Materials Cloud Archive

Augustin Bussy1*,

Ole Schütt2,

Jürg Hutter1*

1 Department of Chemistry, University of Zurich, CH-8057 Zürich, Switzerland

2 CP2K Foundation, CH-8006 Zurich Switzerland

* Corresponding authors emails:,

How to cite this record

Augustin Bussy,
Ole Schütt,
Jürg Hutter,

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., Materials Cloud Archive

2023.50 (2023),

doi: 10.24435/materialscloud:kc-ex.


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.

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Journal reference (The paper is currently under revision.)


Nuclear gradients


Correlated wave function



Sparse tensors




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