Chapter 9: Coordination Compounds
In the closing years of the nineteenth century, chemists were troubled by a set of cobalt compounds that refused to behave. Cobalt chloride reacted with ammonia to give a whole family of solids — one yellow, one purple, and two more with the same composition but different colours, one green and one violet. Each of them already looked like a “finished” compound, yet ammonia kept adding on. The valency rules of the day simply had no room for this.
Alfred Werner, a young Swiss chemist, attacked the puzzle with a beautifully simple experiment. He dissolved each compound in water and added silver nitrate, which throws down chloride ions as a curdy white precipitate of silver chloride. The yellow compound gave three moles of precipitate, the purple gave two, the green gave one. The chlorides were clearly not all alike — some were free to move into solution, others were locked to the cobalt itself.
From this, Werner proposed that a metal has two kinds of valency: one satisfied by ions that ionise away, another satisfied by groups held firmly in a fixed arrangement in space. The idea was resisted for years, but it was right, and in 1913 it earned him the Nobel Prize in Chemistry.
The two spheres Werner imagined around a metal ion are sketched in Fig. 9.0.
Diagram
Fig. 9.0 – A central Co ion with six NH₃ groups bonded around it inside a square bracket (secondary sphere), and three Cl⁻ ions shown loose outside the bracket (primary sphere); label the arrows from N to Co as coordinate bonds.
As you work through this chapter, you will build the ideas needed to reason out each of these questions for yourself.
9.1 Introduction
Most of the compounds you have studied so far are built from a fixed, small number of atoms held together by ionic or covalent bonds. Sodium chloride, water and methane all fit the bonding rules you learnt earlier, and their formulae follow neatly from ordinary valency.
There is, however, a very large family of substances that does not fit those rules so easily. In these, a metal atom or ion sits at the centre and carries a whole set of ions or molecules attached directly around it — often more of them than its ordinary valency seems to allow. These are the coordination compounds.
A familiar example is cisplatin, \(\mathrm{Pt(NH_3)_2Cl_2}\), a chemotherapy drug. It is a coordination compound in which the central platinum metal ion is surrounded by two ammonia molecules and two chloride ions.
The species surrounding the central metal atom or ion are called ligands. In cisplatin, therefore, there are four ligands in all — two \(\mathrm{NH_3}\) molecules and two \(\mathrm{Cl^-}\) ions. The arrangement is drawn in Fig. 9.1.1.
Diagram
Fig. 9.1.1 – Structure of cisplatin: Pt at the centre with two NH₃ groups and two Cl atoms attached; show the lone pairs on N and Cl as dots, with arrows pointing from each donor atom towards Pt.
How the ligands are held
The ligands are linked directly to the central metal ion through coordinate bonds. Recall from your earlier study of chemical bonding that in an ordinary covalent bond, each of the two atoms contributes one electron to the shared pair. A coordinate bond is formed differently: the shared electron pair is contributed entirely by one partner — here, by the ligand.
Because the electrons come from one side only, a coordinate bond is conveniently represented by an arrow \(\rightarrow\), where the arrow head points to the electron acceptor. The central metal atom or ion, usually an electron deficient species, accepts the electron pair, while the ligands serve as electron donors. Coordination compounds having a metal ion in the centre are common.
In cisplatin, the two ammonia molecules and the two chloride ligands utilise their lone pairs of electrons to form bonds with the Pt(II) ion. The donor nitrogen and chlorine atoms of the ligands are directly attached to, and form bonds with, platinum. Note the way the metal is written: the Roman numeral in parentheses, as in Pt(II), states the oxidation state of the metal, a convention used throughout coordination chemistry.
The Lewis acid–base picture
The formation of a coordination compound can be looked upon as a Lewis acid–base interaction. This gives us a single, unifying way of describing every metal–ligand bond in the chapter.
The ligands, being electron pair donors, are Lewis bases. The central metal ion, being an electron pair acceptor, serves as a Lewis acid. Seen this way, it is no accident that the good ligands are exactly those species carrying lone pairs, and the good central atoms are exactly those metal ions that are small, positively charged and short of electrons.
9.2 Types of Ligands
Not every ligand grips the metal ion in the same way. Some can offer only one lone pair, while others carry several donor atoms and can fasten on to the metal at more than one point at the same time. Ligands are therefore classified as monodentate and polydentate ligands, depending on the number of electron donor atoms they have.
9.2.1 Monodentate Ligands
A monodentate ligand is the one where a single donor atom shares an electron pair to form a coordinate bond with the central metal ion. Only one bond to the metal is possible from each such ligand, however many lone pairs the rest of the species may carry.
For example, the ligands \(\mathrm{Cl^{-}}\), \(\mathrm{OH^{-}}\) or \(\mathrm{CN^{-}}\) attached to a metal have the electron pair on Cl, O and N respectively, and these are the donor atoms. Their Lewis structures, with the donatable pair marked, are shown in Fig. 9.2.1.
Diagram
Fig. 9.2.1 – Lewis structures of the monodentate ligands Cl⁻, OH⁻ and CN⁻ (drawn as :C≡N:⁻), with all lone pairs shown as dots and the donor atom in each circled.
9.2.2 Polydentate Ligands
A polydentate ligand has two or more donor atoms linked to the central metal ion. Instead of touching the metal at one point, such a ligand wraps around it and holds it at several points at once.
Ethylenediamine and the oxalate ion are good examples. Each of these ligands possesses two donor atoms, so these are bidentate ligands.
Ethylenediamine binds to a metal using the electron pair on each of its two nitrogens. Its skeleton, \(\mathrm{H_2N\!-\!CH_2\!-\!CH_2\!-\!NH_2}\), places the two nitrogen atoms just far enough apart to reach the metal comfortably, as drawn in Fig. 9.2.2. In formulae it is usually abbreviated to en.
Similarly, the oxalate ion \(\mathrm{(C_2O_4)^{2-}}\) utilises the electron pair on each of its negatively charged oxygen atoms upon linking with the metal.
Diagram
Fig. 9.2.2 – (a) ethylenediamine, H₂N–CH₂–CH₂–NH₂, with lone pairs on both N atoms and arrows to a metal M; (b) oxalate ion, with the two negatively charged O atoms each sending an arrow to the same M, forming a five-membered ring.
- Ethylenediaminetetraacetate ion, \((\text{EDTA})^{4-}\), binds to a metal ion by the electron pairs of four oxygen and two nitrogen atoms. It is therefore a hexadentate ligand — a single ion that can occupy six positions around one metal centre, as shown in Fig. 9.2.3.
Diagram
Fig. 9.2.3 – Structure of the EDTA⁴⁻ ion: central N–CH₂–CH₂–N backbone with four CH₂COO⁻ arms; mark the two N atoms and the four negatively charged O atoms as the six donor atoms.
9.2.3 Ambidentate Ligands
Some ligands carry two different donor atoms but are able to use only one of them at a time. The ligands which have two donor atoms and use the electron pair of either donor atom to form a coordinate bond with the metal ion are called ambidentate ligands.
For example, the ligand \(\mathrm{NO_2^{-}}\) links to a metal ion through nitrogen or through oxygen. Both possibilities are drawn in Fig. 9.2.4.
Similarly, \(\mathrm{SCN^{-}}\) has two donor atoms, nitrogen and sulfur, either of which links to the metal. The two arrangements are depicted as \(\mathrm{M \leftarrow SCN}\) and \(\mathrm{M \leftarrow NCS}\), the atom written next to the metal being the one actually bonded to it.
Diagram
Fig. 9.2.4 – Two pairs of structures: (a) M←N(=O)O and M←O–N=O for the nitrite ligand; (b) M←SCN and M←NCS for the thiocyanate ligand; label the donor atom in each case.
This small choice of donor atom has real consequences. Two compounds with exactly the same formula can be built, differing only in which atom of the ambidentate ligand faces the metal, and they turn out to be different substances. You will meet them in Section 9.7 as linkage isomers.
9.3 Terms Used in Coordination Chemistry
Coordination chemistry has a vocabulary of its own. Before any structure or theory can be discussed, you need to be able to look at a written formula and say at once which part is the complex, which part is free to ionise, what charge the metal carries and how many bonds hold it. The following terms are used for describing coordination compounds.
9.3.1 Coordination Sphere
The central metal ion and the ligands linked to it are enclosed in a square bracket. This bracket is not decoration — it marks off a discrete structural unit called the coordination sphere, which travels through solution as a single particle.
When the coordination sphere comprising the central metal ion and the surrounding ligands together carries a net charge, it is called the complex ion. The ionisable groups shown outside the bracket are the counter ions.
For example, the compound \(\mathrm{K_4[Fe(CN)_6]}\) has the \(\mathrm{[Fe(CN)_6]^{4-}}\) coordination sphere, with the ionisable \(\mathrm{K^{+}}\) ions representing counter ions. The compound ionises as :
\[\mathrm{K_4[Fe(CN)_6]} \longrightarrow 4\,\mathrm{K^{+}} + \mathrm{[Fe(CN)_6]^{4-}}\]
Read that equation carefully. The four potassium ions leave, but the iron and the six cyanide ligands stay together. Everything inside the bracket survives dissolution as one unit; only what is written outside it breaks away.
9.3.2 Charge Number of Complex Ion and Oxidation State of Metal Ion
The net charge residing on the complex ion is its charge number. It is the algebraic sum of the charges carried by the metal ion and the ligands. The charge carried by the metal ion is its oxidation state (O.S.).
Two points make this sum easy to handle. Neutral ligands such as \(\mathrm{NH_3}\), \(\mathrm{H_2O}\) and \(\mathrm{CO}\) contribute zero, so they never affect the arithmetic. Anionic ligands contribute their own charge — \(-1\) for each \(\mathrm{Cl^{-}}\), \(\mathrm{CN^{-}}\) or \(\mathrm{OH^{-}}\), and \(-2\) for each \(\mathrm{(C_2O_4)^{2-}}\).
The complex \(\mathrm{[Fe(CN)_6]^{4-}}\) has charge number of \(-4\). It can be utilised to calculate the O.S. of Fe. Thus,
\[\text{charge number of complex} = -4\] \[= (\text{O.S. of Fe} + \text{charge of ligands})\] \[= (\text{O.S. of Fe} + 6 \times \text{charge of }\mathrm{CN^{-}}\text{ ion})\] \[= (\text{O.S. of Fe} + 6 \times (-1))\]
Therefore, O.S. of \(\mathrm{Fe} = -4 + 6 = +2\).
9.3.3 Coordination Number (C.N.) of Central Metal Ion
Look at the complex \(\mathrm{[Co(NH_3)_4Cl_2]^{+}}\). Here four ammonia molecules and two chloride ions, that is, a total of six ligands, are attached to the cobalt ion. All these are monodentate since each has only one donor atom.
There are therefore six donor atoms in the complex, and the coordination number of the \(\mathrm{Co^{3+}}\) ion in the complex is six. Thus, the coordination number of a metal attached to monodentate ligands is equal to the number of ligands bound to it.
With polydentate ligands the two counts part company. Consider the bidentate ligand \(\mathrm{(C_2O_4)^{2-}}\) or ethylenediamine (en). The complexes \(\mathrm{[Fe(C_2O_4)_3]^{3-}}\) and \(\mathrm{[Co(en)_3]^{3+}}\) have three bidentate ligands each. The total number of donor atoms in three of these ligands is six, and so the C.N. of \(\mathrm{Fe^{3+}}\) and \(\mathrm{Co^{3+}}\) in these complexes is six.
This is exactly the trap that examiners set. A complex with three ligands can have a coordination number of six, and one with two ligands can have a coordination number of four. Always count donor atoms, never ligand molecules.
9.3.4 Double Salt and Coordination Complex
Combination of two or more stable compounds in stoichiometric ratio can give two types of substances, namely, double salts and coordination complexes. On paper their formulae look alike; the difference shows up only when they are dissolved in water.
Double salts
A double salt dissociates in water completely into simple ions. Nothing survives as a bonded unit.
For example, (i) Mohr’s salt, \(\mathrm{FeSO_4(NH_4)_2SO_4{\cdot}6H_2O}\), dissociates as :
\[\mathrm{FeSO_4(NH_4)_2SO_4{\cdot}6H_2O} \xrightarrow{\ \text{water}\ } \mathrm{Fe^{2+}}\text{(aq)} + 2\,\mathrm{NH_4^{+}}\text{(aq)} + 2\,\mathrm{SO_4^{2-}}\text{(aq)}\]
- Carnallite, \(\mathrm{KCl{\cdot}MgCl_2{\cdot}6H_2O}\), dissociates as :
\[\mathrm{KCl{\cdot}MgCl_2{\cdot}6H_2O} \xrightarrow{\ \text{water}\ } \mathrm{K^{+}}\text{(aq)} + \mathrm{Mg^{2+}}\text{(aq)} + 3\,\mathrm{Cl^{-}}\text{(aq)}\]
Because the solution now contains free \(\mathrm{Fe^{2+}}\) ions, Mohr’s salt solution gives every ordinary test for iron(II).
