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(II)Cl(2)X + Pd(II)Cl(3) --> Pd(II)Cl(2) + Pd(II)Cl(3)X have been designed to study the trans influence of a variety of 'X' ligands (X = H(2)O, NH(3), Py, CO, SMe(2), C(2)H(4), AsH(3), PH(3), AsMe(3), PMe(3), PEt(3), ONO(-), F(-), Cl(-), Br(-), N(3)(-), NO(2)(-), OH(-), CN(-), Ph(-), H(-), CH(3)(-), SiH(3)(-)) using density functional theory (MPWB1K) and COSMO continuum solvation model. We find that the isodesmic reaction energy E(1) is a good quantitative measure of the trans influence of X. E(1) showed good linear relationships to trans Pd-Cl bond length and the electron density rho(r) at the (3, -1) bond critical point of the trans Pd-Cl bond. On the basis of E(1) values, ligands are classified into three trans influencing groups, viz. strong, moderate, and weak. Isodesmic reactions of the type Pd(II)Cl(2)X + Pd(II)Cl(2)Y --> Pd(II)Cl(2) + Pd(II)Cl(2)X(Y) with ligands 'X' and 'Y' in the trans positions are also modelled to obtain the energy of the reaction E(2). E(2) 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)) E(2) are observed for X = Y = SiH(3)(-) and X = Y = H(2)O, respectively. Using the E(1) values of X (E(1X)) and Y (E(1Y)), the empirical equation 0.02026(E(1X) + (E(1Y)/radical2))(2) is derived for predicting the E(2) values (standard error = 2.33 kcal mol(-1)). Further, using the rho(r) of the trans Pd-Cl bond in [Pd(II)Cl(3)X](n-) (rho(1X)) and [Pd(II)Cl(3)Y](n-) (rho(1Y)), and a multiple linear regression (MLR) approach with rho(1X), rho(1Y), and rho(1X)rho(1Y) as variables, accurate prediction is made for predicting E(2) 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(II)Cl(2)X(Y)](n-) can be quantified in terms of E(1X) and E(1Y) or the corresponding rho(1X) and rho(1Y). The calculated E(1) values may find use in the development of new trans influence-incorporated force field models for palladium.