CHAPTER 3 STRUCTURES OF METAL COMPLEXES

3.1 Introduction…………………………………………………………………………………..1

3.2 General Characteristics of Coordination Compounds………………………………...…..23.2.1 Coordination Compounds………………………………………………………… 23.2.2 Lewis Structures and the EAN Rule……………………………………………… 33.2.3 Types of Ligand Coordination…………………………………………………….43.2.4 Types of Ligands…………………………………………………………………..5

3.3 Molecular Orbital and Crystal Field Theories……………………………………………..83.3.1 Molecular Orbitals of Metal-Ligand Complexes………………………………….83.3.2 Ligand Field Splitting and the Spectrochemical Series…………………………. 103.3.3 Crystal Field Theory…………………………………………………………….. 113.3.4 Electron Configurations………………………………………………………….123.3.5 Crystal Field Stabilization Energy………………………………………………. 17

3.4 Hard and Soft Acids and Bases…………………………………………………………… 19______________________________________________________________________________

3.1 IntroductionIn general, a metal ion exists in compounds and in aqueous solution, not as a naked ion, but

as an aggregated entity consisting typically of a central metal ion bound to a certain number of anions or molecules. This entity is called a complex or coordination compound, and the bound anions and molecules are termed ligands . The ligands occupy the coordination sphere of the central metal ion and the number of bound ions and molecules associated with a given central ion represents the coordination number of the metal ion. The metal complex may be neutral, anionic or cationic, depending on the combination of charges on the central metal ion and the ligands. Complexing ligands are exploited in several aqueous-based unit processes, such as dissolution, chemical precipitation, electrodeposition, solvent extraction, ion-exchange, and adsorption.

This chapter deals with the structures of metal-ligand complexes, with emphasis on transition metals. We begin by considering how we can understand the structures of coordination compounds through the Lewis concept of the electron-pair bond. We then examine how molecular orbital theory can be extended to metal-ligand complexes. Finally, some useful generalizations are presented which should aid in the selection of ligands for specific metal ions.

3.2 General Characteristics of Coordination Compounds3.2.1 Coordination Compounds

The serious study of coordination compounds did not begin till the end of the 18th century. At this time the available theory of chemical bonding could not explain why compounds such as CoCl3 and NH3, with apparently saturated valences, would combine to give a new stable compound with stoichiometry CoC13•6NH3. Hence such compounds were termed complex,

recognition of their unknown and apparently baffling bonding mechanism. It is now recognized that the structural chemistry of a complex is based in part on two key properties of the central metal ion, i.e., its oxidation state, and its coordination number. Thus, in the case of CoCl3•6NH3, the structural formula may be expressed as [Co(NH3)6]Cl3, with the following

interpretation. The oxidation state of cobalt in this complex is +3 (i.e., Co(III)) and hence three negatively charged chloride ions are needed to satisfy this charge. On the other hand, the ammonia molecules provide the necessary ligands to satisfy the coordination number of six; that is, these molecules are bound directly to the metal ion.

The unique character of coordination compounds often manifests itself in the different solution behavior of stoichiometrically similar compounds. Take for example the two compounds with the similar stoichiometric formulas: 2KCl•HgCl2 and 2KCl•MgCl2. These two

materials dissolve in water differently:

2KCl•HgCl2 = 2K+ + HgCl42- (3.1)

2KCl•MgCl2 = 2K+ + Mg2+ + 4Cl- (3.2)

The first compound, 2KCl•HgCl2, is a coordination compound since the chloride ions are not

released as free ions into the aqueous phase but rather are retained in the coordination sphere of the Hg2+ cation. Accordingly, to emphasize the intimate association of the chloride and mercuric ions, the structural formula for this compound may be expressed as K2[HgCl4]. On the

other hand in the case of the second compound, all the chloride ions report as free ions into the aqueous phase. Therefore this compound is a double salt (rather than a coordination compound) and its structural formula can be legitimately expressed as 2KCl•MgCl2.

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EXAMPLE 3.1 Identification of bound and free chloride ions in cobaltic ammine chloride solutions

Cobaltic ammine chlorides have the general stoichiometric formula CoCl3•nNH3. In these coordination compounds cobalt has an oxidation state of +3 and a coordination number of 6. Also, of the potential ligands NH3

and Cl-, ammonia molecules are bound preferentially to cobalt ions.

(a) Write down the structural formulas of the following complexes: (i) CoCl3•6NH3, (ii) CoCl3•5NH3,

(iii) CoCl3•4NH3.(b) When a solution of silver nitrate is added to a solution of CoCl3•nNH3, the silver ions react with the

unbound chloride ions to give an insoluble precipitate of silver chloride (AgCl(s)). For each of the complexes listed above, indicate the number of chloride ions precipitated.

Solution

(a) According to the problem statement, all the available NH3 will first bind to Co3+ before Cl- can enter the coordination sphere. Therefore, since Co3+ has a coordination number of 6, the coordination sphere of Co3+ in CoCl3•6NH3. will consist entirely of NH3 molecules. Thus, there will be three unbound Cl- ions. Therefore, the coordination formula is [Co(NH3)6]•Cl3. Similar considerations result in appropriate coordination formulas for the other cobaltic ammine chloride complexes, as summarized in the table below.

(b) Since the silver ion will only react with the unbound chloride ions, it is necessary to identify the number of free chloride ions associated with each cobaltic ammine chloride. The results of the analysis are summarized in the table below.