Coordination complexes
A coordination complex dissociates in water with at least one complex ion. For example, \(\mathrm{K_4[Fe(CN)_6]}\) dissociates as the complex ion and the counter ion.
\[\mathrm{K_4[Fe(CN)_6]} \longrightarrow 4\,\mathrm{K^{+}}\text{(aq)} + \mathrm{[Fe(CN)_6]^{4-}}\text{(aq)}\]
Here \(\mathrm{K^{+}}\) is the counter ion and \(\mathrm{[Fe(CN)_6]^{4-}}\) is the complex ion. The two possible outcomes of dissolving such an addition compound are set out in FC 9.3.1.
Flowchart
FC 9.3.1 – Addition compound dissolved in water → branch A: breaks up completely into simple ions (Fe²⁺, NH₄⁺, SO₄²⁻) → double salt, gives tests of all its ions; branch B: breaks up into counter ions + one intact complex ion ([Fe(CN)₆]⁴⁻) → coordination complex, does not give the ordinary tests of the metal.
9.3.5 Werner Theory of Coordination Complexes
The first attempt to explain the nature of bonding in coordination compounds was put forth by Werner. His problem was a real one: a metal salt that had apparently used up all its combining power could still take on several more molecules of ammonia. The postulates of Werner theory are as follows.
Postulate (i) Unlike metal salts, the metal in a complex possesses two types of valencies : primary (ionizable) valency and secondary (nonionizable) valency.
Postulate (ii) The ionizable sphere consists of entities which satisfy the primary valency of the metal. Primary valencies are generally satisfied by anions.
Postulate (iii) The secondary coordination sphere consists of entities which satisfy the secondary valencies and are non ionizable. The secondary valencies for a metal ion are fixed and satisfied by either anions or neutral ligands. The number of secondary valencies is equal to the coordination number.
Postulate (iv) The secondary valencies have a fixed spatial arrangement around the metal ion.
The two spheres of attraction in the complex \(\mathrm{[Co(NH_3)_6]Cl_3}\) are shown in Fig. 9.3.1. The six ammonia molecules sit in the coordination (secondary) sphere, bonded directly to cobalt, while the three chloride ions lie in the ionization (primary) sphere, outside the bracket.
Diagram
Fig. 9.3.1 – [Co(NH₃)₆]Cl₃ drawn as two spheres: an inner box with Co at the centre and six NH₃ groups arrowed to it, labelled “coordination (secondary) sphere”, and a separate outer box containing Cl₃, labelled “ionization (primary) sphere”.
Shape follows the coordination number
Werner’s fourth postulate carries a consequence worth noting now, because the whole of Section 9.7 depends on it. If the secondary valencies point in fixed directions, then the coordination number decides the shape of the complex.
A complex with coordination number six has an octahedral structure. When four coordinating groups are attached to the metal ion, the complex would either be with square planar or tetrahedral structure. These geometries are drawn in Fig. 9.3.2.
Diagram
Fig. 9.3.2 – Three shapes side by side: octahedral (six ligands, C.N. 6), square planar (four ligands in one plane, C.N. 4) and tetrahedral (four ligands at the corners of a tetrahedron, C.N. 4), each with M at the centre and the coordination number labelled below.
9.4 Classification of Complexes
The coordination complexes are classified according to the types of ligands present and the sign of the charge on the complex ion. These are two independent ways of sorting the same compound, so every complex can be described under both headings at once.
9.4.1 Classification on the Basis of Types of Ligands
i. Homoleptic complexes : Consider \(\mathrm{[Co(NH_3)_6]^{3+}}\). Here only one type of ligand surrounds the \(\mathrm{Co^{3+}}\) ion — six identical ammonia molecules. The complexes in which the metal ion is bound to only one type of ligand are homoleptic.
ii. Heteroleptic complexes : Look at the complex \(\mathrm{[Co(NH_3)_4Cl_2]^{+}}\). There are two types of ligands, \(\mathrm{NH_3}\) and \(\mathrm{Cl^{-}}\), attached to the \(\mathrm{Co^{3+}}\) ion. Such complexes, in which the metal ion is surrounded by more than one type of ligand, are heteroleptic.
Only what lies inside the square bracket matters for this test. The counter ions written outside are not ligands at all, so they never make a complex heteroleptic.
9.4.2 Classification on the Basis of Charge on the Complex
i. Cationic complexes : A positively charged coordination sphere, or a coordination compound having a positively charged coordination sphere, is called a cationic sphere complex.
For example, the cation \(\mathrm{[Zn(NH_3)_4]^{2+}}\) and the compound \(\mathrm{[Co(NH_3)_5Cl]SO_4}\) are cationic complexes. The latter has the coordination sphere \(\mathrm{[Co(NH_3)_5Cl]^{2+}}\); the anion \(\mathrm{SO_4^{2-}}\) makes it electrically neutral.
ii. Anionic sphere complexes : A negatively charged coordination sphere, or a coordination compound having a negatively charged coordination sphere, is called an anionic sphere complex.
For example, \(\mathrm{[Ni(CN)_4]^{2-}}\) and \(\mathrm{K_3[Fe(CN)_6]}\) have an anionic coordination sphere; in the latter, \(\mathrm{[Fe(CN)_6]^{3-}}\) and three \(\mathrm{K^{+}}\) ions together make it electrically neutral.
iii. Neutral sphere complexes : A neutral coordination complex does not possess a cationic or anionic sphere. \(\mathrm{[Pt(NH_3)_2Cl_2]}\) or \(\mathrm{[Ni(CO)_4]}\) have neither cation nor anion but are neutral sphere complexes.
Notice how these are written : a neutral complex has no counter ions at all, so nothing appears outside the square bracket. That absence is itself the clue.
Both classifications can be applied in a single sweep, working from the inside of the bracket outwards, as set out in FC 9.4.1.
Flowchart
FC 9.4.1 – Classifying a complex: write the formula → look inside the square bracket → branch 1: one kind of ligand → homoleptic; more than one kind → heteroleptic → then add the metal’s oxidation state to the ligand charges to get the charge on the sphere → branch 2: charge positive → cationic; charge negative → anionic; charge zero (nothing written outside the bracket) → neutral.
9.5 IUPAC Nomenclature of Coordination Compounds
A coordination compound can contain a metal, several kinds of ligand and a counter ion, so its name has to carry a good deal of information in a fixed order. Once you know that order, a name tells you the whole formula, and a formula tells you the whole name. Tables 9.1, 9.2 and 9.3 summarize the IUPAC nomenclature of coordination compounds.
The rules of naming
The rules for naming coordination compounds recommended by IUPAC are as follows.
1. In naming the complex ion or neutral molecule, name the ligand first and then the metal. This is the reverse of the way the formula is written, where the metal comes first inside the bracket.
2. The names of anionic ligands are obtained by changing the ending -ide to -o and -ate to -ato. So chloride becomes chloro, cyanide becomes cyano, sulphate becomes sulphato and oxalate becomes oxalato.
3. The name of a complex is one single word. There must not be any space between different ligand names, nor between the ligand name and the name of the metal.
4. After the name of the metal, write its oxidation state in Roman numerals, which appears in parentheses without any space between the metal name and the parentheses.
5. If the complex has more than one ligand of the same type, the number is indicated with the prefixes di-, tri-, tetra-, penta-, hexa- and so on.
6. For a complex having more than one type of ligand, the ligands are written in alphabetical order. Suppose two ligands with prefixes are tetraaqua and dichloro. While naming in alphabetical order, tetraaqua is first and then dichloro. Note carefully what is being alphabetised — the ligand name itself, aqua against chloro, and not the multiplying prefix in front of it.
7. If the name of the ligand itself contains a numerical prefix, then display the number by the prefixes bis for 2, tris for 3, tetrakis for 4 and so forth, and put the ligand name in parentheses. For example, (ethylenediamine)\(_3\) or (en)\(_3\) would appear as tris(ethylenediamine) or tris(ethane-1,2-diamine).
8. The metal in a cationic or neutral complex is specified by its usual name, while in an anionic complex the name of the metal ends with ‘ate’.
Names of the ligands and of the metals
Table 9.1 : IUPAC names of anionic and neutral ligands
| Anionic ligand | IUPAC name | Anionic ligand | IUPAC name |
|---|---|---|---|
| \(\mathrm{Br^{-}}\), Bromide | Bromo | \(\mathrm{CO_3^{2-}}\), Carbonate | Carbonato |
| \(\mathrm{Cl^{-}}\), Chloride | Chloro | \(\mathrm{OH^{-}}\), Hydroxide | Hydroxo |
| \(\mathrm{F^{-}}\), Fluoride | Fluoro | \(\mathrm{C_2O_4^{2-}}\), Oxalate | Oxalato |
| \(\mathrm{I^{-}}\), Iodide | Iodo | \(\mathrm{NO_2^{-}}\), Nitrite | Nitro (for N-bonded ligand) |
| \(\mathrm{CN^{-}}\), Cyanide | Cyano | \(\mathrm{ONO^{-}}\), Nitrite | Nitrito (for O-bonded ligand) |
| \(\mathrm{SO_4^{2-}}\), Sulphate | Sulphato | \(\mathrm{SCN^{-}}\), Thiocyanate | Thiocyanato (for ligand donor atom S) |
| \(\mathrm{NO_3^{-}}\), Nitrate | Nitrato | \(\mathrm{NCS^{-}}\), Thiocyanate | Isothiocyanato (for ligand donor atom N) |
| Neutral ligand | IUPAC name | Neutral ligand | IUPAC name |
|---|---|---|---|
| \(\mathrm{NH_3}\), Ammonia | Ammine (note the spelling) | \(\mathrm{H_2O}\), water | Aqua |
| \(\mathrm{CO}\), Carbon monoxide | Carbonyl | en, Ethylene diamine | Ethylenediamine |
Notice the two pairs at the right of Table 9.1. Both members of each pair are the same ambidentate ligand met in Section 9.2, and the name records which donor atom is actually bonded to the metal — nitro against nitrito, thiocyanato against isothiocyanato.
Table 9.2 : IUPAC names of metals in anionic complexes
| Metal | IUPAC name | Metal | IUPAC name |
|---|---|---|---|
| Aluminium, Al | Aluminate | Chromium, Cr | Chromate |
| Cobalt, Co | Cobaltate | Copper, Cu | Cuprate |
| Gold, Au | Aurate | Iron, Fe | Ferrate |
| Manganese, Mn | Manganate | Nickel, Ni | Nickelate |
| Platinum, Pt | Platinate | Zinc, Zn | Zincate |
Several of these are built on the Latin name of the metal rather than the English one — ferrate from ferrum, cuprate from cuprum, aurate from aurum. They appear only when the coordination sphere carries a negative charge.
Naming a whole compound
When counter ions are present, the compound’s name is written in two words, exactly as for an ordinary salt : the cation is named first and the anion second. Which of the two happens to be the complex makes no difference to that order. So \(\mathrm{Na_3[Co(NO_2)_6]}\) becomes sodium hexanitrocobaltate(III), with the simple cation first, while \(\mathrm{[PtBr_2(NH_3)_4]Br_2}\) becomes tetraamminedibromoplatinum(IV) bromide, with the complex cation first. The whole order of assembly is summarised in FC 9.5.1.
Flowchart
FC 9.5.1 – Building a name: identify the coordination sphere → work out the metal’s oxidation state from the charge on the sphere → list the ligand names (Table 9.1) → arrange them in alphabetical order of ligand name → attach the multiplying prefixes di/tri/tetra, or bis/tris/tetrakis with parentheses if the ligand name already contains a number → add the metal name; branch: sphere positive or neutral → usual metal name; sphere negative → metal name ending in -ate (Table 9.2) → add the oxidation state in Roman numerals in parentheses → finally, if counter ions are present, write cation first and anion second as two separate words.
