Scalar Relativistic Calculations of Hyperfine Coupling Constants Using Ab Initio Density Matrix Renormalization Group Method in Combination with Third-Order Douglas–Kroll–Hess Transformation: Case Studies on 4d Transition Metals

We have developed a new computational scheme for high-accuracy prediction of the isotropic hyperfine coupling constant (HFCC) of heavy molecules, accounting for the high-level electron correlation effects, as well as the scalar-relativistic effects. For electron correlation, we employed the ab initio density matrix renormalization group (DMRG) method in conjunction with a complete active space model. The orbital-optimization procedure was employed to obtain the optimized orbitals required for accurately determining the isotropic HFCC. For the scalar-relativistic effects, we initially derived and implemented the Douglas-Kroll-Hess (DKH) hyperfine coupling operators up to the third order (DKH3) by using the direct transformation scheme. A set of 4d transition-metal radicals consisting of Ag atom, PdH, and RhH2 were chosen as test cases. Good agreement between the isotropic HFCC values obtained from DMRG/DKH3 and experiment was archived. Because there are no available gas-phase values for PdH and RhH2 radicals in the literature, the results from the present high-level theory may serve as benchmark data.