The moving-grid effect in density functional calculations of harmonic vibration frequencies using numeric atom-centered grids

When using atom-centered integration grids, the portion of the grid that belongs to a certain atom also moves when this atom is displaced. In the paper, we investigate the moving-grid effect for harmonic vibrational frequencies for all-electron full-potential numeric basis set calculation. We found that, unlike the first derivatives (i.e., forces) , this moving-grid effect plays an essential role for second derivatives (i.e., vibrational frequencies). Further analysis reveals that predominantly diagonal force constant terms are affected, which can be bypassed efficiently by invoking translational symmetry.