Molecular No. of No. of Coordination No. of Cl- ionsFormula Bound NH3 Bound Cl- Formula Precipitated _____________________________________________

CoCl3•6NH3 6 0 [Co(NH3)6]Cl3 3CoCl3•5NH3 5 1 [Co(NH3)5Cl]Cl2 2CoCl3•4NH3 4 2 [Co(NH3)4Cl2]Cl 1

_____________________________________

3.2.2 Lewis Structures and the EAN RuleComparison of the Lewis diagrams obtained in Chapter 2 for NH3 and H2O shows that

NH3 possesses an unshared electron pair, while in the case of H2O there are two pairs of

unshared electrons. These lone electron pairs can be shared in the formation of new compounds. Thus an ammonium (NH4+) ion forms when the electron pair on NH3 is shared with a hydrogen

ion:

H+ + :NH3= [H3N:H]+ = NH4+ (3.3)

Similarly, the oxonium ion (H3O+) results when a water molecule shares one of its two lone

electron pairs with a proton:

H+ + :OH2= [H2O:H]+ = H3O+ (3.4)

Equations 3.3 and 3.4 represent Lewis acid-base reactions. According to the Lewis theory of acids and bases, an acid is a substance that can accept an electron pair, whereas a base is a substance that can donate an electron pair. According to this terminology, one may refer to an acid as an acceptor and a base as a donor. Thus, the formation of a complex or a coordination

compound can be viewed in terms of an acid-base reaction:

A + :B = B: A (3.5)(Acid; acceptor) (Base; donor) (Complex)

In the case of metal complexes, the metal ions represent the acids while the ligands represent the bases. Thus the formation of the cobaltic hexammine complex can be represented as:

(3.6)

It will be noticed that for He (Z = 2), Ne (Z = 10), and Ar (Z = 18), the atomic numbers change in increments of 8. In contrast, for Ar (Z = 10), Kr (Z = 36), and Xe (Z = 54), the corresponding increment is 18. This difference translates to a modification of the Lewis eight-electron rule to an Effective Atomic Number (EAN) rule for transition metal complexes. According to the EAN rule, the ligands in the coordination sphere of a transition metal complex must provide the necessary number of electrons that will give the central metal ion the electronic configuration of a rare gas.______________________________________________________________________________

EXAMPLE 3.2 The EAN rule and the structure of Co(III) hexammine

Is the coordination of Co(NH3)63+ consistent with the EAN rule?

Solution

The atomic number of Co is 27. Thus 24 electrons are associated with the Co(III) ion. Each NH3 ligand can offer a lone-pair, i.e., a total of 12 electrons from six ligand molecules. Therefore in the hexammine complex, the Co(III) ion has a total of 36 electrons. This matches the electronic structure of Kr.

Alternatively, we recall from Table 2.2 that the electronic structure of Co is [Ar] 3d74s2. Thus Co(III) has 6 valence electrons. If we now add the 12 electrons provided by the ligands, we get a total of 18 electrons in the valence shell of Co(III) in the complex. Thus we see that the EAN rule can be viewed, in this case, as an 18-electron rule.____________________________________________________________________________________________

Co3+ + 6NH3 =

H3N NH3

NH3

NH3

H3NH3N

Co

3+

3.2.3 Types of Ligands For most ligands the coordinating atom of the anion or molecule (i.e., the atom of the

ligand that is directly bound to the central metal ion) comes from Groups V, VI, or VII of the Periodic Table, particularly N, P for groups V; O, S for group VI; and F, Cl, Br, I for group VII. Table 3.1 presents a collection of common ligands and ligand atoms. We can distinguish between monodentate ligands, characterized by the presence of only one binding site, and polydentate ligands, which carry two or more binding sites. Examples of monodentate ligands

are cyanide (CN-), halide (F-, Cl-, Br

-, I

-), and ammonia (NH3). Bidentate ligands include

ethylene diamine, and acetylacetonate. Some polydentate ligands have binding atoms consisting of different elements, e.g., glycinate (N, O), ethylenediaminetetracetate (EDTA; N,O).

In Table 3.1, certain ligands are associated with more than one ligand atom. Thus NO2-

appears under both nitrogen (N) and oxygen (O), SCN- is grouped with nitrogen (N) ligands as

well as with sulfur (S) ligands, both SO32-

and S2O32-

appear with the oxygen (O) and sulfur (S)

ligands. Ions or molecules which possess alternative donor atoms are given the name ambidentate.

3.2.4 Types of Ligand Coordination The coordination numbers encountered in metal complexes range from 2 to 9, the most

common being 6. There is only a limited number of complex ions with a coordination number of 2, and these are typically found among Group IB M(I) and Hg(II) complexes. The geometrical arrangement of these complexes tends to be linear. In general, these bis complexes readily accept additional ligands to give complexes with higher coordination. Three coordination in metal complexes is also unusual. Thus, attempts to deduce three-coordination from

stoichiometry can be misleading. Thus, the 3-coordinate complex CuCl3- does not exist in the

compound CsCuCl3. In fact, in this compound, Cu(II) has a coordination number of 4. Similarly, in KCuCl3, the coordination number of Cu(II) is 6 not 3.