Table 9.3 : IUPAC names of some complexes
| Complex | IUPAC name |
|---|---|
| i. Anionic complexes | |
| a. \(\mathrm{[Ni(CN)_4]^{2-}}\) | Tetracyanonickelate(II) ion |
| b. \(\mathrm{[Co(C_2O_4)_3]^{3-}}\) | Trioxalatocobaltate(III) ion |
| c. \(\mathrm{[Fe(CN)_6]^{4-}}\) | Hexacyanoferrate(II) ion |
| ii. Compounds containing complex anions and metal cations | |
| a. \(\mathrm{Na_3[Co(NO_2)_6]}\) | Sodium hexanitrocobaltate(III) |
| b. \(\mathrm{K_3[Al(C_2O_4)_3]}\) | Potassium trioxalatoaluminate(III) |
| c. \(\mathrm{Na_3[AlF_6]}\) | Sodium hexafluoroaluminate(III) |
| iii. Cationic complexes | |
| a. \(\mathrm{[Cu(NH_3)_4]^{2+}}\) | Tetraamminecopper(II) ion |
| b. \(\mathrm{[Fe(H_2O)_5(NCS)]^{2+}}\) | Pentaaquaisothiocyanatoiron(III) ion |
| c. \(\mathrm{[Pt(en)_2(SCN)_2]^{2+}}\) | Bis(ethylenediamine)dithiocyanatoplatinum(IV) |
| iv. Compounds containing complex cations and anion | |
| a. \(\mathrm{[PtBr_2(NH_3)_4]Br_2}\) | Tetraamminedibromoplatinum(IV) bromide |
| b. \(\mathrm{[Co(NH_3)_5CO_3]Cl}\) | Pentaamminecarbonatocobalt(III) chloride |
| c. \(\mathrm{[Co(H_2O)(NH_3)_5]I_3}\) | Pentaammineaquacobalt(III) iodide |
| v. Neutral complexes | |
| a. \(\mathrm{[Co(NO_2)_3(NH_3)_3]}\) | Triamminetrinitrocobalt(III) |
| b. \(\mathrm{Fe(CO)_5}\) | Pentacarbonyliron(0) |
| c. \(\mathrm{[Rh(NH_3)_3(SCN)_3]}\) | Triamminetrithiocyanatorhodium(III) |
9.6 Effective Atomic Number (EAN) Rule
Why should a metal ion stop taking on ligands at six, or at four, rather than continuing indefinitely? An early attempt to explain the stability of coordination compounds was made by Sidgwick, who proposed an empirical rule known as the effective atomic number (EAN) rule.
EAN equals the total number of electrons around the central metal ion in the complex. Every coordinate bond brings a lone pair — two electrons — into the metal’s neighbourhood, so the count includes both the electrons the metal ion already has and those the ligands hand over.
The rule states that a metal ion continues to accept electron pairs till it attains the electronic configuration of the next noble gas. Thus if the EAN is equal to 18 (Ar), 36 (Kr), 54 (Xe) or 86 (Rn), then the EAN rule is obeyed.
Calculating the EAN
EAN can be calculated with the following formula.
\[\text{EAN} = \text{number of electrons of metal ion} + \text{total number of electrons donated by ligands}\]
Written in terms of quantities you can look up, this becomes
\[\text{EAN} = \text{atomic number of metal }(Z) - \text{number of electrons lost by metal to form the ion }(X) + \text{number of electrons donated by ligands }(Y)\]
\[\text{EAN} = Z - X + Y\]
Two of these three terms need a moment’s care. \(X\) is simply the oxidation state of the metal, since a metal in the \(+3\) state has lost three electrons. \(Y\) is not the number of ligands but twice the number of donor atoms, because every coordinate bond is made from one lone pair, and a lone pair is two electrons.
Consider \(\mathrm{[Co(NH_3)_6]^{3+}}\). The oxidation state of cobalt is \(+3\), and six ligands donate 12 electrons.
\[Z = 27; \quad X = 3; \quad Y = 12\] \[\text{EAN of }\mathrm{Co^{3+}} = 27 - 3 + 12 = 36\]
Since 36 is the atomic number of krypton, this complex obeys the EAN rule.
How far the rule holds
\(\mathrm{Cr(CO)_6}\) and \(\mathrm{[Fe(CN)_6]^{4-}}\) are some examples of coordination compounds which obey the EAN rule. Certain other coordination compounds, however, do not obey the EAN rule. For example, \(\mathrm{[Fe(CN)_6]^{3-}}\) and \(\mathrm{[Cu(NH_3)_4]^{2+}}\) have EAN 35.
The last two entries are worth dwelling on. \(\mathrm{[Fe(CN)_6]^{3-}}\) is a perfectly stable, well-known complex ion, yet its EAN falls one short of krypton. A rule that a stable compound can break is clearly not the whole story, and this is exactly why the bonding theories of Section 9.9 were developed.
9.7 Isomerism in Coordination Compounds
One of the interesting aspects of coordination chemistry is the existence of isomers. Isomers are different compounds that have the same molecular formula. Their chemical reactivities and physical properties such as colour, solubility and melting point are different.
This is a striking idea. Two bottles may hold solids of identical composition, right down to the last atom, and yet one is violet and the other green, one dissolves readily and the other does not. Everything depends on how the atoms are joined or where they sit in space.
Broadly speaking, isomers are classified into two types, namely stereoisomers and constitutional (or structural) isomers, as displayed in Fig. 9.1.
Diagram
Fig. 9.1 – Classification of isomers in coordination compounds: a tree with “Isomers” at the top branching into “Stereo isomers” and “Constitutional or structural isomers”; Stereo isomers branches into “Geometric or diastereoisomers” and “Optical isomers or enantiomers”; Constitutional isomers branches into “Linkage isomers”, “Coordination isomers”, “Ionization isomers” and “Solvate isomers”.
9.7.1 Stereoisomers
Stereoisomers have the same links among the constituent atoms, however the arrangements of atoms in space are different. Nothing is bonded to anything new — only the geometry has changed.
There are two kinds of stereoisomers in coordination compounds : (a) geometric isomers or diastereoisomers and (b) enantiomers or optical isomers.
a. Geometric isomers or diastereoisomers
Geometric isomers differ in the relative positions the ligands occupy around the central metal ion. They are stereoisomers that are not mirror images of one another — this is exactly what separates them from the enantiomers you will meet next. They are possible in heteroleptic complexes, since a complex with only one kind of ligand offers nothing to rearrange. In these isomers, there are cis and trans types of arrangements of ligands.
Cis and trans isomers have different properties. Cis–trans isomerism is observed in square planar and octahedral complexes.
i. Cis and trans isomers in square planar complexes
The square planar complexes of \(\mathrm{MA_2B_2}\) and \(\mathrm{MA_2BC}\) type exist as cis and trans isomers, where A, B and C are monodentate ligands and M is the metal. For example, \(\mathrm{Pt(NH_3)_2Cl_2}\) is of the \(\mathrm{MA_2B_2}\) type, and its two forms are drawn in Fig. 9.7.1.
Diagram
Fig. 9.7.1 – Square planar Pt(NH₃)₂Cl₂: cis isomer with the two Cl on adjacent corners and the two NH₃ on the other two adjacent corners; trans isomer with the two Cl across from each other and the two NH₃ across from each other; label each “cis isomer” and “trans isomer”.
Here the cis isomer is more soluble in water than the trans isomer. The cis isomer, named cisplatin, is an anticancer drug, while the trans isomer is physiologically inactive.
The dipole moments explain the difference in solubility. The cis isomer is polar, with a non-zero dipole moment. The trans isomer has zero dipole moment as a result of the two opposite Pt–Cl and two Pt–\(\mathrm{NH_3}\) bond moments, which cancel each other. A molecule with no net dipole has little to attract polar water molecules, so it dissolves poorly.
The \(\mathrm{MA_2BC}\) type behaves in the same way. In \(\mathrm{[Pt(NH_3)(H_2O)Cl_2]}\) the two chloride ligands may again be adjacent or opposite, giving the pair drawn in Fig. 9.7.2.
Diagram
Fig. 9.7.2 – Square planar [Pt(NH₃)(H₂O)Cl₂] (MA₂BC type): cis isomer with the two Cl adjacent, and trans isomer with the two Cl opposite; label H₂O and NH₃ in each.
Four coordinate tetrahedral complexes do not show cis and trans isomers.
ii. Cis and trans isomers in octahedral complexes
The octahedral complexes of the type \(\mathrm{MA_4B_2}\), \(\mathrm{MA_4BC}\) and \(\mathrm{M(AA)_2B_2}\) exist as cis and trans isomers, where (AA) is a bidentate ligand.
For the \(\mathrm{MA_4B_2}\) type, consider \(\mathrm{[Co(NH_3)_4Cl_2]^{+}}\), shown in Fig. 9.7.3. The two chloride ligands may sit next to each other or at the two ends of a straight line through the cobalt.
Diagram
Fig. 9.7.3 – Octahedral [Co(NH₃)₄Cl₂]⁺ (MA₄B₂ type): cis isomer with the two Cl on adjacent vertices, trans isomer with the two Cl on opposite vertices along one axis; four NH₃ fill the remaining positions in each.
For the \(\mathrm{MA_4BC}\) type, \(\mathrm{[Pt(NH_3)_4ClBr]^{2+}}\) has the Cl and Br ligands either adjacent or opposite, as in Fig. 9.7.4.
Diagram
Fig. 9.7.4 – Octahedral [Pt(NH₃)₄ClBr]²⁺ (MA₄BC type): cis isomer with Cl and Br on adjacent vertices, trans isomer with Cl and Br on opposite vertices.
For the \(\mathrm{M(AA)_2B_2}\) type, \(\mathrm{[Co(en)_2Cl_2]^{+}}\) carries two bidentate ethylenediamine ligands and two chlorides, drawn in Fig. 9.7.5. A bidentate ligand cannot stretch across the metal, so it always occupies two adjacent positions; it is the two chlorides that decide the geometry.
Diagram
Fig. 9.7.5 – Octahedral [Co(en)₂Cl₂]⁺ (M(AA)₂B₂ type): cis isomer with the two Cl adjacent and the two en rings spanning the remaining positions; trans isomer with the two Cl opposite and the two en rings in the equatorial plane.
b. Optical isomers (Enantiomers)
The complex molecules or ions that are nonsuperimposable mirror images of each other are enantiomers. Such nonsuperimposable mirror images are described as chiral. A more elaborate discussion on chirality and optical isomerism is included in Chapter 10.
Your own hands are the everyday example. The left hand and the right hand are mirror images, and when you hold your left hand up to a mirror the image looks like a right hand — yet no matter how you turn them, one hand will not lie exactly on top of the other. That failure to superimpose is precisely what makes a species chiral.
Enantiomers have identical properties, however they differ in their response to plane-polarized light. The enantiomer that rotates the plane of plane-polarized light to the right (clockwise) is called the dextro (d) isomer, while the other, which rotates the plane to the left (anticlockwise), is called the laevo (l) isomer.
i. Optical isomers in octahedral complexes
The complex \(\mathrm{[Co(en)_3]^{3+}}\), with three bidentate ethylenediamine ligands wrapped around the cobalt, exists as a pair of enantiomers. The two forms are shown facing each other across a mirror in Fig. 9.7.6.
Diagram
Fig. 9.7.6 – The d and l enantiomers of [Co(en)₃]³⁺ drawn on either side of a vertical mirror line, each with three en rings spanning the octahedron; label them d and l and mark the mirror.
ii. Octahedral complexes existing as both geometric and optical isomers
Some complexes show both kinds of stereoisomerism at once. Consider \(\mathrm{[PtCl_2(en)_2]^{2+}}\), drawn in Fig. 9.7.7. In this type of complex, only the cis isomer exists as a pair of enantiomers; the trans isomer is superimposable on its own mirror image and so is not chiral.
Diagram
Fig. 9.7.7 – [PtCl₂(en)₂]²⁺: the cis isomer drawn twice on either side of a mirror line as the d and l enantiomers, and the trans isomer drawn separately with the two Cl on opposite vertices, labelled as not chiral.
Square planar complexes do not show enantiomers, since they have a mirror plane and an axis of symmetry. Any species that contains a plane of symmetry is superimposable on its mirror image, and therefore cannot be chiral.
9.7.2 Structural Isomers (Constitutional Isomers)
Structural isomers possess different linkages among their constituent atoms, while their chemical formulae are the same. Here the difference is not one of geometry but of what is joined to what.
