6.1: Prelude to Coordination Chemistry I - Structure and Isomers

What is a coordination compound?

Coordination compounds consist of one or more metals bound to one or more Lewis base ligands. For example, hexamineruthenium (3+) ion is a coordination complex in which six ammonia ligands coordinate a Co³⁺ ion, as shown in Scheme \(\sf{\PageIndex{1}}\).

Scheme \(\sf{\PageIndex{1}}\): Formation of hexamineruthenium(3+) ion from Co³⁺ and NH₃. (CC BY 4.0; Stephen Contakes)

Such complexes are called coordination complexes because the ligand-metal bond may be thought of as a coordinate covalent bond in which both of the bonding electrons come from the ligand, which is then said to coordinate the metal. This coordinate covalent model is a very useful formalism for understanding the basic features of coordination chemistry, although it does not always accurately reflect the actual details of the bonding in every coordination complex. Nevertheless, even in those cases where the simple coordinate covalent bond model breaks down, the coordinate covalent bond concept supplies the language sophisticated models employ to describe the more complex bonding involved.

Additional important terms

Some of the common widely used terms that follow from the coordinate covalent model of bonding in coordination complexes include:

• Coordination compounds are also called coordination complexes, metal complexes, or just complexes. The term complex refers to coordination compounds' composite nature, in that they may be thought of as comprising multiple ligand and metal ion parts that can be restored by breaking the coordinate covalent bonds holding the complex together. This is in contrast to inorganic or organic molecules which are more commonly thought about as whole molecules held together by the sharing of electrons contributed by all the atoms.
• Coordination complexes that are ions are called complex ions.
• Ligands bound to the coordination complex are said to reside in the primary or inner coordination sphere. These bound ligands are not readily exchangeable, in contrast to nearby counterions and solvent molecules, which are said to reside in the secondary or outer coordination sphere.
• The portion of the complex contributing the electron pairs is said to be the donor and the portion which receives them the acceptor. In conventional coordination compounds the ligand is the donor and the metal the acceptor. In these cases it would be equally convenient to refer to the ligand donor as the Lewis base and the metal acceptor as the Lewis acid. However, in more complex bonding scenarios there may be multiple electron pair donation and acceptance interactions taking place between each pair of atoms and donor-acceptor language will be more convenient.
• The number of ligand sites donating lone pairs to the central atom is referred to as the coordination number. For most complexes this will just be equal to the number of ligand atoms bound to the metal. In simple complexes it is just equal to the number of ligands. For instance, the cobalt in Scheme \(\sf{\PageIndex{1}}\) has a coordination number of six.
• Although technically compounds with metal-carbon bonds are coordination complexes, the term coordination complex is sometimes used to refer to complexes which do not possess metal-carbon bonds in their primary coordination sphere. Complexes which possess metal-carbon bonds are called organometallic compounds instead. The use of the terms organometallic and coordination to distinguish organometallic compounds from other types of coordination compounds is often convenient since many organometallic ligands engage in more than simple \(\sigma\) donor-acceptor coordinate covalent bond formation with the metal center. However, this is true of some wholly inorganic ligands too, so it should always be kept in mind that organometallic compounds are just a type of coordination compound and that inorganic ligands can in principle be tuned to interact with a metal center in much the same way an organic ligand does.

A summary of some of the concepts and terms used to describe coordination compounds is given in Scheme \(\sf{\PageIndex{2}}\).

Scheme \(\sf{\PageIndex{2}}\): Some terms used to describe coordination compounds. (CC BY 4.0; Stephen Contakes)

The formulae of coordination complexes

The way the formulae of coordination complexes are written reflects the fact that it is often convenient to think of coordination compounds as a composite of metals and ligands. When writing the formula of a complex

• the atoms of a ligand are not added to those of the rest of the compound. Instead, the ligand atoms are kept together, if necessary by enclosing the ligand formula in parentheses or giving an abbreviation for the ligand.
• For complex ions the metal and ligands are enclosed in square brackets. Sometimes this is also done for neutral coordination compounds as well. In either case the brackets enclose those parts of the compound which comprise the primary coordination sphere; anything else is in the secondary coordination sphere outside.

A careful perusal of the examples in Scheme \(\sf{\PageIndex{3}}\) should make the important features of this system clear.

Scheme \(\sf{\PageIndex{3}}\): Formulae of coordination compounds and complex ions. (CC BY 4.0; Stephen Contakes)

History of the Coordination Compounds

Coordination compounds have been known and used since antiquity; one of the oldest synthetic pigments is the blue pigment Egyptian blue, a copper complex of formula CaCuSi₄O₁₀ used by the Egyptians since the third Millenium B.C. (in ancient China the Ba analogue, Han blue, was discovered independently). The blue color of Egyptian blue is due to interlocked Cu(Si₂O₇)₄ units in which each copper is coordinated by four O atoms in a square planar arrangement. Later, in 1706, the Berlin painter Diesbach would discover another deep blue pigment, Prussian blue: \(\ce{KFe2(CN)6}\).