Two different coordination polyhedra are associated with a coordination number of 4, i.e., tetrahedral and square planar structures. The tendency towards the formation of a tetrahedral structure can be rationalized in terms of steric constraints. That is, as ligands increase in charge and/or size, there is a need for the ligands to be as far away from each other as possible. Due to steric constraints, square planar structures are not favored by relatively large ligands. Relatively small ligands do not favor square structures either; the ligands may be so small that two-additional ligands may be readily accommodated below and above the square plane, giving an octahedral complex. Thus, only a select group of metal ions can form square planar complexes.

Complexes with a coordination number of 5 are few. As with coordination number 3, many complexes which appear from stoichiometry to be 5-coordinate may not have this

coordination at all. Examples of 5-coordination polyhedra are the trigonal bypyramid, and the square pyramid. The coordination number 6 is the most common.

Table 3.1 Common Ligands and Ligand Atoms

Ligand Atom Common Ligands

Carbon (C) CN-

Nitrogen (N) NH3, NO2, SCN-, RNH2, R2NH, R3N

ORC (Amide), RN=O (Nitroso),

NH2

RC = N - OH (Oxime)

Oxygen (O) H2O, OH-, O2-, NO , NO3, CO3, PO4,

S2O3, SO3, SO4, ClO4, R-O-R (ether),

R-OH (Alcohol), RC=O (Ketone),

OR - O O (Alkyl phosphate), RC — OH (Carboxylate) P HO O-

Sulfur (S) HS-, S2-, SO3, S2O3, SCN-, R-S-R- (Thioether),

R-SH (Mercaptan), R-S-,

O SRC (Monothiocarboxylate), RC (Dithiocarboxylate) S- S-

R S N — C (Dialkyl dithiocarbamate)R S-

R — O S

P (Dialkyl dithiophosphate)

R — O S-

H2N

C = S- (Thiourea)H2N

Halogen (F, Cl, Br, I) F-, Cl-, Br-, I-

Table 3.2 Coordination numbers of metal complexes.

Coord. No. Typical Examples2 Group IB M(I) complexes, e.g.

M(NH3)2+, where M(I) = Cu

+ , Ag

+

MCl2-, where M(I) = Cu

+, Ag

+, Au

+

M(CN)2-, where M(I) = Ag

+, Au

+

Hg(II) complexes, eg., Hg(CN)2

3 KCu(CN)2 chain, [-CN-Cu(CN)-CN-Cu(CN)-CN-]

Triiodomercurate (II) anion, Hg I3-

4 (Square) d8 metal ions (e.g., Ni

2+, Pd

2+, Pt

2+, Au

3+)

4(Tetrahedral) Large ligands (e.g., Cl-, Br

-, I

-) bonded to

(a) small metal ions with noble gas configuration,

ns2np

6, e.g., Be

2+

(b) metal ions with pseudo-noble gas configuration,

ns2np

6 and (n-1)d

10, e.g. Zn

2+, Ga

3+.

(c) transition metal ions which, for energetic reasons, have no strong preference for other structures, e.g.,

Co2+

(d7)

5 Pentachlorocuprate (III) anion, CuCl53-

Pentacyanonickelate (III) anion, Ni(CN)53-

6 Most Cr (III) and Co(III) complexes78 Relatively small ligands (e.g., with C, N, O, F as

ligating atoms) bonded to relatively large metal cationswith high oxidation state: lanthanides, actinides, Zr, Hf, Nb, Ta, Mo, W

9 Ln(H2O)93+,

, Ln = early lanthanide metal

_____________________________ ______________________________________________

3.3 Molecular Orbital and Crystal Field Theories3.3.1 Molecular Orbitals of Metal-Ligand Complexes

As discussed previously above (Section 2.5), we can view the formation of molecules as the interaction between the valence orbitals of the constituent atoms. We shall now extend this concept to metal-ligand complexes. Let us consider a d-metal atom, M, which forms a complex MLn with six molecules of the ligand L. Nine atomic valence orbitals are available on the metal:

one s, three p, and five d. Suppose each ligand provides a single s-type atomic orbital, then for the complex MLn, there will be (9+n) atomic orbitals in all. Corresponding to the n metal-ligand

bonds are n bonding and n antibonding orbitals. This leaves (9-n) orbitals, which then constitute the nonbonding orbitals. The energy levels will be expected to increase in the order, bonding < nonbonding < antibonding.

Figures 3.1, 3.2, and 3.3 present schematic diagrams which illustrate the molecular orbital energy level schemes for octahedral, tetrahedral, and square planar complexes, respectively.

Figure 3.1 Energy level diagram for a sigma-bonded octahedral complex (Huheey, p.417).

Figure 3.2 Energy level diagram for a sigma-bonded tetrahedral complex (Huheey).

Figure 3.3 Energy level diagram for a sigma-bonded square planar complex (Huheey).

Application of molecular orbital theory to octahedral complexes requires the construction of seven-centered molecular orbitals. In the case of both tetrahedral and square-planar complexes, five-centered molecular orbitals are involved. It must be noted that the linear combination of atomic orbitals is feasible only if the metal and ligand orbitals have the same symmetry.

The subscripts g (gerard), and u (even, ungerard) were encountered previously above. The following additional labels are useful in describing the symmetry properties of metal-ligand complexes. The subscript 1 indicates that the orbital does not undergo a sign change when rotated about the Cartesian axes. The subscript 2 is used to indicate that there is no sign change when the axis of rotation is diagonal to the Cartesian axes. For a particular energy level, the labels a, e, and t respectively signify that, there is a single orbital, a set of two orbitals, and a set of three orbitals. Thus the appropriate symmetry labels for the d-metal atomic orbitals are: a1g

for s, t1u for px, py, pz, t2g for dxy, dyz, dzx, and eg for dx2-y2, dz2.

