Geometries of Second-Row Transition-Metal Complexes from Density-Functional Theory

A data set of 19 second-row transition-metal complexes has been collated from sufficiently precise gas-phase electron-diffraction experiments and used for evaluating errors in DFT optimized geometries. Equilibrium geometries have been computed using 15 different combinations of exchange-correlation functionals in conjunction with up to three different effective core potentials. Most DFT levels beyond the local density approximation can reproduce the 29 metal-ligand bond distances selected in this set with reasonable accuracy and precision, as assessed by the mean and standard deviations of optimized vs experimentally observed bond lengths. The pure GGAs tested in this study all have larger standard deviations than their corresponding hybrid variants. In contrast to previous findings for first-row transition-metal complexes, the TPSSh hybrid meta-GGA is slightly inferior to the best hybrid GGAs. The ranking of some popular density functionals, for second-row transition-metal complexes, ordered according to decreasing standard deviation, is VSXC ≈ LSDA > BLYP > BP86 > B3LYP ≈ TPSSh > PBE hybrid ≈ B3PW91 ≈ B3P86. When zero-point vibrational corrections, computed at the BP86/SDD level, are added to equilibrium bond distances obtained from a number of density-functional/basis-set combinations, the overall performance in terms of mean and standard deviations from experiment is not improved. For a combined data set comprised of the first- and second-row transition-metal complexes the hybrid functionals B3P86, B3PW91, and the meta-GGA hybrid TPSSh afford the lowest standard deviations.