Factors Influencing Stability of Metal Complexes

We can identify a number of factors that contribute to the size of stability constants, and it is appropriate to summarize and review effects. In doing so we will also attempt to divide the effects into those more associated with the metal and those more associated with the ligand, since both contribute to the partnership and inevitably each brings something to the metal–ligand marriage.

5.1.2.1.1 Size and Charge

Several factors based on pure electrostatic arguments contribute to a strong stability con- stant. First, since we are bringing together a positively-charged metal ion and anionic or polar neutral ligands carrying high electron density in their lone pairs there is certainly going to be a purely electrostatic contribution. We can see this experimentally as shown above in Table 5.1. As the charge on cations all of similar size, varies from 1+ to 4+ across the series, the size of log K increases.

When the metal ion charge is fixed but the metal ion size is increased, the surface charge density decreases as the ionic radius increases. This means a less effective attractive force for the ligand applies which leads to a fall in the size of log K (Table 5.1). The role of surface charge density is seen also if one plots stability constant against charge/surface ratio for a range of M(OH)(n-1)+ complexes (Figure 5.1). Obviously, the effect of charge

Figure 5.1

Variation of stability constant (K) with charge/radius ratio for some M(OH)(n-1) + complexes. This is a reasonable representation of how K varies will ion charge and size, but obviously the effect of charge has some dominance, given the drop in K for Al³⁺ and Be²⁺ ions despite their large charge/radius ratio.

appears more important than that of ionic radius, from the fall in log K values for very small but lower-charged ions (A¹³⁺ and Be²⁺). Of course, our simple model of the cations as hard spheres applied in this analysis is also imperfect; overall, nevertheless, it is possible to predict stability adequately if not finitely from the charge/radius ratio relationship. As a result, a large K is favoured by a large charge/radius ratio, or the smaller the ion and the larger its charge, the more stable will be its metal complexes.

Although our focus currently is on the metal, it should be recognized that the size (or molar volume) of the ligand plays a role in the electrostatic effect on stability of a complex, particularly for anionic ligands. This is sensible, since the ligand can be assigned a surface charge density (when anionic) in the same way that we have done for the cation and obviously an anion with a high surface charge density should form stronger complexes from an electrostatic perspective. This is best illustrated by examining halide monatomic anions, where spherical surfaces have some meaning. With F (radius 133 pm) and C1- (radius 181 pm) Fe³⁺ forms complexes with log K of 6.0 and 1.3 respectively, reflecting the greater charged/surface ratio for the former. The concept of ion radius becomes diffuse when we move to molecular anions however whose shape may not be anywhere near spherical. However, at least for large reasonably symmetrically-shaped and thus pseudo- spherical anions like CIO4 the very low stability of its complexes is fairly consistent with an electrostatic model, since this ion has a much greater radius than simple halide ions of the same charge.

5.1.2.1.2 Metal Class and Ligand Preference

We have examined the hard/soft acid/base 'like prefers like' concept as it applies to metal-ligand binding already in Chapter 3, so it is simply necessary to revise aspects here. Electropositive metals (lighter and/or more highly charged ones from the s, d and f block such as Mg²⁺. Ti⁺ and Eu³⁺ belonging to Class A) tend to prefer lighter p-block donors (such as N, O and F donors). Less electropositive metals (heavier and/or lower-charged ones such as Ag+ and Pt2+ belonging to Class B) prefer heavier p-block donors from the same families (such as P, S and I donors). A more significant M-L covalent contribution is asserted to apply in the latter case, along with other effects such as back-bonding. Of course, in any situation where there are only two categories, there is a 'grey' area of metals and ligands who do not sit easily in either set. A summary is given in Table 5.2 below in which a large number of the metal ions and simple ligands you are likely to meet appear.

Table 5.2 Examples for both ligands and metals of ‘hard’ and ‘soft’ character, with some less clearly defined intermediate cases also included.

