Density functional predictions for magnetizabilities and nuclear shielding constants

Abstract

There are now many density functionals which are recommended for use in the literature. Most of them have been parametrized or designed with the calculation of energetic properties in mind. This paper looks at their predictions for magnetic properties, specifically magnetizabilities and nuclear shielding constants; the latter are one of the most useful predictions provided by computational chemistry. The results demonstrate that functionals do best for the properties for which they were optimized. It is therefore important to investigate the cause of errors in the calculated magnetic response properties bearing in mind that previous uncoupled DFT studies on nuclear shielding constants found them to be too deshielded and this was rationalized in terms of the known deficiency of existing functionals in underestimating the ∊ _a —∊ _i energy differences, which in turn leads to an overestimation of the paramagnetic shielding terms. The work reported tests whether the improvement of the low lying and higher lying virtual orbitals and eigenvalues using the recently developed HCTH and asymptotically corrected HCTH(AC) functionals, respectively, produces improved predictions of the magnetizabilities and nuclear shielding constants with reference to the other GGA functionals LDA, BLYP and the hybrid functionals B97, B97-1, B3LYP and B3P86. In addition, these results are compared with Malkin's sum-over-states density functional perturbation theory (SOS-DFPT) NMR shielding tensor calculations, where a level shift correction is applied to the DFT orbital energies leading to a substantial improvement in the shieldings. For the magnetizabilities, HCTH and HCTH(AC) give results inferior to BLYP, but the hybrid density functionals produce a significant improvement in the calculated DFT magnetizabilities (with an accuracy equivalent to MP2 level). For the nuclear shielding constants, HCTH and HCTH(AC) give the best results amongst all the DFT functionals, with an accuracy intermediate between the coupled-perturbed Hartree-Fock SCF and the reference MP2 values. This implies that DFT is not yet competitive with ab initio correlated calculations for these shielding constants.