Density functional predictions for metal and ligand nuclear shielding constants in diamagnetic closed-shell first-row transition-metal complexes

Abstract

We use the well-established functionals LDA, BLYP, BP86, BP91 and B3LYP as well as the more recent HCTH, PBE and PBE0 functionals to investigate the density functional theory (DFT) metal nuclear magnetic shieldings in ten transition-metal complexes ([Co(CN)₆]³⁻, [Co(NH₃)₆]³⁺, Cr(CO)₆, [CrO₄]²⁻, Fe(CO)₅ , Fe(C₅H₅)₂, [MnO₄]⁻, [Mn(CO)₆]⁺, VOCl₃, VF₅). We also investigate the ¹³C and ¹⁷O ligand shielding parameters in three first-row transition-metal carbonyl complexes [Cr(CO)₆ , Ni(CO)₄ and Fe(CO)₅] as well as the ¹⁷O shielding parameters in three first-row transition-metal oxo complexes ([CrO₄]²⁻, [MnO₄]⁻, FeO₄). We apply Malkin's sum-over-states density functional perturbation theory (SOS-DFPT) to our own HCTH functional and discuss the effect of the level shift correction to the DFT orbital energies on the calculated metal and ligand shieldings. For the metal chemical shifts the hybrid functionals are superior in quality to the non-hybrid functionals. Amongst this latter group HCTH and LDA provide the least errors. The large discrepancy between hybrid and non-hybrid functional paramagnetic shieldings is rationalised in terms of differences in the magnitude of their matrix element terms and eigenvalue differences. Our analysis of the dominant paramagnetic shielding contributions from the occupied-virtual MO excitations indicates that the poor performance of the non-hybrid functionals originates from their underestimation of the numerator (b∣l^α∣j)(j∣l_A^βr_A⁻³∣b) term rather than any deficiency in their description of the eigenvalue differences ε_b–ε_j. The relative increase in the magnitude of ε_b–ε_j following inclusion of a fraction of exact Hartree-Fock exchange is less than the corresponding increase in the (b∣l^α∣j)(j∣l_A^βr_A⁻³∣b) term. The net effect is a significant increase in the paramagnetic shielding terms for hybrid functionals. For the metal carbonyls the GGA functional ¹³C and ¹⁷O shielding parameters are superior in quality compared to the non-hybrid functionals with HCTH providing the best agreement with experiment. For the metal-oxo complexes, the ¹⁷O shieldings produced by the hybrid and non-hybrid functionals were found to be too deshielded and too shielded respectively, where the latter lie closer to the experimental values.