Number of Coordinated Solvent Molecules

Horrocks and co-workers measured emission hfetimes of aqueous solutions of complexes of Eu(III) and Tb(III) with known numbers of water molecules in their first coordination sphere and compared them to the lifetimes measured in D2O [12,50]. They were able to derive the empirical Equation 2.14 from these measurements, which is now regularly used to determine the number of water molecules q coordinated to Eu(III) and Tb(III) in other compounds. 

The coefficients A and B were empirically determined and are summarised in Table 2.2. Since methanol contains one O—H oscillator, the equation can be extended for this solvent. This equation has been expanded by several authors, to include quenching effects by second sphere solvent molecules, as well as other oscillators, N—H in amines and amides and C-H [51-53]. 

Bunzli, J.-C. G. Choppin, G. R. (eds) Lanthanide Probes in Life, Chemical and Earth Sciences — Theory and Practice Elsevier Amsterdam, 1989. 

In Lanthanide Luminescence Photophysical, Analytical and Biological Aspects Hanninen, P., Harma, H., Eds. Springer Heidelberg, 2010 Vol. 7. 

Patterson, G. Davidson, M. Manley, S. Lippincott-Schwartz, i.Annu. Rev. Phys. Chem. 2010, 61, 345-368. 

---

Figure 6 schematically shows the ligands of the Eu3+ and Tb3+ cryptates examined. Some photophysical data and the number of coordinated solvent molecules of these complexes are gathered in Table 1. 

Complexes of the Eu3+ and Tb3+ ions with different types of macrocyclic ligands have been obtained and their properties, in particular luminescence, have been reported by different authors [4, 15, 80-82]. For this class of complexes, we discuss only the complexes of macrocyclic ligands incorporating chromophores, since such ligands can play the role of antennas. Figure 11 schematically shows the macrocyclic ligands of the Eu3+ and Tb3+ complexes examined. Some photophysical data and the number of coordinated solvent molecules of these complexes are gathered in Table 2. 

As described earlier, the lifetimes and quantum yields of emissive Ln complexes vary dramatically due to the extremely sensitive nature of the 4/-centred excited states to 0-H, N-H and C-H vibrational manifolds, which can provide efficient, non-radiative deactivation pathways the efficiency of energy transfer between the antenna and lanthanide ion also determines overall quantum yields. A classical approach to maximising the emissivity of Ln complexes is to therefore inhibit the approach of water solvent to the inner coordination sphere (and where q denotes the number of coordinated solvent molecules) high denticity, metal ion encapsulating ligands with hydrophobic peripheries can achieve this very effectively, reducing q to zero [4]. 

Encapsulation of the and ions by cage-type ligands was also achieved using functionalized calixarenes. Metal luminescenee properties were studied mostly for complexes of calix[4]arenes, while few results are available for complexes of calix[6]arenes and calix[8]arenes, the latter being dinuclear complexes. Figure 13 shows schematically the calixarene ligands of the Eu and Tb complexes examined. Some photophysical data and the number of coordinated solvent molecules of these complexes are gathered in table 4. 

Entropy effects. The replacement of the coordination shell of the cation by a multidentate ligand has also the very important effect of decreasing the free energy of the system by the increase in translational entropy of the displaced water molecules. If there were no variation in solvation and internal entropies of the free ligand and of the complexes, the increase in translational entropy would amount to about 8 e.u., where x is the number of displaced solvent molecules minus one (38). This estimate is, however, very inaccurate large deviations are expected, especially in the case of complicated multidentate ligands for which complex formation may produce appreciable internal and solvation entropy changes. 

The vibronic decay pathway to the D oscillator is much less efficient. Thus, by comparison of the luminescence lifetimes in H2O and D2O an approximation for the number of coordinated solvent water molecules, q, in aqueous solution can be calculated by Eq. (1). 

The formation of luminescent lanthanide complexes relies on a number of factors. The choice of coordinating ligand and the method by which the antenna chromophore is attached to it, as well as the physical properties of the antenna, are important. In order to fully coordinate a lanthanide ion, either a high-level polydentate ligand such as a cryptate 1 or a number of smaller ligands (such as 1,3-diketones, 2) working in cooperation are required. Both 1 and 2 are two of the simplest coordination complexes possible for lanthanide ions. In both cases there are no antennae present. However, the number of bound solvent molecules is decreased considerably from nine (for lanthanide ions in solution) to one to two for the cryptate and three for the 1,3-diketone complexes. 

