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

Abstract

Isodesmic reactions of the type PdIICl2X + PdIICl3→ PdIICl2 + PdIICl3X 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 PdIICl2X + PdIICl2Y → PdIICl2 + PdIICl2X(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 (E1X) and Y (E1Y), the empirical equation 0.02026(E1X + (E1Y/√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 [PdIICl3X]n− (ρ1X) and [PdIICl3Y]n− (ρ1Y), and a multiple linear regression (MLR) approach with ρ1X, ρ1Y, and ρ1Xρ1Y 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 [PdIICl2X(Y)]n− can be quantified in terms of E1X and E1Y or the corresponding ρ1X and ρ1Y. The calculated E1 values may find use in the development of new trans influence-incorporated force field models for palladium.