Linear Scaling Self-Consistent Field Calculations with Millions of Atoms in the Condensed Phase
Abstract
In this work, the applicability and performance of a linear scaling algorithm is investigated for three-dimensional condensed phase systems. A simple but robust approach based on the matrix sign function is employed together with a thresholding matrix multiplication that does not require a prescribed sparsity pattern. Semiempirical methods and density functional theory have been tested. We demonstrate that self-consistent calculations with 1 million atoms are feasible for simple systems. With this approach, the computational cost of the calculation depends strongly on basis set quality. In the current implementation, high quality calculations for dense systems are limited to a few hundred thousand atoms. We report on the sparsities of the involved matrices as obtained at convergence and for intermediate iterations. We investigate how determining the chemical potential impacts the computational cost for very large systems.
Cited By
This article is cited by 130 publications.
- Xiaohe Lei, Annabelle Canestraight, Vojtech Vlcek. Exceptional Spatial Variation of Charge Injection Energies on Plasmonic Surfaces. The Journal of Physical Chemistry Letters 2023, 14 (38) , 8470-8476. https://doi.org/10.1021/acs.jpclett.3c02223
- Brad A. Steele, Mao-Xi Zhang, I-Feng W. Kuo. Single-Step Mechanism for Regioselective Nitration of 9,10-BN-Naphthalene with Acetyl Nitrate in the Gas Phase. The Journal of Physical Chemistry A 2022, 126 (31) , 5089-5098. https://doi.org/10.1021/acs.jpca.2c02124
- Michela Pauletti, Vladimir V. Rybkin, Marcella Iannuzzi. Subsystem Density Functional Theory Augmented by a Delta Learning Approach to Achieve Kohn–Sham Accuracy. Journal of Chemical Theory and Computation 2021, 17 (10) , 6423-6431. https://doi.org/10.1021/acs.jctc.1c00592
- Aurora E. Clark, Henry Adams, Rigoberto Hernandez, Anna I. Krylov, Anders M. N. Niklasson, Sapna Sarupria, Yusu Wang, Stefan M. Wild, Qian Yang. The Middle Science: Traversing Scale In Complex Many-Body Systems. ACS Central Science 2021, 7 (8) , 1271-1287. https://doi.org/10.1021/acscentsci.1c00685
- Arno Förster, Lucas Visscher. Low-Order Scaling G0W0 by Pair Atomic Density Fitting. Journal of Chemical Theory and Computation 2020, 16 (12) , 7381-7399. https://doi.org/10.1021/acs.jctc.0c00693
- Bela Bauer, Sergey Bravyi, Mario Motta, Garnet Kin-Lic Chan. Quantum Algorithms for Quantum Chemistry and Quantum Materials Science. Chemical Reviews 2020, 120 (22) , 12685-12717. https://doi.org/10.1021/acs.chemrev.9b00829
- Tammie R. Nelson, Alexander J. White, Josiah A. Bjorgaard, Andrew E. Sifain, Yu Zhang, Benjamin Nebgen, Sebastian Fernandez-Alberti, Dmitry Mozyrsky, Adrian E. Roitberg, Sergei Tretiak. Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials. Chemical Reviews 2020, 120 (4) , 2215-2287. https://doi.org/10.1021/acs.chemrev.9b00447
- Ganna Shchygol, Alexei Yakovlev, Tomáš Trnka, Adri C. T. van Duin, Toon Verstraelen. ReaxFF Parameter Optimization with Monte-Carlo and Evolutionary Algorithms: Guidelines and Insights. Journal of Chemical Theory and Computation 2019, 15 (12) , 6799-6812. https://doi.org/10.1021/acs.jctc.9b00769
