl thiolates and no inorganic sulfide, so it releases none. A 2Fe–2S ferredoxin releases two equivalents and a 4Fe–4S ferredoxin releases four.

Dioxygen carriers in heme and copper proteins

Heme and copper proteins bind O_2 in different forms, and the O–O bond order can be read from the resonance Raman stretching frequency. In oxy-hemoglobin the iron(II) centre binds O_2 end-on in a superoxo-like form, and the O–O stretch appears in the region near 1100 cm^{-1}. In oxy-hemocyanin, dioxygen is bridged side-on between two copper(II) centres as a peroxo ligand. Its O–O bond is weaker, so the stretch lies much lower, near 740 cm^{-1}. Myoglobin is a monomeric heme protein. Deoxy-Mb contains high-spin Fe(II), which lies out of the porphyrin plane, while oxy-Mb contains low-spin Fe(II). In oxy-Mb the O_2 is bound end-on, and its terminal oxygen is hydrogen-bonded to the NH group of a distal histidine. Hemoglobin is an allosteric tetramer with two properties that are tested often. The Bohr effect means that lowering the pH stabilizes the T state and lowers O_2 affinity, which is most noticeable at low oxygen partial pressure. Hemoglobin also shows positive cooperativity, so binding the first O_2 increases, rather than decreases, the affinity for the next O_2 molecules.

Metal centres in metalloenzymes

Each metalloenzyme uses one characteristic metal at its active site, so the correct pairing of metal and enzyme must be learned. Copper occurs in tyrosinase as a binuclear type-3 centre. Molybdenum occurs in nitrate reductase through the molybdenum cofactor. Cobalt is the central metal of cobalamin, the vitamin B_{12} coenzyme. Zinc is the catalytic Zn(II) of carboxypeptidase. Cytochrome P-450 is a heme enzyme, and its active-site metal is iron, not copper, zinc, cobalt or molybdenum. The proximal axial ligand of the P-450 heme iron is a cysteinate thiolate, whereas globins such as myoglobin use an imidazole nitrogen from histidine. Dioxygen is activated by reduction. One oxygen atom becomes a high-valent iron(IV)-oxo porphyrin radical cation, known as Compound I, which abstracts a hydrogen atom from a C–H bond. The other oxygen atom is reduced to water.

Crystal field stabilization energy

Crystal field stabilization energy (CFSE) is the net energy gained when d electrons occupy the split orbital sets, measured relative to the barycentre. In an octahedral field each electron in the t_{2g} set contributes -0.4\Delta_o and each electron in the e_g set contributes +0.6\Delta_o. The general form is CFSE = (-0.4\,n_{t_{2g}} + 0.6\,n_{e_g})\Delta_o, with an extra pairing-energy term for strong-field cases. For weak-field ligands such as water, the complexes are high-spin. High-spin d^5 ions such as Mn^{2+} and Fe^{3+} therefore have zero CFSE. High-spin d^4 (Mn^{3+}, t_{2g}^3e_g^1) gives -0.6\Delta_o, and high-spin d^6 (Fe^{2+}, t_{2g}^4e_g^2) gives -0.4\Delta_o. As a worked example, a d^3 ion such as Cr^{3+} places all three electrons in t_{2g}, so CFSE = 3(-0.4)\Delta_o = -1.2\Delta_o. If \Delta_o = 21600 cm^{-1}, then CFSE = -25920 cm^{-1}, and its magnitude is 25920 cm^{-1}.

18-electron rule and metal–metal bond order

The 18-electron rule states that stable d-block organometallic complexes have a total valence count of 18, found by adding the metal's valence electrons, the electrons donated by ligands, and one electron for each metal–metal bond. For example, in Mn_2(CO)_{10} each Mn(0) is d^7, the five CO ligands donate 10 electrons, and the Mn–Mn sigma bond adds one, giving 7 + 10 + 1 = 18. For a metal–metal bond, the bond order is (n_{\text{bonding}} - n_{\text{antibonding}})/2. The number of metal d electrons in the M_2 unit equals 2 \times (\text{group number}) - (\text{sum of oxidation states}), and these electrons fill the \sigma, \pi, \delta and \delta^* levels in order. An Mo_2 unit with 7 d electrons in \sigma^2\pi^4\delta^1 has bond order 3.5. A Cr_2 unit with 8 electrons in \sigma^2\pi^4\delta^2 has bond order 4. The same method gives a quadruple bond for [Re_2Cl_8]^{2-}, with 8 electrons in \sigma^2\pi^4\delta^2 and bond order 4, and a bond order of 3 for [Os_2Cl_8]^{2-}, which has \delta^{*2} electrons that reduce the order. Triple bonds are also found, as in W_2 amides with 6 electrons in \sigma^2\pi^4.

