## 2 Materials and Methods
### Synthesis of the Complexes  
An amount of 0.560 g of Nd(ClO)\({}_{3}\) (0.119 mmol) and 0.435 g of UO\({}_{2}\)(ClO)\({}_{4}\) (0.2196 mmol) stock solutions were added to 10.0 mg (0.0521 mmol) and 5.0 mg of coumarin-3-carboxylic acid, respectively, and then dissolved in water (i.e., 100 mL) under constant stirring and at 37 \({}^{\circ}\)C over a period of 24 h.  
Taking into account the distribution diagrams of the metal ions in the presence of HCCA, the pH of these solutions was controlled (i.e., pH = 6 and pH = 4 for neodymium and uranyl, respectively). The complexation resulted in pallid yellow aqueous solutions and two solids, white for neodymium and orange for uranyl, the latter removed by filtration. Aqueous solutions, as well as solids, dissolved in DMSO, and opportunely diluted with water, were analyzed by UV-Visible spectroscopy. were evidence that some additional species are present. The probable composition of the complexes, responsible for these deviations, was obtained by numerical treatment by the least-square program SUPERQUAD [27], to seek the minimum of the function:  
\[U=\sum{(E_{\rm i}^{\rm obs}-E_{\rm i}^{\rm cal})^{2}} \tag{2}\]  
where \(E^{\rm obs}=E+j\) [H\({}_{3}\)O\({}^{+}\)] = \(E^{\circ}\) + 0.06154 log [H\({}_{3}\)O\({}^{+}\)] and \(E^{\rm cal}\) is a value calculated for a given set of parameters. The most probable \(p\), \(q\) and \(r\) values and the corresponding constants log \(\beta_{pqr}\) (Equation (2)) were achieved by varying systematically the stability constants of a chosen ternary species (\(p\),\(q\),\(r\)) to obtain the best data fitting. In the numerical treatments, the acidic constant of coumarin-3-carboxylic acid, according to equilibrium (5) and reported with the relative standard deviation (3\(\sigma\)), was kept invariant. \[\rm HCCA\leftrightarrows CCA^{-}+H^{+}\qquad\qquad\log{K_{a}}=-3.08\pm 0.01 \tag{5}\]  
This constant, unknown from the literature, was determined by potentiometric measurements under the same experimental conditions used for the evaluation of the stability constants between ligand and metal ions (i.e., at 37 \({}^{\circ}\)C and in 0.16 mol/L NaClO\({}_{4}\)). Considering the low solubility of HCCA in an aqueous solution [20], all the experiments were carried out by adding an exactly weighed quantity of solid ligand in the titration's apparatus. When equilibria (2) and (5) take place, HCCA dissolved into the aqueous medium. In the numerical treatment, the constants of the predominant hydrolysis products of Nd\({}^{3+}\) and UO\({}_{2}\)\({}^{2+}\), taken from the literature [28], (i.e., Nd(OH)\({}^{2+}\) and Nd\({}_{2}\)(OH)\({}_{2}\)\({}^{4+}\), (UO\({}_{2}\))\({}_{2}\)(OH)\({}_{2}\)\({}^{2+}\), (UO\({}_{2}\))\({}_{3}\)(OH)\({}_{5}\)\({}^{+}\), UO\({}_{2}\)(OH)\({}^{+}\) and (UO\({}_{2}\))\({}_{3}\)(OH)\({}_{4}\)\({}^{2+}\), respectively), were kept invariant and were used to construct the distribution diagrams reported in Figure 3a,b. In the construction of these diagrams, the same pH range investigated for the study of the complexes was considered. As can be seen in Figure 3a, the only hydrolytical species of neodymium is Nd(OH)\({}^{2+}\), which nevertheless does not reach percentages greater than 10%. In regard to uranyl ion (Figure 3b), the complexes (UO\({}_{2}\))\({}_{2}\)(OH)\({}_{2}\)\({}^{2+}\) and (UO\({}_{2}\))\({}_{3}\)(OH)\({}_{5}\)\({}^{+}\) are the predominant hydrolytical species, while (UO\({}_{2}\))\({}_{3}\)(OH)\({}_{4}\)\({}^{2+}\) and (UO\({}_{2}\))(OH)\({}^{+}\) are minor species, with percentages that do not exceed 10% and 1%, respectively. The results obtained for the neodymium- and uranyl-HCCA systems are reported in Table 1. For the neodymium-HCCA system, experimental data were explained with the formation of one complex, and the best minimum was obtained with the Nd(OH)CCA\({}^{+}\) species. A substantial decrease in the square error sum \(U\) (66.85%) was obtained considering also the presence of Nd(OH)(CCA)\({}_{2}\). No other complexes improved the fit.