  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 in the calculation of the harmonic
vibrational frequencies when using all-electron full-potential numeric
atomic-centered orbitals as the basis set. We find that, unlike the first order
derivative (i.e., forces), the moving-grid effect plays an essential role for
the second order 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. Our approaches
have been demonstrated in both finite (molecules) and extended (periodic)
systems.