They can be classified as linkage isomers, ionization isomers, coordination isomers and solvate isomers.
a. Linkage isomers
These isomers are formed when the ligand has two different donor atoms. Such a ligand — the ambidentate ligand of Section 9.2 — coordinates to the metal via different donor atoms. Thus the nitrite ion \(\mathrm{NO_2^{-}}\), having two donor atoms, shows isomers as :
\[\mathrm{[Co(NH_3)_5(NO_2)]^{2+}} \quad \text{and} \quad \mathrm{[Co(NH_3)_5(ONO)]^{2+}}\]
The nitro complex has a Co–N bond and the nitrito complex is linked through a Co–O bond. These are linkage isomers.
b. Ionization isomers
Ionization isomers involve an exchange of ligands between the coordination and the ionization spheres. What was a bonded ligand in one isomer becomes a free counter ion in the other. For example :
\[\mathrm{[Co(NH_3)_5SO_4]Br} \quad \text{(I)} \qquad \text{and} \qquad \mathrm{[Co(NH_3)_5Br]SO_4} \quad \text{(II)}\]
In compound I, the anion \(\mathrm{SO_4^{2-}}\), bonded to Co, is in the coordination sphere while \(\mathrm{Br^{-}}\) is in the ionization sphere. In compound II, the anion \(\mathrm{Br^{-}}\) is in the coordination sphere linked to Co, while \(\mathrm{SO_4^{2-}}\) is in the ionisation sphere.
These complexes in solution ionize to give different ions :
\[\mathrm{[Co(NH_3)_5SO_4]Br} \longrightarrow \mathrm{[Co(NH_3)_5SO_4]^{+}} + \mathrm{Br^{-}}\]
\[\mathrm{[Co(NH_3)_5Br]SO_4} \longrightarrow \mathrm{[Co(NH_3)_5Br]^{2+}} + \mathrm{SO_4^{2-}}\]
I and II are examples of ionization isomers. Notice that the two solutions can be told apart by ordinary tests : only the second gives a precipitate of barium sulphate with barium chloride, and only the first gives free bromide ion.
c. Coordination isomers
Coordination isomers show an interchange of ligands between the cationic and anionic spheres of different metal ions. This kind of isomerism needs a compound in which both the cation and the anion are complex ions. For example :
\[\mathrm{[Co(NH_3)_6][Cr(CN)_6]} \quad \text{(I)} \qquad \text{and} \qquad \mathrm{[Cr(NH_3)_6][Co(CN)_6]} \quad \text{(II)}\]
In isomer I, cobalt is linked to the ammine ligands and chromium to the cyanide ligands. In isomer II the ligands coordinating to the metals are interchanged : cobalt coordinates with the cyanide ligands and chromium with the \(\mathrm{NH_3}\) ligands. I and II are examples of coordination isomers.
d. Solvate isomers (hydrate isomers when water is the solvent)
These are similar to ionization isomers, except that the species exchanged between the two spheres is a solvent molecule. Look at the complexes :
\[\mathrm{[Cr(H_2O)_6]Cl_3} \quad \text{(I)} \qquad \text{and} \qquad \mathrm{[Cr(H_2O)_5Cl]Cl_2{\cdot}H_2O} \quad \text{(II)}\]
In compound I the solvent water is directly bonded to Cr. In compound II, one \(\mathrm{H_2O}\) appears as the free solvent molecule, and a chloride has moved into the coordination sphere to take its place. I and II represent solvate (hydrate) isomers.
9.8 Stability of the Coordination Compounds
Some complexes survive dilution, heating and the presence of competing ions; others fall apart at once. The stability of coordination compounds can be explained by knowing their stability constants.
Stability is governed by metal–ligand interactions. In these, the metal serves as the electron pair acceptor while the ligand acts as a Lewis base, since it is the electron donor. The metal–ligand interaction can therefore be realised as a Lewis acid–Lewis base interaction, exactly as described in Section 9.1. The stronger the interaction, the greater is the stability of the complex.
Measuring stability with an equilibrium constant
Complex formation is a reversible reaction, so it settles into an equilibrium between free metal ions, free ligands and the assembled complex. Consider the equilibrium for the metal–ligand interaction :
\[\mathrm{M^{a+}} + n\,\mathrm{L^{x-}} \rightleftharpoons \mathrm{[ML_n]^{(a+)+(nx-)}}\]
where \(a\), \(x\) and \((a+)+(nx-)\) denote the charge on the metal, on the ligand and on the complex respectively. Now the equilibrium constant \(K\) is given by
\[K = \frac{[\mathrm{ML_n}]}{[\mathrm{M^{a+}}]\,[\mathrm{L^{x-}}]^{n}}\]
Stability of the complex can be explained in terms of \(K\). The higher the value of \(K\), the larger is the thermodynamic stability of the complex.
The equilibria for complex formation, with the corresponding \(K\) values, are given below.
\[\mathrm{Ag^{+}} + 2\,\mathrm{CN^{-}} \rightleftharpoons \mathrm{[Ag(CN)_2]^{-}} \qquad K = 5.5\times10^{18}\]
\[\mathrm{Cu^{2+}} + 4\,\mathrm{CN^{-}} \rightleftharpoons \mathrm{[Cu(CN)_4]^{2-}} \qquad K = 2.0\times10^{27}\]
\[\mathrm{Co^{3+}} + 6\,\mathrm{NH_3} \rightleftharpoons \mathrm{[Co(NH_3)_6]^{3+}} \qquad K = 5.0\times10^{33}\]
From the above data, \(\mathrm{[Co(NH_3)_6]^{3+}}\) is more stable than \(\mathrm{[Ag(CN)_2]^{-}}\) and \(\mathrm{[Cu(CN)_4]^{2-}}\).
Because these numbers differ by many powers of ten, they are far easier to compare on a logarithmic scale, as plotted in Fig. 9.8.1.
Diagram
Fig. 9.8.1 – Bar chart of log K for the three complexes: [Ag(CN)₂]⁻ ≈ 18.7, [Cu(CN)₄]²⁻ ≈ 27.3, [Co(NH₃)₆]³⁺ ≈ 33.7; y-axis labelled “log K”, each bar labelled with the formula of the complex.
9.8.1 Factors Which Govern Stability of the Complex
Stability of a complex is governed by (a) the charge to size ratio of the metal ion and (b) the nature of the ligand. The first concerns how strongly the metal can pull, the second how readily the ligand can give.
a. Charge to size ratio of the metal ion
The higher the ratio, the greater is the stability. A small ion carrying a large positive charge concentrates that charge into a small volume, so it attracts the ligand’s lone pair much more strongly than a large ion of the same charge would.
For the divalent metal ion complexes, their stability shows the trend :
\[\mathrm{Cu^{2+}} > \mathrm{Ni^{2+}} > \mathrm{Co^{2+}} > \mathrm{Fe^{2+}} > \mathrm{Mn^{2+}} > \mathrm{Cd^{2+}}\]
The above stability order is called the Irving–Williams order.
In the above list both Cu and Cd have the charge \(+2\); however, the ionic radius of \(\mathrm{Cu^{2+}}\) is 69 pm and that of \(\mathrm{Cd^{2+}}\) is 97 pm. The charge to size ratio of \(\mathrm{Cu^{2+}}\) is therefore greater than that of \(\mathrm{Cd^{2+}}\), and so \(\mathrm{Cu^{2+}}\) forms more stable complexes than \(\mathrm{Cd^{2+}}\).
b. Nature of the ligand
A second factor that governs the stability of complexes is related to how easily the ligand can donate its lone pair of electrons to the central metal ion — that is, the basicity of the ligand. Ligands that are stronger bases tend to form more stable complexes.
This follows directly from the Lewis picture. A stronger base holds its lone pair more loosely and offers it more readily, so the coordinate bond it forms with the metal is stronger and the resulting complex harder to break apart.
9.9 Theories of Bonding in Complexes
So far we have described what complexes look like and how stable they are, but not why a metal ion should bind six ligands in an octahedron, why one complex is magnetic and another is not, or why so many of them are coloured. The metal–ligand bonding in coordination compounds has been described by Valence Bond Theory (VBT) and Crystal Field Theory (CFT), and between them these two theories answer those questions.
9.9.1 Valence Bond Theory (VBT)
The hybridized state is a theoretical step that describes how complexes are formed. VBT is based on the concept of hybridization. The hybrid orbitals neither exist nor can be detected spectroscopically; these orbitals, however, help us to describe the structure of coordination compounds. In other words, hybridisation here is a bookkeeping device that works, not a physical object you could isolate.
The steps involved in describing bonding in coordination compounds using the VBT are given below.
The metal ion provides vacant d orbitals for the formation of coordinate bonds with ligands.
The vacant d orbitals, along with the s and p orbitals of the metal ion, take part in hybridisation.
The number of vacant hybrid orbitals formed is equal to the number of ligand donor atoms surrounding the metal ion, which equals the coordination number of the metal.
Overlap between the vacant hybrid orbitals of the metal and the filled orbitals of the ligand leads to the formation of the metal–ligand coordinate bonds.
The hybrid orbitals used by the metal ion point in the direction of the ligand.
The \((n-1)\mathrm{d}\) or \(n\mathrm{d}\) orbitals used in hybridisation allow the complexes to be classified as (a) inner orbital and (b) outer orbital complexes respectively.
Point vi deserves unpacking, because it is the heart of the method. If the metal uses d orbitals of the shell below its outermost one — the \(3\mathrm{d}\) orbitals of a first-row transition metal, for instance — the complex is called an inner orbital complex. If instead it reaches outward and uses \(4\mathrm{d}\) orbitals, it is an outer orbital complex.
The type of hybridisation decides the structure of the complex. For example, when the hybridisation is \(\mathrm{d^2sp^3}\) the structure is octahedral.
Working through a complex step by step
The steps to understand the metal–ligand bonding include :
Find the oxidation state of the central metal ion.
Write the valence shell electronic configuration of the free metal ion.
See whether the complex is low spin or high spin. (This applies only to octahedral complexes with \(\mathrm{d^4}\) to \(\mathrm{d^8}\) electronic configurations.)
From the number of ligands, find the number of metal ion orbitals required for bonding.
Identify the orbitals of the metal ion available for hybridisation and the type of hybridisation involved.
Write the electronic configuration after hybridisation.
Show the filling of orbitals after complex formation.
Determine the number of unpaired electrons and predict the magnetic behaviour of the complex.
Two terms in step iii are new. A low spin complex is one in which the metal’s d electrons pair up as far as possible before bonding, leaving the smallest possible number of unpaired electrons. A high spin complex is one in which no such pairing occurs and the electrons stay spread out with parallel spins, as they were in the free ion. VBT itself does not tell you which of the two will happen — that information has to be supplied, which is one of its weaknesses.
Step viii connects the theory to a laboratory measurement. A species with one or more unpaired electrons is attracted into a magnetic field and is called paramagnetic; a species with all its electrons paired is weakly repelled and is called diamagnetic. Counting unpaired electrons on paper therefore predicts something that can actually be measured.
The order of work is summarised in FC 9.9.1.
Flowchart
FC 9.9.1 – VBT treatment of a complex: find the oxidation state of the metal → write the valence shell configuration of the free ion → decide high spin or low spin → count the ligand donor atoms to fix the number of orbitals needed → branch: pairing occurs (low spin) → inner (n−1)d orbitals available → d²sp³ hybridisation; no pairing (high spin) → outer nd orbitals used → sp³d² hybridisation → fill the hybrid orbitals with ligand lone pairs → count unpaired electrons → paramagnetic if any remain, diamagnetic if none.
| Coordination number | Geometry of complex | Hybridisation |
|---|---|---|
| 2 | sp | |
| 4 | Tetrahedral | |
| 4 | Square planar | |
| 6 | \(\mathrm{d^2sp^3}\) / \(\mathrm{sp^3d^2}\) |
9.9.2 Octahedral Complexes
a. \(\mathrm{[Co(NH_3)_6]^{3+}}\), low spin
The oxidation state of cobalt is \(+3\).
The valence shell electronic configuration of \(\mathrm{Co^{3+}}\) is represented in the box diagram of Fig. 9.9.1. Cobalt has 27 electrons; removing three leaves \(\mathrm{Co^{3+}}\) with a \(\mathrm{3d^6}\) arrangement, drawn as one pair and four unpaired electrons in the five 3d boxes, with 4s and 4p empty.
Diagram
Fig. 9.9.1 – Box orbital diagram of free Co³⁺: five 3d boxes filled as ↑↓, ↑, ↑, ↑, ↑; one empty 4s box; three empty 4p boxes.
The number of ammine ligands is 6, so the number of vacant metal ion orbitals required for bonding with the ligands must be six.
The complex is low spin, so pairing of electrons will take place prior to hybridisation.
The electronic configuration after pairing would be three filled 3d orbitals and two empty ones, as in Fig. 9.9.2.
Diagram
Fig. 9.9.2 – Box orbital diagram of Co³⁺ after pairing: three 3d boxes each ↑↓ and two 3d boxes empty; 4s and 4p empty.
The six orbitals available for hybridisation are two 3d, one 4s and three 4p orbitals, giving \(\mathrm{d^2sp^3}\) hybridisation. The orbitals for hybridization are decided from the number of ammine ligands, which is six. Here \((n-1)\mathrm{d}\) orbitals participate in hybridization since it is a low spin complex — making this an inner orbital complex.