- Ole Schütt, Joost VandeVondele. Machine Learning Adaptive Basis Sets for Efficient Large Scale Density Functional Theory Simulation. Journal of Chemical Theory and Computation 2018, 14 (8) , 4168-4175. https://doi.org/10.1021/acs.jctc.8b00378
- Amartya S. Banerjee, Lin Lin, Phanish Suryanarayana, Chao Yang, John E. Pask. Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations. Journal of Chemical Theory and Computation 2018, 14 (6) , 2930-2946. https://doi.org/10.1021/acs.jctc.7b01243
- A. Erba, J. Baima, I. Bush, R. Orlando, and R. Dovesi . Large-Scale Condensed Matter DFT Simulations: Performance and Capabilities of the CRYSTAL Code. Journal of Chemical Theory and Computation 2017, 13 (10) , 5019-5027. https://doi.org/10.1021/acs.jctc.7b00687
- Vojtěch Vlček, Eran Rabani, Daniel Neuhauser, and Roi Baer . Stochastic GW Calculations for Molecules. Journal of Chemical Theory and Computation 2017, 13 (10) , 4997-5003. https://doi.org/10.1021/acs.jctc.7b00770
- Daria R. Galimberti, Alberto Milani, Matteo Tommasini, Chiara Castiglioni, and Marie-Pierre Gaigeot . Combining Static and Dynamical Approaches for Infrared Spectra Calculations of Gas Phase Molecules and Clusters. Journal of Chemical Theory and Computation 2017, 13 (8) , 3802-3813. https://doi.org/10.1021/acs.jctc.7b00471
- Maria Karelina and Heather J. Kulik . Systematic Quantum Mechanical Region Determination in QM/MM Simulation. Journal of Chemical Theory and Computation 2017, 13 (2) , 563-576. https://doi.org/10.1021/acs.jctc.6b01049
- Anastasia Kruchinina, Elias Rudberg, and Emanuel H. Rubensson . Parameterless Stopping Criteria for Recursive Density Matrix Expansions. Journal of Chemical Theory and Computation 2016, 12 (12) , 5788-5802. https://doi.org/10.1021/acs.jctc.6b00626
- Cannada A. Lewis, Justus A. Calvin, and Edward F. Valeev . Clustered Low-Rank Tensor Format: Introduction and Application to Fast Construction of Hartree–Fock Exchange. Journal of Chemical Theory and Computation 2016, 12 (12) , 5868-5880. https://doi.org/10.1021/acs.jctc.6b00884
- Heather J. Kulik, Jianyu Zhang, Judith P. Klinman, and Todd J. Martínez . How Large Should the QM Region Be in QM/MM Calculations? The Case of Catechol O-Methyltransferase. The Journal of Physical Chemistry B 2016, 120 (44) , 11381-11394. https://doi.org/10.1021/acs.jpcb.6b07814
- Olle Björneholm, Martin H. Hansen, Andrew Hodgson, Li-Min Liu, David T. Limmer, Angelos Michaelides, Philipp Pedevilla, Jan Rossmeisl, Huaze Shen, Gabriele Tocci, Eric Tyrode, Marie-Madeleine Walz, Josephina Werner, and Hendrik Bluhm . Water at Interfaces. Chemical Reviews 2016, 116 (13) , 7698-7726. https://doi.org/10.1021/acs.chemrev.6b00045
- Christian F. A. Negre, Susan M. Mniszewski, Marc J. Cawkwell, Nicolas Bock, Michael E. Wall, and Anders M. N. Niklasson . Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations. Journal of Chemical Theory and Computation 2016, 12 (7) , 3063-3073. https://doi.org/10.1021/acs.jctc.6b00154
- Samuel Andermatt, Jinwoong Cha, Florian Schiffmann, and Joost VandeVondele . Combining Linear-Scaling DFT with Subsystem DFT in Born–Oppenheimer and Ehrenfest Molecular Dynamics Simulations: From Molecules to a Virus in Solution. Journal of Chemical Theory and Computation 2016, 12 (7) , 3214-3227. https://doi.org/10.1021/acs.jctc.6b00398