5.1.2.1.3 Crystal Field Effects

The above simple effects are not the sole metal-centric influences on K as is evident from examining trends in experimental values with a wide range of ligands. This is particularly evident when one examines a series of transition metal 2+ ions forming complexes with ligands; data with ammonia appears in Table 5.1. Overall, between Mn2+ and Zn²⁺, there is a general trend in K values essentially irrespective of ligand of the order:

Mn²⁺ <Fe²⁺ <Co²⁺ < Ni²⁺ <Cu²⁺ > Zn²⁺.

The relative sizes of the cations vary in a not so different fashion with radii following the trend:

Mn²⁺ > Fe²⁺> Co²⁺ > Ni²⁺ < Cu²⁺ <Zn²⁺

so the change is in part (but only in part) assignable to charge/radius ratio ideas. Across this series of metal ions, the number of protons in the nucleus is increasing, but shielding by the electron clouds is imperfect, so that as Z increases there is a progressively higher apparent nuclear charge 'seen' by the ligands, despite the common formal charge. This also contributes to a steady climb in the stability constants from left to right across the periodic block. However, there is an obvious discontinuity between Cu²⁺ and Zn²⁺, with a drop that is consistently observed regardless of ligand type. The source of this effect is tied to the presence of an incomplete set of d electrons except for Zn²⁺ and we shall return to it below.

5.1.2.1.4 The Natural Order of Stabilities for Transition Metal Ions

For transition metal ions with incomplete sets of d electrons, there is a contribution to stability from the crystal field stabilization energy (CFSE) whereas for d1o metal ions (such as Zn²⁺) with a full set, there is no such stabilization energy. Crystal field stabilization energies of metal ions in complexes have been asserted to have a key influence on values of K for transition metals, reflected in the experimentally-determined stabilities for the series of metal ions from Mn2+ across to Zn²⁺. This effect is overlaid on the general 'upward' trend from left to right across the row with increasing Z, associated with imperfect shielding of the nucleus, discussed earlier, and leads to what is usually called the natural order of stabilities (also called the Irving-Williams Series). This experimentally-based order states that the accessible water-stable M²⁺ octahedral first-row transition metal ions exhibit an order of stabilities with any given ligand which is essentially invariant regardless of the ligand employed, that is

Mn²⁺ <Fe²⁺ <Co²⁺ <Ni²⁺ < Cu²⁺ > Zn²⁺.

This means the same trend in K values is seen regardless of ligand (unless some other special effect overrides it). This trend identifies copper(II) as the metal ion that forms the most stable complexes, irrespective of ligand. The series predicts a fall in K values in each direction from Cu²⁺, irrespective of ligand. The trend is preserved for the series of metal ions with didentate chelates even when the type of donor atom or the size of the chelate ring is varied (Figure 5.2).

In this series, we are dealing, for high-spin complexes, with octahedral systems. Only for Cu²⁺ do we have an especially distorted octahedral shape. Electrons placed in the lower t2g level are stabilized by 0.4Δo whereas those placed in the upper e level are destabilized

Figure 5.2 The natural order of stabilities in operation: consistent variation of measured stability constant with different chelate ligands for the series of transition metal (II) ions from manganese across to zinc.

by 0.6Δo. Overall the calculated CFSE follows the order:

Mn²⁺<Fe²⁺<Co²⁺<Ni²⁺>Cu²⁺>Zn²⁺

with the ions at each end each having zero CFSE as a result of half-filled or filled d shells. This behaviour closely follows the observed (experimental) behaviour of K with varying M2+ (Figure 5.2) except for Cu²⁺ where the apparently anomalous behaviour is related to the axially elongated structure met for this ion. This leads to an enhanced CFSE for Cu²⁺ as a result of a different d-orbital energy arrangement to that operating in the pure octahedral environment. Thus the influence of the d-electron configuration, through the CFSE is important in understanding the natural order of stabilities for light transition metal ions; it links the basic crystal field theory to experimental observations effectively.