The electronic configuration after complex formation shows each of the six \(\mathrm{d^2sp^3}\) hybrid orbitals occupied by a lone pair donated by an ammonia molecule, as in Fig. 9.9.3. The resulting octahedral shape is drawn in Fig. 9.9.4.
Diagram
Fig. 9.9.3 – Box orbital diagram of [Co(NH₃)₆]³⁺ after complex formation: three 3d boxes ↑↓ (metal electrons), then two 3d, one 4s and three 4p boxes each holding a donated pair, bracketed and labelled d²sp³.
Diagram
Fig. 9.9.4 – Octahedral structure of [Co(NH₃)₆]³⁺ with Co at the centre, six NH₃ groups at the vertices and the overall 3+ charge shown outside the bracket.
- As all the electrons are paired, the complex is diamagnetic.
b. \(\mathrm{[CoF_6]^{3-}}\), high spin
The oxidation state of the central metal Co is \(+3\).
The valence shell electronic configuration of \(\mathrm{Co^{3+}}\) is the same \(\mathrm{3d^6}\) arrangement already drawn in Fig. 9.9.1.
There are six fluoride \(\mathrm{F^{-}}\) ligands, thus the number of vacant metal ion orbitals required for bonding with the ligands would be six.
The complex is high spin, which means pairing of electrons will not take place prior to hybridisation. The electronic configuration would remain the same as in the free state shown above — one pair and four unpaired electrons in the 3d orbitals.
Since the 3d orbitals are still occupied and cannot be used, the six orbitals available for the hybridisation are one 4s, three 4p and two of the 4d orbitals, as shown in Fig. 9.9.5. Six metal orbitals bonding with six \(\mathrm{F^{-}}\) ligands led to \(\mathrm{sp^3d^2}\) hybridization. The d orbitals participating in hybridisation for this complex are \(n\mathrm{d}\), making this an outer orbital complex.
Diagram
Fig. 9.9.5 – Box orbital diagram of Co³⁺ for [CoF₆]³⁻: 3d boxes as ↑↓, ↑, ↑, ↑, ↑ unchanged; one 4s, three 4p and two 4d boxes empty and bracketed, labelled sp³d².
Six vacant \(\mathrm{sp^3d^2}\) hybrid orbitals of \(\mathrm{Co^{3+}}\) overlap with six orbitals of fluoride, forming Co–F coordinate bonds.
The configuration after complex formation fills those six hybrid orbitals with the fluoride lone pairs, as in Fig. 9.9.6, and the octahedral shape is drawn in Fig. 9.9.7.
Diagram
Fig. 9.9.6 – Box orbital diagram of [CoF₆]³⁻ after complex formation: 3d as ↑↓, ↑, ↑, ↑, ↑; one 4s, three 4p and two 4d boxes each holding a donated pair, bracketed and labelled sp³d².
Diagram
Fig. 9.9.7 – Octahedral structure of [CoF₆]³⁻ with Co at the centre and six F at the vertices, overall charge 3− shown outside the bracket.
- The complex is octahedral and has four unpaired electrons and hence is paramagnetic.
Read that table across and one point stands out. The metal, its oxidation state and the coordination number are identical in the two complexes; only the ligand has changed, and yet the magnetic behaviour is completely different. VBT records this difference faithfully but cannot explain it, and that gap is what leads to crystal field theory.
9.9.3 Tetrahedral Complex
Consider \(\mathrm{[Ni(Cl)_4]^{2-}}\).
The oxidation state of nickel is \(+2\).
The valence shell electronic configuration of \(\mathrm{Ni^{2+}}\) is \(\mathrm{3d^8}\) — three paired and two unpaired electrons in the five 3d orbitals — as drawn in Fig. 9.9.8.
Diagram
Fig. 9.9.8 – Box orbital diagram of free Ni²⁺: 3d boxes as ↑↓, ↑↓, ↑↓, ↑, ↑; empty 4s and 4p boxes.
The number of \(\mathrm{Cl^{-}}\) ligands is 4. Therefore the number of vacant metal ion orbitals required for bonding with the ligands must be four.
The four orbitals on the metal available for hybridisation are one 4s and three 4p. The complex is tetrahedral. The four metal ion orbitals for bonding with \(\mathrm{Cl^{-}}\) ligands are derived from \(\mathrm{sp^3}\) hybridization.
Four vacant \(\mathrm{sp^3}\) hybrid orbitals of \(\mathrm{Ni^{2+}}\) overlap with four orbitals of \(\mathrm{Cl^{-}}\) ions.
The configuration after complex formation would be as shown in Fig. 9.9.9, with the tetrahedral shape drawn in Fig. 9.9.10.
Diagram
Fig. 9.9.9 – Box orbital diagram of [NiCl₄]²⁻: 3d as ↑↓, ↑↓, ↑↓, ↑, ↑ unchanged; one 4s and three 4p boxes each holding a donated pair, bracketed and labelled sp³.
Diagram
Fig. 9.9.10 – Tetrahedral structure of [NiCl₄]²⁻ with Ni at the centre and four Cl at the corners, charge 2− outside the bracket.
- The complex has two unpaired electrons and hence is paramagnetic.
9.9.4 Square Planar Complex
Consider \(\mathrm{[Ni(CN)_4]^{2-}}\).
The oxidation state of nickel is \(+2\).
The valence shell electronic configuration of \(\mathrm{Ni^{2+}}\) is the \(\mathrm{3d^8}\) arrangement of Fig. 9.9.8.
The number of \(\mathrm{CN^{-}}\) ligands is 4, so the number of vacant metal ion orbitals required for bonding with the ligands would be four.
The complex is square planar, so the \(\mathrm{Ni^{2+}}\) ion uses \(\mathrm{dsp^2}\) hybrid orbitals.
The 3d electrons are paired prior to the hybridisation, and the electronic configuration of \(\mathrm{Ni^{2+}}\) becomes four filled 3d orbitals with one 3d orbital empty, as in Fig. 9.9.11.
Diagram
Fig. 9.9.11 – Box orbital diagram of Ni²⁺ after pairing: 3d boxes as ↑↓, ↑↓, ↑↓, ↑↓ and one empty 3d box; empty 4s and 4p.
The orbitals available for hybridisation are one 3d, one 4s and two 4p, which give \(\mathrm{dsp^2}\) hybridization.
Four vacant \(\mathrm{dsp^2}\) hybrid orbitals of \(\mathrm{Ni^{2+}}\) overlap with four orbitals of \(\mathrm{CN^{-}}\) ions to form Ni–CN coordinate bonds. The configuration after the complex formation becomes that of Fig. 9.9.12, and the square planar shape is drawn in Fig. 9.9.13.
Diagram
Fig. 9.9.12 – Box orbital diagram of [Ni(CN)₄]²⁻: four 3d boxes ↑↓; then one 3d, one 4s and two 4p boxes each holding a donated pair, bracketed and labelled dsp².
Diagram
Fig. 9.9.13 – Square planar structure of [Ni(CN)₄]²⁻ with Ni at the centre and four CN groups at the corners of a square, charge 2− outside the bracket.
- The complex has no unpaired electrons and hence is diamagnetic.
9.9.5 Limitations of VBT
It does not explain the high spin or low spin nature of the complexes. In other words, strong and weak field nature of ligands cannot be distinguished.
It does not provide any explanation for the colour of coordination compounds.
The structure of the complexes predicted from VBT would not always match necessarily with those determined from experiments.
To overcome these difficulties in VBT, the Crystal field theory has been proposed, which has been widely accepted.
9.9.6 Crystal Field Theory (CFT)
C.F.T. is based on the following assumptions.
i. The ligands are treated as point charges. The interaction between metal ion and ligand is purely electrostatic, or in other words there are no orbital interactions between metal and ligand. This is a deliberate simplification — the ligand is reduced to a negative charge sitting at a point, and the whole theory then follows from how that charge repels the metal’s d electrons.
In an isolated gaseous metal ion the five d orbitals, \(\mathrm{d}_{x^2-y^2}\), \(\mathrm{d}_{z^2}\), \(\mathrm{d}_{xy}\), \(\mathrm{d}_{yz}\) and \(\mathrm{d}_{zx}\), have the same energy, that is, they are degenerate.
ii. When ligands approach the metal ion they create a crystal field around the metal ion. If it were symmetrical, the degeneracy of the d orbitals would remain intact.
Usually the field created is not symmetrical and the degeneracy is destroyed. The d orbitals thus split into two sets, namely \((\mathrm{d}_{xy}, \mathrm{d}_{yz}, \mathrm{d}_{xz})\), usually referred to as \(t_{2g}\), and \((\mathrm{d}_{x^2-y^2}, \mathrm{d}_{z^2})\), called \(e_g\). These two sets of orbitals now have different energies. The separation of the energies of these two sets of d orbitals is the crystal field splitting parameter, denoted by \(\Delta_o\) (the subscript O standing for octahedral).
iii. The value of \(\Delta_o\) depends on the strength of the ligands. The ligands are then classified as (a) strong field and (b) weak field ligands.
Strong field ligands are those in which the donor atoms are C, N or P. Thus \(\mathrm{CN^{-}}\), \(\mathrm{NC^{-}}\), \(\mathrm{CO}\), \(\mathrm{NH_3}\), EDTA and en (ethylenediamine) are considered to be strong ligands. They cause larger splitting of d orbitals, and pairing of electrons is favoured. These ligands tend to form low spin complexes.
Weak field ligands are those in which the donor atoms are halogens, oxygen or sulphur. For example, \(\mathrm{F^{-}}\), \(\mathrm{Cl^{-}}\), \(\mathrm{Br^{-}}\), \(\mathrm{I^{-}}\), \(\mathrm{SCN^{-}}\) and \(\mathrm{C_2O_4^{2-}}\). In the case of these ligands the \(\Delta_o\) parameter is smaller compared to the energy required for the pairing of electrons, which is called the electron pairing energy.
The ligands can then be arranged in order of their increasing field strength as
\[\mathrm{I^{-}} < \mathrm{Br^{-}} < \mathrm{Cl^{-}} < \mathrm{S^{2-}} < \mathrm{F^{-}} < \mathrm{OH^{-}} < \mathrm{C_2O_4^{2-}} < \mathrm{H_2O} < \mathrm{NCS^{-}} < \text{EDTA} < \mathrm{NH_3} < \text{en} < \mathrm{CN^{-}} < \mathrm{CO}\]
Splitting of d orbitals and formation of octahedral complexes
In an octahedral environment the central metal ion is surrounded by six ligands. The ligands approach the metal ion along the \(x\), \(y\) and \(z\) axes, and as they approach, the degeneracy of the d orbitals is resolved.
With the closer approach of ligands along the axes, the doubly degenerate \(\mathrm{d}_{x^2-y^2}\) and \(\mathrm{d}_{z^2}\) (\(e_g\)) orbitals experience larger repulsion than the triply degenerate \(t_{2g}\) orbitals. The reason lies in their shapes : the \(e_g\) orbitals point directly along the axes, straight at the incoming ligands, while the \(t_{2g}\) orbitals point between the axes and so avoid the worst of the repulsion.
As shown in Fig. 9.2, the \(e_g\) set has higher energy than the \(t_{2g}\) set by the amount \(\Delta_o\). The \(\Delta_o\) parameter is equal to 10 Dq units of splitting of the \(t_{2g}\) and \(e_g\) levels.
Diagram
Fig. 9.2 – Crystal field splitting in an octahedral complex: five degenerate d orbitals of the free ion at the left, splitting into an upper e_g pair raised by 3/5 Δ₀ and a lower t₂g set of three lowered by 2/5 Δ₀; mark the gap as Δ₀; add the notes that e_g comprises d_z² and d_x²−y², t₂g comprises d_xy, d_yz and d_zx, that Δ₀ = 10 Dq, that e_g is repelled by 0.6 Δ₀ and t₂g is stabilised to the extent of 0.4 Δ₀.
The splitting is not symmetrical about the original level. The two \(e_g\) orbitals are pushed up by \(0.6\,\Delta_o\) each while the three \(t_{2g}\) orbitals are lowered by \(0.4\,\Delta_o\) each, so that the total energy of the five orbitals taken together is unchanged.
For the electronic configurations \(\mathrm{d^1}\), \(\mathrm{d^2}\) and \(\mathrm{d^3}\), the electrons occupy \(t_{2g}\) orbitals and obey Hund’s rule. For the electronic configurations \(\mathrm{d^1}\), \(\mathrm{d^2}\), \(\mathrm{d^3}\) and \(\mathrm{d^8}\), \(\mathrm{d^9}\), \(\mathrm{d^{10}}\) the high spin and low spin configurations cannot be distinguished, because in each of these cases there is only one way of filling the levels. Only the electronic configurations \(\mathrm{d^4}\) to \(\mathrm{d^7}\) render the high and low spin complexes. These are depicted in Table 9.5.
