Chapter 23 The d-Block Elements

Electronic Structure and Reactivity of the Transition Metals

The valence electron configurations of the first-row transition metals are given in Table 23.1 "Valence Electron Configurations of the First-Row Transition Metals". As we go across the row from left to right, electrons are added to the 3d subshell to neutralize the increase in the positive charge of the nucleus as the atomic number increases. With two important exceptions, the 3d subshell is filled as expected based on the aufbau principle and Hund’s rule. Unexpectedly, however, chromium has a 4s¹3d⁵ electron configuration rather than the 4s²3d⁴ configuration predicted by the aufbau principle, and copper is 4s¹3d¹⁰ rather than 4s²3d⁹. In Chapter 7 "The Periodic Table and Periodic Trends", we attributed these anomalies to the extra stability associated with half-filled subshells. Because the ns and (n − 1)d subshells in these elements are similar in energy, even relatively small effects are enough to produce apparently anomalous electron configurations.

In the second-row transition metals, electron–electron repulsions within the 4d subshell cause additional irregularities in electron configurations that are not easily predicted. For example, Nb and Tc, with atomic numbers 41 and 43, both have a half-filled 5s subshell, with 5s¹4d⁴ and 5s¹4d⁶ valence electron configurations, respectively. Further complications occur among the third-row transition metals, in which the 4f, 5d, and 6s orbitals are extremely close in energy. Although La has a 6s²5d¹ valence electron configuration, the valence electron configuration of the next element—Ce—is 6s²5d⁰4f². From this point through element 71, added electrons enter the 4f subshell, giving rise to the 14 elements known as the lanthanides. After the 4f subshell is filled, the 5d subshell is populated, producing the third row of the transition metals. Next comes the seventh period, where the actinides have three subshells (7s, 6d, and 5f) that are so similar in energy that their electron configurations are even more unpredictable.

As we saw in the s-block and p-block elements, the size of neutral atoms of the d-block elements gradually decreases from left to right across a row, due to an increase in the effective nuclear charge (Z_eff) with increasing atomic number. In addition, the atomic radius increases down a group, just as it does in the s and p blocks. Because of the lanthanide contraction, however, the increase in size between the 3d and 4d metals is much greater than between the 4d and 5d metals (Figure 23.1 "The Metallic Radii of the First-, Second-, and Third-Row Transition Metals"). (For more information on the lanthanides, see Chapter 7 "The Periodic Table and Periodic Trends", Section 7.3 "Energetics of Ion Formation".) The effects of the lanthanide contraction are also observed in ionic radii, which explains why, for example, there is only a slight increase in radius from Mo³⁺ to W³⁺.

Figure 23.1 The Metallic Radii of the First-, Second-, and Third-Row Transition Metals

Because of the lanthanide contraction, the second- and third-row transition metals are very similar in size.

As you learned in Chapter 7 "The Periodic Table and Periodic Trends", electrons in (n − 1)d and (n − 2)f subshells are only moderately effective at shielding the nuclear charge; as a result, the effective nuclear charge experienced by valence electrons in the d-block and f-block elements does not change greatly as the nuclear charge increases across a row. Consequently, the ionization energies of these elements increase very slowly across a given row (Figure 7.10 "A Plot of Periodic Variation of First Ionization Energy with Atomic Number for the First Six Rows of the Periodic Table"). In addition, as we go from the top left to the bottom right corner of the d block, electronegativities generally increase, densities and electrical and thermal conductivities increase, and enthalpies of hydration of the metal cations decrease in magnitude, as summarized in Figure 23.2 "Some Trends in Properties of the Transition Metals". Consistent with this trend, the transition metals become steadily less reactive and more “noble” in character from left to right across a row. The relatively high ionization energies and electronegativities and relatively low enthalpies of hydration are all major factors in the noble character of metals such as Pt and Au.

Figure 23.2 Some Trends in Properties of the Transition Metals

The electronegativity of the elements increases, and the hydration energies of the metal cations decrease in magnitude from left to right and from top to bottom of the d block. As a result, the metals in the lower right corner of the d block are so unreactive that they are often called the “noble metals.”

Trends in Transition Metal Oxidation States

The similarity in ionization energies and the relatively small increase in successive ionization energies lead to the formation of metal ions with the same charge for many of the transition metals. This in turn results in extensive horizontal similarities in chemistry, which are most noticeable for the first-row transition metals and for the lanthanides and actinides. Thus all the first-row transition metals except Sc form stable compounds that contain the 2+ ion, and, due to the small difference between the second and third ionization energies for these elements, all except Zn also form stable compounds that contain the 3+ ion. The relatively small increase in successive ionization energies causes most of the transition metals to exhibit multiple oxidation states separated by a single electron. Manganese, for example, forms compounds in every oxidation state between −3 and +7. Because of the slow but steady increase in ionization potentials across a row, high oxidation states become progressively less stable for the elements on the right side of the d block. The occurrence of multiple oxidation states separated by a single electron causes many, if not most, compounds of the transition metals to be paramagnetic, with one to five unpaired electrons. This behavior is in sharp contrast to that of the p-block elements, where the occurrence of two oxidation states separated by two electrons is common, which makes virtually all compounds of the p-block elements diamagnetic.

The electronegativities of the first-row transition metals increase smoothly from Sc (χ = 1.4) to Cu (χ = 1.9). Thus Sc is a rather active metal, whereas Cu is much less reactive. The steady increase in electronegativity is also reflected in the standard reduction potentials: thus E° for the reaction M²⁺(aq) + 2e⁻ → M⁰(s) becomes progressively less negative from Ti (E° = −1.63 V) to Cu (E° = +0.34 V). Exceptions to the overall trends are rather common, however, and in many cases, they are attributable to the stability associated with filled and half-filled subshells. For example, the 4s²3d¹⁰ electron configuration of zinc results in its strong tendency to form the stable Zn²⁺ ion, with a 3d¹⁰ electron configuration, whereas Cu⁺, which also has a 3d¹⁰ electron configuration, is the only stable monocation formed by a first-row transition metal. Similarly, with a half-filled subshell, Mn²⁺ (3d⁵) is much more difficult to oxidize than Fe²⁺ (3d⁶). The chemistry of manganese is therefore primarily that of the Mn²⁺ ion, whereas both the Fe²⁺ and Fe³⁺ ions are important in the chemistry of iron.

The transition metals form cations by the initial loss of the ns electrons of the metal, even though the ns orbital is lower in energy than the (n − 1)d subshell in the neutral atoms. This apparent contradiction is due to the small difference in energy between the ns and (n − 1)d orbitals, together with screening effects. The loss of one or more electrons reverses the relative energies of the ns and (n − 1)d subshells, making the latter lower in energy. Consequently, all transition-metal cations possess dⁿ valence electron configurations, as shown in Table 23.2 for the 2+ ions of the first-row transition metals.

The most common oxidation states of the first-row transition metals are shown in Table 23.3 "Common Oxidation States of the First-Row Transition Metals*". The second- and third-row transition metals behave similarly but with three important differences:

1. The maximum oxidation states observed for the second- and third-row transition metals in groups 3–8 increase from +3 for Y and La to +8 for Ru and Os, corresponding to the formal loss of all ns and (n − 1)d valence electrons. As we go farther to the right, the maximum oxidation state decreases steadily, reaching +2 for the elements of group 12 (Zn, Cd, and Hg), which corresponds to a filled (n − 1)d subshell.
2. Within a group, higher oxidation states become more stable down the group. For example, the chromate ion ([CrO₄]²⁻) is a powerful oxidant, whereas the tungstate ion ([WO₄]²⁻) is extremely stable and has essentially no tendency to act as an oxidant.
3. Cations of the second- and third-row transition metals in lower oxidation states (+2 and +3) are much more easily oxidized than the corresponding ions of the first-row transition metals. For example, the most stable compounds of chromium are those of Cr(III), but the corresponding Mo(III) and W(III) compounds are highly reactive. In fact, they are often pyrophoric, bursting into flames on contact with atmospheric oxygen. As we shall see, the heavier elements in each group form stable compounds in higher oxidation states that have no analogues with the lightest member of the group.

Binary transition-metal compounds, such as the oxides and sulfides, are usually written with idealized stoichiometries, such as FeO or FeS, but these compounds are usually cation deficient and almost never contain a 1:1 cation:anion ratio. Thus a substance such as ferrous oxide is actually a nonstoichiometric compound with a range of compositions.

The acid–base character of transition-metal oxides depends strongly on the oxidation state of the metal and its ionic radius. Oxides of metals in lower oxidation states (less than or equal to +3) have significant ionic character and tend to be basic. Conversely, oxides of metals in higher oxidation states are more covalent and tend to be acidic, often dissolving in strong base to form oxoanions.

Groups 3, 4, and 5

Group 4 (Ti, Zr, and Hf)

Because the elements of group 4 have a high affinity for oxygen, all three metals occur naturally as oxide ores that contain the metal in the +4 oxidation state resulting from losing all four ns²(n − 1)d² valence electrons. They are isolated by initial conversion to the tetrachlorides, as shown for Ti:

Equation 23.2

2FeTiO₃(s) + 6C(s) + 7Cl₂(g) → 2TiCl₄(g) + 2FeCl₃(g) + 6CO(g)

followed by reduction of the tetrachlorides with an active metal such as Mg.

Note the Pattern

The chemistry of the group 4 metals is dominated by the +4 oxidation state. Only Ti has an extensive chemistry in lower oxidation states.

In contrast to the elements of group 3, the group 4 elements have important applications. Titanium (melting point = 1668°C) is often used as a replacement for aluminum (melting point = 660°C) in applications that require high temperatures or corrosion resistance. For example, friction with the air heats the skin of supersonic aircraft operating above Mach 2.2 to temperatures near the melting point of aluminum; consequently, titanium is used instead of aluminum in many aerospace applications. The corrosion resistance of titanium is increasingly exploited in architectural applications, as shown in the chapter-opening photo. Metallic zirconium is used in UO₂-containing fuel rods in nuclear reactors, while hafnium is used in the control rods that modulate the output of high-power nuclear reactors, such as those in nuclear submarines.

Consistent with the periodic trends shown in Figure 23.2 "Some Trends in Properties of the Transition Metals", the group 4 metals become denser, higher melting, and more electropositive down the column (Table 23.4 "Some Properties of the Elements of Groups 3, 4, and 5"). Unexpectedly, however, the atomic radius of Hf is slightly smaller than that of Zr due to the lanthanide contraction. Because of their ns²(n − 1)d² valence electron configurations, the +4 oxidation state is by far the most important for all three metals. Only titanium exhibits a significant chemistry in the +2 and +3 oxidation states, although compounds of Ti²⁺ are usually powerful reductants. In fact, the Ti²⁺(aq) ion is such a strong reductant that it rapidly reduces water to form hydrogen gas.

Reaction of the group 4 metals with excess halogen forms the corresponding tetrahalides (MX₄), although titanium, the lightest element in the group, also forms dihalides and trihalides (X is not F). The covalent character of the titanium halides increases as the oxidation state of the metal increases because of increasing polarization of the anions by the cation as its charge-to-radius ratio increases. Thus TiCl₂ is an ionic salt, whereas TiCl₄ is a volatile liquid that contains tetrahedral molecules. All three metals react with excess oxygen or the heavier chalcogens (Y) to form the corresponding dioxides (MO₂) and dichalcogenides (MY₂). Industrially, TiO₂, which is used as a white pigment in paints, is prepared by reacting TiCl₄ with oxygen at high temperatures:

Equation 23.3

TiCl₄(g) + O₂(g) → TiO₂(s) + 2Cl₂(g)

The group 4 dichalcogenides have unusual layered structures with no M–Y bonds holding adjacent sheets together, which makes them similar in some ways to graphite (Figure 23.3 "The Layered Structure of TiS"). The group 4 metals also react with hydrogen, nitrogen, carbon, and boron to form hydrides (such as TiH₂), nitrides (such as TiN), carbides (such as TiC), and borides (such as TiB₂), all of which are hard, high-melting solids. Many of these binary compounds are nonstoichiometric and exhibit metallic conductivity.

Figure 23.3 The Layered Structure of TiS₂

Each titanium atom is surrounded by an octahedral arrangement of six sulfur atoms that are shared to form extended layers of atoms. Because the layers are held together by only van der Waals forces between adjacent sulfur atoms, rather than covalent bonds, the layers slide past one another relatively easily when a mechanical stress is applied.

Group 5 (V, Nb, and Ta)

Like the group 4 elements, all group 5 metals are normally found in nature as oxide ores that contain the metals in their highest oxidation state (+5). Because of the lanthanide contraction, the chemistry of Nb and Ta is so similar that these elements are usually found in the same ores.

Three-fourths of the vanadium produced annually is used in the production of steel alloys for springs and high-speed cutting tools. Adding a small amount of vanadium to steel results in the formation of small grains of V₄C₃, which greatly increase the strength and resilience of the metal, especially at high temperatures. The other major use of vanadium is as V₂O₅, an important catalyst for the industrial conversion of SO₂ to SO₃ in the contact process for the production of sulfuric acid. (For more information on sulfuric acid production, see Chapter 2 "Molecules, Ions, and Chemical Formulas", Section 2.6 "Industrially Important Chemicals".) In contrast, Nb and Ta have only limited applications, and they are therefore produced in relatively small amounts. Although niobium is used as an additive in certain stainless steels, its primary application is in superconducting wires such as Nb₃Zr and Nb₃Ge, which are used in superconducting magnets for the magnetic resonance imaging of soft tissues. Because tantalum is highly resistant to corrosion, it is used as a liner for chemical reactors, in missile parts, and as a biologically compatible material in screws and pins for repairing fractured bones.

Note the Pattern

The chemistry of the two heaviest group 5 metals (Nb and Ta) is dominated by the +5 oxidation state. The chemistry of the lightest element (V) is dominated by lower oxidation states, especially +4.

As indicated in Table 23.4 "Some Properties of the Elements of Groups 3, 4, and 5", the trends in properties of the group 5 metals are similar to those of group 4. Only vanadium, the lightest element, has any tendency to form compounds in oxidation states lower than +5. For example, vanadium is the only element in the group that forms stable halides in the lowest oxidation state (+2). All three metals react with excess oxygen, however, to produce the corresponding oxides in the +5 oxidation state (M₂O₅), in which polarization of the oxide ions by the high-oxidation-state metal is so extensive that the compounds are primarily covalent in character. Vanadium–oxygen species provide a classic example of the effect of increasing metal oxidation state on the protonation state of a coordinated water molecule: vanadium(II) in water exists as the violet hydrated ion [V(H₂O)₆]²⁺; the blue-green [V(H₂O)₆]³⁺ ion is acidic, dissociating to form small amounts of the [V(H₂O)₅(OH)]²⁺ ion and a proton; and in water, vanadium(IV) forms the blue vanadyl ion [(H₂O)₄VO]²⁺, which contains a formal V=O bond (Figure 23.4 "Aqueous Solutions of Vanadium Ions in Oxidation States of +2 to +5"). Consistent with its covalent character, V₂O₅ is acidic, dissolving in base to give the vanadate ion ([VO₄]³⁻), whereas both Nb₂O₅ and Ta₂O₅ are comparatively inert. Oxides of these metals in lower oxidation states tend to be nonstoichiometric.

