The Thermodynamic Stability of Complexes

The thermodynamic stability of coordination compounds is relatively easy to determine, and provides us with a valuable pool of data from which we may assess the importance of ligand-field and other effects upon the overall properties of transition-metal compounds. The bulk of this chapter will be concerned with the thermodynamic stability of transition-metal compounds, but we will briefly consider kinetic factors at the close. 

The stability of a complex is conveniently expressed in terms of the thermodynamic stepwise stability constant K as defined in Eq. (8.1). 

We should note at this point, that the above reaction implicitly refers to aqueous solutions, and that, for convenience, we have explicitly excluded free and coordinated solvent molecules. Strictly, the above relationships should be written as in Eq. (8.2). 

For obvious reasons, we tend to use the simpler form, although we will discuss some of the limitations shortly. We may also consider overall stability constants, (5 (Eq. 8.3). 

Transition-metal complexes span an enormous range of stabilities. One of the principal aims of this chapter is to attempt to understand some of the factors which control these, and to determine the importance of ligand-field effects. Very extensive compilations of stability constants are available. 

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The reaction control should be emphasized amongst the conditions of reactions of competitive complex formation [19,23], It is necessary to take into account that it is possible to determine, and frequently predict, the direction of the electrophilic attack to the donor center of di- and polyfunctional donors (ligands) only in the case when the thermodynamically stable products are formed under conditions of kinetic control. Thus, the thermodynamic stability of complexes is discussed, when the bond between the metal and di- and polydentate ligands is localized in the place of primary attack on one of any of the donor centers by the electrophilic reagent, without further change of coordination mode in the reaction of complex formation. 

This introductory section has touched only briefly on the nature of complexes and their behavior in aqueous environments. The rest of the chapter expands on such topics, with particular emphasis on how to at least qualitatively predict the thermodynamic stabilities of complexes. This is a meaningful topic in that the stabilities of many potentially important complexes are poorly known. 

Ligand shape has an impact on the resultant complex shape, the number of possible isomers that could form, and the thermodynamic stability of complexes formed. 

Alfred Werner studied the "strengthening of the primary valence force by the saturation of the secondary valence force," but he failed to explain fully this phenomenon. To elucidate the stabilization of unstable oxidation states by complex formation two aspects should be taken into account the thermodynamic stability of complexes and their kinetic redox lability. Such factors as ligand field stabilization energy for M" and and the geometry of the donor atoms spatial orientation also affects the stability of a given oxidation state. Macrocyclic ligands are especially suitable for the stabilization of unstable metal oxidation states, both from the thermodynamic and kinetic viewpoints. 

Crystal field stabilization energy is a factor that contributes to the thermodynamic stability of complexes with predominantly ionic metal-ligand interactions, and also to the variation in properties of d metals and their compounds. Some of these properties are the size of di- and trivalent ions, hydration enthalpies, lattice energies, and stability of oxidation states. 

In tetraazamacrocyclic Co(II) complexes, the formation of /<-peroxo-Co(III) complexes following coordination of O2 to Co(II) complexes can be suppressed if the macrocycle is functionalized to inhibit face-to-face approach of the Co(II) centers. The thermodynamic stabilities of complexes [(X)LCo] (X =SCN or Q", L = C-meso-5,7,7,12,14,14-hexamethyl-l,4,8,ll-tetraaza-cyclotetradecane) have been determined and the effects of the anion X on the rate of dioxygen binding have been studied by laser flash photolysis after the flash, there is an immediate bleaching of the solution at the absorbance wavelength of the complex, followed by a slower return of absorbance. Reestablishment of the equilibrium for SCN can be analyzed in terms of Eq. (4) to (6) an analogous sequence applies when the anion is Cl . 

The terms labile and inert are not related to the thermodynamic stabilities of complex ions or to the equilibrium constants for ligand-substitution reactions. The terms are kinetic terms, referring to the rates at which ligands are exchanged. 

