*3.5. NMR Spectroscopy Studies*

The NMR spectroscopy is a very important tool for the investigation of the structure of an unknown compound in solutions. Data of two-dimensional 1H NMR make it possible not only to obtain information confirming the presence of chelate binding in the products of reaction (1), but also to determine the number of porphyrinate fragments in the resulting porphyrin oligomers. The formation of chelating bonds of porphyrinate axial ligands with Cu2+ is evidenced by characteristic shifts in the signals of the ligand protons located in close proximity to the inner coordination sphere of the copper cations. The NMR study results are presented in Table 6.The absence of signals of protons of the -COOH and -OH groups indicates the formation of the corresponding Cu(II)-complexes (due to the replacement of H<sup>+</sup> with the metal ion). The signal of the protons at the carbon atom, which was closer to the NH2 group, was significantly shifted (by 0.5 ppm) in a strong field.

Diffusion-ordered spectroscopy (DOSY) was used to determine the composition of the reaction (1) products between Sn(IV)-porphyrin axial complexes and Cu2+. It has been reported in recent works [30,49–54] that this method is among the most effective in the analysis of supramolecular complexes of macrocyclic compounds. This method makes it possible to confirm the structures of the formed supramolecular complexes by comparing the diffusion coefficients of the systems obtained by self-assembly with the diffusion coefficients of the initial compounds (before the self-assembly) taken as objects of comparison. In our case, diaxial complexes I and II were employed as the reference compounds. The diffusion coefficients (D) of complexes I and II and the products of their interaction with Cu2+ (in 1:1 and 1:5 ratios) were measured by the stimulated echo method, with a bipolar gradient and a WATERGATE pulsed water suppression unit [55] in an H2O/D2O mixture (in a 90:10 ratio) at 298 K. The results are presented in Table 7 and Figure 10.


**Table 6.** Relevant 1H-NMR signals for studied compounds.

**Table 7.** Diffusion coefficients (D×10<sup>−</sup>10, m2s<sup>−</sup>1) of the complexes I and II and the products of their interaction with Cu2+ at the 1:1 and 1:5 concentration ratios of the reagents.


The measurement error is equal to ±0.04 ÷ 0.09 × 10<sup>−</sup>10, m2s<sup>−</sup>1.

**Figure 10.** 1H NMR diffusion-ordered spectroscopy (DOSY) spectra of products of interaction the complex I (**a**) and porphyrin dimers with Cu2+I-Cu-I (**b**).

The high accuracy of these measurements clearly indicates that the DOSY method is sensitive enough for us to speak with confidence about the difference between the complexes of the monomeric porphyrinates and oligomeric porphyrin systems and to confirm the complexation process in the studied systems.

For the sake of simplicity of interpretation of the DOSY experiments, we conducted a graphical analysis, which has been successfully applied to related/similar molecular systems earlier [56–58]. This graphical analysis is based on a model of a mass dependence on the coefficient of translational diffusion, obtained from the Einstein–Smoluchowski relation [59,60]. Thus, it is shown that the ratio of the diffusion coefficients for two different molecular particles (Di/Dj) is inversely proportional to the square root or cubic root of the ratio of their molecular masses (Mj/Mi) for rod-like and spherical forms of molecules, and can be calculated by the formula:

$$
\sqrt[2]{\frac{\mathcal{M}\_{\dot{j}}}{\mathcal{M}\_{\dot{i}}}} \ge \ \frac{D\_{\dot{i}}}{D\_{\dot{j}}} \ge \ \sqrt[3]{\frac{\mathcal{M}\_{\dot{j}}}{\mathcal{M}\_{\dot{i}}}} \tag{3}
$$

This ratio can be used to calculate a set of theoretical diffusion coefficients (upper and lower limits) for each supramolecular complex based on the diffusion coefficients of starting complexes I and II (monomers). As shown by Cabrita and Berger [61], the use of a reference compound is effective for solving problems associated with qualitative and quantitative analysis of intermolecular interactions. For graphical analysis, in addition to the theoretical curves of the solvent diffusion coefficients shown in Figure 11 (the black line refers to the simulated theoretical dependence for rod-shaped oligomeric particles, the dotted line refers to the simulated theoretical dependence for spherical oligomeric particles), we indicated the experimental values of the self-diffusion coefficients determined both for initial complexes I and II and the products of their interaction with Cu2+. The performed graphical analysis showed that the experimental values of the diffusion coefficients of the reaction (1) products at 1:1 and 1:5 ratios of the starting compounds fit well in the range of the calculated theoretical curves. The data obtained indicate that the products of reaction (1), with an equivalent ratio of reactants in the case of both complex I and complex II, were most likely dimers with molecular weights of 2877.57 g/mol (I-Cu-I) and 2715.37 g/mol (II-Cu-II). The systems formed with a five-fold excess of copper cations were characterized by the formation of Cu-[I-Cu-]6 oligomers with molecular weights of 8892.89 g/mol and Cu-[II-Cu-]6 oligomers with molecular weights of 8400.3 g/mol.

**Figure 11.** Graphical analysis of self-diffusion coefficients of the products of SnP(L)2 interaction with Cu2+ cations at the 1:1 and 1:5 ratios with monomer complexes taken as the reference standard: (**a**)-I, (**b**)-II. The solid lines represent the theoretical values calculated by the Formula (3).