It is generally the case, as shown in the above diagrams, that the ligand energy level is lower than the metal energy levels. The implication is that the bonding molecular orbitals tend to be ligand-like in character.

3.3.2 Ligand Field Splitting and the Spectrochemical SeriesIt can be seen from Figures 3.1 and 3.2 that one outcome of the presence of ligands around

the central metal ion is that the five d-type molecular orbitals are split into two groups, separated by an energy gap identified as o for octahedral coordination and as t for tetrahedral structures.

This effect is termed ligand field splitting. In the case of the square-planar energy level diagram...

Ligands differ in the extent to which their orbitals interact with metal orbitals. A ligand whose orbitals interact strongly with metal orbitals is termed a strong-field ligand. Such a ligand will produce a large ligand field splitting. On the other hand, a weak-field ligand interacts weakly and the resulting ligand field splitting is small. Table 3.3 presents ligand field splitting data for selected octahedral complexes (Table 7.4 SAL, p.211). It can be seen that o varies with

both the metal and ligand. An empirically determined order of ligand fields, termed a spectrochemical series, has been established for both ligands and metals. In the case of ligands, the order is as follows:

I- < Br-< S2- < SCN- < Cl- < NO3- < F- < C2O42- < H2O < NCS- < CH3CN < NH3 < en < bipy < phen < NO2- < PPh3 < CN- < CO

In cases where there may be some ambiguity, the binding site on the ligand is underlined. For metal ions, the following order has been established:

Mn2+ < V2+ < Co2+ < Fe2+ < Ni2+ < Fe3+ < Co3+ < Mn4+ < Mo3+ < Rh3+ < Ru3+ < Pd4+ < Ir3+ < Pt4+ (SAL, p.212).

Table 3.3 Ligand field splittings (o) of ML6 complexes*

Ions Ligands Cl - H 2O NH 3 en CN -

d3 Cr3+ 13.7 17.4 21.5 21.9 26.6d2 Mn2+ 7.5 8.5 10.1 30d5 Fe3+ 11.0 14.3 (35)d6 Fe2+ 10.4 (32.8)d6 Co3+ (20.7) (22.9) (23.2) (34.8)d6 Rh3+ (20.4) (27.0) (34.0) (34.6) (45.5)d8 Ni2+ 7.5 8.5 10.8 11.5 *"Values are in multiples of 1000 cm-1; entries in parentheses are for low spin complexes.""Source: H. B. Gray, Electrons and Chemical Bonding, Benjamin, Menlo Park (1965)."(SAL, P.211)

The empirical trends exemplified by the spectrochemical series can be rationalized with the aid of molecular orbital theory. Three important factors are: (a) the relative energies of the metal and ligand orbitals, (b) the degree of overlap between metal and ligand orbitals, and (c) the extent of metal-ligand pi bonding. ______________________________________________________________________________

EXAMPLE 3.3 Metal - ligand combinations giving strong-field and weak-field complexes

Speculate on whether the following metal-ligand combinations are most likely to give weak-field or strong-field complexes.

Solution

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3.3.3 Crystal Field TheoryIt was noted above that one outcome of the presence of ligands around the central metal ion

is the splitting of the d-type orbitals into two main groups. Crystal field theory (CFT) focuses on this characteristic feature of the energy level diagram. In the CFT approach to bonding in metal-ligand complexes, the development of the energy gap is viewed electrostatically: A metal complex is considered as consisting of a central metal ion embedded in a cluster of the negative ions and molecular dipoles which constitute the ligands. The bonding between the central metal ion and the surrounding ligands is attributed to electrostatic interaction arising from the electric field of the metal ion and that of the ligands. The electrostatic field emanating from the negative charges and the negative ends of the dipoles will tend to repel the outer electrons, particularly, the d electrons of the central metal ion. That is, the greater the proximity of a ligand to a metal orbital, the harder it is for an electron to occupy that orbital. A consequence of this repulsion is an increase in the energy of the d-orbitals of the central ion.

As would be expected, the geometrical arrangement (e.g., octahedral, tetrahedral, square-planar) of the ligands around the central ion has a significant influence on the electrostatic field experienced by the central metal ion. Let us consider an octahedral complex. We envision the six ligand ions or molecules to be distributed along the x, y, z Cartesian axes as illustrated in Figure 3.4a. It can be seen that the ligand-metal orbital interactions will be greatest for the dx2-

y2 and dz2 orbitals (i.e., the eg group) since these lie along the x, y, z axes. In contrast, there is a

smaller interaction with the dxy, dxz and dyz orbitals (i.e., the t2g group) since these lie in between the ligands. Accordingly the eg orbitals acquire a greater energy than the t2g orbitals.

In the language of crystal field theory, this effect is termed crystal field splitting; it corresponds to the ligand field splitting encountered previously above. Crystal field splitting for an octahedral complex is illustrated in Figure 3.4b; the difference in energy between the eg and t2g orbitals is denoted as o. If one considers the energy of a hypothetical complex with degenerate d orbitals (i.e. orbitals with the same energy), then it can be demonstrated that the eg and t2g orbitals are respectively 0.6 o and 0.4 o above and below this hypothetical energy level. A

similar analysis can also be performed for other ligand geometries, e.g., tetrahedral, and planar. For tetrahedral complexes the ligand field effect causes a splitting of the d sublevel with the t2g orbitals lying above the eg orbitals. In general the crystal field splitting of the tetrahedral arrangement (t) is about a half of the corresponding octahedral value (o).