Table 9.5 : d orbital diagrams for high spin and low spin complexes
| d orbital electronic configuration | High spin | Low spin |
|---|---|---|
| \(\mathrm{d^4}\) | \(t_{2g}^{\,3}\,e_g^{\,1}\) — 4 unpaired | \(t_{2g}^{\,4}\) — 2 unpaired |
| \(\mathrm{d^5}\) | \(t_{2g}^{\,3}\,e_g^{\,2}\) — 5 unpaired | \(t_{2g}^{\,5}\) — 1 unpaired |
| \(\mathrm{d^6}\) | \(t_{2g}^{\,4}\,e_g^{\,2}\) — 4 unpaired | \(t_{2g}^{\,6}\) — 0 unpaired |
| \(\mathrm{d^7}\) | \(t_{2g}^{\,5}\,e_g^{\,2}\) — 3 unpaired | \(t_{2g}^{\,6}\,e_g^{\,1}\) — 1 unpaired |
9.9.7 Factors Affecting Crystal Field Splitting Parameter (\(\Delta_o\))
a. The magnitude of crystal field splitting depends on the strength of the ligands. The strong ligands that appear high in the spectrochemical series approach closer to the central metal, which results in a large crystal field splitting.
b. Oxidation state of the metal : A metal with a higher positive charge is able to draw ligands closer to it than one with a lower charge. Thus a metal in a higher oxidation state results in a larger separation of the \(t_{2g}\) and \(e_g\) sets of orbitals. The trivalent metal ions cause larger crystal field splitting than the corresponding divalent ones.
Both factors say the same thing in the end : whatever brings the ligand point charges nearer to the metal’s d orbitals increases the repulsion, and therefore widens the gap.
9.9.8 Colour of the Octahedral Complexes
As discussed above, the formation of an octahedral complex is accompanied by the splitting of d orbitals into \(t_{2g}\) and \(e_g\) sets. The separation of these two sets of orbitals is \(\Delta_o\), which can be measured from experiments.
The \(\Delta_o\) corresponds to a certain frequency of electromagnetic radiation, usually in the visible region. When white light passes through the complex, exactly that frequency is absorbed to lift an electron from the lower set to the upper set, and the light that emerges is missing it. A colour complementary to the absorbed frequency is thus observed.
Consider the \(\mathrm{[Ti(H_2O)_6]^{3+}}\) complex. The central metal ion titanium has the electronic configuration \(\mathrm{3d^1}\) and the electron occupies one of the \(t_{2g}\) orbitals, as in Fig. 9.3.
Diagram
Fig. 9.3 – d–d transition in a d¹ system: on the left, the ground state with a single electron in one t₂g orbital and empty e_g orbitals; an arrow labelled “Energy” pointing to the right; on the right, the excited state with the electron promoted into an e_g orbital.
The absorption of the wavelength of light corresponding to the \(\Delta_o\) parameter promotes an electron from the \(t_{2g}\) level. Such an energy gap in the case of the \(\mathrm{[Ti(H_2O)_6]^{3+}}\) complex is \(20{,}300\ \text{cm}^{-1}\) (520 nm, 243 kJ/mol), and a colour complementary to this is imparted to the complex. The violet colour of the \(\mathrm{[Ti(H_2O)_6]^{3+}}\) complex arises from such a d–d transition.
A wavelength of 520 nm is green light. Green is therefore the colour removed from the white light, and what reaches the eye is the complementary colour, violet — which is exactly what the solution looks like.
9.9.9 Tetrahedral Complexes
A pattern of splitting of d orbitals, which is a key idea in crystal field theory, is dependent on the ligand field environment. This is illustrated here for the tetrahedral ligand field environment.
The tetrahedral structure, having the metal atom M at the centre and four ligands occupying the corners of a tetrahedron, is displayed in Fig. 9.4.
Diagram
Fig. 9.4 – Tetrahedral structure: a cube with the x, y and z axes drawn through the centre, M marked at the centre, and four ligands at alternate corners of the cube forming a tetrahedron.
Here the geometry reverses the octahedral result. The \(\mathrm{d}_{xy}\), \(\mathrm{d}_{yz}\) and \(\mathrm{d}_{zx}\) orbitals, with their lobes lying in between the axes, point towards the ligands. On the other hand, the \(\mathrm{d}_{x^2-y^2}\) and \(\mathrm{d}_{z^2}\) orbitals lie in between the metal–ligand bond axes. The \(\mathrm{d}_{xy}\), \(\mathrm{d}_{yz}\) and \(\mathrm{d}_{zx}\) orbitals therefore experience more repulsion from the ligands compared to that experienced by the \(\mathrm{d}_{x^2-y^2}\) and \(\mathrm{d}_{z^2}\) orbitals.
Due to these larger repulsions, the \(\mathrm{d}_{xy}\), \(\mathrm{d}_{yz}\) and \(\mathrm{d}_{zx}\) orbitals are of higher energy, while the \(\mathrm{d}_{x^2-y^2}\) and \(\mathrm{d}_{z^2}\) orbitals are of relatively lower energy.
Each electron entering one of the \(\mathrm{d}_{xy}\), \(\mathrm{d}_{yz}\) and \(\mathrm{d}_{zx}\) orbitals raises the energy by 4 Dq, whereas one occupying the \(\mathrm{d}_{x^2-y^2}\) and \(\mathrm{d}_{z^2}\) orbitals lowers it by 6 Dq, compared to the energy of the hypothetical degenerate d orbitals in the ligand field.
A splitting of d orbitals in tetrahedral crystal fields (assumed to be 10 Dq) is thus much less — typically \(4/9\) — compared to that for the octahedral environment. The crystal field splitting of d orbitals in a tetrahedral ligand field is compared with the octahedral one in Fig. 9.5.
Diagram
Fig. 9.5 – Splitting of d orbitals in tetrahedral and octahedral complexes: the free-ion level in the centre; to the left the tetrahedral case with the lower e_g pair and upper t₂g set separated by the small gap Δ_tet; to the right the octahedral case with the lower t₂g set and upper e_g pair separated by the larger gap Δ₀.
Because \(\Delta_{\text{tet}}\) is so much smaller, it is almost always less than the electron pairing energy. Thus the pairing of electrons is not favoured in a tetrahedral structure. For example, in a \(\mathrm{d^4}\) configuration an electron would occupy one of the \(t_{2g}\) orbitals rather than pair up. The low spin tetrahedral complexes are thus not found.
Typically, metal complexes possessing a central metal ion with the \(\mathrm{d^8}\) electronic configuration — for example, \(\mathrm{Ni(CO)_4}\) — favour the tetrahedral structure.
9.10 Applications of Coordination Compounds
Everything in this chapter — the coordinate bond, the coordination sphere, the way a polydentate ligand grips a metal, the stability constant — turns up in practice. The applications below are the reason coordination chemistry matters outside the classroom.
a. In biology
Several biologically important natural compounds are metal complexes. They play an important role in a number of processes occurring in plants and animals.
For example, chlorophyll present in plants is a complex of Mg. Haemoglobin present in blood is a complex of iron. In each case the metal ion sits at the centre of a large ring ligand whose nitrogen atoms act as the donor atoms, as sketched in Fig. 9.10.1.
Diagram
Fig. 9.10.1 – Two simplified ring structures side by side: a flat four-nitrogen ring with Mg at the centre labelled “chlorophyll”, and the same ring type with Fe at the centre labelled “haem, in haemoglobin”; show the coordinate bonds from the N atoms to the metal.
b. In medicines
The Pt complex cisplatin is used in the treatment of cancer.
EDTA is used for the treatment of lead poisoning.
c. To estimate hardness of water
Hardness of water is due to the presence of \(\mathrm{Ca^{2+}}\) and \(\mathrm{Mg^{2+}}\) ions. The ligand EDTA forms stable complexes with \(\mathrm{Ca^{2+}}\) and \(\mathrm{Mg^{2+}}\). It can therefore be used to estimate the hardness of water.
The estimation works because the reaction goes essentially to completion : since the complexes are so stable, every \(\mathrm{Ca^{2+}}\) and \(\mathrm{Mg^{2+}}\) ion present is captured, and the amount of EDTA needed is a direct measure of how many such ions the sample contained.
d. In electroplating
Usually stable coordination complexes, on dissolution, dissociate to a small extent and furnish a controlled supply of metal ions. The metal ions, when reduced, clump together to form clusters or nanoparticles.
When coordination complexes are used, the ligands in the complex keep the metal atoms well separated from each other. These metal atoms tend to form a protective layer on the surface.
Certain cyanide complexes, \(\mathrm{K[Ag(CN)_2]}\) and \(\mathrm{K[Au(CN)_2]}\), find applications in the electroplating of these noble metals. The sequence is set out in FC 9.10.1.
Flowchart
FC 9.10.1 – Electroplating from a complex: complex salt such as K[Ag(CN)₂] dissolved in the bath → dissociates only to a small extent → low, steady concentration of free Ag⁺ ions → ions reduced at the article being plated → metal atoms, kept apart by the ligands, deposit evenly → smooth, adherent protective layer of silver.
9.11 Summary
A coordination compound consists of a central metal atom or ion surrounded by ions or molecules called ligands, which are bonded directly to it. Cisplatin, \(\mathrm{Pt(NH_3)_2Cl_2}\), is a familiar example.
Ligands are joined to the metal by coordinate bonds, in which the shared pair of electrons is supplied entirely by the ligand. The bond is shown by an arrow whose head points to the electron acceptor.
Complex formation is a Lewis acid–base interaction : the ligand donates a lone pair and is the Lewis base, while the electron deficient central metal ion accepts it and is the Lewis acid.
Ligands are classified by the number of donor atoms they carry. A monodentate ligand has one donor atom (\(\mathrm{Cl^{-}}\), \(\mathrm{OH^{-}}\), \(\mathrm{CN^{-}}\), \(\mathrm{NH_3}\), \(\mathrm{H_2O}\)).
A polydentate ligand has two or more donor atoms. Ethylenediamine and the oxalate ion are bidentate; \((\text{EDTA})^{4-}\), with four oxygen and two nitrogen donor atoms, is hexadentate.
An ambidentate ligand has two different donor atoms but binds through only one at a time — \(\mathrm{NO_2^{-}}\) through N or O, and \(\mathrm{SCN^{-}}\) through S or N.
The metal ion and its ligands, written inside a square bracket, form the coordination sphere. If this unit carries a net charge it is a complex ion, and the ionisable ions outside the bracket are counter ions.
The charge number of a complex ion is the algebraic sum of the charge on the metal and the charges on the ligands. Neutral ligands contribute zero. From it the oxidation state of the metal is found : for \(\mathrm{[Fe(CN)_6]^{4-}}\), \(-4 = (\text{O.S. of Fe}) + 6 \times (-1)\), so the O.S. of Fe is \(+2\).
The coordination number is the number of ligand donor atoms bonded directly to the metal, that is, the number of electron pairs involved in coordinate bonds. Count donor atoms, not ligand molecules : \(\mathrm{[Co(en)_3]^{3+}}\) has three ligands but a coordination number of six.
A double salt dissociates completely in water into simple ions (Mohr’s salt, carnallite), while a coordination complex gives at least one intact complex ion in solution (\(\mathrm{K_4[Fe(CN)_6]} \longrightarrow 4\,\mathrm{K^{+}} + \mathrm{[Fe(CN)_6]^{4-}}\)).
Werner’s theory states that a metal in a complex has a primary, ionizable valency satisfied by anions outside the coordination sphere, and a secondary, non-ionizable valency, equal in number to the coordination number, satisfied by ligands held in fixed positions in space.
Only the chlorides in the ionization sphere are precipitated by silver nitrate. Counting the moles of \(\mathrm{AgCl}\) formed therefore reveals the formula of a complex : two moles of \(\mathrm{AgCl}\) from one mole of a \(\mathrm{CoCl_3}\)–\(\mathrm{NH_3}\) complex of coordination number 6 fixes it as \(\mathrm{[Co(NH_3)_5Cl]Cl_2}\).
Coordination number decides shape : six gives an octahedral structure, while four gives either a square planar or a tetrahedral structure.
Complexes are homoleptic if the metal is bound to only one type of ligand and heteroleptic if more than one type is present.
By charge on the coordination sphere, complexes are cationic (\(\mathrm{[Zn(NH_3)_4]^{2+}}\)), anionic (\(\mathrm{[Ni(CN)_4]^{2-}}\)) or neutral (\(\mathrm{[Pt(NH_3)_2Cl_2]}\), \(\mathrm{[Ni(CO)_4]}\)).