Figure 23.4 Aqueous Solutions of Vanadium Ions in Oxidation States of +2 to +5

Because vanadium ions with different oxidation states have different numbers of d electrons, aqueous solutions of the ions have different colors: in acid V(V) forms the pale yellow [VO₂]⁺ ion; V(IV) is the blue vanadyl ion [VO]²⁺; and V(III) and V(II) exist as the hydrated V³⁺ (blue-green) and V²⁺ (violet) ions, respectively.

Although group 5 metals react with the heavier chalcogens to form a complex set of binary chalcogenides, the most important are the dichalcogenides (MY₂), whose layered structures are similar to those of the group 4 dichalcogenides. The elements of group 5 also form binary nitrides, carbides, borides, and hydrides, whose stoichiometries and properties are similar to those of the corresponding group 4 compounds. One such compound, tantalum carbide (TiC), has the highest melting point of any compound known (3738°C); it is used for the cutting edges of high-speed machine tools.

Groups 6 and 7

Group 6 (Cr, Mo, and W)

As an illustration of the trend toward increasing polarizability as we go from left to right across the d block, in group 6 we first encounter a metal (Mo) that occurs naturally as a sulfide ore rather than as an oxide. Molybdenite (MoS₂) is a soft black mineral that can be used for writing, like PbS and graphite. Because of this similarity, people long assumed that these substances were all the same. In fact, the name molybdenum is derived from the Greek molybdos, meaning “lead.” More than 90% of the molybdenum produced annually is used to make steels for cutting tools, which retain their sharp edge even when red hot. In addition, molybdenum is the only second- or third-row transition element that is essential for humans. The major chromium ore is chromite (FeCr₂O₄), which is oxidized to the soluble [CrO₄]²⁻ ion under basic conditions and reduced successively to Cr₂O₃ and Cr with carbon and aluminum, respectively. Pure chromium can be obtained by dissolving Cr₂O₃ in sulfuric acid followed by electrolytic reduction; a similar process is used for electroplating metal objects to give them a bright, shiny, protective surface layer. Pure tungsten is obtained by first converting tungsten ores to WO₃, which is then reduced with hydrogen to give the metal.

Consistent with periodic trends, the group 6 metals are slightly less electropositive than those of the three preceding groups, and the two heaviest metals are essentially the same size because of the lanthanide contraction (Table 23.5 "Some Properties of the Elements of Groups 6 and 7"). All three elements have a total of six valence electrons, resulting in a maximum oxidation state of +6. Due to extensive polarization of the anions, compounds in the +6 oxidation state are highly covalent. As in groups 4 and 5, the lightest element exhibits variable oxidation states, ranging from Cr²⁺, which is a powerful reductant, to CrO₃, a red solid that is a powerful oxidant. For Mo and W, the highest oxidation state (+6) is by far the most important, although compounds in the +4 and +5 oxidation states are known.

Note the Pattern

The metals become increasing polarizable across the d block.

Table 23.5 Some Properties of the Elements of Groups 6 and 7

Group	Element	Z	Valence Electron Configuration	Electronegativity	Metallic Radius (pm)	Melting Point (°C)	Density ${\text{(g/cm}}^{\text{3}}\text{)}$
6	Cr	24	4s13d5	1.66	128	1907	7.15
	Mo	42	5s14d5	2.16	139	2623	10.20
	W	74	6s25d44f14	1.70	139	3422	19.30
7	Mn	25	4s23d5	1.55	127	1246	7.30
	Tc	43	5s24d5	2.10	136	2157	11.50
	Re	75	6s25d54f14	1.90	137	3186	20.80

Note the Pattern

The chemistry of the two heaviest group 6 metals (Mo and W) is dominated by the +6 oxidation state. The chemistry of the lightest element (Cr) is dominated by lower oxidation states.

As observed in previous groups, the group 6 halides become more covalent as the oxidation state of the metal increases: their volatility increases, and their melting points decrease. Recall that as the electronegativity of the halogens decreases from F to I, they are less able to stabilize high oxidation states; consequently, the maximum oxidation state of the corresponding metal halides decreases. Thus all three metals form hexafluorides, but CrF₆ is unstable at temperatures above −100°C, whereas MoF₆ and WF₆ are stable. Consistent with the trend toward increased stability of the highest oxidation state for the second- and third-row elements, the other halogens can oxidize chromium to only the trihalides, CrX₃ (X is Cl, Br, or I), while molybdenum forms MoCl₅, MoBr₄, and MoI₃, and tungsten gives WCl₆, WBr₅, and WI₄.

Both Mo and W react with oxygen to form the covalent trioxides (MoO₃ and WO₃), but Cr reacts to form only the so-called sesquioxide (Cr₂O₃). Chromium will form CrO₃, which is a highly toxic compound that can react explosively with organic materials. All the trioxides are acidic, dissolving in base to form the corresponding oxoanions ([MO₄]²⁻). Consistent with periodic trends, the sesquioxide of the lightest element in the group (Cr₂O₃) is amphoteric. The aqueous chemistry of molybdate and tungstate is complex, and at low pH they form a series of polymeric anions called isopolymetallates, such as the [Mo₈O₂₆]⁴⁻ ion, whose structure is as follows:

An isopolymolybdate cluster. The [Mo₈O₂₆]⁴⁻ ion, shown here in both side and top views, is typical of the oxygen-bridged clusters formed by Mo(VI) and W(VI) in aqueous solution.

Reacting molybdenum or tungsten with heavier chalcogens gives binary chalcogenide phases, most of which are nonstoichiometric and electrically conducting. One of the most stable is MoS₂; it has a layered structure similar to that of TiS₂ (Figure 23.3 "The Layered Structure of TiS"), in which the layers are held together by only weak van der Waals forces, which allows them to slide past one another rather easily. Consequently, both MoS₂ and WS₂ are used as lubricants in a variety of applications, including automobile engines. Because tungsten itself has an extraordinarily high melting point (3380°C), lubricants described as containing “liquid tungsten” actually contain a suspension of very small WS₂ particles.

As in groups 4 and 5, the elements of group 6 form binary nitrides, carbides, and borides whose stoichiometries and properties are similar to those of the preceding groups. Tungsten carbide (WC), one of the hardest compounds known, is used to make the tips of drill bits.

Group 7 (Mn, Tc, and Re)

Continuing across the periodic table, we encounter the group 7 elements (Table 23.5 "Some Properties of the Elements of Groups 6 and 7"). One group 7 metal (Mn) is usually combined with iron in an alloy called ferromanganese, which has been used since 1856 to improve the mechanical properties of steel by scavenging sulfur and oxygen impurities to form MnS and MnO. Technetium is named after the Greek technikos, meaning “artificial,” because all its isotopes are radioactive. One isotope, ^99mTc (m for metastable), has become an important biomedical tool for imaging internal organs. (For more information on biomedical imaging, see Chapter 20 "Nuclear Chemistry", Section 20.5 "Applied Nuclear Chemistry".) Because of its scarcity, Re is one of the most expensive elements, and its applications are limited. It is, however, used in a bimetallic Pt/Re catalyst for refining high-octane gasoline.

All three group 7 elements have seven valence electrons and can form compounds in the +7 oxidation state. Once again, the lightest element exhibits multiple oxidation states. Compounds of Mn in oxidation states ranging from −3 to +7 are known, with the most common being +2 and +4 (Figure 23.5 "Compounds of Manganese in Oxidation States +2 to +7"). In contrast, compounds of Tc and Re in the +2 oxidation state are quite rare. Because the electronegativity of Mn is anomalously low, elemental manganese is unusually reactive. In contrast, the chemistry of Tc is similar to that of Re because of their similar size and electronegativity, again a result of the lanthanide contraction. Due to the stability of the half-filled 3d⁵ electron configuration, the aqueous Mn³⁺ ion, with a 3d⁴ valence electron configuration, is a potent oxidant that is able to oxidize water. It is difficult to generalize about other oxidation states for Tc and Re because their stability depends dramatically on the nature of the compound.

Figure 23.5 Compounds of Manganese in Oxidation States +2 to +7

Like vanadium, compounds of manganese in different oxidation states have different numbers of d electrons, which leads to compounds with different colors: the Mn²⁺(aq) ion is pale pink; Mn(OH)₃, which contains Mn(III), is a dark brown solid; MnO₂, which contains Mn(IV), is a black solid; and aqueous solutions of Mn(VI) and Mn(VII) contain the green manganate ion [MnO₄]²⁻ and the purple permanganate ion [MnO₄]⁻, respectively.

Consistent with higher oxidation states being more stable for the heavier transition metals, reacting Mn with F₂ gives only MnF₃, a high-melting, red-purple solid, whereas Re reacts with F₂ to give ReF₇, a volatile, low-melting, yellow solid. Again, reaction with the less oxidizing, heavier halogens produces halides in lower oxidation states. Thus reaction with Cl₂, a weaker oxidant than F₂, gives MnCl₂ and ReCl₆. Reaction of Mn with oxygen forms only Mn₃O₄, a mixed-valent compound that contains two Mn(II) and one Mn(III) per formula unit and is similar in both stoichiometry and structure to magnetite (Fe₃O₄). In contrast, Tc and Re form high-valent oxides, the so-called heptoxides (M₂O₇), consistent with the increased stability of higher oxidation states for the second and third rows of transition metals. Under forced conditions, manganese will form Mn₂O₇, an unstable, explosive, green liquid. Also consistent with this trend, the permanganate ion [MnO₄]²⁻ is a potent oxidant, whereas [TcO₄]⁻ and [ReO₄]⁻ are much more stable. Both Tc and Re form disulfides and diselenides with layered structures analogous to that of MoS₂, as well as more complex heptasulfides (M₂S₇). As is typical of the transition metals, the group 7 metals form binary nitrides, carbides, and borides that are generally stable at high temperatures and exhibit metallic properties.

Note the Pattern

The chemistry of the group 7 metals (Mn, Tc, and Re) is dominated by lower oxidation states. Compounds in the maximum possible oxidation state (+7) are readily reduced.

Groups 8, 9, and 10

In many older versions of the periodic table, groups 8, 9, and 10 were combined in a single group (group VIII) because the elements of these three groups exhibit many horizontal similarities in their chemistry, in addition to the similarities within each column. In part, these horizontal similarities are due to the fact that the ionization potentials of the elements, which increase slowly but steadily across the d block, have now become so large that the oxidation state corresponding to the formal loss of all valence electrons is encountered only rarely (group 8) or not at all (groups 9 and 10). As a result, the chemistry of all three groups is dominated by intermediate oxidation states, especially +2 and +3 for the first-row metals (Fe, Co, and Ni). The heavier elements of these three groups are called precious metals because they are rather rare in nature and mostly chemically inert.

Group 10 (Ni, Pd, and Pt)

Nickel silicates are easily processed; consequently, nickel has been known and used since antiquity. In fact, a 75:25 Cu:Ni alloy was used for more than 2000 years to mint “silver” coins, and the modern US nickel uses the same alloy. In contrast to nickel, palladium and platinum are rare (their terrestrial abundance is about 10–15 ppb), but they are at least an order of magnitude more abundant than the heavier elements of groups 8 and 9. Platinum and palladium are used in jewelry, the former as the pure element and the latter as the Pd/Au alloy known as white gold.

Over 2000 years ago, the Bactrian civilization in Western Asia used a 75:25 alloy of copper and nickel for its coins. A modern US nickel has the same composition, but a modern Canadian nickel is nickel-plated steel and contains only 2.5% nickel by mass.

Groups 11 and 12

Group 11 (Cu, Ag, and Au)

The coinage metals—copper, silver, and gold—occur naturally (like the gold nugget shown here); consequently, these were probably the first metals used by ancient humans. For example, decorative gold artifacts dating from the late Stone Age are known, and some gold Egyptian coins are more than 5000 yr old. Copper is almost as ancient, with objects dating to about 5000 BC. Bronze, an alloy of copper and tin that is harder than either of its constituent metals, was used before 3000 BC, giving rise to the Bronze Age. Deposits of silver are much less common than deposits of gold or copper, yet by 3000 BC, methods had been developed for recovering silver from its ores, which allowed silver coins to be widely used in ancient times.

This 1 kg gold nugget was found in Australia; in 2005, it was for sale in Hong Kong at an asking price of more than US$64,000.

Deposits of gold and copper are widespread and numerous, and for many centuries it was relatively easy to obtain large amounts of the pure elements. For example, a single gold nugget discovered in Australia in 1869 weighed more than 150 lb. Because the demand for these elements has outstripped their availability, methods have been developed to recover them economically from even very low-grade ores (as low as 1% Cu content for copper) by operating on a vast scale, as shown in the photo of an open-pit copper mine. Copper is used primarily to manufacture electric wires, but large quantities are also used to produce bronze, brass, and alloys for coins. Much of the silver made today is obtained as a by-product of the manufacture of other metals, especially Cu, Pb, and Zn. In addition to its use in jewelry and silverware, silver is used in Ag/Zn and Ag/Cd button batteries. (For more information on button batteries, see Chapter 19 "Electrochemistry", Section 19.5 "Commercial Galvanic Cells".) Gold is typically found either as tiny particles of the pure metal or as gold telluride (AuTe₂). It is used as a currency reserve, in jewelry, in the electronics industry for corrosion-free contacts, and, in very thin layers, as a reflective window coating that minimizes heat transfer.

The Chuquicamata copper mine in northern Chile, the world’s largest open-pit copper mine, is 4.3 km long, 3 km wide, and 825 m deep. Each gigantic truck in the foreground (and barely visible in the lower right center) can hold 330 metric tn (330,000 kg) of copper ore.

Some properties of the coinage metals are listed in Table 23.7 "Some Properties of the Elements of Groups 11 and 12". The electronegativity of gold (χ = 2.40) is close to that of the nonmetals sulfur and iodine, which suggests that the chemistry of gold should be somewhat unusual for a metal. The coinage metals have the highest electrical and thermal conductivities of all the metals, and they are also the most ductile and malleable. With an ns¹(n − 1)d¹⁰ valence electron configuration, the chemistry of these three elements is dominated by the +1 oxidation state due to losing the single ns electron. Higher oxidation states are also known, however: +2 is common for Cu and, to a lesser extent, Ag, and +3 for Au because of the relatively low values of the second and (for Au) third ionization energies. All three elements have significant electron affinities due to the half-filled ns orbital in the neutral atoms. As a result, gold reacts with powerful reductants like Cs and solutions of the alkali metals in liquid ammonia to produce the gold anion Au⁻ with a 6s²5d¹⁰ valence electron configuration.