- S. M. Mniszewski, M. J. Cawkwell, M. E. Wall, J. Mohd-Yusof, N. Bock, T. C. Germann, and A. M. N. Niklasson . Efficient Parallel Linear Scaling Construction of the Density Matrix for Born–Oppenheimer Molecular Dynamics. Journal of Chemical Theory and Computation 2015, 11 (10) , 4644-4654. https://doi.org/10.1021/acs.jctc.5b00552
- Karl A. Wilkinson, Nicholas D. M. Hine, and Chris-Kriton Skylaris . Hybrid MPI-OpenMP Parallelism in the ONETEP Linear-Scaling Electronic Structure Code: Application to the Delamination of Cellulose Nanofibrils. Journal of Chemical Theory and Computation 2014, 10 (11) , 4782-4794. https://doi.org/10.1021/ct500686r
- Anthony Scemama, Nicolas Renon, and Mathias Rapacioli . A Sparse Self-Consistent Field Algorithm and Its Parallel Implementation: Application to Density-Functional-Based Tight Binding. Journal of Chemical Theory and Computation 2014, 10 (6) , 2344-2354. https://doi.org/10.1021/ct500115v
- Timothy J. Giese, Haoyuan Chen, Ming Huang, and Darrin M. York . Parametrization of an Orbital-Based Linear-Scaling Quantum Force Field for Noncovalent Interactions. Journal of Chemical Theory and Computation 2014, 10 (3) , 1086-1098. https://doi.org/10.1021/ct401035t
- Rustam Z. Khaliullin, Joost VandeVondele, and Jürg Hutter . Efficient Linear-Scaling Density Functional Theory for Molecular Systems. Journal of Chemical Theory and Computation 2013, 9 (10) , 4421-4427. https://doi.org/10.1021/ct400595k
- Mauro Del Ben, Jürg Hutter, and Joost VandeVondele . Second-Order Møller–Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach. Journal of Chemical Theory and Computation 2012, 8 (11) , 4177-4188. https://doi.org/10.1021/ct300531w
- Robert Schade, Tobias Kenter, Hossam Elgabarty, Michael Lass, Thomas D. Kühne, Christian Plessl. Breaking the exascale barrier for the electronic structure problem in ab-initio molecular dynamics. The International Journal of High Performance Computing Applications 2023, 37 (5) , 530-538. https://doi.org/10.1177/10943420231177631
- Qiming Sun. Exact exchange with range-separated algorithm for thermodynamic limit of periodic Hartree–Fock theory. The Journal of Chemical Physics 2023, 159 (2) https://doi.org/10.1063/5.0155815
- Phillip Seeber, Sebastian Seidenath, Johannes Steinmetzer, Stefanie Gräfe. Growing Spicy ONIOMs : Extending and generalizing concepts of ONIOM and many body expansions. WIREs Computational Molecular Science 2023, 13 (3) https://doi.org/10.1002/wcms.1644
- 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. The Journal of Chemical Physics 2023, 158 (16) https://doi.org/10.1063/5.0144493
- Yoshifumi Nishimura, Hiromi Nakai. Enabling large-scale quantum path integral molecular dynamics simulations through the integration of D cdftbmd and i-PI codes. The Journal of Chemical Physics 2023, 158 (16) https://doi.org/10.1063/5.0147535
- Kamil Wojtkowiak, Aneta Jezierska. Role of Non-Covalent Interactions in Carbonic Anhydrase I—Topiramate Complex Based on QM/MM Approach. Pharmaceuticals 2023, 16 (4) , 479. https://doi.org/10.3390/ph16040479