In IUPAC nomenclature the ligands are named first and the metal last, all as one word. Anionic ligand endings change from -ide to -o and -ate to -ato; neutral ligands are ammine, aqua, carbonyl and ethylenediamine.
Ligands of the same kind take the prefixes di-, tri-, tetra-, but bis-, tris-, tetrakis- with the name in parentheses when the ligand name already contains a numeral. Different ligands are written in alphabetical order of their own names, ignoring the prefixes.
The oxidation state of the metal follows its name as a Roman numeral in parentheses. The metal keeps its usual name in cationic and neutral complexes, but ends in ‘ate’ in an anionic complex — ferrate, cuprate, aurate, cobaltate, nickelate and so on.
The effective atomic number is the total number of electrons around the central metal ion, given by
\[\text{EAN} = Z - X + Y\]
where \(Z\) is the atomic number of the metal, \(X\) its oxidation state and \(Y\) twice the number of donor atoms.
Sidgwick’s EAN rule states that a metal ion accepts electron pairs until it reaches the electron count of the next noble gas — 18 (Ar), 36 (Kr), 54 (Xe) or 86 (Rn). \(\mathrm{Cr(CO)_6}\) and \(\mathrm{[Fe(CN)_6]^{4-}}\) obey it, while \(\mathrm{[Fe(CN)_6]^{3-}}\) and \(\mathrm{[Cu(NH_3)_4]^{2+}}\), with EAN 35, do not.
Isomers have the same molecular formula but differ in colour, solubility, melting point and chemical behaviour. They fall into stereoisomers and structural (constitutional) isomers.
Geometric isomers differ in the relative positions of the ligands : identical ligands are adjacent in the cis isomer and opposite in the trans isomer. Such isomerism occurs in heteroleptic square planar (\(\mathrm{MA_2B_2}\), \(\mathrm{MA_2BC}\)) and octahedral (\(\mathrm{MA_4B_2}\), \(\mathrm{MA_4BC}\), \(\mathrm{M(AA)_2B_2}\)) complexes, but not in tetrahedral ones.
In \(\mathrm{Pt(NH_3)_2Cl_2}\) the cis isomer is polar, more soluble in water and is the anticancer drug cisplatin, while the trans isomer has zero dipole moment and is physiologically inactive.
Optical isomers, or enantiomers, are nonsuperimposable mirror images and are chiral. They have identical properties but rotate the plane of plane-polarized light in opposite directions — clockwise for the dextro (d) isomer and anticlockwise for the laevo (l) isomer. \(\mathrm{[Co(en)_3]^{3+}}\) is a classic example, and in \(\mathrm{[PtCl_2(en)_2]^{2+}}\) only the cis isomer is chiral. Square planar complexes show no enantiomers, as they possess a mirror plane and an axis of symmetry.
Structural isomers differ in the linkages among their atoms and are of four kinds : linkage isomers (\(\mathrm{[Co(NH_3)_5(NO_2)]^{2+}}\) and \(\mathrm{[Co(NH_3)_5(ONO)]^{2+}}\)), ionization isomers (\(\mathrm{[Co(NH_3)_5SO_4]Br}\) and \(\mathrm{[Co(NH_3)_5Br]SO_4}\)), coordination isomers (\(\mathrm{[Co(NH_3)_6][Cr(CN)_6]}\) and \(\mathrm{[Cr(NH_3)_6][Co(CN)_6]}\)) and solvate or hydrate isomers (\(\mathrm{[Cr(H_2O)_6]Cl_3}\) and \(\mathrm{[Cr(H_2O)_5Cl]Cl_2{\cdot}H_2O}\)).
The stability of a complex is measured by its stability constant, the equilibrium constant for its formation from the free metal ion and free ligands :
\[K = \frac{[\mathrm{ML_n}]}{[\mathrm{M^{a+}}]\,[\mathrm{L^{x-}}]^{n}}\]
The larger the value of \(K\), the greater the thermodynamic stability of the complex.
Stability is governed by the charge to size ratio of the metal ion and by the nature of the ligand. A higher ratio gives greater stability, as in the Irving–Williams order \(\mathrm{Cu^{2+}} > \mathrm{Ni^{2+}} > \mathrm{Co^{2+}} > \mathrm{Fe^{2+}} > \mathrm{Mn^{2+}} > \mathrm{Cd^{2+}}\), and ligands that are stronger bases form more stable complexes.
Valence bond theory describes bonding through hybridisation. The number of hybrid orbitals equals the coordination number, and each overlaps with a filled ligand orbital to form a coordinate bond.
The type of hybridisation fixes the geometry : sp for coordination number 2, \(\mathrm{sp^3}\) for tetrahedral, \(\mathrm{dsp^2}\) for square planar, and \(\mathrm{d^2sp^3}\) or \(\mathrm{sp^3d^2}\) for octahedral complexes.
Complexes using \((n-1)\mathrm{d}\) orbitals are inner orbital complexes and those using \(n\mathrm{d}\) orbitals are outer orbital complexes. \(\mathrm{[Co(NH_3)_6]^{3+}}\) is low spin, \(\mathrm{d^2sp^3}\), inner orbital and diamagnetic, while \(\mathrm{[CoF_6]^{3-}}\) is high spin, \(\mathrm{sp^3d^2}\), outer orbital and paramagnetic with four unpaired electrons.
\(\mathrm{[NiCl_4]^{2-}}\) is tetrahedral and \(\mathrm{sp^3}\) with two unpaired electrons, hence paramagnetic, while \(\mathrm{[Ni(CN)_4]^{2-}}\) is square planar and \(\mathrm{dsp^2}\) with no unpaired electrons, hence diamagnetic.
The route from formula to predicted properties is summarised in FC 9.S.1.
Flowchart
FC 9.S.1 – From formula to properties: write the complex → identify counter ions and coordination sphere → find the oxidation state of the metal → count donor atoms to get the coordination number → coordination number fixes the geometry (6 → octahedral; 4 → square planar or tetrahedral) → look up the ligand in the spectrochemical series → branch: strong field ligand → large Δ₀ → low spin → few or no unpaired electrons → diamagnetic or weakly paramagnetic; weak field ligand → small Δ₀ → high spin → more unpaired electrons → paramagnetic → the size of Δ₀ also fixes the wavelength absorbed and hence the colour observed.
VBT has three limitations : it cannot distinguish high spin from low spin complexes or strong from weak field ligands, it offers no explanation of colour, and its predicted structures do not always agree with experiment. Crystal field theory was proposed to overcome these difficulties.
Crystal field theory treats the ligands as point charges interacting electrostatically with the metal, with no orbital interaction between them.
In an isolated gaseous metal ion the five d orbitals are degenerate. In an octahedral field the ligands approach along the axes, and the degeneracy is destroyed : the \(e_g\) set (\(\mathrm{d}_{x^2-y^2}\), \(\mathrm{d}_{z^2}\)), which points at the ligands, is raised in energy above the \(t_{2g}\) set (\(\mathrm{d}_{xy}\), \(\mathrm{d}_{yz}\), \(\mathrm{d}_{zx}\)), which points between them.
The energy separation between the two sets is the crystal field splitting parameter \(\Delta_o\), equal to 10 Dq. The \(e_g\) orbitals are raised by \(0.6\,\Delta_o\) and the \(t_{2g}\) orbitals lowered by \(0.4\,\Delta_o\).
Strong field ligands, with donor atoms C, N or P (\(\mathrm{CN^{-}}\), \(\mathrm{CO}\), \(\mathrm{NH_3}\), EDTA, en), give a large \(\Delta_o\), favour pairing and form low spin complexes. Weak field ligands, with halogen, oxygen or sulphur donors (\(\mathrm{F^{-}}\), \(\mathrm{Cl^{-}}\), \(\mathrm{Br^{-}}\), \(\mathrm{I^{-}}\), \(\mathrm{SCN^{-}}\), \(\mathrm{C_2O_4^{2-}}\)), give a \(\Delta_o\) smaller than the electron pairing energy and form high spin complexes.
Arranged in order of increasing field strength, the ligands give the series
\[\mathrm{I^{-}} < \mathrm{Br^{-}} < \mathrm{Cl^{-}} < \mathrm{S^{2-}} < \mathrm{F^{-}} < \mathrm{OH^{-}} < \mathrm{C_2O_4^{2-}} < \mathrm{H_2O} < \mathrm{NCS^{-}} < \text{EDTA} < \mathrm{NH_3} < \text{en} < \mathrm{CN^{-}} < \mathrm{CO}\]
High spin and low spin arrangements can be distinguished only for the \(\mathrm{d^4}\) to \(\mathrm{d^7}\) configurations; for \(\mathrm{d^1}\) to \(\mathrm{d^3}\) and \(\mathrm{d^8}\) to \(\mathrm{d^{10}}\) there is only one way of filling the levels.
The magnitude of \(\Delta_o\) increases with the strength of the ligand and with the oxidation state of the metal, so trivalent ions cause larger splitting than the corresponding divalent ones.
Colour arises from a d–d transition. The complex absorbs the frequency of visible light matching \(\Delta_o\), promoting an electron from \(t_{2g}\) to \(e_g\), and the complementary colour is seen. For \(\mathrm{[Ti(H_2O)_6]^{3+}}\), whose \(\mathrm{Ti^{3+}}\) ion is \(\mathrm{3d^1}\), the gap is \(20{,}300\ \text{cm}^{-1}\) (520 nm, 243 kJ/mol) and the complex appears violet.
In a tetrahedral field the pattern is reversed : the \(\mathrm{d}_{xy}\), \(\mathrm{d}_{yz}\) and \(\mathrm{d}_{zx}\) orbitals are raised by 4 Dq and the \(\mathrm{d}_{x^2-y^2}\) and \(\mathrm{d}_{z^2}\) orbitals lowered by 6 Dq. The splitting is only about \(4/9\) of the octahedral value, so pairing is never favoured and low spin tetrahedral complexes are not found. Metal ions with the \(\mathrm{d^8}\) configuration, such as in \(\mathrm{Ni(CO)_4}\), favour the tetrahedral structure.
Coordination compounds matter in biology, where chlorophyll is a complex of magnesium and haemoglobin a complex of iron; in medicine, where cisplatin treats cancer and EDTA treats lead poisoning; in the estimation of the hardness of water, where EDTA forms stable complexes with \(\mathrm{Ca^{2+}}\) and \(\mathrm{Mg^{2+}}\); and in electroplating, where \(\mathrm{K[Ag(CN)_2]}\) and \(\mathrm{K[Au(CN)_2]}\) release metal ions slowly enough to build an even protective layer.
9.12 Objective Questions
- The oxidation state of cobalt ion in the complex \(\mathrm{[Co(NH_3)_5Br]SO_4}\) is
- \(+2\)
- \(+3\)
- \(+1\)
- \(+4\)
- IUPAC name of the complex \(\mathrm{[Pt(en)_2(SCN)_2]^{2+}}\) is
- bis(ethylenediamine dithiocyanatoplatinum (IV) ion
- bis(ethylenediamine) dithiocyantoplatinate (IV) ion
- dicyanatobis(ethylenediamine) platinate IV ion
- bis(ethylenediammine)dithiocynato platinate (IV) ion
- Formula for the compound sodium hexacynoferrate (III) is
- \(\mathrm{[NaFe(CN)_6]}\)
- \(\mathrm{Na_2[Fe(CN)_6]}\)
- \(\mathrm{Na[Fe(CN)_6]}\)
- \(\mathrm{Na_3[Fe(CN)_6]}\)
- Which of the following complexes exist as cis and trans isomers?
- \(\mathrm{[Cr(NH_3)_2Cl_4]^{-}}\) 2. \(\mathrm{[Co(NH_3)_5Br]^{2+}}\) 3. \(\mathrm{[PtCl_2Br_2]^{2-}}\) (square planar) 4. \(\mathrm{[FeCl_2(NCS)_2]^{2-}}\) (tetrahedral)
- 1 and 3
- 2 and 3
- 1 and 3
- 4 only
- Which of the following complexes are chiral?
- \(\mathrm{[Co(en)_2Cl_2]^{+}}\) 2. \(\mathrm{[Pt(en)Cl_2]}\) 3. \(\mathrm{[Cr(C_2O_4)_3]^{3-}}\) 4. \(\mathrm{[Co(NH_3)_4Cl_2]^{+}}\)
- 1 and 3
- 2 and 3
- 1 and 4
- 2 and 4
- On the basis of CFT predict the number of unpaired electrons in \(\mathrm{[CrF_6]^{3-}}\).