Table 23.7 Some Properties of the Elements of Groups 11 and 12

Group	Element	Z	Valence Electron Configuration	Electronegativity	Metallic Radius (pm)	Melting Point (°C)	Density ${\text{(g/cm}}^{\text{3}}\text{)}$
11	Cu	29	4s13d10	1.90	128	1085	8.96
	Ag	47	5s14d10	1.93	144	962	10.50
	Au	79	6s15d104f14	2.40	144	1064	19.30
12	Zn	30	4s23d10	1.65	134	420	7.13
	Cd	48	5s24d10	1.69	149	321	8.69
	Hg	80	6s25d104f14	1.90	151	−38.8	13.53

All group 11 elements are relatively unreactive, and their reactivity decreases from Cu to Au. Hence they are noble metals that are particularly well suited for use in coins and jewelry. Copper reacts with O₂ at high temperatures to produce Cu₂O and with sulfur to form Cu₂S. Neither silver nor gold reacts directly with oxygen, although oxides of these elements can be prepared by other routes. Silver reacts with sulfur compounds to form the black Ag₂S coating known as tarnish. Gold is the only metal that does not react with sulfur; it also does not react with nitrogen, carbon, or boron. All the coinage metals do, however, react with oxidizing acids. Thus both Cu and Ag dissolve in HNO₃ and in hot concentrated H₂SO₄, while Au dissolves in the 3:1 HCl:HNO₃ mixture known as aqua regia. Furthermore, all three metals dissolve in basic cyanide solutions in the presence of oxygen to form very stable [M(CN)₂]⁻ ions, a reaction that is used to separate gold from its ores. (For more information about gold processing, see Chapter 4 "Reactions in Aqueous Solution", Section 4.3 "Stoichiometry of Reactions in Solution".)

Note the Pattern

Although the most important oxidation state for group 11 is +1, the elements are relatively unreactive, with reactivity decreasing from Cu to Au.

All the monohalides except CuF and AuF are known (including AgF). Once again, iodine is unable to stabilize the higher oxidation states (Au³⁺ and Cu²⁺). Thus all the copper(II) halides except the iodide are known, but the only dihalide of silver is AgF₂. In contrast, all the gold trihalides (AuX₃) are known, again except the triiodide. No binary nitrides, borides, or carbides are known for the group 11 elements.

Pyrometallurgy

In pyrometallurgy, an ore is heated with a reductant to obtain the metal. Theoretically, it should be possible to obtain virtually any metal from its ore by using coke, an inexpensive form of crude carbon, as the reductant. An example of such a reaction is as follows:

Unfortunately, many of the early transition metals, such as Ti, react with carbon to form stable binary carbides. Consequently, more expensive reductants, such as hydrogen, aluminum, magnesium, or calcium, must be used to obtain these metals. Many metals that occur naturally as sulfides can be obtained by heating the sulfide in air, as shown for lead in the following equation:

The reaction is driven to completion by the formation of SO₂, a stable gas.

Pyrometallurgy is also used in the iron and steel industries. The overall reaction for the production of iron in a blast furnace is as follows:

The actual reductant is CO, which reduces Fe₂O₃ to give Fe(l) and CO₂(g); the CO₂ is then reduced back to CO by reaction with excess carbon. As the ore, lime, and coke drop into the furnace (Figure 23.7 "A Blast Furnace for Converting Iron Oxides to Iron Metal"), any silicate minerals in the ore react with the lime to produce a low-melting mixture of calcium silicates called slag, which floats on top of the molten iron. Molten iron is then allowed to run out the bottom of the furnace, leaving the slag behind. Originally, the iron was collected in pools called pigs, which is the origin of the name pig iron.

Figure 23.7 A Blast Furnace for Converting Iron Oxides to Iron Metal

(a) The furnace is charged with alternating layers of iron ore (largely Fe₂O₃) and a mixture of coke (C) and limestone (CaCO₃). Blasting hot air into the mixture from the bottom causes it to ignite, producing CO and raising the temperature of the lower part of the blast furnace to about 2000°C. As the CO that is formed initially rises, it reduces Fe₂O₃ to form CO₂ and elemental iron, which absorbs heat and melts as it falls into the hottest part of the furnace. Decomposition of CaCO₃ at high temperatures produces CaO (lime) and additional CO₂, which reacts with excess coke to form more CO. (b) This blast furnace in Magnitogorsk, Russia, was the largest in the world when it was built in 1931.

Iron that is obtained directly from a blast furnace has an undesirably low melting point (about 1100°C instead of 1539°C) because it contains a large amount of dissolved carbon. It contains other impurities (such as Si, S, P, and Mn from contaminants in the iron ore that were also reduced during processing) that must be removed because they make iron brittle and unsuitable for most structural applications. In the Bessemer process, oxygen is blown through the molten pig iron to remove the impurities by selective oxidation because these impurities are more readily oxidized than iron (Figure 23.8 "A Basic Oxygen Furnace for Converting Crude Iron to Steel"). In the final stage of this process, small amounts of other metals are added at specific temperatures to produce steel with the desired combination of properties.

Figure 23.8 A Basic Oxygen Furnace for Converting Crude Iron to Steel

(a) A blast of oxygen is used to agitate the molten iron and oxidize impurities to products that dissolve in the less dense slag layer. The slag and the molten steel are removed by tilting the entire furnace and pouring the liquids out through the taphole. (b) A basic oxygen furnace is being filled with molten iron from a blast furnace.

Hydrometallurgy

The most selective methods for separating metals from their ores are based on the formation of metal complexes. For example, gold is often found as tiny flakes of the metal, usually in association with quartz or pyrite deposits. In those circumstances, gold is typically extracted by using cyanide leaching, which forms a stable gold–cyanide complex—[Au(CN)₂]⁻:

Virtually pure gold can be obtained by adding powdered zinc to the solution:

A related method, which is used to separate Co³⁺, Ni²⁺, and Cu⁺ from Fe, Mn, and Ti, is based on the formation of stable, soluble ammonia complexes of ions of the late transition metals.

History of the Coordination Compounds

Coordination compounds have been known and used since antiquity; probably the oldest is the deep blue pigment called Prussian blue: KFe₂(CN)₆. The chemical nature of these substances, however, was unclear for a number of reasons. For example, many compounds called “double salts” were known, such as AlF₃·3KF, Fe(CN)₂·4KCN, and ZnCl₂·2CsCl, which were combinations of simple salts in fixed and apparently arbitrary ratios. Why should AlF₃·3KF exist but not AlF₃·4KF or AlF₃·2KF? And why should a 3:1 KF:AlF₃ mixture have different chemical and physical properties than either of its components? Similarly, adducts of metal salts with neutral molecules such as ammonia were also known—for example, CoCl₃·6NH₃, which was first prepared sometime before 1798. Like the double salts, the compositions of these adducts exhibited fixed and apparently arbitrary ratios of the components. For example, CoCl₃·6NH₃, CoCl₃·5NH₃, CoCl₃·4NH₃, and CoCl₃·3NH₃ were all known and had very different properties, but despite all attempts, chemists could not prepare CoCl₃·2NH₃ or CoCl₃·NH₃.

The Great Wave Off Kanagawa. The Japanese artist Katsushika Hokusai used Prussian blue to create this famous woodcut.

Although the chemical composition of such compounds was readily established by existing analytical methods, their chemical nature was puzzling and highly controversial. The major problem was that what we now call valence (i.e., the oxidation state) and coordination number were thought to be identical. As a result, highly implausible (to modern eyes at least) structures were proposed for such compounds, including the “Chattanooga choo-choo” model for CoCl₃·4NH₃ shown here.

The modern theory of coordination chemistry is based largely on the work of Alfred Werner (1866–1919; Nobel Prize in Chemistry in 1913). In a series of careful experiments carried out in the late 1880s and early 1890s, he examined the properties of several series of metal halide complexes with ammonia. For example, five different “adducts” of ammonia with PtCl₄ were known at the time: PtCl₄·nNH₃ (n = 2–6). Some of Werner’s original data on these compounds are shown in Table 23.8 "Werner’s Data on Complexes of Ammonia with PtCl". The electrical conductivity of aqueous solutions of these compounds was roughly proportional to the number of ions formed per mole, while the number of chloride ions that could be precipitated as AgCl after adding Ag⁺(aq) was a measure of the number of “free” chloride ions present. For example, Werner’s data on PtCl₄·6NH₃ in Table 23.8 "Werner’s Data on Complexes of Ammonia with PtCl" showed that all the chloride ions were present as free chloride. In contrast, PtCl₄·2NH₃ was a neutral molecule that contained no free chloride ions.

These data led Werner to postulate that metal ions have two different kinds of valence: (1) a primary valence (oxidation state) that corresponds to the positive charge on the metal ion and (2) a secondary valence (coordination number) that is the total number of ligands bound to the metal ion. If Pt had a primary valence of 4 and a secondary valence of 6, Werner could explain the properties of the PtCl₄·NH₃ adducts by the following reactions, where the metal complex is enclosed in square brackets:

Further work showed that the two missing members of the series—[Pt(NH₃)Cl₅]⁻ and [PtCl₆]²⁻—could be prepared as their mono- and dipotassium salts, respectively. Similar studies established coordination numbers of 6 for Co³⁺ and Cr³⁺ and 4 for Pt²⁺ and Pd²⁺.

Werner’s studies on the analogous Co³⁺ complexes also allowed him to propose a structural model for metal complexes with a coordination number of 6. Thus he found that [Co(NH₃)₆]Cl₃ (yellow) and [Co(NH₃)₅Cl]Cl₂ (purple) were 1:3 and 1:2 electrolytes. Unexpectedly, however, two different [Co(NH₃)₄Cl₂]Cl compounds were known: one was red, and the other was green (part (a) in Figure 23.9 "Complexes with Different Arrangements of the Same Ligands Have Different Properties"). Because both compounds had the same chemical composition and the same number of groups of the same kind attached to the same metal, there had to be something different about the arrangement of the ligands around the metal ion. Werner’s key insight was that the six ligands in [Co(NH₃)₄Cl₂]Cl had to be arranged at the vertices of an octahedron because that was the only structure consistent with the existence of two, and only two, arrangements of ligands (part (b) in Figure 23.9 "Complexes with Different Arrangements of the Same Ligands Have Different Properties"). His conclusion was corroborated by the existence of only two different forms of the next compound in the series: Co(NH₃)₃Cl₃.

Figure 23.9 Complexes with Different Arrangements of the Same Ligands Have Different Properties

The [Co(NH₃)₄Cl₂]⁺ ion can have two different arrangements of the ligands, which results in different colors: if the two Cl⁻ ligands are next to each other, the complex is red (a), but if they are opposite each other, the complex is green (b).

Example 4

In Werner’s time, many complexes of the general formula MA₄B₂ were known, but no more than two different compounds with the same composition had been prepared for any metal. To confirm Werner’s reasoning, calculate the maximum number of different structures that are possible for six-coordinate MA₄B₂ complexes with each of the three most symmetrical possible structures: a hexagon, a trigonal prism, and an octahedron. What does the fact that no more than two forms of any MA₄B₂ complex were known tell you about the three-dimensional structures of these complexes?

Given: three possible structures and the number of different forms known for MA₄B₂ complexes

Asked for: number of different arrangements of ligands for MA₄B₂ complex for each structure

Strategy:

Sketch each structure, place a B ligand at one vertex, and see how many different positions are available for the second B ligand.

Solution:

The three regular six-coordinate structures are shown here, with each coordination position numbered so that we can keep track of the different arrangements of ligands. For each structure, all vertices are equivalent. We begin with a symmetrical MA₆ complex and simply replace two of the A ligands in each structure to give an MA₄B₂ complex:

For the hexagon, we place the first B ligand at position 1. There are now three possible places for the second B ligand: at position 2 (or 6), position 3 (or 5), or position 4. These are the only possible arrangements. The (1, 2) and (1, 6) arrangements are chemically identical because the two B ligands are adjacent to each other. The (1, 3) and (1, 5) arrangements are also identical because in both cases the two B ligands are separated by an A ligand.

Turning to the trigonal prism, we place the first B ligand at position 1. Again, there are three possible choices for the second B ligand: at position 2 or 3 on the same triangular face, position 4 (on the other triangular face but adjacent to 1), or position 5 or 6 (on the other triangular face but not adjacent to 1). The (1, 2) and (1, 3) arrangements are chemically identical, as are the (1, 5) and (1, 6) arrangements.

In the octahedron, however, if we place the first B ligand at position 1, then we have only two choices for the second B ligand: at position 2 (or 3 or 4 or 5) or position 6. In the latter, the two B ligands are at opposite vertices of the octahedron, with the metal lying directly between them. Although there are four possible arrangements for the former, they are chemically identical because in all cases the two B ligands are adjacent to each other.

The number of possible MA₄B₂ arrangements for the three geometries is thus: hexagon, 3; trigonal prism, 3; and octahedron, 2. The fact that only two different forms were known for all MA₄B₂ complexes that had been prepared suggested that the correct structure was the octahedron but did not prove it. For some reason one of the three arrangements possible for the other two structures could have been less stable or harder to prepare and had simply not yet been synthesized. When combined with analogous results for other types of complexes (e.g., MA₃B₃), however, the data were best explained by an octahedral structure for six-coordinate metal complexes.

Exercise

Determine the maximum number of structures that are possible for a four-coordinate MA₂B₂ complex with either a square planar or a tetrahedral symmetrical structure.

Answer: square planar, 2; tetrahedral, 1

Structures of Metal Complexes

The coordination numbers of metal ions in metal complexes can range from 2 to at least 9. In general, the differences in energy between different arrangements of ligands are greatest for complexes with low coordination numbers and decrease as the coordination number increases. Usually only one or two structures are possible for complexes with low coordination numbers, whereas several different energetically equivalent structures are possible for complexes with high coordination numbers (n > 6). The following presents the most commonly encountered structures for coordination numbers 2–9. Many of these structures should be familiar to you from our discussion of the valence-shell electron-pair repulsion (VSEPR) model in Chapter 9 "Molecular Geometry and Covalent Bonding Models" because they correspond to the lowest-energy arrangements of n electron pairs around a central atom.

Coordination Number 2

Although it is rare for most metals, this coordination number is surprisingly common for d¹⁰ metal ions, especially Cu⁺, Ag⁺, Au⁺, and Hg²⁺. An example is the [Au(CN)₂]⁻ ion, which is used to extract gold from its ores, as described in Section 23.3 "Metallurgy". As expected based on VSEPR considerations, these complexes have the linear L–M–L structure shown here.

Coordination Number 3

Although it is also rare, this coordination number is encountered with d¹⁰ metal ions such as Cu⁺ and Hg²⁺. Among the few known examples is the HgI₃⁻ ion. Three-coordinate complexes almost always have the trigonal planar structure expected from the VSEPR model.

Coordination Number 4

Two common structures are observed for four-coordinate metal complexes: tetrahedral and square planar. The tetrahedral structure is observed for all four-coordinate complexes of nontransition metals, such as [BeF₄]²⁻, and d¹⁰ ions, such as [ZnCl₄]²⁻. It is also found for four-coordinate complexes of the first-row transition metals, especially those with halide ligands (e.g., [FeCl₄]⁻ and [FeCl₄]²⁻). In contrast, square planar structures are routinely observed for four-coordinate complexes of second- and third-row transition metals with d⁸ electron configurations, such as Rh⁺ and Pd²⁺, and they are also encountered in some complexes of Ni²⁺ and Cu²⁺.