- Xinming Qin, Junshi Chen, Zhaolong Luo, Lingyun Wan, Jielan Li, Shizhe Jiao, Zhenlin Zhang, Qingcai Jiang, Wei Hu, Hong An, Jinlong Yang. High performance computing for first-principles Kohn-Sham density functional theory towards exascale supercomputers. CCF Transactions on High Performance Computing 2023, 5 (1) , 26-42. https://doi.org/10.1007/s42514-022-00120-0
- Mark A. Burton, Brad A. Steele, Jonathan C. Crowhurst, Ana Racoveanu, I‐Feng W. Kuo, William L. Shaw, Richard H. Gee. Vibrational Spectra of HNIW and its Isotopologues: A Combined Experimental and Computational Study. Propellants, Explosives, Pyrotechnics 2023, 48 (4) https://doi.org/10.1002/prep.202200349
- Van-Quan Vuong, Caterina Cevallos, Ben Hourahine, Bálint Aradi, Jacek Jakowski, Stephan Irle, Cristopher Camacho. Accelerating the density-functional tight-binding method using graphical processing units. The Journal of Chemical Physics 2023, 158 (8) https://doi.org/10.1063/5.0130797
- Christian F. A. Negre, Michael E. Wall, Anders M. N. Niklasson. Graph-based quantum response theory and shadow Born–Oppenheimer molecular dynamics. The Journal of Chemical Physics 2023, 158 (7) , 074108. https://doi.org/10.1063/5.0137119
- Brad A. Steele. Initial decomposition mechanisms of 2,4,6-triamino-1,3,5-trinitrobenzene (TATB) and their kinetic isotope effect. Journal of Applied Physics 2023, 133 (7) https://doi.org/10.1063/5.0139625
- Fabian Belleflamme, Anna-Sophia Hehn, Marcella Iannuzzi, Jürg Hutter. A variational formulation of the Harris functional as a correction to approximate Kohn–Sham density functional theory. The Journal of Chemical Physics 2023, 158 (5) https://doi.org/10.1063/5.0122671
- Zhaoyang Du, Yijin Guan, Tianchan Guan, Dimin Niu, Nianxiong Tan, Xiaopeng Yu, Hongzhong Zheng, Jianyi Meng, Xiaolang Yan, Yuan Xie. Predicting the Output Structure of Sparse Matrix Multiplication with Sampled Compression Ratio. 2023, 483-490. https://doi.org/10.1109/ICPADS56603.2022.00069
- Jürg Hutter, Marcella Iannuzzi, Thomas D. Kühne. Ab Initio Molecular Dynamics: A Guide to Applications. 2023https://doi.org/10.1016/B978-0-12-821978-2.00096-9
- Ali Estejab, Rachel B. Getman. Water/Solid Interface in Thermal- and Electrocatalysis for Wetting and Non-Wetting Surfaces: Interactions and Models.. 2023https://doi.org/10.1016/B978-0-12-821978-2.00104-5
- Lenz Fiedler, Zhandos A. Moldabekov, Xuecheng Shao, Kaili Jiang, Tobias Dornheim, Michele Pavanello, Attila Cangi. Accelerating equilibration in first-principles molecular dynamics with orbital-free density functional theory. Physical Review Research 2022, 4 (4) https://doi.org/10.1103/PhysRevResearch.4.043033
- Edward Ditler, Sandra Luber. Vibrational spectroscopy by means of first‐principles molecular dynamics simulations. WIREs Computational Molecular Science 2022, 12 (5) https://doi.org/10.1002/wcms.1605
- Jan Blasius, Paul Zaby, Jürgen Dölz, Barbara Kirchner. Uncertainty quantification of phase transition quantities from cluster weighting calculations. The Journal of Chemical Physics 2022, 157 (1) https://doi.org/10.1063/5.0093057
- Robert Schade, Tobias Kenter, Hossam Elgabarty, Michael Lass, Ole Schütt, Alfio Lazzaro, Hans Pabst, Stephan Mohr, Jürg Hutter, Thomas D. Kühne, Christian Plessl. Towards electronic structure-based ab-initio molecular dynamics simulations with hundreds of millions of atoms. Parallel Computing 2022, 111 , 102920. https://doi.org/10.1016/j.parco.2022.102920