Water plays a crucial role in the inclusion process. Although cyclodextrin does form inclusion complexes in such nonaqueous solvents as dimethyl sulfoxide, the binding is very weak compared with that in water 13 Recently, it has been shown that the thermodynamic stabilities of some inclusion complexes in aqueous solutions decrease markedly with the addition of dimethyl sulfoxide to the solutions 14,15>. Kinetic parameters determined for inclusion reactions also revealed that the rate-determining step of the reactions is the breakdown of the water structure around a substrate molecule and/or within the cyclodextrin cavity 16,17). 

Compared to the sum of covalent radii, metal-silicon single bonds are significantly shortened. This phenomenon is explained by a partial multiple bonding between the metal and silicon [62]. A comparison of several metal complexes throughout the periodic table shows that the largest effects occur with the heaviest metals. However, conclusions drawn concerning the thermodynamic stability of the respective M —Si bonds should be considered with some reservation [146], since in most cases the compared metals show neither the same coordination geometries nor the same oxidation states. 

The rate at which displaceable ligands leave or enter a complex is obviously important and is a quite separate consideration from the thermodynamic stability of the complexes. The reaction... 

The thermodynamic stability of an ML complex is expressed by the equilibrium constant of the formation reaction, A1ML, called the the stability constant ... 

The thermodynamic stability of a complex ML formed from an acceptor metal ion M and ligand groups L may be approached in two different but related ways. (The difference between the two approaches lies in the way in which the formation reaction is presented.) Consistent with preceding sections, an equilibrium constant may be written for the formation reaction. This is the formation constant Kv In a simple approach, the effects of the solvent and ionic charges may be ignored. A stepwise representation of the reaction enables a series of stepwise formation constants to be written (Table 3.5). 

Terminal RCH—CH2 1-Hexene C4H9CH=CH2 is isomerized by complex 1 in accordance with the factors influencing the thermodynamic stability of cis- and trans-2 -hexene [15], At the end of the reaction, the alkyne complex 1 was recovered almost quantitatively. No alkene complexes or coupling products were obtained. The corresponding zirconocene complex 2a did not show any isomerization activity. Propene CH3CH=CH2 reacts with complex 6 with substitution of the alkyne and the formation of zirconacydopentanes as coupling products, the structures of which are non-uniform [16]. 

So far only a few quantitative data on the thermodynamic stability of arenediazonium salts and crown ethers have been reported. Bartsch et al. (1976) calculated the value of the association constant of the complex of 18-crown-6 and 4-t-butylbenzenediazonium tetrafluoroborate from kinetic data on the thermal decomposition of the complex, Kt = 1.56 x 105 1 mol-1 in 1,2-dichloroethane at 50°C. Compared with the corresponding linear polyether this is at least a factor of 30 higher (Bartsch and Juri, 1979). 

Our calculations suggest that the stereoselectivity of the hydrosilylation is determined by the thermodynamic stability of the ri3-allylic complex that forms after styrene insertion. This opens up the possibility of improving the enantioselectivity by modifying the catalyst framework to alter the stability of the exo versus the endo T 3-allylic intermediate. 

Unfortunately, for all these reasons the conclusions cannot be applied quantitatively for description of the pH effects in the RCH-RP process. There are gross differences between the parameters of the measurements in [97] and those of the industrial process (temperature, partial pressure of H2, absence or presence of CO), furthermore the industrial catalyst is preformed from rhodium acetate rather than chloride. Although there is no big difference in the steric bulk of TPPTS and TPPMS [98], at least not on the basis of their respective Tolman cone angles, noticable differences in the thermodynamic stability of their complexes may still arise from the slight alterations in steric and electronic parameters of these two ligands being unequally sulfonated. Nevertheless, the laws of thermodynamics should be obeyed and equilibria like (4.2) should contribute to the pH-effects in the industrial process, too. 

The number of water molecules in the second hydration layer can be increased by a proper ligand design without modifying its denticity and thus preserving the thermodynamic stability of the Gd(III) complex. 

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