Performance of modern density functional theory for the prediction of hyperfine structure: meta-GGA and double hybrid functionals

The performance of modern density functionals for the prediction of molecular hyperfine couplings is investigated for a series of small radicals and transition metal complexes. Besides the established BP86 (GGA) and B3LYP (hybrid) functionals we have tested two prototypical members of emerging classes of density functionals, namely the TPSS meta-GGA functional (together with its hybrid version TPSSh) and the B2PLYP double-hybrid functional. The latter is the first member of a 'fifth-rung' density functional that incorporates a fraction of orbital dependent nonlocal correlation energy estimated at the level of second-order many-body perturbation theory. Since this approach is non-variational, it becomes necessary to derive and implement the so-called 'relaxed' densities in order to properly predict hyperfine couplings. The necessary formalism is described in some detail and the new method has been implemented into the ORCA electronic structure program. The results of extended test calculations reveal that TPSS is superior to BP86. The hybrid variant TPSSh is at least as accurate or better than the B3LYP functional and significantly superior to the non-hybrid TPSS variant. The B2PLYP functional also leads to accurate predictions and is a clear improvement for the difficult metal nucleus HFCs. However, it also showed a few significant outliers in the test set which points to a somewhat reduced stability in the method. The latter effect is largely attributed to the elevated fraction Hartree-Fock exchange (53%) and to some extent also to the perturbative correction.