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First-principles phonon calculations have been widely performed for studyingvibrational properties of condensed matter, where the dynamical matrix iscommonly constructed via supercell force-constant calculations or the linearresponse approach. With different manners, a supercell can be introduced inboth methods. Unless the supercell is large enough, the interpolated phononproperty highly depends on the shape and size of the supercell and the imposedperiodicity could give unphysical results that can be easily overlooked. Alongthis line, the concept of partition of force constants is discussed, andaddressed by NaCl, PbTiO$_3$, monolayer CrI$_3$, and twisted bilayer grapheneas examples for illustrating the effects of the imposed supercell periodicity.To diminish the unphysical effects, a simple method of partitioning forceconstants, which relies only on the translational symmetry and interatomicdistances, is demonstrated to be able to deliver reasonable results. Thepartition method is also compatible with the mixed-space approach fordescribing LO-TO splitting. The proper partition is especially important forstudying moderate-size systems with low symmetry, such as two-dimensionalmaterials on substrates, and useful for the implementation of phononcalculations in first-principles packages using atomic basis functions, wheresymmetry operations are usually not applied owing to the suitability forlarge-scale calculations.

journal of physics. condensed matter

Partitioning interatomic force constants for first-principles phonon  calculations: Applications to NaCl, PbTiO$_3$, monolayer CrI$_3$, and twisted  bilayer graphene