A Benchmark and Basis-Set Extrapolation Study of Hyperfine Coupling Constants from the Random Phase Approximation and σ-Functionals.

Hyperfine coupling constants (HFCCs) provide an important link between theory and experiment; however, their accurate computation at a reasonable computational cost remains challenging. In this work, we present the theory for evaluating HFCCs on the level of the promising σ-functionals developed in the Görling group. We show that the best-performing σ-functional achieves accuracies, relative to coupled-cluster singles doubles and perturbative triples (CCSD(T)) reference values, comparable to those of domain-based local pair-natural orbital coupled-cluster singles doubles (DLPNO-CCSD)─currently among the most accurate methods applicable beyond the few-atoms scale─while being significantly less computationally demanding. We further investigate the influence of the atomic-orbital basis on random phase approximation (RPA), σ-functional, and also CCSD(T) HFCCs, showing that the pcH and pcJ basis-set families developed in the Jensen group are well suited for these methods. The availability of these basis-set families enables systematic complete basis-set (CBS) extrapolations for all HFCC calculations, with different extrapolation schemes producing very similar results. The presented basis-set extrapolated CCSD(T) HFCCs can hence serve as new reference values for future method developments or benchmarks.