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 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

Predicting the Charge Density Response in Metal Electrodes

The computational study of energy storage and conversion processes call for simulation techniques that can reproduce the electronic response of metal electrodes under electric fields. Despite recent advancements in machine-learning methods applied to electronic-structure properties, predicting the non-local behaviour of the charge density in electronic conductors remains a major open challenge. We combine long-range and equivariant kernel methods to predict the Kohn-Sham electron density of metal electrodes decomposed on an atom-centered basis. By taking slabs of gold as an example, we show that including long-range correlations into the learning model is essential to accurately reproduce the charge density and potential in bare electrodes of increasing size. A finite-field extension of the method is then introduced, which allows us to predict the charge transfer and the electrostatic potential drop induced by the application of an external electric field. Finally, we demonstrate the capability of the method to extrapolate the non-local electronic polarization generated by the interaction with an ionic species for electrodes of arbitrary thickness. Our study represents an important step forward in the accurate simulation of energy materials that include metallic interfaces.Comment: 6 pages, 4 figure

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post–Hartree–Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension

First-principles correction scheme for linear-response time-dependent density functional theory calculations of core electronic states

Linear-response time-dependent density functional theory (LR-TDDFT) for core level spectroscopy using standard local functionals suffers from self-interaction error and a lack of orbital relaxation upon creation of the core hole. As a result, LR-TDDFT calculated x-ray absorption near edge structure spectra needed to be shifted along the energy axis to match experimental data. We propose a correction scheme based on many-body perturbation theory to calculate the shift from first-principles. The ionization potential of the core donor state is first computed and then substituted for the corresponding Kohn–Sham orbital energy, thus emulating Koopmans’s condition. Both self-interaction error and orbital relaxation are taken into account. The method exploits the localized nature of core states for efficiency and integrates seamlessly in our previous implementation of core level LR-TDDFT, yielding corrected spectra in a single calculation. We benchmark the correction scheme on molecules at the K- and L-edges as well as for core binding energies and report accuracies comparable to higher order methods. We also demonstrate applicability in large and extended systems and discuss efficient approximations

Efficient and low-scaling linear-response time-dependent density functional theory implementation for core-level spectroscopy of large and periodic systems

We discuss our implementation of linear-response time-dependent density functional theory (LR-TDDFT) for core level near-edge absorption spectroscopy. The method is based on established LR-TDDFT approaches to X-ray absorption spectroscopy (XAS) with additional accurate approximations for increased efficiency. We validate our implementation by reproducing benchmark results at the K-edge and showing that spin–orbit coupling effects at the L2,3-edge are well described. We also demonstrate that the method is suitable for extended systems in periodic boundary conditions and measure a favorable sub-cubic scaling of the calculation cost with system size. We finally show that GPUs can be efficiently exploited and report speedups of up to a factor 2

Dictionarium casuum conscientiae, quos secundum Moralis principia, Ecclesiasticae Disciplinae Consuetudines, Conciliorum, et Caonistarum Auctoritatem, et Regni Jurisprudentiam Domini quondam de Lamet et Fromageau ..., e Gallico idiomate, quo Parisiis prodiit, Latine redditum : In Supplementum Dictionarii ... Jo : Pontas ...

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