Partitioning interatomic force constants for first-principles phonon calculations

First-principles phonon calculations have been widely performed for studying vibrational properties of condensed matter, where the dynamical matrix can be constructed via supercell force-constant calculations or the linear response approach. With different manners, a supercell needs to be introduced in both methods. Unless the supercell is large enough, the 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 a model structure and NaCl as examples for illustrating the effects of the imposed supercell periodicity. To diminish the unphysical effects, a simple partition of force constants, which relies only on the translational symmetry and interatomic distances, is demonstrated to be able to deliver reasonable results. 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.