(a) Metal-ligand orbital interactions

Figure 3.4. Crystal field splitting for an octahedral complex

3.3.4 Electron ConfigurationsA major factor in working out the electron distribution in a metal-ligand complex, is the energy level difference, . Let us return to the molecular orbital energy level diagram for octahedral complexes shown in Figure 3.1. Each of the six ligand atoms supplies a lone pair of electrons. The resulting twelve electrons fill up the six bonding orbitals. There can be a maximum of ten d electrons; therefore, five orbitals are needed and these must be the next lower-lying orbitals, i.e., the t2g and eg* orbitals. The order in which the t2g and eg orbitals are filled by electrons, and the

extent to which electron pairing occurs, are both the combined effects of the energy level difference o, the electrostatic energy (Eel), and the exchange energy (Eex). We recall from Section 2.2.4 that the total energy of a given electronic configuration (Econfig) is given by:

Econfig = Eelt + Eext (3.7)

where Eelt is the total electrostatic energy associated with Pel electron pairs and Eext (= PexEex) is the total energy due to Pex parralel-spin electrons. For the condition o > Econfig, the leading

principle is that based on energy levels, and it is energetically more favorable to first fill up the lower energy levels. On the other hand, when o < Econfig, the leading principle is the constraint

on electron pairing and the electronic configuration is more stable with unpaired electrons.

Table 3.4 Effect of the ligand field on the electron distribution in octahedral complexes

System Weak Field (High Spin) Strong Field (Low Spin)

t 2g e g t 2g e g

d0 d1 d2 d3 d4 d5 d6 d7 d8 d9 d10

The crystal field splitting can lead to modifications in the electron distributions in the five d

orbitals. As noted previously, Hund's rules require that all the d orbitals be occupied singly before electron pairing begins, however, if the ligand field splitting is relatively large, then the eg orbitals will be significantly higher in energy than the t2g orbitals. Under these circumstances the lower t2g orbitals will become completely filled before occupation of the higher eg orbitals

begins. Table 3.4 illustrates the different electron distributions for low and high ligand fields in an octahedral complex. It can be seen that the d4, d5, d6, and d7 systems differ significantly in electron distribution, depending on whether they are subjected to a weak or a strong ligand field. The presence of a weak field does not significantly influence electron pairing, and high-spin complexes are said to form. On the other hand a strong field causes significant electron pairing, and the resulting complexes are termed low-spin complexes.____________________________________________________________________________________________

EXAMPLE 3.4 Effect of ligand field strength on the filling of d-orbitals

For a given central metal ion Mz+, determine the tendency with which the following ligands may form low-spin complexes: F-, phenanthroline, aliphatic amine, CN-, H2O.

Solution

The relative strengths of the ligand fields are given by the spectrochemical series. That is, the ligand field strength increases in the order: F- < H2O < amine < phenanthroline < CN-. The stronger the ligand field, the greater the tendency towards ion-pairing, and therefore the tendency to form low-spin complexes. Thus, low-spin complexes are expected to form in the same order as the spectrochemical series, i.e., CN- complexes are likely to be low-spin and F- complexes high-spin.

EXAMPLE 3.5 Magnetic moments and the structure of metal complexes

The magnetic moment (mM) of a metal complex is a reflection of the number of unpaired electrons (n) that the

central metal ion contains, i.e. mM = (n(n+2))1/2 magnetons (1 Bohr magneton = 9.18 x 10-21 gauss-cm/atom or 5564 gauss-cm/mol).

(a) Determine the magnetic moment (in Bohr magnetons) that corresponds to the following numbers of unpaired electrons 0, 1, 2, 3, 4, 5.

(b) Determine the magnetic moment (in Bohr magnetons) of a free Fe3+ ion.

(c) Given the following magnetic moments (shown in brackets), determine the corresponding number of unpaired electrons for the central metal ion: (i) Fe(CN) (2.3), (ii) FeF (6.0), (iii) Fe(CN) (0).

Solution

(a) Given that mM = (n(n + 2))1/2 magnetons, it follows that: (i) for n = 0, mM = 0; (ii) n = 1, mM = (1(1 + 2))1/2

= 1.73; (iii) n = 2, mM = (2(2 + 2))1/2 = 2.83; (iv) n = 3, mM = (3(3 + 2))1/2 = 3.87; (v) n = 4, mM = (4(4 + 2))1/2

= 4.90; (vi) n = 5, mM = (5(5 + 2))1/2 = 5.92.

(b) Fe has the electronic structure [Ar] 3d64s2. The corresponding structure of Fe3+ is [Ar] 3d54s0. The free Fe3+ ion is situated in a weak field and therefore this ion has five unpaired electrons (see Table 3.4). Thus, it follows

from part (a) that mM = 5.92 magnetons.

(c) (i) Fe(CN) , mM = 2.3 magnetons. From part (a), for n = 1, mM = 1.73 magnetons; this suggests that Fe(CN)

has one unpaired electron.

(ii) FeF , mM = 6.0 magnetons. This suggests a structure with five unpaired electrons.