- Emanuel H. Rubensson, Elias Rudberg, Anastasia Kruchinina, Anton G. Artemov. The Chunks and Tasks Matrix Library. SoftwareX 2022, 19 , 101159. https://doi.org/10.1016/j.softx.2022.101159
- Frederick Stein, Jürg Hutter. Double-hybrid density functionals for the condensed phase: Gradients, stress tensor, and auxiliary-density matrix method acceleration. The Journal of Chemical Physics 2022, 156 (7) https://doi.org/10.1063/5.0082327
- GiovanniMaria Piccini, Mal-Soon Lee, Simuck F. Yuk, Difan Zhang, Greg Collinge, Loukas Kollias, Manh-Thuong Nguyen, Vassiliki-Alexandra Glezakou, Roger Rousseau. Ab initio molecular dynamics with enhanced sampling in heterogeneous catalysis. Catalysis Science & Technology 2022, 12 (1) , 12-37. https://doi.org/10.1039/D1CY01329G
- Zhaoyang Du, Yijin Guan, Tianchan Guan, Dimin Niu, Linyong Huang, Hongzhong Zheng, Yuan Xie. OpSparse: A Highly Optimized Framework for Sparse General Matrix Multiplication on GPUs. IEEE Access 2022, 10 , 85960-85974. https://doi.org/10.1109/ACCESS.2022.3196940
- Yoshifumi Nishimura, Hiromi Nakai. Quantum Chemical Calculations for up to One Hundred Million Atoms Using D cdftbmd Code on Supercomputer Fugaku. Chemistry Letters 2021, 50 (8) , 1546-1550. https://doi.org/10.1246/cl.210263
- Anton G. Artemov, Emanuel H. Rubensson. Sparse approximate matrix-matrix multiplication for density matrix purification with error control. Journal of Computational Physics 2021, 438 , 110354. https://doi.org/10.1016/j.jcp.2021.110354
- Aaron Welch, Oscar Hernandez, Barbara Chapman. Combining Static and Dynamic Analysis to Query Characteristics of HPC Applications. 2021, 420-429. https://doi.org/10.1109/IPDPSW52791.2021.00071
- Lingyun Wan, Xiaofeng Liu, Jie Liu, Xinming Qin, Wei Hu, Jinlong Yang. Hybrid MPI and OpenMP parallel implementation of large-scale linear-response time-dependent density functional theory with plane-wave basis set. Electronic Structure 2021, 3 (2) , 024004. https://doi.org/10.1088/2516-1075/abfd1f
- Ming Chen, Roi Baer, Daniel Neuhauser, Eran Rabani. Stochastic density functional theory: Real- and energy-space fragmentation for noise reduction. The Journal of Chemical Physics 2021, 154 (20) https://doi.org/10.1063/5.0044163
- Victor Wen-zhe Yu, Jonathan Moussa, Pavel Kůs, Andreas Marek, Peter Messmer, Mina Yoon, Hermann Lederer, Volker Blum. GPU-acceleration of the ELPA2 distributed eigensolver for dense symmetric and hermitian eigenproblems. Computer Physics Communications 2021, 262 , 107808. https://doi.org/10.1016/j.cpc.2020.107808
- Emanuel H Rubensson, Anton G Artemov, Anastasia Kruchinina, Elias Rudberg. Localized inverse factorization. IMA Journal of Numerical Analysis 2021, 41 (1) , 729-763. https://doi.org/10.1093/imanum/drz075
- Wei Hu, Xinming Qin, Qingcai Jiang, Junshi Chen, Hong An, Weile Jia, Fang Li, Xin Liu, Dexun Chen, Fangfang Liu, Yuwen Zhao, Jinlong Yang. High performance computing of DGDFT for tens of thousands of atoms using millions of cores on Sunway TaihuLight. Science Bulletin 2021, 66 (2) , 111-119. https://doi.org/10.1016/j.scib.2020.06.025
