Substitution Reactions of Solvated Metal Ions

Stephen F. Lincoln; André E. Merbach    Department of Chemistry, University of Adelaide, Australia; and Institut de Chimie Minérale et Analytique, Université de Lausanne, Switzerland

I Introduction

A GENERAL ASPECTS

The most common ligand substitution on a solvated metal ion is the exchange of a water molecule in the first coordination sphere of a metal ion with a water molecule from the second coordination sphere. Water exchange on metal ions may also be viewed as being particularly fundamental, as it is through the intervention of another type of ligand in this process that the stoichiometry of the first coordination sphere is changed and a vast range of metal complexes is formed. Accordingly, it is appropriate to review the water exchange process and the 18 orders of magnitude variation in the water exchange rate constant, H2O, and lability exhibited by metal ions towards this process. This is most effectively commenced through an inspection of Fig. 1, which in its evolving forms has been one of the most intellectually focusing compilations of information about ligand substitution since it was published by Eigen in 1963 (1). At one end of the lability scale it is seen that the mean lifetime of a water molecule in the first coordination sphere of [Rh(H2O)6]3 +, H2O=1/kH2O, is 14.4 years, whereas at the other extreme, that of a water molecule bound to Cs+ is ~2 × 10− 10 s, during which time light travels ~6 cm. Clearly the microscopic interpretation of the macroscopic kinetic and related observations of water exchange and its substitution in the first coordination sphere by other ligands, the ligand substitution mechanism, must account for this great variation in lability reflected in the range of H2O characterizing the metal ions in Fig. 1.

The metal ions may be conveniently considered in three categories, the first of which is the main group metal ions which, for a given ionic charge, exhibit an increase in H2O with an increase in ionic radius, rM(2). Thus, the lability of the alkali metal ions increases by an order of magnitude as rM increases from Li+ to Cs+, and in general terms these ions are particularly labile coincident with their low ionic charge-to-rM ratio. In contrast, the lability of the alkaline earth metal ions spans approximately seven orders of magnitude, coincident with their higher charge and larger variation in rM. At this point it is appropriate to note that the more labile of the metal ions in these two sets are particularly difficult to characterize in terms of their numbers of coordinated water molecules. Thus, the coordination number of Li+ is variously quoted as 4 and 6, and that of Cs+ as 9, while intermediate values are quoted for Na+, K+, and Rb+. For Be2 + and Mg2 +, coordination numbers of 4 and 6, respectively, are well established, but a range from 6 to 10 is quoted for Ca2 + and similar or greater values are anticipated for Sr2 + and Ba2 +(3–5). As rM increases with coordination number, so the metal ion–water dipole interaction weakens and lability increases. The labilities exhibited by the six-coordinate sets—Zn2 +, Cd2 +, and Hg2 +(1) and Al3 +, Ga3 +, and In3 +(6–8)—vary over two and six orders of magnitude, respectively, and it is not surprising that the smallest of these ions, Al3 +, is the least labile in the light of the preceding discussion.

The second category is the transition metal ions, all of which in Fig. 1 are six-coordinate with the exception of Pt2 + and Pd2 +, which are square-planar four-coordinate (6–9). Their labilities are strongly influenced by the electronic occupancy of their d orbitals. This is illustrated by the divalent first-row transition metal ions, which should exhibit similar labilities to Zn2 + on the basis of their rM; instead, however, their labilities encompass seven orders of magnitude. On a similar basis, the trivalent first-row transition metal ions might be expected to be of similar lability to Ga3 +, but instead they exhibit a lability variation of 11 orders of magnitude, with Cr3 + being at the lower end of this lability scale. Second-row Ru3 + and Rh3 + are slightly more labile and three orders of magnitude less labile than Cr3 +, respectively.

The third category is the heavy eight-coordinate trivalent lanthanides, whose lability decreases with the progressive filling of the 4f orbitals and the resulting lanthanide contraction, and which are very labile as a consequence of their large rM(7, 10, 11).

B THE FORMATION OF METAL COMPLEXES

It is generally considered that some orientation of water in the second coordination sphere of the archetypal aqua ion, [M(H2O)n]m +, occurs (4, 12), but exchange of this water with bulk water appears to occur at close to diffusion-controlled rates. Hence, it is only in the case of the most labile metal ions that the rate of entry of a substituting ligand, Lx−, into the first coordination sphere is within an order of magnitude or so of its rate of entry into the second coordination sphere. Usually, the entry of Lx− into the first coordination sphere is preceded by the formation of an outer-sphere complex (13), in which Lx− resides in the second coordination sphere of [M(H2O)n]m+. An impressive armory of kinetic techniques has facilitated the study of ligand substitution processes in solution, ranging from those occurring at close to diffusioncontrolled rates to those taking place over extended times (14–16). However, it is seldom the case that more than one stage of the movement of a monodentate ligand from the bulk water environment into the first coordination sphere is observed, except in ultrasonic studies where as many as three steps have been detected. It is such studies which have provided the basis for most current discussion of the mechanisms of metal complexation. Thus, the formation of metal complexes has been conveniently formalized in a mechanism proposed by Eigen and Tamm (17), and illustrated by Eq. (1), where Mm+ is the metal ion, Lx− is the substituting ligand, and only those water molecules interposed between Mm+ and Lx−are shown. Initially, in a diffusioncontrolled step, Mm+ and Lx− form a species (1) in which they are separated by two layers of water molecules. This is followed by a fast step in which Lx− enters the second solvation sphere or second coordination sphere of Mm+ to form an outer-sphere complex (2), and the inner-sphere complex (3) is formed in the final and slowest step characterized by k23, which is frequently denoted ki because it indicates the step in which Lx− interchanges between the second and first coordination spheres. By analogy, k32 is often denoted k− i. The formation of (1) is seldom detected (18), and as a consequence, the simpler mechanism shown in Eq. (2) is often discussed instead and is sometimes referred to as the Eigen–Wilkins mechanism (19).

12Mm++Lx−⇌k10k01M⋅OH2⋅OH2⋅Lm−x+⇌k21k12M⋅OH2⋅Lm−x+MLm−x+k23⇌k323

m++Lx−⇌k21k12M⋅OH2⋅Lm−x+⇌k32k23MLm−x+

12=K0=4πNR3/3000exp−zMzLe02/εRkT

m++Lx−⇌kbkfMLm−x+

obs=k1K0[Lx−]1+K0[Lx−]+k−i

The successive equilibria are characterized by K12 and K23, respectively, and when K12 (often denoted K0) cannot be directly determined, it may be estimated from the Fuoss equation (3), where R is the distance of closest approach of Mz+ and Lx− (considered as spherical species) in M · OH2 · L(m − x)+, ε is the solvent dielectric constant, and zM and zL are the...