Quantification of mutual trans influence of ligands in Pd(II) complexes: a combined approach using isodesmic reactions and AIM analysis

Isodesmic reactions of the type Pd^IICl₂X + Pd^IICl₃→ Pd^IICl₂ + Pd^IICl₃X have been designed to study the trans influence of a variety of ‘X’ ligands (X = H₂O, NH₃, Py, CO, SMe₂, C₂H₄, AsH₃, PH₃, AsMe₃, PMe₃, PEt₃, ONO⁻, F⁻, Cl⁻, Br⁻, N₃⁻, NO₂⁻, OH⁻, CN⁻, Ph⁻, H⁻, CH₃⁻, SiH₃⁻) using density functional theory (MPWB1K) and COSMO continuum solvation model. We find that the isodesmic reaction energy E₁ is a good quantitative measure of the trans influence of X. E₁ showed good linear relationships to trans Pd–Cl bond length and the electron density ρ(r) at the (3, −1) bond critical point of the trans Pd–Cl bond. On the basis of E₁ values, ligands are classified into three trans influencing groups, viz. strong, moderate, and weak. Isodesmic reactions of the type Pd^IICl₂X + Pd^IICl₂Y → Pd^IICl₂ + Pd^IICl₂X(Y) with ligands ‘X’ and ‘Y’ in the trans positions are also modelled to obtain the energy of the reaction E₂. E₂ is a measure of the mutual trans influence of X and Y and the highest (99.65 kcal mol⁻¹) and the lowest (−3.95 kcal mol⁻¹) E₂ are observed for X = Y = SiH₃⁻ and X = Y = H₂O, respectively. Using the E₁ values of X (E_1X) and Y (E_1Y), the empirical equation 0.02026(E_1X + (E_1Y/√2))² is derived for predicting the E₂ values (standard error = 2.33 kcal mol⁻¹). Further, using the ρ(r) of the trans Pd–Cl bond in [Pd^IICl₃X]ⁿ⁻ (ρ_1X) and [Pd^IICl₃Y]ⁿ⁻ (ρ_1Y), and a multiple linear regression (MLR) approach with ρ_1X, ρ_1Y, and ρ_1Xρ_1Y as variables, accurate prediction is made for predicting E₂ of any combination of X and Y (standard error = 2.20 kcal mol⁻¹). We also find that the contribution of trans influence to the bond dissociation energy of ligands X or Y in complexes of the type [Pd^IICl₂X(Y)]ⁿ⁻ can be quantified in terms of E_1X and E_1Y or the corresponding ρ_1X and ρ_1Y. The calculated E₁ values may find use in the development of new trans influence-incorporated force field models for palladium.