- Christian F. A. Negre, Anders M. N. Niklasson, Antonio Redondo. Quantum-Based Molecular Dynamics Simulations with Applications to Industrial Problems. 2021, 289-314. https://doi.org/10.1007/978-3-030-18778-1_15
- Zhaolong Luo, Xinming Qin, Lingyun Wan, Wei Hu, Jinlong Yang. Parallel Implementation of Large-Scale Linear Scaling Density Functional Theory Calculations With Numerical Atomic Orbitals in HONPAS. Frontiers in Chemistry 2020, 8 https://doi.org/10.3389/fchem.2020.589910
- Michael Lass, Robert Schade, Thomas D. Kuhne, Christian Plessl. A Submatrix-Based Method for Approximate Matrix Function Evaluation in the Quantum Chemistry Code CP2K. 2020, 1-14. https://doi.org/10.1109/SC41405.2020.00084
- Julio Daniel Carvalho Maia, Lucidio dos Anjos Formiga Cabral, Gerd Bruno Rocha. GPU algorithms for density matrix methods on MOPAC: linear scaling electronic structure calculations for large molecular systems. Journal of Molecular Modeling 2020, 26 (11) https://doi.org/10.1007/s00894-020-04571-6
- Victor Wen-zhe Yu, Carmen Campos, William Dawson, Alberto García, Ville Havu, Ben Hourahine, William P. Huhn, Mathias Jacquelin, Weile Jia, Murat Keçeli, Raul Laasner, Yingzhou Li, Lin Lin, Jianfeng Lu, Jonathan Moussa, Jose E. Roman, Álvaro Vázquez-Mayagoitia, Chao Yang, Volker Blum. ELSI — An open infrastructure for electronic structure solvers. Computer Physics Communications 2020, 256 , 107459. https://doi.org/10.1016/j.cpc.2020.107459
- Rita P. Magalhães, Henriques S. Fernandes, Sérgio F. Sousa. Modelling Enzymatic Mechanisms with QM/MM Approaches: Current Status and Future Challenges. Israel Journal of Chemistry 2020, 60 (7) , 655-666. https://doi.org/10.1002/ijch.202000014
- Thomas D. Kühne, Marcella Iannuzzi, Mauro Del Ben, Vladimir V. Rybkin, Patrick Seewald, Frederick Stein, Teodoro Laino, Rustam Z. Khaliullin, Ole Schütt, Florian Schiffmann, Dorothea Golze, Jan Wilhelm, Sergey Chulkov, Mohammad Hossein Bani-Hashemian, Valéry Weber, Urban Borštnik, Mathieu Taillefumier, Alice Shoshana Jakobovits, Alfio Lazzaro, Hans Pabst, Tiziano Müller, Robert Schade, Manuel Guidon, Samuel Andermatt, Nico Holmberg, Gregory K. Schenter, Anna Hehn, Augustin Bussy, Fabian Belleflamme, Gloria Tabacchi, Andreas Glöß, Michael Lass, Iain Bethune, Christopher J. Mundy, Christian Plessl, Matt Watkins, Joost VandeVondele, Matthias Krack, Jürg Hutter. CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations. The Journal of Chemical Physics 2020, 152 (19) https://doi.org/10.1063/5.0007045
- Ayako Nakata, Jack S. Baker, Shereif Y. Mujahed, Jack T. L. Poulton, Sergiu Arapan, Jianbo Lin, Zamaan Raza, Sushma Yadav, Lionel Truflandier, Tsuyoshi Miyazaki, David R. Bowler. Large scale and linear scaling DFT with the CONQUEST code. The Journal of Chemical Physics 2020, 152 (16) https://doi.org/10.1063/5.0005074
- Anton G. Artemov, Elias Rudberg, Emanuel H. Rubensson. Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model. Parallel Computing 2019, 89 , 102548. https://doi.org/10.1016/j.parco.2019.102548
- Ilia Sivkov, Alfio Lazzaro, Jurg Hutter. DBCSR: A Library for Dense Matrix Multiplications on Distributed GPU-Accelerated Systems. 2019, 0799-0803. https://doi.org/10.1109/SIBIRCON48586.2019.8958035
