Kohn-Sham Density Functional Perturbation Theory at Unprecedented Scale and Accuracy

Kohn-Sham density functional theory based calculations have become a cornerstone for material research and discovery. Despite the great advancements in numerical approaches and computational power, performing large scale first-principles DFT calculations is a daunting task. This issue becomes even more prominent while calculating the higher derivatives of energy using linear response theory. In this work, we develop a real-space density functional perturbation theory formulation for phonon calculation for systems with arbitrary boundary conditions and implement it in large-scale massively parallel state-of-the-art real-space DFT code SPARC. The highly efficient parallel architecture of the ground state calculation of the code is leveraged upon and extended to perform large-scale DFPT calculation. Furthermore, we symmetry-adapt the above formulation to non-affine coordinate system to study systems with cyclic and/or helical symmetry. This opens avenues for studying the low-dimensional systems which have been predicted as future thermoelectric and photovoltaic materials. Finally, we study the effect of different functionals (local as well as nonlocal) on phononic properties for a wide variety of systems. Overall, this work opens avenues for first-principles based large scale data generation related to phononic properties of materials as well as understanding the physics of complex materials.