VFe3S4X3] (X = Cl, Br, and I), (Me4N)2[TpVFeS4Cl3], and (Me4N)[(NH3)-(bipy)Fe3S4Cl3]. A study of the catalytic reduction of hydrazine (a nitrogenase substrate) to ammonia in the presence of an external source of electrons and protons shows that the rate of reduction decreases as the number of labile solvent molecules coordinated to the V atom decreases but does not depend on the nature of the atom attached to the Fe atoms. 

So = organic solvent component w = number of water molecules coordinated to metal n = number of organic solvent molecules coordinated to metal (g) = gas... 

Finally, we discuss the importance of the nonradiative decay via vibronic coupling with the OH oscillators of the solvent, by considering the number of solvent (water or methanol) molecules coordinated to the metal ion obtained from the decay rate constants (Table 6). First, it is interesting to notice that the numbers of coordinated water molecules, varying from about... 

The first method is based on the statistical distribution of an iso-topically-labelled solvent such that the ratio of the concentration of isotopic solvent in the coordinated solvent to its concentration in the bulk solvent is equal to the ratio of coordinated solvent molecules to bulk solvent molecules. One obvious requirement is that the half-life of solvent exchange must be considerably longer than the time required for isotopic sampling. Furthermore, there must be an efficient means of separating the coordinated solvent from the bulk solvent. This approach was first used by Hunt and Taube [13] to establish the existence of Cr(H2 0)g as a distinct species in aqueous solution. Although only of limited application to metal ions more labile than Cr the method has been employed to determine the solvation number of the hydrated Al ion using a flow... 

In Guggenheim s terms a lattice consists of N — Ni + rN sites, standing for the number of monomer (solvent) molecules each of which takes one site, and JVg for the number of r-mer (polymer) molecules each taking r successive sites. Assume that all configurations have the same energy. Let z retain its significance, i.e. the coordination number of the lattice (each monomer molecule has z nearest neighbours). However the... 

With bulky carboxylate anions, the mononuclear compound formed can be expressed [REL3(sol) ], where sol is a coordinating solvent, such as H2O, EtOH, MeOH, DMF, or DMSO. In most cases, the three carboxylates are in the chelating rf-) mode, and n is 2 or 3, CN = 8 or 9. However, when the ligand is too bulky, there would be not enough room for all of the three carboxylates to be in the chelating mode, and one or two of them have to be in the monodentate( 7 ) mode, and the number of the solvent molecules (n) becomes 3 or 4. Figure 3 shows the structures... 

The first solvation shell of the methyl cation in water and HF can satisfactorily be represented by five and that of the fluorine anion—by six solvent molecules, i.e., the total number of the solvent molecules included in the supermolecular approximation is 11. The C—X distance was taken as the reaction coordinate and all other geometry parameters, includingg those of the solute environment, were optimized. The most important result of the calculations of Eq. (5.7) by the CNDO/2 and ab initio (STO-3G basis set) methods is the detection of three minima along the MERP. The first of these characterized by the distance r( p= 1.388 A corresponds to the hydrated undissociated molecule CH3F. The second minimum corresponds to rcp = 3.480 A. There are no solvent molecules between the ions CHj and F , hence they are located in one cage and may be structurally described as a contact ion pair of type IV. The third minimum corresponds to a completely dissociated system (r< p = 5.463 A), i.e., the solvent-separated ion pair V with each ion surrounded by its own solvation shell with n = 11, j = 5, and k = 6 in Eq. (5.7). 

The definition of solvent exchange rates has sometimes led to misunderstandings in the literature. In this review kjs 1 (or fc2lsolvent]), sometimes also referred to as keJ s 1, is the rate constant for the exchange of a particular coordinated solvent molecule in the first coordination sphere (for example, solvent molecule number 2, if the solvent molecules are numbered from 1 to n, where n is the coordination number for the solvated metal ion, [MS ]m+). Thus, the equation for solvent exchange may be written ... 

---