Application of the Adiabatic Connection Random Phase Approximation to Electron-Nucleus Hyperfine Coupling Constants

The electron-nucleus hyperfine coupling constant is a challenging property for density functional methods. For accurate results, hybrid functionals with a large amount of exact exchange are often needed and there is no clear "one-for-all" functional, which describes the hyperfine coupling interaction for a large set of nuclei. To alleviate this unfavorable situation, we apply the adiabatic connection random phase approximation (RPA) in its post-Kohn-Sham fashion to this property as a first test. For simplicity, only the Fermi-contact and spin--dipole terms are calculated within the non-relativistic and the scalar-relativistic exact two-component framework. This requires to solve a single coupled-perturbed Kohn-Sham equation to evaluate the relaxed density matrix, which comes with a modest increase in computational demands. RPA performs remarkably well and substantially improves upon its Kohn-Sham (KS) starting point while also reducing the dependence on the KS reference. For main-group systems, RPA outperforms global, range-separated, and local hybrid functionals—at similar computational costs. For transition-metal compounds and lanthanide complexes, a similar performance as for hybrid functionals is observed. In contrast, related post-Hartree-Fock methods such as Mølller-Plesset perturbation theory or CC2 perform worse than semilocal density functionals.