Despite their long use, the chemical nature of coordination compounds was unclear for a number of reasons. For example, many compounds called “double salts” were known, such as \(\ce{AlF3·3KF}\), \(\ce{Fe(CN)2·4KCN}\), and \(\ce{ZnCl2·2CsCl}\), which were combinations of simple salts in fixed and apparently arbitrary ratios. Why should \(\ce{AlF3·3KF}\) exist but not \(\ce{AlF3·4KF}\) or \(\ce{AlF3·2KF}\)? And why should a 3:1 KF:\(\ce{AlF3}\) 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, \(\ce{CoCl3·6NH3}\), 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, \(\ce{CoCl3·6NH3}\), \(\ce{CoCl3·5NH3}\), \(\ce{CoCl3·4NH3}\), and \(\ce{CoCl3·3NH3}\) were all known and had very different properties, but despite all attempts, chemists could not prepare \(\ce{CoCl3·2NH3}\) or \(\ce{CoCl3·NH3}\).

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. Of these the most influential was the Blomstrand-Jørgensen chain theory of bonding in coordination compounds, which predicted the “Chattanooga choo-choo” model for CoCl₃·4NH₃ shown in Scheme \(\sf{\PageIndex{I}}\).

Scheme \(\sf{\PageIndex{I}}\). Blomstrand-Jørgensen chain theory model of bonding in CoCl₃·4NH₃.

Nevertheless, this theory was not wholly illogical and, in fact, explained much of the analytical data on coordination compounds available to chemists of the time. This data included the electrical conductivity of aqueous solutions of these compounds, which was roughly proportional to the number of ions formed per mole, and the number of free chloride ions present, which could be determined by precipitating them gravimetrically as AgCl. In the case of CoCl₃·4NH₃, two ions and one chloride were produced when the compound was dissolved in water, which Jørgensen was able to explain using the chain structure shown above by postulating that chlorides attached to NH₃ could dissociate while those attached to Co could not. The modern theory of coordination chemistry, which overthrew the chain theory, 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 \(\PageIndex{1}\). Werner’s data on PtCl₄·6NH₃ in Table \(\PageIndex{1}\) showed that all the chloride ions were present as free chloride. In contrast, PtCl₄·2NH₃, was a neutral molecule that did not give free chloride ions when dissolved in water.

Alfred Werner (1866–1919)

Werner, the son of a factory worker, was born in Alsace. He developed an interest in chemistry at an early age, and he did his first independent research experiments at age 18. While doing his military service in southern Germany, he attended a series of chemistry lectures, and he subsequently received his PhD at the University of Zurich in Switzerland, where he was appointed professor of chemistry at age 29. He won the Nobel Prize in Chemistry in 1913 for his work on coordination compounds, which he performed as a graduate student and first presented at age 26. Apparently, Werner was so obsessed with solving the riddle of the structure of coordination compounds that his brain continued to work on the problem even while he was asleep. In 1891, when he was only 25, he woke up in the middle of the night and, in only a few hours, had laid the foundation for modern coordination chemistry.

Table \(\PageIndex{1}\): Werner’s Data on Complexes of Ammonia with \(PtCl_4\)

Complex	Conductivity (ohm^−1)	Number of Ions per Formula Unit	Number of Cl^− Ions Precipitated by Ag^+
PtCl4·6NH3	523	5	4
PtCl4·5NH3	404	4	3
PtCl4·4NH3	299	3	2
PtCl4·3NH3	97	2	1
PtCl4·2NH3	0	0	0

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:

\[\begin{align} \mathrm{[Pt(NH_3)_6]Cl_4} &\rightarrow \mathrm{[Pt(NH_3)_6]^{4+}(aq)+4Cl^-(aq)} \\[4pt]
\mathrm{[Pt(NH_3)_5Cl]Cl_3} &\rightarrow \mathrm{[Pt(NH_3)_5Cl]^{3+}(aq) +3Cl^-(aq)}\\[4pt]
\mathrm{[Pt(NH_3)_4Cl_2]Cl_2} &\rightarrow \mathrm{[Pt(NH_3)_4Cl_2]^{2+}(aq) +2Cl^-(aq)}\\[4pt]
\mathrm{[Pt(NH_3)_3Cl_3]Cl} &\rightarrow \mathrm{[Pt(NH_3)_3Cl_3]^+(aq) + Cl^-(aq)}\\[4pt]
\mathrm{[Pt(NH_3)_2Cl_4]} &\rightarrow \mathrm{[Pt(NH_3)_2Cl_4]^0(aq)} \end{align} \nonumber \]

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⁺.

Exercise \(\PageIndex{1}\). The CoCl₃xNH₃ series.

The series CoCl₃·xNH₃ was particularly important in establishing the correctness of Werner's coordination theory over the rival chain theory. By ~1900 conductivity measurements suggested that the members of the series gave the number of ions shown in Table \(\sf{\PageIndex{1}}\).

Table \(\sf{\PageIndex{1}}\). The CoCl3·xNH3 series according to coordination theory, chain theory, and experiment.