5.1.2.2.1 Base Strength One aspect of complex formation that became apparent at an early date was the relationship between the Brønsted base strength of a ligand and its ability to form strong complexes. This is sensible, in the sense that base strength is a measure of a capacity to bind a proton. Making a substitution of H+ by Mn+ seems reasonable permitting basicity to define likely complex strength. From this perspective, the better base NH3 should be a better ligand than PH₃ orH₂O and F− should be superi or to other halide ions. This predicted behaviour holds quite well for s-block, lighter (first-row) d-block, and f-block metal ions, which have been defined as ‘hard’ or Class A metal ions. We can say with some certainty that the greater is the base strength of a ligand (that is its affinity for H+) the greater is its affinity for (and hence stability of complexes of) at least Class A metal ions. Unfortunately, when one examines heavier metal ions and those in low oxidation states, the behaviour is not the same (hence their definition as ‘soft’ or Class B metals). Obviously, there are electrostatic contributions applying, but other influences are now important. A classical example is the reaction of the relatively large, low-charged Ag+ ion in forming AgX which follows the order (log values of the formation constant in parentheses):

F−(0.3) <Cl−(3.3) <Br−(4.5) <I−(8.0).

Clearly, this does not follow the trend expected on electrostatic grounds, which should be opposite to that observed. The trend is thought to reflect increased covalent character in the Ag X bond in moving from fluoride to iodide. The steric bulk of ligands also introduces an influence that can act counter to a pure base strength effect. This has been discussed earlier for NR3 compounds (Chapter 2.2.2). Substituted pyridines present another example of this influence; 2.6-dimethylpyridine is a poor ligand due to the location of the two methyl groups either side of the pyridine N-donor atom, despite a similar base strength to unsubstituted pyridine.

5.1.2.2.2 Chelate Effect From a purely thermodynamic viewpoint, the equilibrium constant is reporting the heat released (the enthalpy change, H0) in the reaction and the amount of disorder (called the entropy change, S0) resulting from the reaction, related to the reaction free energy as defined in Equation (5.7). The greater the amount of energy evolved in a reaction the more stable are the reaction products; this heat change can sometimes be felt when holding a test-tube in which a reaction has been initiated, and is certainly experimentally measurable to high levels of accuracy. Further, the greater the amount of disorder resulting from a reaction the greater is the entropy change and the greater the stability of the products. This is a harder concept to grasp than some, but think of it in terms of particles involved in a reaction– if there are more particles present at the end of the reaction than at the start, or even if those present at the end are less structured or restricted in their locations, there is increased disorder and hence a positive entropy change. Again, this is experimentally measurable but not as directly as a simple heat change associated with reaction enthalpy. In the coming together of two oppositely charged ions to form a comple there is both a release of heat (increased enthalpy ΔH⁰) and a release of solvent molecules from the ordered and compressed layers around the ions (increased entropy ΔS⁰) on complexation. Moreover, the higher the charge on the metal ion, the greater is the effect. When we employ molecules as ligands where they offer more than one donor group capable of binding to metal ions there is the strong possibility that more than one donor group will coordinate to the one metalion. We have entered the realm of poly dentate ligands. Just because a ligand offers two donor groups does not mean that both can coordinate to the one metal ion. For example, the para and ortho diaminobenzene isomers can both act as didentate ligands, but the former must attach to two different metal ions because of the direction in which the rigidly attached donors point. Only the ortho form has the two donors directed in such a way that they can occupy two adjacent coordination sites around a metal ion. This isomer has achieved chelation. The same behaviour is displayed by the linked pyridine molecules 2.2-bipyridine and 4.4-bipyridine (Figure 5.3). In general, chelation is beneficial for complex stability, and chelating ligands form stronger complexes than comparable monodentate ligand sets. For example, consider Equa tions (5.9) and (5.10):

Figure 5.3 Lone pairs of ortho-diaminobenzene (top left) and 2.2-bipyridine (bottom left) and para diaminobenzene (top right) and 4.4-bipyridine (bottom right) are arranged in space so that only the former pair can chelate to a single metal centre. The latter pair can only bind to two separate metal centres.

