Equilibrium studies

Thermodynamic data for scandium(III) complexes with polydentate ligands are scarce; only some stability constant data have been published for Sc(III) complexes of DTPA [46] and DOTA.[17,19] As the data seemed to be not fully reliable, in previous work we determined stability constants for both complexes by combination of potentiometry and NMR spectrometry.[26]The methods have to be combined as potentiometry itself led to misleading results due to quantitative complex formation at pH below 1.5, thus, out of potentiometry pH range. In addition for Sc(III)-DOTA system, slow complex formation complicated the measurements and out-of-cell titration method has to be used. The stability constants, logKScL

27.43 and 30.79, for DTPA and DOTA complexes, respectively, are several orders of magnitude higher than those of lanthanide(III) complexes of the same ligands. As the title ligands are DOTA analogues the same problems with stability constant determination were expected.

First, pH range where the complexes are formed and time necessary to establish equilibrium were examined by ⁴⁵Sc and/or ³¹P{¹H} NMR spectroscopy. It was found that equilibrium at pH >1.8 (in-cage complexes) is established during several days and the rate of complexation being faster with higher pH (Figure S1). Equilibria in very acidic solutions (out- of-cage complexes) seemed to be established almost immediately; but anyway, the spectra were recorded after standing the samples at room temperature for at least six days. Both phoshinate ligands behave similarly each other as well as to DOTA; Sc(III)-aqua complex disappeared above pH ~1.8. Unlike the Sc(III)-DOTA system, some complex formation starting between pH 0 and 0.5 (Figure S2) was indicated by a broad ⁴⁵Sc NMR peak (~35 ppm) observed in the acidic solutions. This chemical shift suggests purely oxygen coordination sphere. Therefore, the species can be assigned as out-of-cage complexes where Sc(III) ion is coordinated by oxygen atom(s) from one or more pendant arms of the ligands.

Their formation can be caused by the presence of rather acidic phosphinic acid group able to bind metal ions even in very acidic solutions (see also below). Once the in-cage complexes (scandium(III) ion is sandwiched between N4 and O4 planes as in the [Sc(DOTA)]^– complex) [47] are formed ⁴⁵Sc NMR signal of the out-of-cage complexes start to broaden and decrease in intensity and, finally, no ⁴⁵Sc NMR signal is observed. In parallel, two broad closely located ³¹P{¹H} NMR signals assignable to the Sc(III)-bound phosphinate group in the isomeric in-cage complexes (see below) start to be observed. Behavior of Sc(III)-DO3AP system was analogous to that observed for the Sc(III) complexes of monophosphinic acid

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DOTA analogues above pH ~3.8; no ⁴⁵Sc and two ³¹P{¹H} NMR peaks were observed confirming formation of the in-cage complex (Figure 2). However, unexpected results were obtained for Sc(III)-DO3AP system and, in more acidic solutions, another peaks appeared in both NMR spectra - Sc ~23 ppm, and P –8.3 ppm (Figure 2). The ⁴⁵Sc NMR signal of Sc(III)-aqua complex start to be observable below pH ~0.8; surprisingly, the signal at Sc ~23 ppm was present even in extremely acidic solutions (up to 1:1 aq. HCl). Most probably, the NMR signal can be assigned to out-of-cage complex species where at least the phosphonate group (and possibly the acetate group(s) as well) is bound to scandium(III) ion; it has been confirmed that phosphonate group can interact with metal ions (e.g. trivalent lanthanides) even under highly acidic conditions. [48] Overall stoichiometry of the Sc(III)-DO3AP species present in the acidic solutions can be roughly estimated as 1 : 2 from a Job-like plot of NMR signal intensities (Figure S3). However, the equilibria are rather complicated as several species are present at different overall Sc(III):DO3AP molar ratios (Figure S3). At equimolar Sc(III)-DO3AP ratio and at pH around zero, it also leads to an observation of the ―free‖

Sc(III) which is rather consequence of formation of the complexes with higher ligand-to- metal ratio than caused by vanishing interaction with the ligand. Unfortunately, such solution behavior (not determinable correct Sc/DO3AP stoichiometry as well as a number of protons in the species) precluded determination of the value of the Sc(III)-DO3AP complex stability constants (see below).