Coordination Number 5

This coordination number is less common than 4 and 6, but it is still found frequently in two different structures: trigonal bipyramidal and square pyramidal. Because the energies of these structures are usually rather similar for most ligands, many five-coordinate complexes have distorted structures that lie somewhere between the two extremes.

Coordination Number 6

This coordination number is by far the most common. The six ligands are almost always at the vertices of an octahedron or a distorted octahedron. The only other six-coordinate structure is the trigonal prism, which is very uncommon in simple metal complexes.

Coordination Number 7

This relatively uncommon coordination number is generally encountered for only large metals (such as the second- and third-row transition metals, lanthanides, and actinides). At least three different structures are known, two of which are derived from an octahedron or a trigonal prism by adding a ligand to one face of the polyhedron to give a “capped” octahedron or trigonal prism. By far the most common, however, is the pentagonal bipyramid.

Coordination Number 8

This coordination number is relatively common for larger metal ions. The simplest structure is the cube, which is rare because it does not minimize interligand repulsive interactions. Common structures are the square antiprism and the dodecahedron, both of which can be generated from the cube.

Coordination Number 9

This coordination number is found in larger metal ions, and the most common structure is the tricapped trigonal prism, as in [Nd(H₂O)₉]³⁺.

Stability of Metal Complexes

The thermodynamic stability of a metal complex depends greatly on the properties of the ligand and the metal ion and on the type of bonding. Recall that the metal–ligand interaction is an example of a Lewis acid–base interaction. Lewis bases can be divided into two categories: hard basesA type of Lewis base with small, relatively nonpolarizable donor atoms., which contain small, relatively nonpolarizable donor atoms (such as N, O, and F), and soft basesA type of Lewis base with large, relatively polarizable donor atoms., which contain larger, relatively polarizable donor atoms (such as P, S, and Cl). Metal ions with the highest affinities for hard bases are hard acidsAn acid with the highest affinity for hard bases. It is relatively nonpolarizable and has a relatively high charge-to-radius ratio., whereas metal ions with the highest affinity for soft bases are soft acidsAn acid with the highest affinity for soft bases. It tends to be a cation of a less electropositive metal.. Some examples of hard and soft acids and bases are given in Table 23.9 "Examples of Hard and Soft Acids and Bases". Notice that hard acids are usually cations of electropositive metals; consequently, they are relatively nonpolarizable and have higher charge-to-radius ratios. Conversely, soft acids tend to be cations of less electropositive metals; consequently, they have lower charge-to-radius ratios and are more polarizable. Chemists can predict the relative stabilities of complexes formed by the d-block metals with a remarkable degree of accuracy by using a simple rule: hard acids prefer to bind to hard bases, and soft acids prefer to bind to soft bases.

Because the interaction between hard acids and hard bases is primarily electrostatic in nature, the stability of complexes involving hard acids and hard bases increases as the positive charge on the metal ion increases and as its radius decreases. For example, the complex of Al³⁺ (r = 53.5 pm) with four fluoride ligands (AlF₄⁻) is about 10⁸ times more stable than InF₄⁻, the corresponding fluoride complex of In³⁺ (r = 80 pm). In general, the stability of complexes of divalent first-row transition metals with a given ligand varies inversely with the radius of the metal ion, as shown in the following series:The inversion in the order at copper is due to the anomalous structure of copper(II) complexes, which will be discussed shortly.

Because a hard metal interacts with a base in much the same way as a proton, by binding to a lone pair of electrons on the base, the stability of complexes of hard acids with hard bases increases as the ligand becomes more basic. For example, because ammonia is a stronger base than water, metal ions bind preferentially to ammonia. Consequently, adding ammonia to aqueous solutions of many of the first-row transition-metal cations results in the formation of the corresponding ammonia complexes.

In contrast, the interaction between soft metals (such as the second- and third-row transition metals and Cu⁺) and soft bases is largely covalent in nature. Most soft-metal ions have a filled or nearly filled d subshell, which suggests that metal-to-ligand π bonding is important. Complexes of soft metals with soft bases are therefore much more stable than would be predicted based on electrostatic arguments.

The hard acid–hard base/soft acid–soft base concept also allows us to understand why metals are found in nature in different kinds of ores. Recall from Section 23.2 "A Brief Survey of Transition-Metal Chemistry" that most of the first-row transition metals are isolated from oxide ores but that copper and zinc tend to occur naturally in sulfide ores. This is consistent with the increase in the soft character of the metals across the first row of the transition metals from left to right. Recall also that most of the second- and third-row transition metals occur in nature as sulfide ores, consistent with their greater soft character.

Ligands like chloride, water, and ammonia are said to be monodentate (one-toothed, from the Greek mono, meaning “one,” and the Latin dent-, meaning “tooth”): they are attached to the metal via only a single atom. Ligands can, however, be bidentate (two-toothed, from the Greek di, meaning “two”), tridentate (three-toothed, from the Greek tri, meaning “three”), or, in general, polydentate (many-toothed, from the Greek poly, meaning “many”), indicating that they are attached to the metal at two, three, or several sites, respectively. Ethylenediamine (H₂NCH₂CH₂NH₂, often abbreviated as en) and diethylenetriamine (H₂NCH₂CH₂NHCH₂CH₂NH₂, often abbreviated as dien) are examples of a bidentate and a tridentate ligand, respectively, because each nitrogen atom has a lone pair that can be shared with a metal ion. When a bidentate ligand such as ethylenediamine binds to a metal such as Ni²⁺, a five-membered ring is formed. A metal-containing ring like that shown is called a chelate ring (from the Greek chele, meaning “claw”). Correspondingly, a polydentate ligand is a chelating agent, and complexes that contain polydentate ligands are called chelate complexes.

Experimentally, it is observed that metal complexes of polydentate ligands are significantly more stable than the corresponding complexes of chemically similar monodentate ligands; this increase in stability is called the chelate effect. For example, the complex of Ni²⁺ with three ethylenediamine ligands, [Ni(en)₃]²⁺, should be chemically similar to the Ni²⁺ complex with six ammonia ligands, [Ni(NH₃)₆]²⁺. In fact, the equilibrium constant for the formation of [Ni(en)₃]²⁺ is almost 10 orders of magnitude larger than the equilibrium constant for the formation of [Ni(NH₃)₆]²⁺:

The stability of a chelate complex depends on the size of the chelate rings. For ligands with a flexible organic backbone like ethylenediamine, complexes that contain five-membered chelate rings, which have almost no strain, are significantly more stable than complexes with six-membered chelate rings, which are in turn much more stable than complexes with four- or seven-membered rings. For example, the complex of copper(II) with two ethylenediamine ligands is about 1000 times more stable than the corresponding complex with triethylenediamine (H₂NCH₂CH₂CH₂NH₂, abbreviated as trien):

Isomers of Metal Complexes

As we discussed earlier in this section, the existence of coordination compounds with the same formula but different arrangements of the ligands was crucial in the development of coordination chemistry. Two or more compounds with the same formula but different arrangements of the atoms are called isomersTwo or more compounds with the same molecular formula but different arrangements of their atoms.. Because isomers usually have different physical and chemical properties, it is important to know which isomer we are dealing with if more than one isomer is possible. Recall from Chapter 2 "Molecules, Ions, and Chemical Formulas" that in many cases more than one structure is possible for organic compounds with the same molecular formula; examples discussed previously include n-butane versus isobutane and cis-2-butene versus trans-2-butene. As we will see, coordination compounds exhibit the same types of isomers as organic compounds, as well as several kinds of isomers that are unique. (For more information on isomers in organic compounds, see Chapter 24 "Organic Compounds", Section 24.2 "Isomers of Organic Compounds".)

Geometrical Isomers

Metal complexes that differ only in which ligands are adjacent to one another (cisA type of geometrical isomer in which the ligands or the substituents are adjacent to one another in a rigid molecule or a metal complex.) or directly across from one another (transA type of geometrical isomer in which the ligands or the substituents are directly across from each other in a rigid molecule or a metal complex.) in the coordination sphere of the metal are called geometrical isomersComplexes that differ only in which ligands are adjacent to one another or directly across from one another in the coordination sphere of a metal.. They are most important for square planar and octahedral complexes.

Because all vertices of a square are equivalent, it does not matter which vertex is occupied by the ligand B in a square planar MA₃B complex; hence only a single geometrical isomer is possible in this case (and in the analogous MAB₃ case). All four structures shown here are chemically identical because they can be superimposed simply by rotating the complex in space:

For an MA₂B₂ complex, there are two possible isomers: either the A ligands can be adjacent to one another (cis), in which case the B ligands must also be cis, or the A ligands can be across from one another (trans), in which case the B ligands must also be trans. Even though it is possible to draw the cis isomer in four different ways and the trans isomer in two different ways, all members of each set are chemically equivalent:

Because there is no way to convert the cis structure to the trans by rotating or flipping the molecule in space, they are fundamentally different arrangements of atoms in space. Probably the best-known examples of cis and trans isomers of an MA₂B₂ square planar complex are cis-Pt(NH₃)₂Cl₂, also known as cisplatin, and trans-Pt(NH₃)₂Cl₂, which is actually toxic rather than therapeutic.

The anticancer drug cisplatin and its inactive trans isomer. Cisplatin is especially effective against tumors of the reproductive organs (the testes in males and the ovaries in females), which primarily affect individuals in their 20s and were notoriously difficult to cure. For example, after being diagnosed with metastasized testicular cancer in 1991 and given only a 50% chance of survival, Lance Armstrong was cured by treatment with cisplatin and went on to win an unprecedented seven Tour de France bicycle races.

Square planar complexes that contain symmetrical bidentate ligands, such as [Pt(en)₂]²⁺, have only one possible structure, in which curved lines linking the two N atoms indicate the ethylenediamine ligands:

Octahedral complexes also exhibit cis and trans isomers. Like square planar complexes, only one structure is possible for octahedral complexes in which only one ligand is different from the other five (MA₅B). Even though we usually draw an octahedron in a way that suggests that the four “in-plane” ligands are different from the two “axial” ligands, in fact all six vertices of an octahedron are equivalent. Consequently, no matter how we draw an MA₅B structure, it can be superimposed on any other representation simply by rotating the molecule in space. Two of the many possible orientations of an MA₅B structure are as follows:

If two ligands in an octahedral complex are different from the other four, giving an MA₄B₂ complex, two isomers are possible. The two B ligands can be cis or trans. Cis- and trans-[Co(NH₃)₄Cl₂]Cl are examples of this type of system:

Replacing another A ligand by B gives an MA₃B₃ complex for which there are also two possible isomers. In one, the three ligands of each kind occupy opposite triangular faces of the octahedron; this is called the facAn isomer in which three ligands occupy opposite triangular faces of an octahedron. isomer (for facial). In the other, the three ligands of each kind lie on what would be the meridian if the complex were viewed as a sphere; this is called the merAn isomer in which three ligands lie on a spherical meridian. isomer (for meridional):

Example 6

Draw all the possible geometrical isomers for the complex [Co(H₂O)₂(ox)BrCl]⁻, where ox is ⁻O₂CCO₂⁻, which stands for oxalate.

Given: formula of complex

Asked for: structures of geometrical isomers

Solution:

This complex contains one bidentate ligand (oxalate), which can occupy only adjacent (cis) positions, and four monodentate ligands, two of which are identical (H₂O). The easiest way to attack the problem is to go through the various combinations of ligands systematically to determine which ligands can be trans. Thus either the water ligands can be trans to one another or the two halide ligands can be trans to one another, giving the two geometrical isomers shown here:

In addition, two structures are possible in which one of the halides is trans to a water ligand. In the first, the chloride ligand is in the same plane as the oxalate ligand and trans to one of the oxalate oxygens. Exchanging the chloride and bromide ligands gives the other, in which the bromide ligand is in the same plane as the oxalate ligand and trans to one of the oxalate oxygens:

This complex can therefore exist as four different geometrical isomers.

Exercise

Draw all the possible geometrical isomers for the complex [Cr(en)₂(CN)₂]⁺.

Answer:

Two geometrical isomers are possible: trans and cis.

Summary

Transition metals form metal complexes, polyatomic species in which a metal ion is bound to one or more ligands, which are groups bound to a metal ion. Complex ions are electrically charged metal complexes, and a coordination compound contains one or more metal complexes. Metal complexes with low coordination numbers generally have only one or two possible structures, whereas those with coordination numbers greater than six can have several different structures. Coordination numbers of two and three are common for d¹⁰ metal ions. Tetrahedral and square planar complexes have a coordination number of four; trigonal bipyramidal and square pyramidal complexes have a coordination number of five; and octahedral complexes have a coordination number of six. At least three structures are known for a coordination number of seven, which is generally found for only large metal ions. Coordination numbers of eight and nine are also found for larger metal ions. The stability of metal complexes with first-row transition metals in a +2 oxidation state varies inversely with their ionic radius. Lewis bases can be hard bases, which have small, relatively nonpolarizable donor atoms, or soft bases, with larger, relatively polarizable donor atoms. Hard acids have the highest affinity for hard bases, and soft acids have the highest affinity for soft bases. Soft metals and soft bases form complexes that are more stable than would be predicted based on electrostatic arguments, which suggests that metal-to-ligand π bonding is important. Ligands that are strong bases form the most stable complexes with metal ions that are hard acids. Exceptionally stable complexes are formed by chelates, which are polyatomic ligands with two or more donor atoms; this enhanced stability is known as the chelate effect. Many metal complexes form isomers, which are two or more compounds with the same formula but different arrangements of atoms. Structural isomers differ in which atoms are bonded to one another, while geometrical isomers differ only in the arrangement of ligands around the metal ion. Ligands adjacent to one another are cis, while ligands across from one another are trans.

Key Takeaways

• Coordination compounds are a major feature of the chemistry of over half the elements.
• Coordination compounds have important roles as industrial catalysts in controlling reactivity, and they are essential in biochemical processes.

Conceptual Problems

1. Give two reasons a metal can bind to only a finite number of ligands. Based on this reasoning, what do you predict is the maximum coordination number of Ti? of Ac?

2. Can a tetrahedral MA₂B₂ complex form cis and trans isomers? Explain your answer.

3. The group 12 elements are never found in their native (free) form but always in combination with one other element. What element is this? Why? Which of the group 12 elements has the highest affinity for the element you selected?

Answer

3. The group 12 metals are rather soft and prefer to bind to a soft anion such as sulfide rather than to a hard anion like oxide; hence they are usually found in nature as sulfide ores. Because it is the softest of these metals, mercury has the highest affinity for sulfide.

Structure and Reactivity

1. Complexes of metals in the +6 oxidation state usually contain bonds to which two Lewis bases? Why are these bonds best described as covalent rather than ionic? Do Ca, Sr, and Ba also form covalent bonds with these two Lewis bases, or is their bonding best described as ionic?

2. Cr, Mn, Fe, Co, and Ni form stable CO complexes. In contrast, the earlier transition metals do not form similar stable complexes. Why?

3. The transition metals Cr through Ni form very stable cyanide complexes. Why are these complexes so much more stable than similar compounds formed from the early transition metals?

4. Of Co(en)₃³⁺, CoF₆³⁻, Co(NH₃)₆³⁺, and Co(dien)₂³⁺, which species do you expect to be the most stable? Why?

5. Of Ca²⁺, Ti²⁺, V²⁺, Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, and Zn²⁺, which divalent metal ions forms the most stable complexes with ligands such as NH₃? Why?