The three didentate chelate ethane-1.2-diamine ligands occupy six sites as do the six monodentate ammonia molecules, and amine nitrogen donors are involved in each case; however, it is the chelation of the former that causes the enhanced stability. However, direct comparison of the overall stability constants reported above is inappropriate since as a result of the different terms in the equations for each n, the units are not equivalent, being M−3β for β3 and M−6β for β6. A better but still not perfect approach is to examine the experimental results for direct ligand exchange of two ammines by an ethane-1.2-diamine such as reaction (5.11).

It is obvious that there is a strong driving force for this ligand replacement reaction with formation thermodynamically favourable as seen by the negative ΔG0 value. Introducing one H₂NCH₂CH₂NH₂ chelate in place of two ammine ligands leads to a complex that is ∼300-fold more stable than the analogue with two ammonia molecules bound; this is enhanced substantially once all sites around the octahedron are occupied by chelated amine donors as exemplified by the overall reaction (5.12).

For this overall reaction the components of ΔG are ΔH-16.8 kJ mol1 and (at 298 K) TAS +36.2 kJ mol. Both contribute to the overall negative ΔG", but the contribution from the entropy-based term TAS is larger. The smaller AH" contribution is in part associated with increased crystal field stabilization, seen experimentally as a change in the maximum in the visible spectrum. We can interpret this reaction as dominated by a favourable entropy change associated with chelation (i.e. an increase in disorder and 'particles' or participating molecules) as exemplified in (5.13) and (5.14).

Another way of viewing the process leads to an equivalent interpretation. Adding the first amine of an ethane-1.2-diamine molecule or adding an ammonia molecule in place of a water molecule should occur with similar facility, as they are both strong basic N- donor ligands. However, the next substitution step in each molecular assembly is distinctly different as there is no special advantage for a second ammonia entering, whereas the second amine group of the partly-bound ethane-1.2-diamine molecule is required to be closely located to a second substitution site as a result of the anchoring effect of the first substitution. Less translational energy is required and the coordination is more probable. Some reactions appear to be driven almost entirely by a positive entropy effect. For the two related reactions (5.15) and (5.16) below, each leading to four Cd-N bonds forming, the AH values are equivalent (-57 kJ mol-' for the monodentate -56 kJ mol' for the didentate chelate), and only the -TΔS terms differ (+20 kJ mol1 for the monodentate -4 kJ mol for the didentate chelate) favouring the latter.

However, it is not correct to assume that a favourable entropy change always drives ligand substitution reactions, as there are examples where the overall entropy change opposes reaction, which is driven rather by a substantial negative enthalpy change. Factors that can contribute to the latter include CFSE variation, reduction in electrostatic repulsion terms on reaction, and solvation and hydrogen-bonding changes that favour reaction. However, entropy-based effects are both easier to visualize and comprehend and more often the dominant contributor, and so tend to attract greater attention. With higher multidentates a favourable entropy change can account for an equilibrium lying to the right (favouring the ligand with more donor groups) for example (where NN=didentate and NNNN = tetradentate ligands) in (5.17):

The growing stability with number of potential donor groups can be seen by looking at the change in stability constants for occupying four coordination sites with four ammine molecules two ethane-1.2-diamine (en) molecules

or one N,N'-bis(2-aminoethane)-ethane-1,2-diamine (trien) ligand. The overall sta- bility constant (log ẞ value) for the substitution of [Ni(NH₃)₄(OH₂)₂]²⁺ to form [Ni(H₂NCH₂CH₂NH₂)₂(OH)²⁺ is 5.7 and for [Ni(H₂NCH₂CH₂NH₂)₂(OH₂)₂]₂ + to [Ni(H₂NCH₂CH₂NHCH₂CH₂NHCH₂CH₂NH₂) (OH₂)₂]²⁺ is 4.0. Clearly, as a general rule, the higher the denticity (or number of bound donor atoms) of a ligand, the higher will be its stability constant with a particular metal ion.