- 1
- 2
- 3
- 4
- When an excess of \(\mathrm{AgNO_3}\) is added to the complex, one mole of \(\mathrm{AgCl}\) is precipitated. The formula of the complex is
- \(\mathrm{[CoCl_2(NH_3)_4]Cl}\)
- \(\mathrm{[CoCl(NH_3)_4]Cl_2}\)
- \(\mathrm{[CoCl_3(NH_3)_3]}\)
- \(\mathrm{[Co(NH_3)_4]Cl_3}\)
- The sum of coordination number and oxidation number of M in \(\mathrm{[M(en)_2C_2O_4]Cl}\) is
- 6
- 7
- 9
- 8
9.13 Check Your Concepts
A coordinate bond is drawn as an arrow rather than a line. What does the direction of the arrow record, and does the arrow imply that the bond is weaker than an ordinary covalent bond? Justify your answer.
Explain why \(\mathrm{SCN^{-}}\) is described as an ambidentate ligand and not as a bidentate ligand, even though it possesses two donor atoms.
A student states that the coordination number of a metal ion is equal to the number of ligands attached to it. State when this is true and when it fails, giving one example of each case.
Assertion : An aqueous solution of \(\mathrm{K_4[Fe(CN)_6]}\) does not give the usual tests for \(\mathrm{Fe^{2+}}\) ions. Reason : \(\mathrm{K_4[Fe(CN)_6]}\) does not dissolve in water. Select the correct option : (a) both assertion and reason are true and the reason is the correct explanation; (b) both are true but the reason is not the correct explanation; (c) the assertion is true and the reason is false; (d) both are false. Justify your choice.
Mohr’s salt and potassium hexacyanoferrate(II) are both made by combining two simple compounds, yet they behave very differently in water. Explain the difference and name the class to which each belongs.
According to Werner’s theory, a metal in a complex has two kinds of valency. Explain how a single experiment with silver nitrate can distinguish between the two, and state what is being counted in that experiment.
Why can the multiplying prefix be ignored when arranging ligand names in alphabetical order, and when must “bis”, “tris” and “tetrakis” be used instead of “di”, “tri” and “tetra”?
The complex \(\mathrm{[Fe(CN)_6]^{4-}}\) obeys the EAN rule while \(\mathrm{[Fe(CN)_6]^{3-}}\) does not, although both are well known and can be handled in the laboratory. What does this tell you about the status of the EAN rule?
Match the following.
| Column A | Column B |
|---|---|
| a. \(\mathrm{[Co(NH_3)_5(NO_2)]^{2+}}\) and \(\mathrm{[Co(NH_3)_5(ONO)]^{2+}}\) | i. coordination isomers |
| b. \(\mathrm{[Co(NH_3)_5SO_4]Br}\) and \(\mathrm{[Co(NH_3)_5Br]SO_4}\) | ii. hydrate isomers |
| c. \(\mathrm{[Co(NH_3)_6][Cr(CN)_6]}\) and \(\mathrm{[Cr(NH_3)_6][Co(CN)_6]}\) | iii. linkage isomers |
| d. \(\mathrm{[Cr(H_2O)_6]Cl_3}\) and \(\mathrm{[Cr(H_2O)_5Cl]Cl_2{\cdot}H_2O}\) | iv. ionization isomers |
The trans isomer of \(\mathrm{Pt(NH_3)_2Cl_2}\) has a zero dipole moment while the cis isomer does not. Explain how this difference arises, and how it accounts for their different solubilities in water.
Tetrahedral complexes of the type \(\mathrm{MA_2B_2}\) show no cis and trans isomers, although square planar complexes of the same type do. Give the geometrical reason.
Explain why square planar complexes do not exhibit enantiomerism, while an octahedral complex such as \(\mathrm{[Co(en)_3]^{3+}}\) does.
Two complexes of the same metal ion in the same oxidation state are formed with two different ligands. State the two factors given in this chapter that decide which of the two complexes is more stable, and explain the reasoning behind each.
\(\mathrm{[Co(NH_3)_6]^{3+}}\) and \(\mathrm{[CoF_6]^{3-}}\) contain cobalt in the same oxidation state with the same coordination number, yet one is diamagnetic and the other paramagnetic. Explain this on the basis of VBT, naming the hybridisation in each case.
State the limitations of valence bond theory, and explain for each limitation how crystal field theory improves on it.
In an octahedral field the \(e_g\) orbitals are raised in energy while the \(t_{2g}\) orbitals are lowered, but in a tetrahedral field the order is reversed. Explain this reversal in terms of the directions in which the two sets of orbitals point.
Why are low spin tetrahedral complexes not found? Support your answer by comparing the size of \(\Delta_{\text{tet}}\) with the electron pairing energy.
Assertion : \(\mathrm{[Ti(H_2O)_6]^{3+}}\) appears violet in solution. Reason : The complex absorbs light of wavelength 520 nm to promote its single d electron from the \(t_{2g}\) to the \(e_g\) level. Select the correct option from those listed in question 4 and justify your choice.
Arrange \(\mathrm{I^{-}}\), \(\mathrm{NH_3}\), \(\mathrm{H_2O}\), \(\mathrm{CN^{-}}\) and \(\mathrm{F^{-}}\) in order of increasing field strength, and state which of them would be most likely to give a low spin octahedral complex.
Explain why a complex of a trivalent metal ion generally shows a larger crystal field splitting than the corresponding complex of a divalent ion of the same metal.
Both chlorophyll and haemoglobin hold a metal ion inside a ring of nitrogen donor atoms. Explain, in terms of the number of donor atoms and the stability constant, why such an arrangement suits a biological role.
Explain why a cyanide complex such as \(\mathrm{K[Ag(CN)_2]}\) gives a better electroplated coating than a simple, fully ionised silver salt would.
Write the formula for tetraammineplatinum (II) chloride.
Predict whether the \(\mathrm{[Cr(en)_2(H_2O)_2]^{3+}}\) complex is chiral. Write the structure of its enantiomer.
Name the Lewis acids and bases in the complex \(\mathrm{[PtCl_2(NH_3)_2]}\).
What is the shape of a complex in which the coordination number of the central metal ion is 4?
Is the complex \(\mathrm{[CoF_6]}\) cationic or anionic if the oxidation state of cobalt ion is \(+3\)?
Consider the complexes \(\mathrm{[Cu(NH_3)_4][PtCl_4]}\) and \(\mathrm{[Pt(NH_3)_4][CuCl_4]}\). What type of isomerism do these two complexes exhibit?
Mention two applications of coordination compounds.
What are bidentate ligands? Give one example.
What is the difference between a double salt and a complex? Give an example.
Classify the following complexes as homoleptic and heteroleptic : \(\mathrm{[Cu(NH_3)_4]SO_4}\), \(\mathrm{[Cu(en)_2(H_2O)Cl]^{2+}}\), \(\mathrm{[Fe(H_2O)_5(NCS)]^{2+}}\), tetraammine zinc (II) nitrate.
Write formulae of the following complexes :
- Potassium amminetrichloroplatinate (II)
- Dicyanoaurate (I) ion
What are ionization isomers? Give an example.
What are the high-spin and low-spin complexes?
\(\mathrm{[CoCl_4]^{2-}}\) is a tetrahedral complex. Draw its box orbital diagram. State which orbitals participate in hybridization.
What are strong field and weak field ligands? Give one example of each.
With the help of a crystal field energy-level diagram, explain why the complex \(\mathrm{[Cr(en)_3]^{3+}}\) is coloured.
Give the valence bond description for the bonding in the complex \(\mathrm{[VCl_4]^{-}}\). Draw box diagrams for the free metal ion. Which hybrid orbitals are used by the metal? State the number of unpaired electrons.
Draw qualitatively the energy-level diagram showing d-orbital splitting in the octahedral environment. Predict the number of unpaired electrons in the complex \(\mathrm{[Fe(CN)_6]^{4-}}\). Is the complex diamagnetic or paramagnetic? Is it coloured? Explain.
Draw isomers in each of the following :
- \(\mathrm{[Pt(NH_3)_2ClNO_2]}\)
- \(\mathrm{[Ru(NH_3)_4Cl_2]}\)
- \(\mathrm{[Cr(en_2)Br_2]^{+}}\)
- Draw geometric isomers and enantiomers of the following complexes :
- \(\mathrm{[Pt(en)_3]^{4+}}\)
- \(\mathrm{[Pt(en)_2ClBr]^{2+}}\)
What are ligands? What are their types? Give one example of each type.
What are cationic, anionic and neutral complexes? Give one example of each.
How can the stability of coordination compounds be explained in terms of equilibrium constants?
The reaction of chromium metal with \(\mathrm{H_2SO_4}\) in the absence of air gives a blue solution of chromium ion.
\[\mathrm{Cr}\text{(s)} + 2\,\mathrm{H^{+}}\text{(aq)} \longrightarrow \mathrm{Cr^{2+}}\text{(aq)} + \mathrm{H_2}\text{(s)}\]
\(\mathrm{Cr^{2+}}\) forms an octahedral complex with \(\mathrm{H_2O}\) ligands. a. Write the formula of the complex. b. Describe the bonding in the complex using CFT and VBT. Draw the crystal field splitting and valence bond orbital diagrams.
- The reaction of the complex \(\mathrm{[Co(NH_3)_3(NO_2)_3]}\) with HCl gives a complex \(\mathrm{[Co(NH_3)_3H_2OCl_2]^{+}}\) in which two chloride ligands are trans to one another.
- Draw the possible stereoisomers of the starting material.
- Assuming that the \(\mathrm{NH_3}\) groups remain in place, which of the two starting isomers would give the observed product?
9.14 Practice With Numericals
Calculate the oxidation state of the central metal ion and state its coordination number in each of the following : (a) \(\mathrm{K_3[Co(NO_2)_6]}\) (b) \(\mathrm{[Cr(en)_3]Cl_3}\) (c) \(\mathrm{[Ni(CO)_4]}\) (d) \(\mathrm{Na_3[AlF_6]}\)
A complex ion is formed from one \(\mathrm{Fe^{3+}}\) ion, three oxalate ions and no other ligand. Calculate the charge number of the complex ion, write its formula, and state the coordination number of iron.
One mole of a cobalt(III) complex formed from \(\mathrm{CoCl_3}\) and \(\mathrm{NH_3}\) gives three moles of \(\mathrm{AgCl}\) on treatment with excess \(\mathrm{AgNO_3}\). Given that the coordination number of cobalt is 6, write the formula of the complex and the equation for its ionisation in water.
Calculate the EAN of the central metal ion in each of the following and state whether the EAN rule is obeyed : (a) \(\mathrm{[Cr(CO)_6]}\) (b) \(\mathrm{[Ni(NH_3)_6]^{2+}}\) (c) \(\mathrm{[Pt(NH_3)_6]^{4+}}\) (Atomic numbers : Cr = 24, Ni = 28, Pt = 78)
A complex contains one \(\mathrm{Co^{3+}}\) ion bonded to two ethylenediamine molecules and two chloride ions. Calculate (a) the total number of donor atoms, (b) the coordination number, (c) the total number of electrons donated by the ligands and (d) the EAN of cobalt. (Atomic number of Co = 27)
The stability constants of two complexes of the same metal ion are \(1.6 \times 10^{7}\) and \(5.5 \times 10^{18}\). State which complex is the more stable and calculate how many times larger the greater stability constant is.
Using crystal field theory, work out the \(t_{2g}\) and \(e_g\) occupation, the number of unpaired electrons and the magnetic behaviour of each of the following octahedral complexes : (a) \(\mathrm{[Cr(H_2O)_6]^{3+}}\) (b) \(\mathrm{[Fe(CN)_6]^{3-}}\) (c) \(\mathrm{[CoF_6]^{3-}}\) (Atomic numbers : Cr = 24, Fe = 26, Co = 27)
For an octahedral complex the crystal field splitting parameter is \(\Delta_o = 10\) Dq. Calculate, in Dq units, (a) the energy by which each \(e_g\) orbital is raised, (b) the energy by which each \(t_{2g}\) orbital is lowered, and (c) show that the total energy of the five d orbitals taken together is unchanged.
The crystal field splitting in an octahedral complex of a certain metal ion is \(18\,000\ \text{cm}^{-1}\). Estimate the splitting expected for a tetrahedral complex of the same metal ion with the same ligands, taking \(\Delta_{\text{tet}}\) to be \(4/9\) of \(\Delta_o\).
For the complex \(\mathrm{[Cr(en)_2(C_2O_4)]Br}\), calculate the oxidation number of chromium and its coordination number, and hence find the sum of the two.
What is the coordination number and oxidation state of the metal ion in the complex \(\mathrm{[Pt(NH_3)Cl_5]^{-}}\)?