6. Match each Lewis base with the metal ions with which it is most likely to form a stable complex:

   Lewis bases: NH₃, F⁻, RS⁻, OH⁻, and Cl⁻

   Metals: Sc³⁺, Cu⁺, W⁶⁺, Mg²⁺, V³⁺, Fe³⁺, Zr⁴⁺, Co²⁺, Ti⁴⁺, Au⁺, Al³⁺, and Mn⁷⁺

7. Of ReF₂, ReCl₅, MnF₆, Mn₂O₇, and ReO, which are not likely to exist?

8. Of WF₂, CrF₆, MoBr₆, WI₆, CrO₃, MoS₂, W₂S₃, and MoH, which are not likely to exist?

Answers

1. Metals in the +6 oxidation state are stabilized by oxide (O²⁻) and fluoride (F⁻). The M−F and M−O bonds are polar covalent due to extreme polarization of the anions by the highly charged metal. Ca, Sr, and Ba can be oxidized only to the dications (M²⁺), which form ionic oxides and fluorides.

3. Cyanide is a relatively soft base, and the early transition-metal cations are harder acids than the later transition metals.

5. The formation of complexes between NH₃ and a divalent cation is largely due to electrostatic interactions between the negative end of the ammonia dipole moment and the positively charged cation. Thus the smallest divalent cations (Ni²+, Zn²⁺, and Cu²⁺) will form the most stable complexes with ammonia.

7. Re²⁺ is a very soft cation, and F⁻ and O²⁻ are very hard bases, so ReO and ReF₂ are unlikely to exist. MnF₆ is also unlikely to exist: although fluoride should stabilize high oxidation states, in this case Mn⁶⁺ is probably too small to accommodate six F⁻ ions.

d-Orbital Splittings

CFT focuses on the interaction of the five (n − 1)d orbitals with ligands arranged in a regular array around a transition-metal ion. We will focus on the application of CFT to octahedral complexes, which are by far the most common and the easiest to visualize. Other common structures, such as square planar complexes, can be treated as a distortion of the octahedral model. According to CFT, an octahedral metal complex forms because of the electrostatic interaction of a positively charged metal ion with six negatively charged ligands or with the negative ends of dipoles associated with the six ligands. In addition, the ligands interact with one other electrostatically. As you learned in our discussion of the valence-shell electron-pair repulsion (VSEPR) model in Chapter 9 "Molecular Geometry and Covalent Bonding Models", the lowest-energy arrangement of six identical negative charges is an octahedron, which minimizes repulsive interactions between the ligands.

We begin by considering how the energies of the d orbitals of a transition-metal ion are affected by an octahedral arrangement of six negative charges. Recall from Chapter 6 "The Structure of Atoms" that the five d orbitals are initially degenerate (have the same energy). If we distribute six negative charges uniformly over the surface of a sphere, the d orbitals remain degenerate, but their energy will be higher due to repulsive electrostatic interactions between the spherical shell of negative charge and electrons in the d orbitals (part (a) in Figure 23.10 "An Octahedral Arrangement of Six Negative Charges around a Metal Ion Causes the Five "). Placing the six negative charges at the vertices of an octahedron does not change the average energy of the d orbitals, but it does remove their degeneracy: the five d orbitals split into two groups whose energies depend on their orientations. As shown in part (b) in Figure 23.10 "An Octahedral Arrangement of Six Negative Charges around a Metal Ion Causes the Five ", the $d_{z^2}$ and $d_{x^2-y^2}$ orbitals point directly at the six negative charges located on the x, y, and z axes. Consequently, the energy of an electron in these two orbitals (collectively labeled the e_g orbitals) will be greater than it will be for a spherical distribution of negative charge because of increased electrostatic repulsions. In contrast, the other three d orbitals (d_xy, d_xz, and d_yz, collectively called the t_2g orbitals) are all oriented at a 45° angle to the coordinate axes, so they point between the six negative charges. The energy of an electron in any of these three orbitals is lower than the energy for a spherical distribution of negative charge.

Figure 23.10 An Octahedral Arrangement of Six Negative Charges around a Metal Ion Causes the Five d Orbitals to Split into Two Sets with Different Energies

(a) Distributing a charge of −6 uniformly over a spherical surface surrounding a metal ion causes the energy of all five d orbitals to increase due to electrostatic repulsions, but the five d orbitals remain degenerate. Placing a charge of −1 at each vertex of an octahedron causes the d orbitals to split into two groups with different energies: the $d_{x^2-y^2}$ and $d_{z^2}$ orbitals increase in energy, while the, d_xy, d_xz, and d_yz orbitals decrease in energy. The average energy of the five d orbitals is the same as for a spherical distribution of a −6 charge, however. Attractive electrostatic interactions between the negatively charged ligands and the positively charged metal ion (far right) cause all five d orbitals to decrease in energy but does not affect the splittings of the orbitals. (b) The two e_g orbitals (left) point directly at the six negatively charged ligands, which increases their energy compared with a spherical distribution of negative charge. In contrast, the three t_2g orbitals (right) point between the negatively charged ligands, which decreases their energy compared with a spherical distribution of charge.

The difference in energy between the two sets of d orbitals is called the crystal field splitting energyThe difference in energy between the $e_g$ set of $d$ orbitals $(d_{z_2}$ and $d_{x_2-y_2})$ and the ${\text{t}}_{\text{2g}}$ set of $d$ orbitals $(d_{xy}$, $d_{xz}$, $d_{yz})$ that results when the five $d$ orbitals are placed in an octahedral crystal field. (Δ_o), where the subscript o stands for octahedral. As we shall see, the magnitude of the splitting depends on the charge on the metal ion, the position of the metal in the periodic table, and the nature of the ligands. (Crystal field splitting energy also applies to tetrahedral complexes: Δ_t.) It is important to note that the splitting of the d orbitals in a crystal field does not change the total energy of the five d orbitals: the two e_g orbitals increase in energy by 0.6Δ_o, whereas the three t_2g orbitals decrease in energy by 0.4Δ_o. Thus the total change in energy is 2(0.6Δ_o) + 3(−0.4Δ_o) = 0.

Thus far, we have considered only the effect of repulsive electrostatic interactions between electrons in the d orbitals and the six negatively charged ligands, which increases the total energy of the system and splits the d orbitals. Interactions between the positively charged metal ion and the ligands results in a net stabilization of the system, which decreases the energy of all five d orbitals without affecting their splitting (as shown at the far right in part (a) in Figure 23.10 "An Octahedral Arrangement of Six Negative Charges around a Metal Ion Causes the Five ").

Electronic Structures of Metal Complexes

We can use the d-orbital energy-level diagram in Figure 23.10 "An Octahedral Arrangement of Six Negative Charges around a Metal Ion Causes the Five " to predict electronic structures and some of the properties of transition-metal complexes. We start with the Ti³⁺ ion, which contains a single d electron, and proceed across the first row of the transition metals by adding a single electron at a time. We place additional electrons in the lowest-energy orbital available, while keeping their spins parallel as required by Hund’s rule. As shown in Figure 23.11 "The Possible Electron Configurations for Octahedral ", for d¹–d³ systems—such as [Ti(H₂O)₆]³⁺, [V(H₂O)₆]³⁺, and [Cr(H₂O)₆]³⁺, respectively—the electrons successively occupy the three degenerate t_2g orbitals with their spins parallel, giving one, two, and three unpaired electrons, respectively. We can summarize this for the complex [Cr(H₂O)₆]³⁺, for example, by saying that the chromium ion has a d³ electron configuration or, more succinctly, Cr³⁺ is a d³ ion.

Figure 23.11 The Possible Electron Configurations for Octahedral dⁿ Transition-Metal Complexes (n = 1–10)

Two different configurations are possible for octahedral complexes of metals with d⁴, d⁵, d⁶, and d⁷ configurations; the magnitude of Δ_o determines which configuration is observed.

When we reach the d⁴ configuration, there are two possible choices for the fourth electron: it can occupy either one of the empty e_g orbitals or one of the singly occupied t_2g orbitals. Recall from Chapter 6 "The Structure of Atoms" that placing an electron in an already occupied orbital results in electrostatic repulsions that increase the energy of the system; this increase in energy is called the spin-pairing energy (P)The energy that must be overcome to place an electron in an orbital that already has one electron.. If Δ_o is less than P, then the lowest-energy arrangement has the fourth electron in one of the empty e_g orbitals. Because this arrangement results in four unpaired electrons, it is called a high-spin configuration, and a complex with this electron configuration, such as the [Cr(H₂O)₆]²⁺ ion, is called a high-spin complex. Conversely, if Δ_o is greater than P, then the lowest-energy arrangement has the fourth electron in one of the occupied t_2g orbitals. Because this arrangement results in only two unpaired electrons, it is called a low-spin configuration, and a complex with this electron configuration, such as the [Mn(CN)₆]³⁻ ion, is called a low-spin complex. Similarly, metal ions with the d⁵, d⁶, or d⁷ electron configurations can be either high spin or low spin, depending on the magnitude of Δ_o.

In contrast, only one arrangement of d electrons is possible for metal ions with d⁸–d¹⁰ electron configurations. For example, the [Ni(H₂O)₆]²⁺ ion is d⁸ with two unpaired electrons, the [Cu(H₂O)₆]²⁺ ion is d⁹ with one unpaired electron, and the [Zn(H₂O)₆]²⁺ ion is d¹⁰ with no unpaired electrons.

Factors That Affect the Magnitude of Δ_o

The magnitude of Δ_o dictates whether a complex with four, five, six, or seven d electrons is high spin or low spin, which affects its magnetic properties, structure, and reactivity. Large values of Δ_o (i.e., Δ_o > P) yield a low-spin complex, whereas small values of Δ_o (i.e., Δ_o < P) produce a high-spin complex. As we noted, the magnitude of Δ_o depends on three factors: the charge on the metal ion, the principal quantum number of the metal (and thus its location in the periodic table), and the nature of the ligand. Values of Δ_o for some representative transition-metal complexes are given in Table 23.10 "Crystal Field Splitting Energies for Some Octahedral (Δ".

Colors of Transition-Metal Complexes

The striking colors exhibited by transition-metal complexes are caused by excitation of an electron from a lower-energy d orbital to a higher-energy d orbital, which is called a d–d transition (Figure 23.12 "A "). For a photon to effect such a transition, its energy must be equal to the difference in energy between the two d orbitals, which depends on the magnitude of Δ_o.

Figure 23.12 A d–d Transition

In a d–d transition, an electron in one of the t_2g orbitals of an octahedral complex such as the [Cr(H₂O)₆]³⁺ ion absorbs a photon of light with energy equal to Δ_o, which causes the electron to move to an empty or singly occupied e_g orbital.

Recall from Chapter 6 "The Structure of Atoms" that the color we observe when we look at an object or a compound is due to light that is transmitted or reflected, not light that is absorbed, and that reflected or transmitted light is complementary in color to the light that is absorbed. Thus a green compound absorbs light in the red portion of the visible spectrum and vice versa, as indicated by the color wheel in End-of-Chapter Application Problem 6 in Chapter 6 "The Structure of Atoms". Because the energy of a photon of light is inversely proportional to its wavelength, the color of a complex depends on the magnitude of Δ_o, which depends on the structure of the complex. For example, the complex [Cr(NH₃)₆]³⁺ has strong-field ligands and a relatively large Δ_o. Consequently, it absorbs relatively high-energy photons, corresponding to blue-violet light, which gives it a yellow color. A related complex with weak-field ligands, the [Cr(H₂O)₆]³⁺ ion, absorbs lower-energy photons corresponding to the yellow-green portion of the visible spectrum, giving it a deep violet color.

We can now understand why emeralds and rubies have such different colors, even though both contain Cr³⁺ in an octahedral environment provided by six oxide ions. Although the chemical identity of the six ligands is the same in both cases, the Cr–O distances are different because the compositions of the host lattices are different (Al₂O₃ in rubies and Be₃Al₂Si₆O₁₈ in emeralds). In ruby, the Cr–O distances are relatively short because of the constraints of the host lattice, which increases the d orbital–ligand interactions and makes Δ_o relatively large. Consequently, rubies absorb green light and the transmitted or reflected light is red, which gives the gem its characteristic color. In emerald, the Cr–O distances are longer due to relatively large [Si₆O₁₈]¹²⁻ silicate rings; this results in decreased d orbital–ligand interactions and a smaller Δ_o. Consequently, emeralds absorb light of a longer wavelength (red), which gives the gem its characteristic green color. It is clear that the environment of the transition-metal ion, which is determined by the host lattice, dramatically affects the spectroscopic properties of a metal ion.

Gem-quality crystals of ruby and emerald. The colors of both minerals are due to the presence of small amounts of Cr³⁺ impurities in octahedral sites in an otherwise colorless metal oxide lattice.

Crystal Field Stabilization Energies

Recall from Chapter 9 "Molecular Geometry and Covalent Bonding Models" that stable molecules contain more electrons in the lower-energy (bonding) molecular orbitals in a molecular orbital diagram than in the higher-energy (antibonding) molecular orbitals. If the lower-energy set of d orbitals (the t_2g orbitals) is selectively populated by electrons, then the stability of the complex increases. For example, the single d electron in a d¹ complex such as [Ti(H₂O)₆]³⁺ is located in one of the t_2g orbitals. Consequently, this complex will be more stable than expected on purely electrostatic grounds by 0.4Δ_o. The additional stabilization of a metal complex by selective population of the lower-energy d orbitals is called its crystal field stabilization energy (CFSE)The additional stabilization of a metal complex by selective population of the lower-energy $d$ orbitals (the t_2g orbitals).. The CFSE of a complex can be calculated by multiplying the number of electrons in t_2g orbitals by the energy of those orbitals (−0.4Δ_o), multiplying the number of electrons in e_g orbitals by the energy of those orbitals (+0.6Δ_o), and summing the two. Table 23.11 "CFSEs for Octahedral Complexes with Different Electron Configurations (in Units of Δ" gives CFSE values for octahedral complexes with different d electron configurations. The CFSE is highest for low-spin d⁶ complexes, which accounts in part for the extraordinarily large number of Co(III) complexes known. The other low-spin configurations also have high CFSEs, as does the d³ configuration.

CFSEs are important for two reasons. First, the existence of CFSE nicely accounts for the difference between experimentally measured values for bond energies in metal complexes and values calculated based solely on electrostatic interactions. Second, CFSEs represent relatively large amounts of energy (up to several hundred kilojoules per mole), which has important chemical consequences.