Tetrahedral vs square planar Ni(II) complexes

Ni(II) is a d^8 ion, and its geometry determines its magnetism and colour. Square planar d^8 complexes are diamagnetic, because the eight electrons fill the lower d orbitals and leave the d_{x^2-y^2} orbital empty, with a large splitting between the filled levels and that orbital. Tetrahedral d^8 complexes have a small splitting, so they are high-spin with two unpaired electrons and are paramagnetic. The same formula can therefore give isomers with different geometries. Bulky ligands such as triphenylphosphine favour the tetrahedral arrangement. Thus [NiBr_2(PPh_3)_2] can exist as a red, diamagnetic square planar form and as a green, paramagnetic tetrahedral form.

Spectrochemical series

The spectrochemical series ranks ligands by their ability to split the d orbitals. Among the common ligands, the order runs \text{F}^- < \text{H}_2\text{O} < \text{NH}_3 < \text{CN}^-, with CO at the strong end. Because \Delta_o depends on the metal, its oxidation state, and the ligand, comparisons are meaningful only when the metal and its oxidation state are the same. For Cr(III) complexes the series predicts \Delta_o in the order [\text{Cr(CN)}_6]^{3-} > [\text{Cr(H}_2\text{O)}_6]^{3+} > [\text{CrF}_6]^{3-}. Cyanide is a strong-field ligand, water is intermediate, and fluoride is a weak-field ligand. Remember that the series ranks ligand field strength and does not depend on the metal's identity.

Spin-only magnetic moment

The spin-only magnetic moment ignores orbital contributions and depends only on the number of unpaired electrons n, through \mu = \sqrt{n(n+2)} Bohr magnetons. Useful values are \mu = 1.73 BM for n = 1, 2.83 BM for n = 2, 3.87 BM for n = 3, 4.90 BM for n = 4 and 5.92 BM for n = 5. For a high-spin octahedral d^7 ion, such as Co(II) in the aqua complex, there are three unpaired electrons. Its spin-only moment is therefore \sqrt{15} \approx 3.9 BM. Orbital contributions can make the observed moment larger than the spin-only value, particularly in octahedral Co(II) complexes.

Biological Na+ and K+ distribution

Animal cells maintain a large difference in the concentrations of Na^+ and K^+ across the membrane. K^+ is concentrated inside the cell, at roughly 140 mM inside against 4 to 5 mM outside. Na^+ is concentrated outside, at roughly 145 mM outside against 10 to 15 mM inside. These gradients are maintained by the Na^+/K^+-ATPase, which uses ATP to pump three Na^+ ions out and two K^+ ions in per cycle. Thus [\text{K}^+]_{\text{in}} > [\text{K}^+]_{\text{out}} and [\text{Na}^+]_{\text{in}} < [\text{Na}^+]_{\text{out}}. The Na^+ gradient drives Na^+ influx through channels, which is the basis of the action potential.

Metal content in ore stoichiometry

To find the mass of ore needed to supply a given mass of metal, first calculate the molar mass of the ore formula, including the water of hydration. Then find the mass fraction of metal, which is (number of metal atoms × atomic mass) divided by the molar mass of the ore. The mass of ore required is the desired metal mass divided by this fraction. Count every oxygen atom, including those in the anion groups and those in the water of hydration. For example, in Fe_2O_3 the metal mass fraction is 112/160 = 0.70. To obtain 1 kg of iron, about 1/0.70 \approx 1.43 kg of Fe_2O_3 is needed.

Metal–metal quadruple bonding in Mo2 dimers

A quadruple metal–metal bond consists of one \sigma component, two \pi components and one \delta component. In a dimeric molybdenum(II) carboxylate such as Mo_2(O_2CR)_4, each Mo contributes d orbitals. Overlap of the d_{z^2} orbitals gives the \sigma bond, overlap of d_{xz} and d_{yz} gives two \pi bonds, and overlap of the in-plane d_{xy} orbitals gives the \delta bond. Each Mo(II) is d^4, so the unit has eight bonding electrons in \sigma^2\pi^4\delta^2. The bond therefore consists of 1 \sigma, 2 \pi and 1 \delta components. The \delta component is weak, which explains why such bonds are sensitive to ligand and geometry.

Qualitative tests for transition metal cations

Potassium hexacyanoferrate(II), K_4[Fe(CN)_6], is a group reagent for identifying several cations by the colour and solubility of the precipitate formed. Cu^{2+} gives a chocolate-brown precipitate of Cu_2[Fe(CN)_6], which is insoluble in dilute mineral acid. The reaction is 2\,\text{Cu}^{2+} + [\text{Fe(CN)}_6]^{4-} \rightarrow \text{Cu}_2[\text{Fe(CN)}_6]\downarrow. Fe^{3+} gives Prussian blue, which is deep blue, and Th^{4+} gives a white gelatinous precipitate. Uranyl gives a reddish-brown precipitate. Identification therefore depends on both the colour of the precipitate and its stability in dilute acid.