Preliminary investigations showed that stability constants of scandium(III) complexes can be determined only for DO3AP^ABn and DO3AP^PrA ligands. As complexation of scandium(III) ion by these ligands starts in very acidic solutions, protonation constants having values logK_a < 2 are important in for stability constant evaluations, they were re-determined for both ligands with emphasize on acidic region (see SI); only two constants different from those previously published were obtained for the most acidic ones of DO3AP^PrA, logK₅ 2.94 and logK₆ 1.54.

The complex formation range is behind a range suitable for potentiometry and, therefore, NMR spectrometry (as in the case of Sc(III)-DOTA system) [26] had to be used to acquire equilibrium data in acid solutions necessary for evaluation of stability of the out-of-cage complex. Potentiometry is the most suitable method to cover pH range above 1.5 where in- cage / out-of-cage complex equilibrium is expected. As complex formation rate is slow in the less acidic pH region, out-of-cell titration method has to be used. However, this method cannot be used at pH < 4 due to some precipitation (probably Sc(OH)3, due to slow complex formation kinetics) during hydroxide addition. This pH region is important for evaluation of equilibrium between protonated and fully deprotonated in-cage complexes. Therefore, normal titration of pre-formed complexes was carried out; one protonation constant corresponding to

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protonation of amino/carboxy group in the side chain was considered below pH 7. Only combination of all the data allowed correct description of the Sc(III)-DO3AP^ABn and - DO3AP^PrA systems; in addition, the titration of the pre-formed complex ending above pH 12 enabled determination of stability constant of a hydroxide-complex. To quantify abundance of Sc(III)-aqua ion in the systems, previously suggested secondary standard ,[26] [Sc(ox)₄]^5– (ox

= oxalate), cannot be used as peaks of the out-of-cage were too broad and overlapping with the standard. Therefore, [Sc(tmu)₆]³⁺ was used as secondary standard. [49] The experimentally determined overall stability constants are presented in Table S2.

The stability constants are collected and compare with data for similar systems in Table 1 and corresponding distribution diagrams are shown in Figure 3. The Sc(III)- DO3AP^ABn and -DO3AP^PrA complexes are more stable than their lanthanide(III) complexes (logKLuL 24.0 and 25.5, respectively) [31] but less stable than the [Sc(DOTA)]^– complex.[26]

The difference in stability constants between the lutetium(III) and scandium(III) complexes is similar for all ligands. In slightly acidic pH, the amino or carboxylate group in the side chain are protonated and the protonation constant are almost identical as for their lutetium(III) complexes.[31] The next two protons should be bound to ring nitrogen protons and the scandium(III) ion should be bound to pendant arm oxygen atom(s) in out-of-cage complex.

Protonation over two steps gave much better fit of experimental data. Such chemical model has been suggested for Ln(III)-DO3AP systems [30] and such diprotonated out-of-cage species has been observed for lanthanide(III) complexes in the solid state as well as in solution; [50] the species should correspond to monoprotonated [Sc(HDOTA)] species. The very high abundance of the diprotonated species (Figure 3) can be caused by a strong preference of trivalent scandium for oxygen donors and, mainly, to coordination of the hard phosphinate group in the out-of-cage species. Their value (logK_a ~2 for a hypothetical double monoprotonation) is higher than the corresponding protonation constant of [Sc(DOTA)]^– illustrating again stronger interaction of the pedant arms involving phosphinate group for the DOTA phosphinic acid analogues.

The interaction between Sc(III) ion and the pendant arm(s) in out-of-cage complex is even stronger for DO3AP. The out-of-cage complex is formed at even higher pH and up to two ligand molecules can be bound to the central ion in acidic solutions, probably each of them at least through protonated phosphonate group. At such low pH, ring nitrogen atoms should be protonated as well. [26] The out-of-cage species could be stabilized by intramolecular hydrogen bonds between the coordinated phosphonate groups. Such coordination mode has been suggested for stabilization of lanthanide (III) complexes with bis(phosphonate)- containing ligands in very acidic solutions.[47] Unfortunately, stability constants for Sc(III)-

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DO3AP systems cannot be determined by the same method as for phosphinate ligands as speciation in the acidic solution is too complex to be modeled by equilibrium constant calculations. As stability constant of fully deprotonated complex, logK(Sc-DO3AP), cannot be determined by common procedure, competition method with trivalent ytterbium (as metal ion with very high stability constant of the Yb(III)-DO3AP complex, logK ~28.5) [30] as well as transchelation with DTPA were tested. In both cases, the determination failed due to problems with kinetics of the (trans) metallation or transchelation.