Real-space density functional theory on graphical processing units: computational approach and comparison to Gaussian basis set methods
Xavier Andrade,Alán Aspuru-Guzik +1 more
TL;DR: Results for current-generation GPUs from AMD and Nvidia show that the implementation, implemented in the free code Octopus, can reach a sustained performance of up to 90 GFlops for a single GPU, representing a significant speed-up when compared to the CPU version of the code.
read more
Abstract: We discuss the application of graphical processing units (GPUs) to accelerate real-space density functional theory (DFT) calculations. To make our implementation efficient, we have developed a scheme to expose the data parallelism available in the DFT approach; this is applied to the different procedures required for a real-space DFT calculation. We present results for current-generation GPUs from AMD and Nvidia, which show that our scheme, implemented in the free code Octopus, can reach a sustained performance of up to 90 GFlops for a single GPU, representing a significant speed-up when compared to the CPU version of the code. Moreover, for some systems our implementation can outperform a GPU Gaussian basis set code, showing that the real-space approach is a competitive alternative for DFT simulations on GPUs.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Figures
Figure 9. Numerical throughput of the calculation of the finite-difference fourth-order Laplacian as a function of the size of the block of orbitals (block-size) for different processors. Calculation for β-cyclodextrin with 256 orbitals and 260k grid points. 
Figure 10. Numerical throughput of the application of the local potential as a function of size of the block of orbitals (block-size) for different processors. Calculation for β-cyclodextrin with 256 orbitals and 260k grid points. 
Figure 18. Speed-up of the GPU calculation with the respect to the CPU for different molecules as a function of the number of valence electrons. a) Speed-up calculated from the total calculation time. b) Speed-up computed from the time spent in the SCF-cycle (without considering initializations). The reference CPU is an Intel Core i7 3820 using 8 threads. 
Figure 17. Performance of our CPU and GPU implementations for a set of 40 molecules of different sizes. a) Numerical throughput of the self-consistency cycle. b) Total execution time for a single-point energy calculation. The list of molecules and the calculation times are given in table I. 
Figure 12. Numerical throughput of the application of the non-local potential as a function of the size of the block of orbitals (block-size). Calculation for β-cyclodextrin with 256 orbitals and 260k grid points. 
Figure 11. Division of the atoms of a C60 molecule in groups (represented by different colors) whose pseudopotential spheres do not overlap.
Citations
Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems
Xavier Andrade,Xavier Andrade,David A. Strubbe,Umberto De Giovannini,Ask Hjorth Larsen,Micael J. T. Oliveira,Joseba Alberdi-Rodriguez,Alejandro Varas,Iris Theophilou,Nicole Helbig,Matthieu J. Verstraete,Lorenzo Stella,Fernando Nogueira,Alán Aspuru-Guzik,Andrea Castro,Miguel A. L. Marques,Angel Rubio,Angel Rubio +17 more
TL;DR: This article discusses how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems, and the exact solution of the Schrödinger equation for low-dimensionality systems.
Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems.
John A. Keith,Valentin Vassilev-Galindo,Bingqing Cheng,Stefan Chmiela,Michael Gastegger,Klaus-Robert Müller,Alexandre Tkatchenko +6 more
TL;DR: A critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design are reviewed.
334
Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems.
John A. Keith,Valentin Vassilev-Galindo,Bingqing Cheng,Stefan Chmiela,Michael Gastegger,Klaus-Robert Müller,Alexandre Tkatchenko +6 more
TL;DR: In this paper, the authors provide a review of the applications of computational chemistry and machine learning in molecular and materials modeling, retrosyntheses, catalysis, and drug design.
308
Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems
Nicolas Tancogne-Dejean,Micael J. T. Oliveira,Xavier Andrade,Heiko Appel,Carlos H. Borca,Carlos H. Borca,Guillaume Le Breton,Florian Buchholz,Andrea Castro,Stefano Corni,Alfredo A. Correa,Umberto De Giovannini,Alain Delgado,F. G. Eich,Johannes Flick,Gabriel Gil,Adrián Gomez,Nicole Helbig,Hannes Hübener,René Jestädt,Joaquim Jornet-Somoza,Ask Hjorth Larsen,Irina V. Lebedeva,M. Lüders,Miguel A. L. Marques,Sebastian T. Ohlmann,Silvio Pipolo,Markus Rampp,Carlo Andrea Rozzi,David A. Strubbe,Shunsuke A. Sato,Shunsuke A. Sato,Christian Schäfer,Iris Theophilou,Alicia Rae Welden,Angel Rubio,Angel Rubio +36 more
TL;DR: The Octopus project as mentioned in this paper provides a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory.
288
Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems
Nicolas Tancogne-Dejean,Micael J. T. Oliveira,Xavier Andrade,Heiko Appel,Carlos H. Borca,Carlos H. Borca,Guillaume Le Breton,Florian Buchholz,Andrea Castro,Stefano Corni,Alfredo A. Correa,Umberto De Giovannini,Alain Delgado,F. G. Eich,Johannes Flick,Gabriel Gil,Adrián Gomez,Nicole Helbig,Hannes Hübener,René Jestädt,Joaquim Jornet-Somoza,Ask Hjorth Larsen,Irina V. Lebedeva,M. Lüders,Miguel A. L. Marques,Sebastian T. Ohlmann,Silvio Pipolo,Markus Rampp,Carlo Andrea Rozzi,David A. Strubbe,Shunsuke A. Sato,Shunsuke A. Sato,Christian Schäfer,Iris Theophilou,Alicia Rae Welden,Angel Rubio,Angel Rubio +36 more
TL;DR: The major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light-matter hybrid states are described.
199
References
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set.
Georg Kresse,Jürgen Furthmüller +1 more
TL;DR: An efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set is presented and the application of Pulay's DIIS method to the iterative diagonalization of large matrices will be discussed.
107K
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
TL;DR: Numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, show that density-functional formulas for the correlation energy and correlation potential give correlation energies within a few percent.
94.9K
Self-Consistent Equations Including Exchange and Correlation Effects
Walter Kohn,L. J. Sham +1 more
TL;DR: In this paper, the Hartree and Hartree-Fock equations are applied to a uniform electron gas, where the exchange and correlation portions of the chemical potential of the gas are used as additional effective potentials.
Density-functional exchange-energy approximation with correct asymptotic behavior.
TL;DR: This work reports a gradient-corrected exchange-energy functional, containing only one parameter, that fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.
Inhomogeneous Electron Gas
P. C. Hohenberg,Walter Kohn +1 more
TL;DR: In this article, the ground state of an interacting electron gas in an external potential was investigated and it was proved that there exists a universal functional of the density, called F[n(mathrm{r})], independent of the potential of the electron gas.
49.6K