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 (rho(1X)) and Pd(II)Cl(3)Y (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) 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.