Complex Formation in the Ternary System Tl(III)−CN^-−Cl^- in Aqueous Solution. A ²⁰⁵Tl NMR Study

The existence of mixed complexes of the general formula Tl(CN)_mCl_n^3-m-n (m + n ≤ 4) in aqueous solution containing 3 M ionic medium {(H⁺+Li⁺),ClO₄^-} has been established by means of ²⁰⁵Tl NMR. All six ternary complexes have been identified, and their compositions, chemical shifts, ²⁰⁵Tl−¹³C spin−spin coupling constants, and peak integrals were determined and used to calculate the stability constants, β = [Tl(CN)_mCl_n^3-m-n]/{[Tl³⁺][CN^-]^m[Cl^-]ⁿ}. Very good agreement was obtained between the equilibrium constants determined in this work and those estimated by a theoretical formula using the stability constants for the binary complexes and a statistical factor. Specific interaction coefficients have been calculated for the Tl(CN)_m^3-m (1 ≤ m ≤ 4) complexes. Some interesting correlations were found for the obtained NMR parameters. The stepwise formation constants for addition of one cyanide ligand, log K_CN, show linear dependence on both the spin−spin coupling constants, ¹J(²⁰⁵Tl−¹³C), and the chemical shifts, δ_Tl. Also the interatomic distance, d(Tl−C), is linearly correlated to the spin−spin coupling constant. The correlations are discussed in terms of the Ramsey equation, involving bond properties, stereochemistry, and stability of the complexes. Since ¹J(²⁰⁵Tl−¹³C) also shows linear dependence on the Tl−CN force constant, it is concluded that the above correlations reflect the Tl−CN bond strength. Thus, the most important factor contributing to the thermodynamic stability of the complexes is the enthalpy term, dominated by formation of very strong σ-bonds between cyanide and thallium. These trends may prove useful for spectral/structural assignments but also for estimation of metal-to-ligand bond distances and stability constants for complexes which exist only in low concentration.