Implementation of hyperfine coupling in all-electron mixed basis approach

In order to accurately evaluate hyperfine interaction (HFI) (both the isotropic, Fermi contact term and the anisotropic, dipole interaction term) of spin-polarized atoms and molecules, we newly implement the cubic harmonics routines for calculating HFI in the all-electron mixed basis code, TOMBO, in which both plane waves (PWs) and atomic orbitals (AOs) are used as basis functions, and AOs are restricted inside the non-overlapping atomic spheres and composed of the numerical radial function on a logarithmic radial mesh and analytic cubic harmonics. The method has a distinct merit of describing the cusp behavior near the nucleus position, which is essential for the Fermi contact term, and of significantly reducing the required cutoff energy for PWs compared to the usual PW expansion approach accompanied with the pseudopotential or PAW method. We also considered the contributions from surrounding atoms in the dipole interaction. Calculated results show excellent agreement with the experimental data, indicating the excellent performance of the code.