(iii) Fe(CN) , mM = 0 magnetons. In this case there are no unpaired electrons.

EXAMPLE 3.6 Exchangeable electron pairs in high and low spin complexes(a) Determine the number of exchangeable pairs for high spin and low spin complexes of (i) a d6 ion, (ii) a d5 ion.

(b) For both ions, determine the value of Econfig.

Solution

(a) (i) d 6 (high spin): The relevant electronic configuration is: . Thus, 5 spin down electrons (i.e., N = 5) and 1 spin up electron (N = 1). Thus, the number of exchangeable pairs is given by (Equation 2.2):

Pex() = N(N-1)/2 = 5(4)/2 = 10Pex = N(N-1)/2 = 1(0)/2 = 0

Thus the total number of exchangeable pairs is

Pex = Pex() + Pex = 10 + 0 = 10

d 6 (low spin ): The electronic configuration is: . Accordingly, N() = 3, N = 3.

Thus,

Pex() = Pex= N(N-1)/2 = 3(2)/2 = 3

and,

Pex = Pex() + Pex() = 3 + 3 = 6.

(ii) d 5 (high spin) : The electronic configuration is: . Therefore, N() = 5, N() = 0. Thus,

Pex = Pex() = N(N-1)/2 = 5(4)/2) = 10.

d5(low spin): __ __. There are 3 spin-down electrons (N()=3) and two spin-up electrons(N() = 2). Thus,

Pex = [3(3-1)/2] + [2(2-1)/2] = 3+1 = 4.

EXAMPLE 3.7 Spin configuration of aquo complexes

Presented below are orbital splitting (o ) and mean pairing energy (Epair) data for aquo ions (cm-1). On the basis of these data, speculate on the likelihood of the formation of low spin configurations.

Ion o Epair Ion o Epair

d1 Ti3+ 20,300

d2 V3+ 18,000

d1 Ti3+ 20,300

Solution____________________________________________________________________________________________

3.3.5 Crystal Field Stabilization EnergyThe amount of energy by which d orbitals are lowered in comparison with the hypothetical

undisturbed d orbitals is designated the crystal field stabilization energy (CFSE) of the complex. Referring to Figure 3.4b, let us assign the zero of energy to the degenerate d levels in the hypothetical homogeneous ligand field. Then, the energy of the eg orbitals is 0.6∆, while that of the t2g orbitals is -0.4∆o. Thus, for a given electronic configuration t 2g

a egb , the net energy relative

to the degenerate levels, i.e., the crystal field stabilization energy (CFSE), is defined as:

CFSE = -(0.4a + 0.6b) ∆o = 0.4a - 0.6b) (3.8)

Table 3.5 presents crystal field stabilization energies (in units of o) for octahedral, tetrahedral,

and square complexes.

Table 3.5 Crystal field stabilization energies for octahedral, tetrahedral, and square complexes (in units of o).

Weak Field (High Spin) Strong Field (Low Spin)

System Examples Oct. Tet. Square Oct. Tet. Square

d0 Ca2+, Sc3+ 0 0 0 0 0 0d1 Ti3+ U4+ 0.4 0.27 0.51 0.4 0.27 0.57d2 Ti2+,V3+ 0.8 0.54 1.02 0.8 0.54 1.02d3 V2+, Cr3+ 1.2 0.36 1.45 1.2 0.81 1.45d4 Cr2+,Mn3+ 0.6 0.18 1.22 1.6 1.08 1.96d5 Mn2+,Fe3+,Os3+ 0 0 0 2.0 0.90 2.47d6 Fe2+,Co3+,Ir3+ 0.4 0.27 0.51 2.4 0.72 2.90d7 Co2+,Ni3+,Rh2+ 0.8 0.54 1.02 1.8 0.54 2.67d8 Ni2+,Pd2+,Pt2+,Au3+ 1.2 0.36 1.45 1.2 0.36 2.44d9 Cu2+,Ag2+ 0.6 0.18 1.22 0.6 0.18 1.22d10 Cu+,Zn2+,Cd2+, 0 0 0 0 0 0

Ag+,Hg2+,Ga3+

EXAMPLE 3.8 Crystal Field Stabilization Energies for Metal ions in Octahedral Complexes.

By assigning a value of 0.4o for each electron in a t orbital, and -0.6 o for each electron in an e orbital (see Figure 3.4b), the crystal field stabilization energy of an octahedral complex can be calculated. Determine the CFSE for the following octahedral complexes:

(a) high spin d4 (b) low spin d4

(c) high spin d7 (d) low spin d7

Solution

(a) High spin d4: In this case the d electrons experience a weak field and therefore are unpaired. Thus the electrondistribution is t e . Therefore if nt and ne respectively represent the number of electrons in the t and eg orbitals, then the crystal field stabilizing energy is given by:

CFSE = nt(0.4o) + ne (-0.6o)= (3) (0.4o) + (1) (-0.6o) = 0.6o

(b) Low spin d4: Now all the electrons are paired and they reside only in the t orbitals (see Table 3.4). Thus

CFSE = (4)(0.4) o

(c) High spin d7: The corresponding electron distribution is t e . Thus

CFSE = (5) (0.4o) + 2(-0.6o) = 0.8o

(d) Low spin d7: the electron distribution is t e . Accordingly

CFSE = (6) (0.4o) + 1(-0.6o) = 1.8o

EXAMPLE 3.9 Crystal field theory and the structure of complexes

With the acid of crystal field theory rationalize the following observations.