Invariably, for occupancy of the same number of coordination sites around a metal ion, the outcome is greater stability (larger stability constants) for the chelate system over a set of monodentates [B(chelate) > B(monodentates)]. As the number of coordinated donor atoms in a ligand rises, almost invariably the size of the stability constant likewise grows. This effect is assigned in large part, as discussed above, to entropy considerations, associated with favourable entropy change (or disorder) in the system as a chelate ligand replaces a set of monodentate ligands. Examples of stability constants and reaction energies for monodentate and analogous chelate ligands appear in Table 5.3. Recall however that direct comparisons of data for monodentate/chelate substitution of the aqua metal ion are of limited value.

A more sophisticated aspect of chelation relates to the chelates 'readiness' for binding as a chelate. This is illustrated in Figure 5.4 where one didentate chelate is rigidly fixed into an orientation immediately appropriate for chelation (that is, it is 'pre-organized") whereas the other requires rotation of one component part (which costs energy) from its

Figure 5.4

How a pre-defined appropriate ligand shape (pre-organization) provides chelation at less energy cost than in circumstances where energy-demanding ligand re-arrangement must accompany chelation.

Figure 5.5 Influence of ring size on the stability of first-row d-block metal complexes; five-membered saturated rings are more stable. The exception is for chelation of unsaturated conjugated ligands where six membered rings (such as the acetylacetonate ligand illustrated) form complexes of enhanced stability. preferred free ligand conformation prior to adopting a shape suitable for chelation. Usually, systems that are pre-organized for binding metal ions exhibit stronger stability constants than comparable systems where ligand rearrangement is required.

5.1.2.2.3 Chelate Ring Size Notwithstanding the above discussion, the size of the chelate ring also influences the size of the stability constant, an aspect we have already touched on earlier, being at its largest for five-membered rings and conjugated six-membered rings. Since we are constraining the metal by binding to two linked donor atoms, it can be hardly surprising that there is a relationship between the formed chelate ring size and stability. For example, the smallest chelate ring practicable (three-membered) will reflect a tension between the preferred metal donor length and the preferred donor–donor length, since perfect compatibility is rarely reached. Compromise resulting, seen in terms of variation in intraligand angles and bond distances, has an influence on the stability of the assembly, as obviously a system under great strain is hardly likely to be of high stability. Simply, the size of the stability constant depends on the number of atoms or bonds in the ring. For saturated rings, five-membered rings where ligand donor ‘bite’ and preferred angles within the chelate ring are optimized are preferred for the lighter metal ions, with smaller or larger rings being of lower stability (Figure 5.5). The exception to this observed preference for five-membered rings comes when unsatu rated conjugated ligands are coordinated, where very stable complexes with six-membered chelate rings can exist with some light metal ions. This is associated with a shift from tetrahedral to trigonal planar geometry of ring carbons, with associated opening out of preferred angles around each carbon leading to a more appropriate ligand ‘bite’. When the chelate ring size grows very large, there is no particular stability arising from chelation. As a consequence most examples of the chelate effect feature chelates with five or six members in the ring; indeed as one moves to lower or higher chelate ring size the chelate effect rapidly becomes modest.