Tetragonal and Square Planar Complexes

If two trans ligands in an octahedral complex are either chemically different from the other four, as in the trans-[Co(NH₃)₄Cl₂]⁺ ion, or at a different distance from the metal than the other four, the result is a tetragonally distorted octahedral complex. The electronic structures of such complexes are best viewed as the result of distorting an octahedral complex. Consider, for example, an octahedral complex such as [Co(NH₃)₆]³⁺ and then slowly remove two trans NH₃ molecules by moving them away from the metal along the ±z axes, as shown in the top half of Figure 23.13. As the two axial Co–N distances increase simultaneously, the d orbitals that interact most strongly with the two axial ligands will decrease in energy due to a decrease in electrostatic repulsions between electrons in these orbitals and the negative ends of the ligand dipoles. The affected d orbitals are those with a component along the ±z axes—namely, $d_{z^2}$, d_xz, and d_yz. They will not be affected equally, however. Because the $d_{z^2}$ orbital points directly at the two ligands being removed, its energy will decrease much more rapidly than the energy of the other two, as shown in the bottom half of Figure 23.13. In addition, the positive charge on the metal will increase somewhat as the axial ligands are removed, causing the four remaining in-plane ligands to be more strongly attracted to the metal. This will increase their interactions with the other two d orbitals and increase their energy. Again, the two d orbitals will not be affected equally. Because the $d_{x^2-y^2}$ orbital points directly at the four in-plane ligands, its energy will increase more rapidly than the energy of the d_xy orbital, which points between the in-plane ligands. If we remove the two axial ligands to an infinite distance, we obtain a square planar complex. The energies of the $d_{z^2}$ and d_xy orbitals actually cross as the axial ligands are removed, and the largest orbital spliting in a square planar complex is identical in magnitude to Δ_o.

Figure 23.13 d-Orbital Splittings for Tetragonal and Square Planar Complexes

Moving the two axial ligands away from the metal ion along the z axis initially gives an elongated octahedral complex (center) and eventually produces a square planar complex (right). As shown below the structures, an axial elongation causes the $d_{z^2}$ d_xz and d_yz orbitals to decrease in energy and the $d_{x^2-y^2}$ and d_xy orbitals to increase in energy. As explained in the text, the change in energy is not the same for all five d orbitals. Removing the two axial ligands completely causes the energy of the $d_{z^2}$ orbital to decrease so much that the order of the $d_{z^2}$ and d_xy orbitals is reversed.

Tetrahedral Complexes

In a tetrahedral arrangement of four ligands around a metal ion, none of the ligands lies on any of the three coordinate axes (part (a) in Figure 23.14); consequently, none of the five d orbitals points directly at the ligands. Nonetheless, the d_xy, d_xz, and d_yz orbitals interact more strongly with the ligands than do $d_{x^2-y^2}$ and $d_{z^2}$ again resulting in a splitting of the five d orbitals into two sets. The splitting of the energies of the orbitals in a tetrahedral complex (Δ_t) is much smaller than that for Δ_o, however, for two reasons. First, the d orbitals interact less strongly with the ligands in a tetrahedral arrangement. Second, there are only four negative charges rather than six, which decreases the electrostatic interactions by one-third if all other factors are equal. It can be shown that, for complexes of the same metal ion with the same charge, the same ligands, and the same M–L distance, ${\Delta }_{\text{t}}=\frac{4}{9}{\Delta }_{\text{o}}\text{.}$ The relationship between the splitting of the five d orbitals in octahedral and tetrahedral crystal fields imposed by the same ligands is shown schematically in part (b) in Figure 23.14.

Figure 23.14 d-Orbital Splittings for a Tetrahedral Complex

(a) In a tetrahedral complex, none of the five d orbitals points directly at or between the ligands. (b) Because the d_xy, d_xz, and d_yz orbitals (the t_2g orbitals) interact more strongly with the ligands than do the $d_{x^2-y^2}$ and $d_{z^2}$ orbitals (the e_g orbitals), the order of orbital energies in a tetrahedral complex is the opposite of the order in an octahedral complex.

Because Δ_o is so large for the second- and third-row transition metals, all four-coordinate complexes of these metals are square planar due to the much higher CFSE for square planar versus tetrahedral structures. The only exception is for d¹⁰ metal ions such as Cd²⁺, which have zero CFSE and are therefore tetrahedral as predicted by the VSEPR model. Four-coordinate complexes of the first-row transition metals can be either square planar or tetrahedral. The former is favored by strong-field ligands, whereas the latter is favored by weak-field ligands. For example, the [Ni(CN)₄]²⁻ ion is square planar, while the [NiCl₄]²⁻ ion is tetrahedral.

Consequences of d-Orbital Splitting

The splitting of the d orbitals because of their interaction with the ligands in a complex has important consequences for the chemistry of transition-metal complexes; they can be divided into structural effects and thermodynamic effects. Although the two kinds of effects are interrelated, we will consider them separately.

Structural Effects

There are two major kinds of structural effects: effects on the ionic radius of metal ions with regular octahedral or tetrahedral geometries, and structural distortions that are observed for specific electron configurations.

Ionic Radii

Figure 23.15 "The Effect of " is a plot of the ionic radii of the divalent fourth-period metal ions versus atomic number. Only Ca²⁺(d⁰), Mn²⁺ (high-spin d⁵), and Zn²⁺ (d¹⁰) fall on the smooth curve calculated based on the effective nuclear charge (Z_eff), which assumes that the distribution of d electrons is spherically symmetrical. All the other divalent ions fall below this curve because they have asymmetrical distributions of d electrons. (The points shown for Cr²⁺ and Cu²⁺ are only estimated values; as you will learn shortly, these two ions do not form any truly octahedral complexes.) To see why an asymmetrical distribution of d electrons makes a metal ion smaller than expected, consider the Ti²⁺ ion, which has a d² configuration with both electrons in the t_2g orbitals. Because the t_2g orbitals are directed between the ligands, the two d electrons are unable to shield the ligands from the nuclear charge. Consequently, the ligands experience a higher effective nuclear charge than expected, the metal–ligand distance is unusually short, and the ionic radius is smaller than expected. If instead the two electrons were distributed uniformly over all five d orbitals, they would be much more effective at screening the ligands from the nuclear charge, making the metal–ligand distances longer and giving a larger ionic radius.

Figure 23.15 The Effect of d-Orbital Splittings on the Radii of the Divalent Ions of the Fourth-Period Metals

Because these radii are based on the structures of octahedral complexes and Cr²⁺ and Cu²⁺ do not form truly octahedral complexes, the points for these ions are shown as open circles. The dashed line represents the behavior predicted based on the effects of screening and variation in effective nuclear charge (Z_eff), assuming a spherical distribution of the 3d electrons.

A similar effect is observed for the V²⁺ ion, which has a d³ configuration. Because the three electrons in the t_2g orbitals provide essentially no shielding of the ligands from the metal, the ligands experience the full increase of +1 in nuclear charge that occurs in going from Ti²⁺ to V²⁺. Consequently, the observed ionic radius of the V²⁺ ion is significantly smaller than that of the Ti²⁺ ion.

Skipping the Cr²⁺ ion for the moment, we next consider the d⁵ Mn²⁺ ion. Because the nuclear charge increases by +2 from V²⁺ to Mn²⁺, we might expect Mn²⁺ to be smaller than V²⁺. The two electrons that are also added from V²⁺ to Mn²⁺ occupy the e_g orbitals, however, which point directly at the six ligands. Because these electrons are localized directly between the metal ion and the ligands, they are effective at screening the ligands from the increased nuclear charge. As a result, the ionic radius actually increases significantly as we go from V²⁺ to Mn²⁺, despite the higher nuclear charge of the latter.

Exactly the same effects are seen in the second half of the first-row transition metals. In the Fe²⁺, Co²⁺, and Ni²⁺ ions, the extra electrons are added successively to the t_2g orbitals, resulting in poor shielding of the ligands from the nuclear charge and abnormally small ionic radii. Skipping over Cu²⁺, we again see that adding the last two electrons causes a significant increase in the ionic radius of Zn²⁺, despite its higher nuclear charge.

The Jahn–Teller Effect

Because simple octahedral complexes are not known for the Cr²⁺ and Cu²⁺ ions, only estimated values for their radii are shown in Figure 23.15 "The Effect of ". We see in Figure 23.11 "The Possible Electron Configurations for Octahedral " that both the Cr²⁺ and Cu²⁺ ions have electron configurations with an odd number of electrons in the e_g orbitals. Because the single electron (in the case of Cr²⁺) or the third electron (in the case of Cu²⁺) can occupy either one of two degenerate e_g orbitals, they have what is called a degenerate ground state. The Jahn–Teller theoremA theory that states that a non-linear molecule with a spatially degenerate electronic ground state will undergo a geometrical distortion to remove the degeneracy and lower the overall energy of the system. states that such non-linear systems are not stable; they will undergo a distortion that makes the complex less symmetrical and splits the degenerate states, which decreases the energy of the system. The distortion and resulting decrease in energy are collectively referred to as the Jahn–Teller effect. Neither the nature of the distortion nor its magnitude is specified, and in fact, they are difficult to predict. In principle, Jahn–Teller distortions are possible for many transition-metal ions; in practice, however, they are observed only for systems with an odd number of electrons in the e_g orbitals, such as the Cr²⁺ and Cu²⁺ ions.

To see how a geometrical distortion can decrease the energy of such a system, consider an octahedral Cu²⁺ complex, the [Cu(H₂O)₆]²⁺ ion, which has been elongated along the z axis. As indicated in Figure 23.16 "The Jahn–Teller Effect", this kind of distortion splits both the e_g and t_2g sets of orbitals. Because the axial ligands interact most strongly with the $d_{z^2}$ orbital, the splitting of the e_g set (δ₁) is significantly larger than the splitting of the t_2g set (δ₂), but both δ₁ and δ₂ are much, much smaller than the Δ_o. This splitting does not change the center of gravity of the energy within each set, so a Jahn–Teller distortion results in no net change in energy for a filled or half-filled set of orbitals. If, however, the e_g set contains one (as in the d⁴ ions, Cr²⁺ and Mn³⁺) or three (as in the d⁹ ion, Cu²⁺) electrons, the distortion decreases the energy of the system. For Cu²⁺, for example, the change in energy after distortion is 2(−δ₁/2) + 1(δ₁/2) = −δ₁/2. For Cu²⁺ complexes, the observed distortion is always an elongation along the z axis by as much as 50 pm; in fact, many Cu²⁺ complexes are so distorted that they are effectively square planar. In contrast, the distortion observed for most Cr²⁺ complexes is a compression along the z axis. In both cases, however, the net effect is the same: the distorted system is more stable than the undistorted system.

Note the Pattern

Jahn–Teller distortions are most important for d⁹ and high-spin d⁴ complexes; the distorted system is more stable than the undistorted one.

Figure 23.16 The Jahn–Teller Effect

Increasing the axial metal–ligand distances in an octahedral d⁹ complex is an example of a Jahn–Teller distortion, which causes the degenerate pair of e_g orbitals to split in energy by an amount δ₁; δ₁ and δ₂ are much smaller than Δ_o. As a result, the distorted system is more stable (lower in energy) than the undistorted complex by δ₁/2.

Thermodynamic Effects

As we previously noted, CFSEs can be as large as several hundred kilojoules per mole, which is the same magnitude as the strength of many chemical bonds or the energy change in most chemical reactions. Consequently, CFSEs are important factors in determining the magnitude of hydration energies, lattice energies, and other thermodynamic properties of the transition metals.

Hydration Energies

The hydration energy of a metal ion is defined as the change in enthalpy for the following reaction:

Equation 23.12

M²⁺(g) + H₂O(l) → M²⁺(aq)

Although hydration energies cannot be measured directly, they can be calculated from experimentally measured quantities using thermochemical cycles. As shown in part (a) in Figure 23.17 "Thermochemical Effects of ", a plot of the hydration energies of the fourth-period metal dications versus atomic number gives a curve with two valleys. Note the relationship between the plot in part (a) in Figure 23.17 "Thermochemical Effects of " and the plot of ionic radii in Figure 23.15 "The Effect of ": the overall shapes are essentially identical, and only the three cations with spherically symmetrical distributions of d electrons (Ca²⁺, Mn²⁺, and Zn²⁺) lie on the dashed lines. In part (a) in Figure 23.17 "Thermochemical Effects of ", the dashed line corresponds to hydration energies calculated based solely on electrostatic interactions. Subtracting the CFSE values for the [M(H₂O)₆]²⁺ ions from the experimentally determined hydration energies gives the points shown as open circles, which lie very near the calculated curve. Thus CFSEs are primarily responsible for the differences between the measured and calculated values of hydration energies.

Figure 23.17 Thermochemical Effects of d-Orbital Splittings

(a) A plot of the hydration energies of the divalent fourth-period metal ions versus atomic number (solid circles) shows large deviations from the smooth curve calculated, assuming a spherical distribution of d electrons (dashed line). Correcting for CFSE gives the points shown as open circles, which, except for Ti²⁺ and Cr²⁺, are close to the calculated values. The apparent deviations for these ions are caused by the fact that solutions of the Ti²⁺ ion in water are not stable, and Cr²⁺ does not form truly octahedral complexes. (b) A plot of the lattice energies for the fourth-period metal dichlorides versus atomic number shows similar deviations from the smooth curve calculated, assuming a spherical distribution of d electrons (dashed lines), again illustrating the importance of CFSEs.

Lattice Energies

Values of the lattice energies for the fourth-period metal dichlorides are plotted versus atomic number in part (b) in Figure 23.17 "Thermochemical Effects of ". Recall that the lattice energy is defined as the negative of the enthalpy change for the following reaction. Like hydration energies, lattice energies are determined indirectly by using a thermochemical cycle:

Equation 23.13

M²⁺(g) + 2Cl⁻(g) → MCl₂(s)

The shape of the lattice-energy curve is essentially the mirror image of the hydration-energy curve in part (a) in Figure 23.19 "Ferritin, an Iron Storage Protein", with only Ca²⁺, Mn²⁺, and Zn²⁺ lying on the smooth curve. It is not surprising that the explanation for the deviations from the curve is exactly the same as for the hydration energy data: all the transition-metal dichlorides, except MnCl₂ and ZnCl₂, are more stable than expected due to CFSE.

Summary

Crystal field theory (CFT) is a bonding model that explains many properties of transition metals that cannot be explained using valence bond theory. In CFT, complex formation is assumed to be due to electrostatic interactions between a central metal ion and a set of negatively charged ligands or ligand dipoles arranged around the metal ion. Depending on the arrangement of the ligands, the d orbitals split into sets of orbitals with different energies. The difference between the energy levels in an octahedral complex is called the crystal field splitting energy (Δ_o), whose magnitude depends on the charge on the metal ion, the position of the metal in the periodic table, and the nature of the ligands. The spin-pairing energy (P) is the increase in energy that occurs when an electron is added to an already occupied orbital. A high-spin configuration occurs when the Δ_o is less than P, which produces complexes with the maximum number of unpaired electrons possible. Conversely, a low-spin configuration occurs when the Δ_o is greater than P, which produces complexes with the minimum number of unpaired electrons possible. Strong-field ligands interact strongly with the d orbitals of the metal ions and give a large Δ_o, whereas weak-field ligands interact more weakly and give a smaller Δ_o. The colors of transition-metal complexes depend on the environment of the metal ion and can be explained by CFT. Distorting an octahedral complex by moving opposite ligands away from the metal produces a tetragonal or square planar arrangement, in which interactions with equatorial ligands become stronger. Because none of the d orbitals points directly at the ligands in a tetrahedral complex, these complexes have smaller values of the crystal field splitting energy Δ_t. The crystal field stabilization energy (CFSE) is the additional stabilization of a complex due to placing electrons in the lower-energy set of d orbitals. CFSE explains the unusual curves seen in plots of ionic radii, hydration energies, and lattice energies versus atomic number. The Jahn–Teller theorem states that a non-linear molecule with a spatially degenerate electronic ground state will undergo a geometrical distortion to remove the degeneracy and lower the overall energy of the system.

