Evaluating Density Functionals by Examining Molecular Structures, Chemical Bonding, and Relative Energies of Mononuclear Ru–Cl–H–PR₃ Isomers

In order to define a robust level of theory using density functionals for investigating the reactivity of ruthenium complexes, we used benchmark wave function theory, with saturated basis sets to validate generalized gradient approximation (GGA), meta-GGA, and hyper-GGA functionals in the presence and absence of empirical dispersion and range-separated corrections. We first selected potentially suitable functionals that gave accurate predictions of the relative energetics of coordination isomers. These functionals were further evaluated for the chemical accuracy of their predicted geometric and electronic structures. For the latter, both the ionic and covalent interactions were considered. The reference level of theory for comparison was coupled-cluster perturbation theory using full treatment of singles and doubles (CCSD) with a saturated triple-ζ quality basis set (TZVP) and corresponding small-core, effective core potentials for ruthenium. Several population analysis methods were evaluated to predict the ionic interactions. We found that the atomic charges obtained from fitting the electrostatic potential provided the most reasonable estimates for the ruthenium complexes. The covalent interactions were quantified by considering the atomic compositions of Ru 4dx2–y2- and 4dz2-based frontier unoccupied orbitals. Comparison of more than two dozen functionals with reference data from high-level wave function calculations revealed trends that allowed for the formulation of an optimal hybrid density functional: PBE exchange and correlation functionals with 50% HF exchange component. This level of theory was found to reproduce the experimental structure of Ru(II) complexes. These complexes were used to investigate chemical speciation in a simplified model for an ionic liquid environment