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

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Abstract

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 second-order Møller–Plesset (MP2) and direct random phase approximation (dRPA), 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 Hartree–Fock exchange (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 leads to sparsity, allowing for sparse tensor contractions to take place. These operations are efficiently performed with the newly developed Distributed Block-sparse Tensors (DBT) and Distributed Block-sparse Matrices (DBM) libraries, which scale to hundreds of graphics processing unit (GPU) nodes. The resulting methods, resolution-of-the-identity (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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A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu.

Stefan Grimme, Jens Antony, Stephan Ehrlich … (2010)

The method of dispersion correction as an add-on to standard Kohn-Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C(6) coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.