Key Takeaway

• Crystal field theory, which assumes that metal–ligand interactions are only electrostatic in nature, explains many important properties of transition-metal complexes, including their colors, magnetism, structures, stability, and reactivity.

Conceptual Problems

1. Describe crystal field theory in terms of its

   1. assumptions regarding metal–ligand interactions.
   2. weaknesses and strengths compared with valence bond theory.

2. In CFT, what causes degenerate sets of d orbitals to split into different energy levels? What is this splitting called? On what does the magnitude of the splitting depend?

3. Will the value of Δ_o increase or decrease if I⁻ ligands are replaced by NO₂⁻ ligands? Why?

4. For an octahedral complex of a metal ion with a d⁶ configuration, what factors favor a high-spin configuration versus a low-spin configuration?

5. How can CFT explain the color of a transition-metal complex?

Structure and Reactivity

1. Do strong-field ligands favor a tetrahedral or a square planar structure? Why?

2. For each complex, predict its structure, whether it is high spin or low spin, and the number of unpaired electrons present.

   1. [TiCl₆]³⁻
   2. [CoCl₄]²⁻

3. For each complex, predict its structure, whether it is high spin or low spin, and the number of unpaired electrons present.

   1. [Cu(NH₃)₄]²⁺
   2. [Ni(CN)₄]²⁻

4. The ionic radii of V²⁺, Fe²⁺, and Zn²⁺ are all roughly the same (approximately 76 pm). Given their positions in the periodic table, explain why their ionic radii are so similar.

Answer

3. 1. d⁹, square planar, neither high nor low spin, single unpaired electron
   2. d⁸, square planar, low spin, no unpaired electrons

Uptake and Storage of Transition Metals

In Chapter 1 "Introduction to Chemistry", we described the three possible dietary levels for any essential element: deficient, optimal, and toxic, in order of increasing concentration in the diet (Figure 1.27 "Possible Concentrations of an Essential Element in the Diet"). If the concentration of an essential element in the diet is too low, an organism must be able to extract the element from the environment and concentrate it. If the concentration of an essential element in the diet is too high, an organism must be able to limit its intake to avoid toxic effects. Moreover, organisms must be able to switch off the uptake process rapidly if dietary levels rise suddenly, and they must be able to store essential elements for future use.

Three distinct steps are involved in transition metal uptake. First, the metal must be “mobilized” from the environment and brought into contact with a cell in a form that can be absorbed. Second, the metal must be transported across the cell membrane into the cell. Third, the element must be transported to its point of utilization within a cell or to other cells within the organism. In our discussion, we focus on the uptake, transport, and storage of iron, which illustrates the most important points. Because iron deficiency (anemia) is the most widespread nutritional deficiency known in humans, the uptake of iron is especially well understood.

Iron complexes in biological systems. Iron(III) forms very stable octahedral complexes with hydroxamate and catecholate ligands.

In Chapter 17 "Solubility and Complexation Equilibriums", you learned that the solubility of metal ions such as Fe³⁺, which form highly insoluble hydroxides, depends on the pH and the presence of complexing agents. In an oxygen-containing atmosphere, iron exists as Fe(III) because of the positive reduction potential of Fe³⁺ (Fe³⁺ + e⁻ → Fe²⁺; E° = +0.77 V). Because ferric hydroxide [Fe(OH)₃] is highly insoluble (K_sp ≈ 1 × 10⁻³⁹), the equilibrium concentration of Fe³⁺(aq) at pH 7.0 is very low, about 10⁻¹⁸ M. You would have to drink 2 × 10¹³ L of iron-saturated water per day (roughly 5 mi³) to consume the recommended daily intake of Fe for humans, which is about 1 mg/day. Animals such as humans can overcome this problem by consuming concentrated sources of iron, such as red meat, but microorganisms cannot.

Consequently, most microorganisms synthesize and secrete organic molecules called siderophoresAn organic ligand that has a high affinity for Fe(III) and is secreted into the surrounding medium to increase the total concentration of dissolved iron. to increase the total concentration of available iron in the surrounding medium. Siderophores are generally cyclic compounds that use bidentate ligands, such as the hydroxamate and catecholate groups shown here, to bind Fe³⁺ in an octahedral arrangement. Typical siderophores are ferrichrome, a cyclic peptide produced by fungi, and enterobactin, a cyclic ester produced by bacteria (Figure 23.18 "Siderophores"). Attaching the three iron ligands to a cyclic framework greatly increases the stability of the resulting Fe³⁺ complex due to the chelate effect described in Section 23.4 "Coordination Compounds". The formation constants for the Fe³⁺ complexes of ferrichrome and enterobactin are about 10³² and 10⁴⁰, respectively, which are high enough to allow them to dissolve almost any Fe(III) compound.

Figure 23.18 Siderophores

Ferrichrome (a) and enterobactin (b) are siderophores that use hydroxamate and catecholate ligands, respectively, to bind Fe³⁺. The “wrapped” drawing of enterobactin (c) shows how the cyclic ester framework places the three catecholate ligands in the correct orientation to bind to a single Fe³⁺ ion, which is an application of the chelate effect. The actual structure of ferrichrome is similar to that of enterobactin, with the three hydroxamate ligands adjacent to one another for optimal binding of Fe³⁺. Note: For clarity, most or all hydrogen atoms have been omitted in this and the following structures.

Siderophores increase the [Fe³⁺] in solution, providing the bacterium that synthesized them (as well as any competitors) with a supply of iron. In addition, siderophores neutralize the positive charge on the metal ion and provide a hydrophobic “wrapping” that enables the Fe³⁺–siderophore complex to be recognized by a specific protein that transports it into the interior of a cell. Once it is inside a cell, the iron is reduced to Fe²⁺, which has a much lower affinity for the siderophore and spontaneously dissociates.

In contrast, multicellular organisms can increase the concentration of iron in their diet by lowering the pH in the gastrointestinal tract. At pH 1.0 (the approximate pH of the stomach), most Fe(III) salts dissolve to form Fe³⁺(aq), which is absorbed by specific proteins in the intestinal wall. A protein called transferrin forms a complex with iron(III), allowing it to be transported to other cells. Proteins that bind tightly to Fe(III) can also be used as antibacterial agents because iron is absolutely essential for bacterial growth. For example, milk, tears, and egg white all contain proteins similar to transferrin, and their high affinity for Fe³⁺ allows them to sequester iron, thereby preventing bacteria from growing in these nutrient-rich media.

Iron is released from transferrin by reduction to Fe²⁺, and then it is either used immediately (e.g., for the synthesis of hemoglobin) or stored in a very large protein called ferritin for future use (Figure 23.19 "Ferritin, an Iron Storage Protein"). Ferritin uses oxygen to oxidize Fe²⁺ to Fe³⁺, which at neutral pH precipitates in the central cavity of the protein as a polymeric mixture of Fe(OH)₃ and FePO₄. Because a fully loaded ferritin molecule can contain as many as 4500 Fe atoms, which corresponds to about 25% Fe by mass, ferritin is an effective way to store iron in a highly concentrated form. When iron is needed by a cell, the Fe³⁺ is reduced to the much more soluble Fe²⁺ by a reductant such as ascorbic acid (vitamin C). The structure of ferritin contains channels at the junctions of the subunits, which provide pathways for iron to enter and leave the interior of a molecule.

Figure 23.19 Ferritin, an Iron Storage Protein

A schematic drawing of the structure of iron-loaded ferritin, showing the almost spherical protein shell inside which the iron hydroxide/phosphate core is formed.

Metalloproteins and Metalloenzymes

A protein that contains one or more metal ions tightly bound to amino acid side chains is called a metalloproteinA protein that contains one or more tightly bound metal ions.; some of the most common ligands provided by amino acids are shown here. A metalloprotein that catalyzes a chemical reaction is a metalloenzymeA protein that contains one or more tightly bound metal ions and catalyzes a biochemical reaction.. Thus all metalloenzymes are metalloproteins, but the converse is not true. Recent estimates suggest that more than 40% of all known enzymes require at least one metal ion for activity, including almost all the enzymes responsible for the synthesis, duplication, and repair of DNA (deoxyribonucleic acid) and RNA (ribonucleic acid).

Ligands used in biological systems. These metal ligands are commonly found in metalloproteins.

Electron-Transfer Proteins

Proteins whose function is to transfer electrons from one place to another are called electron-transfer proteins. Because they do not catalyze a chemical reaction, electron-transfer proteins are not enzymes; they are biochemical reductants or oxidants consumed in an enzymatic reaction. The general reaction for an electron-transfer protein is as follows:

Because many transition metals can exist in more than one oxidation state, electron-transfer proteins usually contain one or more metal ions that can undergo a redox reaction. Incorporating a metal ion into a protein has three important biological consequences:

1. The protein environment can adjust the redox potential (E⁰′), of the metal ion over a rather large potential range, whereas the redox potential of the simple hydrated metal ion [M_n⁺(aq)], is essentially fixed.
2. The protein can adjust the structure of the metal complex to ensure that electron transfer is rapid.
3. The protein environment provides specificity, ensuring that the electron is transferred to only the desired site.

Three important classes of metalloproteins transfer electrons: blue copper proteins, cytochromes, and iron–sulfur proteins, which generally transfer electrons at high (> 0.20 V), intermediate (±0 V), and low (−0.20 to −0.50 V) potentials, respectively (Table 23.12 "Some Properties of the Most Common Electron-Transfer Proteins"). Although these electron-transfer proteins contain different metals with different structures, they are all designed to ensure rapid electron transfer to and from the metal. Thus when the protein collides with its physiological oxidant or reductant, electron transfer can occur before the two proteins diffuse apart. For electron transfer to be rapid, the metal sites in the oxidized and reduced forms of the protein must have similar structures.

Blue Copper Proteins

Figure 23.20 A Blue Copper Protein

In both the oxidized and reduced forms of a blue copper protein, the copper is coordinated by four ligands (two histidine imidazole nitrogen atoms, a cysteine thiolate sulfur, and a thioether sulfur of a methionine) in a roughly tetrahedral arrangement.

Blue copper proteins were first isolated from bacteria in the 1950s and from plant tissues in the early 1960s. The intense blue color of these proteins is due to a strong absorption band at a wavelength of about 600 nm. Although simple Cu²⁺ complexes, such as [Cu(H₂O)₆]²⁺ and [Cu(NH₃)₄]²⁺, are also blue due to an absorption band at 600 nm, the intensity of the absorption band is about 100 times less than that of a blue copper protein. Moreover, the reduction potential for the Cu²⁺/Cu⁺ couple in a blue copper protein is usually +0.3 to +0.5 V, considerably more positive than that of the aqueous Cu²⁺/Cu⁺ couple (+0.15 V).

The copper center in blue copper proteins has a distorted tetrahedral structure, in which the copper is bound to four amino acid side chains (Figure 23.20 "A Blue Copper Protein"). Although the most common structures for four-coordinate Cu²⁺ and Cu⁺ complexes are square planar and tetrahedral, respectively, the structures of the oxidized (Cu²⁺) and reduced (Cu⁺) forms of the protein are essentially identical. Thus the protein forces the Cu²⁺ ion to adopt a higher-energy structure that is more suitable for Cu⁺, which makes the Cu²⁺ form easier to reduce and raises its reduction potential.

Moreover, by forcing the oxidized and reduced forms of the metal complex to have essentially the same structure, the protein ensures that electron transfer to and from the copper site is rapid because only minimal structural reorganization of the metal center is required. Kinetics studies on simple metal complexes have shown that electron-transfer reactions tend to be slow when the structures of the oxidized and reduced forms of a metal complex are very different, and fast when they are similar. You will see that other metal centers used for biological electron-transfer reactions are also set up for minimal structural reorganization after electron transfer, which ensures the rapid transfer of electrons.

Cytochromes

The cytochromes (from the Greek cytos, meaning “cell”, and chroma, meaning “color”) were first identified in the 1920s by spectroscopic studies of cell extracts. Based on the wavelength of the maximum absorption in the visible spectrum, they were classified as cytochromes a (with the longest wavelength), cytochromes b (intermediate wavelength), and cytochromes c (shortest wavelength). It quickly became apparent that there was a correlation between their spectroscopic properties and other physical properties. For examples, cytochromes c are generally small, soluble proteins with a reduction potential of about +0.25 V, whereas cytochromes b are larger, less-soluble proteins with reduction potentials of about 0 V.

All cytochromes contain iron, and the iron atom in all cytochromes is coordinated by a planar array of four nitrogen atoms provided by a cyclic tetradentate ligand called a porphyrin. The iron–porphyrin unit is called a heme group. The structures of a typical porphyrin (protoporphyrin IX) and its iron complex (protoheme) are shown here. In addition to the four nitrogen atoms of the porphyrin, the iron in a cytochrome is usually bonded to two additional ligands provided by the protein, as shown in Figure 23.21 "A Cytochrome ".

A cytochrome. Shown here is protoporphyrin IX and its iron complex, protoheme.

Figure 23.21 A Cytochrome c

In a cytochrome c, the heme iron is coordinated to the nitrogen atom of a histidine imidazole and the sulfur atom of a methionine thioether, in addition to the four nitrogen atoms provided by the porphyrin.

In contrast to the blue copper proteins, two electron configurations are possible for both the oxidized and reduced forms of a cytochrome, and this has significant structural consequences. Thus Fe²⁺ is d⁶ and can be either high spin (with four unpaired electrons) or low spin (with no unpaired electrons; Figure 23.11 "The Possible Electron Configurations for Octahedral "). Similarly, Fe³⁺ is d⁵ and can also be high spin (with five unpaired electrons) or low spin (with one unpaired electron). In low-spin heme complexes, both the Fe²⁺ and the Fe³⁺ ions are small enough to fit into the “hole” in the center of the porphyrin; hence the iron atom lies almost exactly in the plane of the four porphyrin nitrogen atoms in both cases. Because cytochromes b and c are low spin in both their oxidized and reduced forms, the structures of the oxidized and reduced cytochromes are essentially identical. Hence minimal structural changes occur after oxidation or reduction, which makes electron transfer to or from the heme very rapid.

Note the Pattern

Electron transfer reactions occur most rapidly when minimal structural changes occur during oxidation or reduction.

Iron–Sulfur Proteins

Although all known bacteria, plants, and animals use iron–sulfur proteins to transfer electrons, the existence of these proteins was not recognized until the late 1950s. Iron–sulfur proteins transfer electrons over a wide range of reduction potentials, and their iron content can range from 1 to more than 12 Fe atoms per protein molecule. In addition, most iron–sulfur proteins contain stoichiometric amounts of sulfide (S²⁻).