Compound	Color	Werner formulation	Blomstrand-Jørgensen chain theory formulation	Number of ions in solution
CoCl3·6NH3	yellow	[Co(NH3)6]Cl3		4
CoCl3·5NH3	violet	[Co(NH3)5Cl]Cl2		3
CoCl3·4NH3	green	[Co(NH3)4Cl2]Cl		2
CoCl3·3NH3	orange	[Co(NH3)4Cl3]		0

What does this data suggest about the relative explanatory power of Werner's coordination theory and chain theory? Explain.

Answer

Remember that

• chain theory predicts that the number of ions is the number formed when the Cl atoms bound in a chain with NH₃ dissociate.
• coordination theory predicts the number of ions based on the number of complex ions and their counterions.

Based on this the predictions of coordination theory and chain theory can be compared with the experimental data, as is done in Table \(\sf{\PageIndex{2}}\).

Table \(\sf{\PageIndex{2}}\): Comparison of ions predicted for the CoCl₃·xNH₃ series by coordination theory and chain theory with the number observed experimentally.

Compound	Color	Ions predicted by Werner's coordination theory	Number of ions predicted by coordination theory	Ions predicted by Blomstrand-Jørgensen chain theory	Number of ions predicted by chain theory	Observed Number of ions in solution
CoCl3·6NH3	yellow	[Co(NH3)6]^3+ Cl^- Cl^- Cl^-	4		4	4
CoCl3·5NH3	violet	[Co(NH3)5Cl]^2+ Cl^- Cl^-	3		3	3
CoCl3·4NH3	green	[Co(NH3)4Cl2]^+ Cl^-	2		2	2
CoCl3·3NH3	orange	None	0		2	0

 

As can be seen by comparing the number of ions predicted by coordination and chain theory in Table \(\sf{\PageIndex{2}}\), coordination theory successfully explains all the observed ion counts, while chain theory fails to explain the lack of ions observed for CoCl₃·3NH₃.

 

Nevertheless, as is often the case when developing theoretical models using data from real experimental investigations, these observations did not convince Jørgensen, who could point to the experimental difficulty of determining the number of ions present from solution conductivity data.

What ultimately convinced Jørgensen of the correctness of Werner's coordination model over his own chain theory was how Werner's explanation of the structure of cobalt coordination complexes using an octahedral coordination geometry explained the existence of isomers in Co complexes containing Cl and NH₃ ligands. In the case of [Co(NH₃)₄Cl₂]Cl two isomers were known: one red and the other green. 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, stereoisomers (Figure \(\PageIndex{1}\)). His conclusion was also corroborated by the existence of two and only two stereoisomers of the next compound in the series: Co(NH₃)₃Cl₃.

Figure \(\PageIndex{1}\). 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 (cis), the complex is red (a), but if they are opposite each other (trans), the complex is green (b).

Example \(\PageIndex{1}\): Why did Werner propose an octahedral geometry for 6-coordinate complexes?

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 that this suggests these complexes possess an octahedral geometry, calculate the maximum number of different structures possible for six-coordinate MA₄B₂ complexes with each of the three most symmetrical possible structures the ligands will form about the central metal - a hexagon, a trigonal prism, and an octahedron.

Assuming that the absence of evidence for additional compounds in this case serves as reasonable circumstantial evidence for their absence, what does the fact that no more than two forms of any MA₄B₂ complex were known suggest about the three-dimensional structures of these complexes?

Solution

In this problem you are given

• the stochiometry of the complexes, MA₄B₂
• three possible coordination geometries - hexagonal, trigonal prismatic, and octahedral.

In order to calculate the number of isomers that could be present for each geometry it is best to follow a systematic approach. Since there are fewer B type ligands than A type ligands, the easiest way to do this for each geometry is to start by placing a B ligand at one vertex and then to determine how many different positions are available for the second B ligand.

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:

• position 2 (or 6)
• position 3 (or 5)
• position 4

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. Those of you who remember your ogranic chemistry might recognize that this situation is formally analogous to the ortho-, meta-, and para- isomerism in disubstituted benzenes.

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)
• 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:

• position 2 (or 3 or 4 or 5)
• 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 \(\PageIndex{1}\)

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

Even Werner's explanation of isomerism in coordination complexes in terms of octahedral and other recognized coordination geometries did not convince all chemists until he was able to resolve a racemic mixture of d- and l-[Co{Co(NH3)₄(OH)₂}₃] into its enantiomers, which are shown in Scheme \(\sf{\PageIndex{II}}\). By doing so Werner demonstrated to chemists of his time (virtually none of whom knew group theory) that tetrahedral carbon atoms were not required for chirality; D₃ octahedral complexes were also chiral.

Scheme \(\sf{\PageIndex{II}}\): d- and l-enantiomers of [Co{Co(NH3)₄(OH)₂}₃], colloquially referred to as hexol. This work by Stephen Contakes is licensed under a Creative Commons Attribution 4.0 International License.