(a) If a divalent ion from the first row of transition metals forms a low-spin complex with a coordinationnumber of four, the complex is most likely to be square.

(b) Metal ions from the second and third series of transition elements tend to form square complexes morereadily than those of the first.

(c) In the presence of strong ligand fields, square planar complexes are most likely to be formed by d 8 and d9

metal ions followed by d7.

Solution(a) We are concerned here with a coordination number of four. Thus we need to choose between a square and

a tetrahedral complex. Referring to Table 3.3, it is seen that, for a given d configuration (1< n < 9), the crystal field stabilization energy (CFSE) value for a low-spin square complex is higher than that for the corresponding low-spin tetradedral complex. Thus it is reasonable to expect that square complexes would be preferred.

(b) Since the value of ∆ increases from the first to the second and third transition series, one should expect acorresponding increase in the stability of square complexes.

(c) Ni2+ is a d8 ion. It can be seen from Table 3.3 that square d8 ions exhibit the highest CFSE among thethree possibilities of octahedral, tetrahedral, and square arrangements.

3.4 Hard and Soft Acids and Bases (HSAB)Metal ions may be divided into two groups, i.e., class (a) or class (b), depending on whether

they prefer to bind to (a) the first elements in groups V, VI, and VII, i.e., N, O, F, or (b) the second or later members of groups V, VI and VII. That is, complexes of class (a) metals follow the stability sequence:

F- > Cl- > Br- > I-

O >> S > Se > TeN >> P > As > Sb > B

On the other hand class (b) metals tend to follow the reverse order, i.e.,

I- > Br- > Cl- > F-

Te ~ Se ~ S >> OP >> N

When an atom is subjected to an electric field there is a tendency for the electronic cloud surrounding the atom to experience some distortion and an atom is said to be highly polarizable if its electron cloud is readily distorted. The polarizability of the electron cloud increases, the further removed it is from the atomic nucleus. Thus, large atoms or molecules which are highly resistant towards polarization are termed hard while highly polarizable atoms are called soft. Accordingly, N, O, and F are respectively the hardest (or least polarizable) atoms in groups V, VI, and VII respectively. It can be stated therefore that class (a) metal ions prefer the hardest atom of a group, whereas class (b) metal ions prefer the softest atom of a group.

Class (a) metal ions have a low polarizability while class (b) metal ions are highly polarizable. Thus, class (a) metal ions may be identified as hard Lewis acids while class (b) metal ions are soft Lewis acids. Therefore, the principle of hard and soft acids and bases (the HSAB principle) may be stated thus: hard acids prefer hard bases while soft acids prefer soft bases. Tables 3.6 and 3.7 present a classification of selected ions and molecules according to the HSAB principle.

The most typical group (a) metal cation has a rare-gas configuration (d0 cations), e.g. Be2+, Mg2+, Ca2+, Sr2+, Ba2+ and forms stable aqueous-soluble complexes only with ligands which have F and O as donor atoms. On the other hand the most typical group (b) cation is characterized by an outer shell of 18 electrons (d10), e.g. Cu+, Ag+, Zn2+, Cd2+, Hg2+.

Table 3.6 Selected Hard and Soft Bases Hard Borderline Soft

H2O, OH-, F- C6H5NH2, C5H5N, R2S, RSH, RS-

CH3COO-, PO, SO Br-, NO2-, SOI-, SCN-, S2O

Cl-, CO, ClO, NO R3P, R3As, (RO)3P

ROH, RO-, R2O CN-, RNC, CO

NH3, RNH2, N2H4 C2H4, C6H6, H-, R-

Table 3.7 Selected Hard and Soft Acids Hard Borderline Soft

H+, Li+, Na+, K+ Fe2+, Co2+, Ni2+, Cu2+, Zn2+ Cu+, Ag+, Au+, Tl+, Hg+

Be2+, Mg2+, Ca2+,Sr2+,Mn2+ Pb2+, Sn2+, Sb3+, Bi3+ Pd2+, Cd2+, Pt2+, Hg2+

Al3+, Sc3+, Ga3+, In3+ Rh3+, Ir3+, SO2, CH3Hg+, Co(CN)

La3+, Gd3+, Lu3+ Ru2+, Os2+, GaH3 Pt4+, Te4+

Cr3+, Co3+, Fe3+, As3+, H3Sn3+

Si4+, Ti4+, Zr4+, Th4+, U4+

Pu4+, Ce3+, Hf4+, WO4+, Sn4+

UO, (CH3)2Sn2+, VO2+, MoO3+

A convenient (but admittedly oversimplified) way to rationalize the observed preferential

hard-hard and soft-soft acid-base interaction is to assume that the interactions of hard acids are

primarily via ionic bonding whereas soft acids interact primarily via covalent bonding. It then

follows, from an electrostatic standpoint, that bases which are highly negatively charged and are

small in size will bind most strongly to hard acids. In the case of soft acids, the presence of d

electrons plays a critical role in the bonding interactions. These d electrons may be donated to

appropriate ligands to yield π -bonds. Consequently the most likely ligands are those whose

ligand atom (e.g. P, As, S, I) contains empty d orbitals which can accept d electrons from the

metal.EXAMPLE 3.10 Comparison of stability constants for acid-base reactions.