5.1.2.2.4 Steric Strain Size matters. As ligands can vary so much more in size and shape than metal cations, there must be other consequences, including simply size effects in terms of ‘fitting’ around the central atom. These effects of ligand bulk, resulting from molecules being necessarily required to occupy different regions of space and thus required to avoid ‘bumping’ against each other when confined around a central metal ion, tend to be termed steric effects. As a general rule, the bulkier a molecule the weaker the complex formed when there is a set of ligands involved. Therefore one would expect NH₃ to be a superior ligand to N(CH₃)₃ despite both being strong bases, and this behaviour is experimentally observed in solution. In the gas phase, where there is no metal ion solvation and usually only low coordination number complexes form due in part to a low probability of metal–ligand encounters, discrimination in complex stability based more on base strength than steric bulk may apply. Thus N(CH₃)₃, which is a stronger base than NH3, forms the stronger complexes in the gas phase, the opposite to behaviour in aqueous solution. However, gas phase coordination chemistry is not commonly met, and we will explore only solution chemistry. Nevertheless, even in solution inherently sterically less demanding ligands can display stability constants that reflect basicity effects more; R S R ligands often form stronger complexes than R S H, for example. Overall, we can assume that large, bulky groups that interact sterically (that is ‘bump into’ other ligands) when attempting to occupy coordination sites around a central metal ion usually leads to lower stability. The strain in such systems is seen in distortions of bond lengths and angles away from the ideal for the particular stereochemistry applying. It is possible to model these distortions effectively even with simple molecular mechanics that treats molecules as composed of atomic spheres joined by springs, based on Hooke’s Law principles (see Chapter 8), although more sophisticated modelling evolving from atomic theory has developed in recent years. Ligand bulk is particularly significant with regard to its introduction in the immediate region around the donor atom, as congestion will become greater the closer bulky groups approach the central atom. Thus coordination of N(CH₃))₃ will lead to greater steric interaction with other ligands than will −OOC C(CH₃)₃ as the ligand bulk is displaced further out in space in the latter case. As a consequence the carboxylate is termed a more ‘sterically efficient’ ligand than the amine.

Although we understand complexation reasonably well, and can make experimental mea surements of stability constants using a number of different physical methods with high accuracy, the outcome of a suite of effects influencing the stability of metal complexes is that prediction is an approximate and not a perfect art. There are other effects that arise as a result of molecular shape that add complications. For example, large cyclic ligands that carry at least three donor atoms (macrocycles) have a central cavity or ‘hole’, and the fit of a metal ion into this hole is an important consideration. In fact fit (or misfit) of metal ions into ligands of pre-defined shape (or topology) is an important aspect of modern coordination chemistry, as we now tend to meet more and more sophisticated and designed ligand systems. However it is more appropriate to leave this aspect for an advanced textbook, and we shall restrict ourselves here to an introduction to one type.

5.1.2.3.1 The Macrocycle Effect We have already introduced the hole-fit concept for a macrocyclic ligand in Chapter 4 (see Figure 4.38) which effectively means that the most stable complexes form where the internal diameter of the ring cavity matches the size of the entering cation. The effect can be significant; for example the natural antibiotic valinomycin is a macrocycle that binds potassium ion to form a complex ∼104 times more stable than that formed with the smaller

Figure 5.6

Comparison of the stability constants for (at left) a linear and a cyclic polyether binding to potassium ion and (at right) a linear and cyclic polyamine binding to zinc ion, illustrating the macrocyclic effect in action.

sodium ion, despite the chemical similarity of the cations. There is, however, an aspect of pre-organization that is important to macrocycle complexation also, and comparison of the stability constants for potassium ion binding to a linear polyether and a cyclic polyether with the same number of donors and linkage chain lengths (Figure 5.6) provide a clear illustration. The flexible long-chain linear molecule must undergo significant translational motion to ‘stitch’ itself onto the metal ion, which is not favoured. However, the cyclic molecule has the donors pre-organized in more appropriate positions for binding to the metal ion, and its coordination is thus favoured. The higher stability achieved is mainly entropy-driven, although both enthalpy and entropy can contribute, as measured for the polyamines in Figure 5.6, for which changes in both H0 and S0 occur. This type of enhanced stability for complexation of macrocycles over acyclic analogues is shown by a wide range of macrocycles of different size, donor type and number, and is well established; a typical example involving polyamines appears in Figure 5.6.

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مواضيع ذات صلة

Lability and Inertness in Octahedral Complexes

Kinetic Rate Constants

Thermodynamic and Kinetic Stability

Undergoing Change– Kinetic Stability

Overall Stability Constants

Bedded Down– The rmodynamic Stability

Bedded Down– The rmodynamic Stability

Host–Guest Molecular Assemblies

Encapsulation Compounds

Compounds of Polydentate Ligands

Sophisticated Shapes

Isomer Preferences