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We present an accurate and efficient formulation for the calculation ofphonons in real-space Kohn-Sham density functional theory. Specifically,employing a local exchange-correlation functional, norm-conservingpseudopotential in the Kleinman-Bylander representation, and local form for theelectrostatics, we derive expressions for the dynamical matrix and associatedSternheimer equation that are particularly amenable to the real-spacefinite-difference method, within the framework of density functionalperturbation theory. In particular, the formulation is applicable to insulatingas well as metallic systems of any dimensionality, enabling the efficient andaccurate treatment of semi-infinite and bulk systems alike, for both orthogonaland non-orthogonal cells. We also develop an implementation of the proposedformulation within the high-order finite-difference method. Throughrepresentative examples, we verify the accuracy of the computed phonondispersion curves and density of states, demonstrating excellent agreement withestablished planewave results.

On the calculation of phonons in real-space density functional theory