These properties are due to the presence of four different kinds of iron–sulfur units, which contain one, two, three, or four iron atoms per Fe–S complex (Figure 23.22 "Fe–S Centers in Proteins"). In all cases, the Fe²⁺ and Fe³⁺ ions are coordinated to four sulfur ligands in a tetrahedral environment. Due to tetrahedral coordination by weak-field sulfur ligands, the iron is high spin in both the Fe³⁺ and Fe²⁺ oxidation states, which results in similar structures for the oxidized and reduced forms of the Fe–S complexes. Consequently, only small structural changes occur after oxidation or reduction of the Fe–S center, which results in rapid electron transfer.

Figure 23.22 Fe–S Centers in Proteins

Four kinds of iron–sulfur centers, containing one, two, three, and four iron atoms, respectively, are known in electron-transfer proteins. Although they differ in the number of sulfur atoms provided by cysteine thiolates versus sulfide, in all cases the iron is coordinated to four sulfur ligands in a roughly tetrahedral environment.

Reactions of Small Molecules

Although small molecules, such as O₂, N₂, and H₂, do not react with organic compounds under ambient conditions, they do react with many transition-metal complexes. Consequently, virtually all organisms use metalloproteins to bind, transport, and catalyze the reactions of these molecules. Probably the best-known example is hemoglobin, which is used to transport O₂ in many multicellular organisms.

Myoglobin and Hemoglobin

Myoglobin is a relatively small protein that contains 150 amino acids. The functional unit of myoglobin is an iron–porphyrin complex that is embedded in the protein (Figure 23.23 "The Structure of Deoxymyoglobin, Showing the Heme Group"). In myoglobin, the heme iron is five-coordinate, with only a single histidine imidazole ligand from the protein (called the proximal histidine because it is near the iron) in addition to the four nitrogen atoms of the porphyrin. A second histidine imidazole (the distal histidine because it is more distant from the iron) is located on the other side of the heme group, too far from the iron to be bonded to it. Consequently, the iron atom has a vacant coordination site, which is where O₂ binds. In the ferrous form (deoxymyoglobin), the iron is five-coordinate and high spin. Because high-spin Fe²⁺ is too large to fit into the “hole” in the center of the porphyrin, it is about 60 pm above the plane of the porphyrin. When O₂ binds to deoxymyoglobin to form oxymyoglobin, the iron is converted from five-coordinate (high spin) to six-coordinate (low spin; Figure 23.24 "Oxygen Binding to Myoglobin and Hemoglobin"). Because low-spin Fe²⁺ and Fe³⁺ are smaller than high-spin Fe²⁺, the iron atom moves into the plane of the porphyrin ring to form an octahedral complex. The O₂ pressure at which half of the molecules in a solution of myoglobin are bound to O₂ (P_1/2) is about 1 mm Hg (1.3 × 10⁻³ atm).

Note the Pattern

A vacant coordination site at a metal center in a protein usually indicates that a small molecule will bind to the metal ion, whereas a coordinatively saturated metal center is usually involved in electron transfer.

Figure 23.23 The Structure of Deoxymyoglobin, Showing the Heme Group

The iron in deoxymyoglobin is five-coordinate, with one histidine imidazole ligand from the protein. Oxygen binds at the vacant site on iron.

Figure 23.24 Oxygen Binding to Myoglobin and Hemoglobin

(a) The Fe²⁺ ion in deoxymyoglobin is high spin, which makes it too large to fit into the “hole” in the center of the porphyrin. (b) When O₂ binds to deoxymyoglobin, the iron is converted to low-spin Fe³⁺, which is smaller, allowing the iron to move into the plane of the four nitrogen atoms of the porphyrin to form an octahedral complex.

Hemoglobin consists of two subunits of 141 amino acids and two subunits of 146 amino acids, both similar to myoglobin; it is called a tetramer because of its four subunits. Because hemoglobin has very different O₂-binding properties, however, it is not simply a “super myoglobin” that can carry four O₂ molecules simultaneously (one per heme group). The shape of the O₂-binding curve of myoglobin (Mb; Figure 23.25 "The O") can be described mathematically by the following equilibrium:

Equation 23.15

$$\begin{array}{cc}{\text{MbO}}_2\rightleftharpoons \text{Mb }+{\text{ O}}_2& K_{\text{diss}}=\frac{\text{[Mb]}[{\text{O}}_2]}{[{\text{MbO}}_2]}\end{array}$$

In contrast, the O₂-binding curve of hemoglobin is S shaped (Figure 23.25 "The O"). As shown in the curves, at low oxygen pressures, the affinity of deoxyhemoglobin for O₂ is substantially lower than that of myoglobin, whereas at high O₂ pressures the two proteins have comparable O₂ affinities. The physiological consequences of the unusual S-shaped O₂-binding curve of hemoglobin are enormous. In the lungs, where O₂ pressure is highest, the high oxygen affinity of deoxyhemoglobin allows it to be completely loaded with O₂, giving four O₂ molecules per hemoglobin. In the tissues, however, where the oxygen pressure is much lower, the decreased oxygen affinity of hemoglobin allows it to release O₂, resulting in a net transfer of oxygen to myoglobin.

Figure 23.25 The O₂-Binding Curves of Myoglobin and Hemoglobin

The curve for myoglobin can be described by a simple equilibrium between deoxy- and oxymyoglobin, but the S-shaped curve for hemoglobin can be described only in terms of a cooperative interaction between the four hemes.

The S-shaped O₂-binding curve of hemoglobin is due to a phenomenon called cooperativity, in which the affinity of one heme for O₂ depends on whether the other hemes are already bound to O₂. Cooperativity in hemoglobin requires an interaction between the four heme groups in the hemoglobin tetramer, even though they are more than 3000 pm apart, and depends on the change in structure of the heme group that occurs with oxygen binding. The structures of deoxyhemoglobin and oxyhemoglobin are slightly different, and as a result, deoxyhemoglobin has a much lower O₂ affinity than myoglobin, whereas the O₂ affinity of oxyhemoglobin is essentially identical to that of oxymyoglobin. Binding of the first two O₂ molecules to deoxyhemoglobin causes the overall structure of the protein to change to that of oxyhemoglobin; consequently, the last two heme groups have a much higher affinity for O₂ than the first two.

Oxygen is not unique in its ability to bind to a ferrous heme complex; small molecules such as CO and NO bind to deoxymyoglobin even more tightly than does O₂. The interaction of the heme iron with oxygen and other diatomic molecules involves the transfer of electron density from the filled t_2g orbitals of the low-spin d⁶ Fe²⁺ ion to the empty π* orbitals of the ligand. In the case of the Fe²⁺–O₂ interaction, the transfer of electron density is so great that the Fe–O₂ unit can be described as containing low-spin Fe³⁺ (d⁵) and O₂⁻. We can therefore represent the binding of O₂ to deoxyhemoglobin and its release as a reversible redox reaction:

Equation 23.16

Fe²⁺ + O₂ ⇌ Fe³⁺–O₂⁻

As shown in Figure 23.26 "Binding of O", the Fe–O₂ unit is bent, with an Fe–O–O angle of about 130°. Because the π* orbitals in CO are empty and those in NO are singly occupied, these ligands interact more strongly with Fe²⁺ than does O₂, in which the π* orbitals of the neutral ligand are doubly occupied.

Figure 23.26 Binding of O₂ and CO to the Iron of Myoglobin

Because the Fe–O–O unit is bent, while the Fe–C–O unit is linear, the imidazole group of the distal histidine in hemoglobin interferes with CO binding and decreases the affinity of hemoglobin for CO.

Although CO has a much greater affinity for a ferrous heme than does O₂ (by a factor of about 25,000), the affinity of CO for deoxyhemoglobin is only about 200 times greater than that of O₂, which suggests that something in the protein is decreasing its affinity for CO by a factor of about 100. Both CO and NO bind to ferrous hemes in a linear fashion, with an Fe–C(N)–O angle of about 180°, and the difference in the preferred geometry of O₂ and CO provides a plausible explanation for the difference in affinities. As shown in Figure 23.26 "Binding of O", the imidazole group of the distal histidine is located precisely where the oxygen atom of bound CO would be if the Fe–C–O unit were linear. Consequently, CO cannot bind to the heme in a linear fashion; instead, it is forced to bind in a bent mode that is similar to the preferred structure for the Fe–O₂ unit. This results in a significant decrease in the affinity of the heme for CO, while leaving the O₂ affinity unchanged, which is important because carbon monoxide is produced continuously in the body by degradation of the porphyrin ligand (even in nonsmokers). Under normal conditions, CO occupies approximately 1% of the heme sites in hemoglobin and myoglobin. If the affinity of hemoglobin and myoglobin for CO were 100 times greater (due to the absence of the distal histidine), essentially 100% of the heme sites would be occupied by CO, and no oxygen could be transported to the tissues. Severe carbon-monoxide poisoning, which is frequently fatal, has exactly the same effect. Thus the primary function of the distal histidine appears to be to decrease the CO affinity of hemoglobin and myoglobin to avoid self-poisoning by CO.

Enzymes Involved in Oxygen Activation

Many of the enzymes involved in the biological reactions of oxygen contain metal centers with structures that are similar to those used for O₂ transport. Many of these enzymes also contain metal centers that are used for electron transfer, which have structures similar to those of the electron-transfer proteins discussed previously. In this section, we briefly describe two of the most important examples: dioxygenases and methane monooxygenase.

Dioxygenases are enzymes that insert both atoms of O₂ into an organic molecule. In humans, dioxygenases are responsible for cross-linking collagen in connective tissue and for synthesizing complex organic molecules called prostaglandins, which trigger inflammation and immune reactions. Iron is by far the most common metal in dioxygenases; and the target of the most commonly used drug in the world, aspirin, is an iron enzyme that synthesizes a specific prostaglandin. Aspirin inhibits this enzyme by binding to the iron atom at the active site, which prevents oxygen from binding.

Methane monooxygenase catalyzes the conversion of methane to methanol. The enzyme is a monooxygenase because only one atom of O₂ is inserted into an organic molecule, while the other is reduced to water:

Because methane is the major component of natural gas, there is enormous interest in using this reaction to convert methane to a liquid fuel (methanol) that is much more convenient to ship and store. Because the C–H bond in methane is one of the strongest C–H bonds known, however, an extraordinarily powerful oxidant is needed for this reaction. The active site of methane monooxygenase contains two Fe atoms that bind O₂, but the details of how the bound O₂ is converted to such a potent oxidant remain unclear.

Metal Ions as Lewis Acids

Reactions catalyzed by metal ions that do not change their oxidation states during the reaction are usually group transfer reactionsReactions involving the transfer of a group, catalyzed by metal ions that do not change their oxidation states during the reaction., in which a group such as the phosphoryl group (−PO₃²⁻) is transferred. These enzymes usually use metal ions such as Zn²⁺, Mg²⁺, and Mn²⁺, and they range from true metalloenzymes, in which the metal ion is tightly bound, to metal-activated enzymes, which require the addition of metal ions for activity. Because tight binding is usually the result of specific metal–ligand interactions, metalloenzymes tend to be rather specific for a particular metal ion. In contrast, the binding of metal ions to metal-activated enzymes is largely electrostatic in nature; consequently, several different metal ions with similar charges and sizes can often be used to give an active enzyme.

A metal ion that acts as a Lewis acid can catalyze a group transfer reaction in many different ways, but we will focus on only one of these, using a zinc enzyme as an example. Carbonic anhydrase is found in red blood cells and catalyzes the reaction of CO₂ with water to give carbonic acid.

Although this reaction occurs spontaneously in the absence of a catalyst, it is too slow to absorb all the CO₂ generated during respiration. Without a catalyst, tissues would explode due to the buildup of excess CO₂ pressure. Carbonic anhydrase contains a single Zn²⁺ ion per molecule, which is coordinated by three histidine imidazole ligands and a molecule of water. Because Zn²⁺ is a Lewis acid, the pK_a of the Zn²⁺–OH₂ unit is about 8 versus 14 for pure water. Thus at pH 7–8, a significant fraction of the enzyme molecules contain the Zn²⁺–OH⁻ group, which is much more reactive than bulk water. When carbon dioxide binds in a nonpolar site next to the Zn²⁺–OH⁻ unit, it reacts rapidly to give a coordinated bicarbonate ion that dissociates from the enzyme:

The active site of carbonic anhydrase.

Thus the function of zinc in carbonic anhydrase is to generate the hydroxide ion at pH 7.0, far less than the pH required in the absence of the metal ion.

Enzymes That Use Metals to Generate Organic Radicals

An organic radical is an organic species that contains one or more unpaired electrons. Chemists often consider organic radicals to be highly reactive species that produce undesirable reactions. For example, they have been implicated in some of the irreversible chemical changes that accompany aging. It is surprising, however, that organic radicals are also essential components of many important enzymes, almost all of which use a metal ion to generate the organic radical within the enzyme. These enzymes are involved in the synthesis of hemoglobin and DNA, among other important biological molecules, and they are the targets of pharmaceuticals for the treatment of diseases such as anemia, sickle-cell anemia, and cancer. In this section, we discuss one class of radical enzymes that use vitamin B₁₂.

Vitamin B₁₂ was discovered in the 1940s as the active agent in the cure of pernicious anemia, which does not respond to increased iron in the diet. Humans need only tiny amounts of vitamin B₁₂, and the average blood concentration in a healthy adult is only about 3.5 × 10⁻⁸ M. The structure of vitamin B₁₂, shown in Figure 23.27 "Vitamin B", is similar to that of a heme, but it contains cobalt instead of iron, and its structure is much more complex. In fact, vitamin B₁₂ has been called the most complex nonpolymeric biological molecule known and was the first naturally occurring organometallic compound to be isolated. When vitamin B₁₂ (the form present in vitamin tablets) is ingested, the axial cyanide ligand is replaced by a complex organic group.

Figure 23.27 Vitamin B₁₂

In the body, the axial cyanide ligand found in the vitamin is replaced by a complex organic unit. Heterolytic cleavage of the Co–C bond in the resulting organometallic complex generates an organic radical for the catalysis of rearrangement reactions.

The cobalt–carbon bond in the enzyme-bound form of vitamin B₁₂ and related compounds is unusually weak, and it is particularly susceptible to homolytic cleavage:

Homolytic cleavage of the Co³⁺–CH₂R bond produces two species, each of which has an unpaired electron: a d⁷ Co²⁺ derivative and an organic radical, ·CH₂R, which is used by vitamin B₁₂-dependent enzymes to catalyze a wide variety of reactions. Virtually all vitamin B₁₂-catalyzed reactions are rearrangements in which an H atom and an adjacent substituent exchange positions:

In the conversion of ethylene glycol to acetaldehyde, the initial product is the hydrated form of acetaldehyde, which rapidly loses water:

The enzyme uses the ·CH₂R radical to temporarily remove a hydrogen atom from the organic substrate, which then rearranges to give a new radical. Transferring the hydrogen atom back to the rearranged radical gives the product and regenerates the ·CH₂R radical.

The metal is not involved in the actual catalytic reaction; it provides the enzyme with a convenient mechanism for generating an organic radical, which does the actual work. Many examples of similar reactions are now known that use metals other than cobalt to generate an enzyme-bound organic radical.