Consider the following reactions:

H+ + CH3HgOH = H2O + CH3Hg+ (1)

H+ + CH3HgS- = HS- + CH3Hg+ (2)

Speculate on the relative values of the equilibrium constants for Equations 1 and 2 (see Pearson, Science, 151, 172-177 (1966)).

Solution

According to Tables 3.5 and 3.6, H+ and CH3Hg+ are hard and soft acids respectively, while OH- and S2- are

hard and soft bases respectively. In Equation 1 a hard acid (H+) reacts with a hard base (OH-) to give H2O and this should be a favorable reaction according to the HASB principle. On the other hand, in Equation 2 the hard acid (H+) reacts with the soft base (S2-) and this is less favorable. Thus it is expected that the equilibrium constant (K1) for reaction 1 would be greater that the corresponding value (K2) for reaction 2. (In fact, it is found that log K1 = 6.3, and log K2 = -8.4, in agreement with the predictions of the HASB principle).

EXAMPLE 3.11 Symbiotic behavior and the HSAB principle

It is observed that an acid becomes softer when it is bound to a soft base. This symbiotic effect is attributable to the ability of the soft base to release electrons to the metal ion, thereby causing a decrease in the effective positive charge of this ion.

(a) Compare the effective positive charge on the boron atom in BH3 and in BF3.(b) Discuss the likelihood of forming the complexes BH3CO and BF3CO.

(c) Speculate on the relative stabilities of the following pairs of complexes: (i) Co(NH3)5 F2+, Co(NH3)5 I2+; (ii) Co(CN)5 I3-, Co(CN)5 F3-.

Solution(a) It can be seen from Table 3.5 that the hydride ion (H-) is a soft base whereas the fluoride ion (F-) is a hard

base. Now, the oxidation state of boron is B3+ in both BH3 and BF3. Thus in the case of BH3, there is

partial transfer of negative charge from the soft base H- to the boron and this results in an effective charge of less than +3 on the boron atom. On the other hand, there is little tendency for the hard base F- to lose its electrons. Therefore it would be expected that in BF3 the effective charge on the boron atom would not differ significantly from +3.

(b) According to Table 3.5 CO is a soft base. Furthermore, it was found in part (a) that the effective charge on the boron atom is lower in BH3 compared with BF3. Thus BH3 is a softer acid than BF3. Therefore the soft base CO is more likely to bind to BH3 than to BF3.

(c) (i) From Table 4.4, Co3+ is a hard acid, NH3 is a hard base, F- is a hard base, and I- is a soft base. The

complex Co(NH3)53+ is a hard acid-hard base complex and therefore should be stable. Since NH3 is a

hard base, the charge on the cobalt atom is expected to remain close to +3. Thus Co(NH3)53+ will be

expected to be a hard acid. Combination of this complex with the hard base F- should therefore give a relatively stable complex. On the other hand, the Co(NH3)5I3+ complex involves hard acid-soft base interaction, which is not expected to be highly favored. Thus the relative stabilities are expected to follow the order Co(NH3)5F2+ > Co(NH3)5I2+

(ii) It can be seen from Table 3.5 that Co(CN)is a soft acid. Consequently the complex Co(CN)5I3- is based on

soft acid-soft base interaction and is favorable, whereas the complex Co(CN)5F3- is based on soft acid-hard base interaction, which is unfavorable. Thus the relative stabilities of the complexes are expected to follow the order Co(CN)5I3- > Co(CN)5F3-.

FURTHER READING

1. J. E. Huheey, E.A. Keiter, and R. L. Keiter, Inorganic Chemistry. Principles of Structure and Reactivity, 4th ed., HarperColins, 1993.

2. A. G. Sharpe, Inorganic Chemistry, 3rd. ed., Longman, London, 1992.

3. G. L. Miessler and D. H. Tarr, Inorganic Chemistry, Prentice-Hall, Englewood Cliffs, NJ, 1991.

4. D. E. Shriver, P. W. Atkins, and C. H. Langford, Inorganic Chemistry, Freeman, New York, 1990.

5. D. W. Smith, Inorganic Substances, Cambridge, New York, 1990.

6. B. Webster, Chemical Bonding Theory, Blackwell, Oxford, 1990.

7. K. M. Mackay and R. A. Mackay, Introduction to Modern Inorganic Chemistry, 4th ed., Prentice Hall, Englewood Cliffs, NJ, 1989.

8. F. A. Cotton and G. Wilkinson, Advanced Inorganic Chemistry, 5th ed., Wiley New York, 1988.

9. T. Moeller, Inorganic Chemistry: A Modern Introduction, Wiley, New York, 1982.

10. K. F. Purcell and J. C. Kotz, An Introduction to Inorganic Chemistry, Sauders, Philadelphia, 1980.

11. G. I. Brown, A New Guide to Modern Valency Theory, Longmans, London, 1967.

12. F. Basolo and R. C. Johnson, Coordination Chemistry, 2nd ed., Science Reviews, 1986.

13. R. G. Pearson, ed., Hard and Soft Acids and Bases, Dowden, Hutchinson and Ross, Stroudsburg, PA, 1973.

14. R. G. Pearson, "Hard and Soft Acids and Bases, HSAB, Part I: Fundamental Principles", J. Chem. Educ., 45, 581-587 (1968); "Part II*: Underlying Theories", J. Chem. Educ., 45, 643-648 (1968).

15. L. E. Orgel, An Introduction to Transition - Metal Chemistry: Ligand-Field Theory, 2nd ed., Wiley, New York, 1966.