Benchmark Study of Density Functional Theory Methods in Geometry Optimization of Transition Metal-Dinitrogen Complexes.

The current benchmark study is focused on determining the most precise theoretical method for optimizing the geometry of transition metal-dinitrogen complexes. To accomplish this goal, seven density functional (DF) methods from five distinct classes of density functional theory (DFT) have been selected, including B3LYP-D3(BJ), BP86-D3(BJ), PBE0-D3(BJ), ωB97X-D, M06, M06-L, and TPSSh-D3(BJ). These DFs will be utilized with the Karlsruhe basis set (def2-SVP). To carry out this benchmark study, a total of forty-two structurally diverse transition metal-dinitrogen compounds with experimentally known X-ray data have been selected from the Cambridge Crystallographic Data Centre (CCDC). Based on a comparison of the theoretical data with experimental values (X-ray) of the selected transition metal-dinitrogen compounds, statistical parameters such as root-mean-square deviation (RMSD) and N-N and M-N bond lengths are obtained to evaluate the performance of the seven chosen DFs. According to the obtained results, among all DFT methods used in the study, Minnesota functionals (M06 and M06-L) and TPSSh-D3(BJ) show good performance, with lower RMSD values. This suggests that these three methods are the most reliable for optimizing the geometry of transition metal-dinitrogen complexes. Based on the absolute errors of the N-N and M-N bond lengths relative to the X-ray data, further analysis is conducted, and it is determined that M06-L is the best functional for optimizing the geometry of transition metal-dinitrogen compounds. Additionally, the influence of using a high-level basis set (def2-TZVP) compared to def2-SVP on the calculated RMSD among the seven chosen methods is found to be negligible.