Sparse tensor based nuclear gradients for periodic Hartree–Fock and low-scaling correlated wave function methods in the CP2K software package: A massively parallel and GPU accelerated implementation.

The development of novel double-hybrid density functionals offers new levels of accuracy, and is leading to fresh insights into the fundamental properties of matter. Hartree–Fock exact exchange and correlated wave function methods such as MP2 and direct RPA are usually required to build such functionals. Their high computational cost is a concern, and their application to large and periodic systems is therefore limited. In this work, low-scaling methods for HFX, SOS-MP2 and direct RPA energy gradients are developed and implemented in the CP2K software package. The use of the resolution-of-the-identity approximation with a short range metric and atom-centered basis functions lead to sparsity, allowing for sparse tensor contractions to take place. These operations are efficiently performed with the newly developed DBT and DBM libraries, which scale to hundreds of GPU nodes. The resulting methods, RI-HFX, SOS-MP2 and dRPA, were benchmarked on large supercomputers. They exhibit favorable sub-cubic scaling with system size, good strong scaling performance, and GPU acceleration up to a factor of 3. These developments will allow for double-hybrid level calculations of large and periodic condensed phase systems to take place on a more regular basis. This record contains all CP2K input and output files used for the paper.