  First-principles phonon calculations have been widely performed for studying
vibrational properties of condensed matter, where the dynamical matrix is
commonly constructed via supercell force-constant calculations or the linear
response approach. With different manners, a supercell can be introduced in
both methods. Unless the supercell is large enough, the interpolated phonon
property highly depends on the shape and size of the supercell and the imposed
periodicity could give unphysical results that can be easily overlooked. Along
this line, the concept of partition of force constants is discussed, and
addressed by NaCl, PbTiO$_3$, monolayer CrI$_3$, and twisted bilayer graphene
as examples for illustrating the effects of the imposed supercell periodicity.
To diminish the unphysical effects, a simple method of partitioning force
constants, which relies only on the translational symmetry and interatomic
distances, is demonstrated to be able to deliver reasonable results. The
partition method is also compatible with the mixed-space approach for
describing LO-TO splitting. The proper partition is especially important for
studying moderate-size systems with low symmetry, such as two-dimensional
materials on substrates, and useful for the implementation of phonon
calculations in first-principles packages using atomic basis functions, where
symmetry operations are usually not applied owing to the suitability for
large-scale calculations.
