Relativistic Effects on Electron-Nucleus Hyperfine Coupling Studied with an Exact 2-Component (X2C) Hamiltonian

An exact 2-component (X2C) transformation of the one-electron Hamiltonian is used to transform nuclear hyperfine magnetic field operators from the 4-component Dirac picture to 2-component form. Numerical applications are concerned with hyperfine coupling constants of one-electron and many-electron atoms, as well as the HgH radical, using spin-unrestricted scalar X2C Hartree-Fock and Kohn-Sham theory. Reference data for 2-component generalized-collinear X2C calculations, including spin-orbit coupling, are also provided for selected cases. Calculations for one-electron atomic n s states with n = 1-3 show that the X2C transformed hyperfine operators give accurate hyperfine coupling constants. Kohn-Sham one-electron self-interaction errors for these states are small. The performance of the X2C transformed hyperfine operator for many-electron systems is also promising. The method is straightforward to implement in codes using spin-unrestricted (1-component) or 2-component spinor orbitals.