- Hristo N. Djidjev, Georg Hahn, Susan M. Mniszewski, Christian F. A. Negre, Anders M. N. Niklasson. Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics. Algorithms 2019, 12 (9) , 187. https://doi.org/10.3390/a12090187
- Wenhui Mi, Michele Pavanello. Orbital-free density functional theory correctly models quantum dots when asymptotics, nonlocality, and nonhomogeneity are accounted for. Physical Review B 2019, 100 (4) https://doi.org/10.1103/PhysRevB.100.041105
- Yoshifumi Nishimura, Hiromi Nakai. D cdftbmd : Divide‐and‐Conquer Density Functional Tight‐Binding Program for Huge‐System Quantum Mechanical Molecular Dynamics Simulations. Journal of Computational Chemistry 2019, 40 (15) , 1538-1549. https://doi.org/10.1002/jcc.25804
- Ben Slater, Angelos Michaelides. Surface premelting of water ice. Nature Reviews Chemistry 2019, 3 (3) , 172-188. https://doi.org/10.1038/s41570-019-0080-8
- Lars G. M. Pettersson. A Two-State Picture of Water and the Funnel of Life. 2019, 3-39. https://doi.org/10.1007/978-3-030-21755-6_1
- Taisuke Ozaki, Masahiro Fukuda, Gengping Jiang. Efficient O( N ) divide-conquer method with localized single-particle natural orbitals. Physical Review B 2018, 98 (24) https://doi.org/10.1103/PhysRevB.98.245137
- Ada Sedova, John D. Eblen, Reuben Budiardja, Arnold Tharrington, Jeremy C. Smith. High-Performance Molecular Dynamics Simulation for Biological and Materials Sciences: Challenges of Performance Portability. 2018, 1-13. https://doi.org/10.1109/P3HPC.2018.00004
- Vojtěch Vlček, Wenfei Li, Roi Baer, Eran Rabani, Daniel Neuhauser. Swift G W beyond 10,000 electrons using sparse stochastic compression. Physical Review B 2018, 98 (7) https://doi.org/10.1103/PhysRevB.98.075107
- Hayden Scheiber, Yifei Shi, Rustam Z. Khaliullin. Communication: Compact orbitals enable low-cost linear-scaling ab initio molecular dynamics for weakly-interacting systems. The Journal of Chemical Physics 2018, 148 (23) https://doi.org/10.1063/1.5029939
- William Dawson, Takahito Nakajima. Massively parallel sparse matrix function calculations with NTPoly. Computer Physics Communications 2018, 225 , 154-165. https://doi.org/10.1016/j.cpc.2017.12.010
- Zhentao Wang, Gia-Wei Chern, Cristian D. Batista, Kipton Barros. Gradient-based stochastic estimation of the density matrix. The Journal of Chemical Physics 2018, 148 (9) https://doi.org/10.1063/1.5017741
- Jolyon Aarons, Chris-Kriton Skylaris. Electronic annealing Fermi operator expansion for DFT calculations on metallic systems. The Journal of Chemical Physics 2018, 148 (7) https://doi.org/10.1063/1.5001340
- Heather J. Kulik. Large-scale QM/MM free energy simulations of enzyme catalysis reveal the influence of charge transfer. Physical Chemistry Chemical Physics 2018, 20 (31) , 20650-20660. https://doi.org/10.1039/C8CP03871F
- Victor Wen-zhe Yu, Fabiano Corsetti, Alberto García, William P. Huhn, Mathias Jacquelin, Weile Jia, Björn Lange, Lin Lin, Jianfeng Lu, Wenhui Mi, Ali Seifitokaldani, Álvaro Vázquez-Mayagoitia, Chao Yang, Haizhao Yang, Volker Blum. ELSI: A unified software interface for Kohn–Sham electronic structure solvers. Computer Physics Communications 2018, 222 , 267-285. https://doi.org/10.1016/j.cpc.2017.09.007
- Teruo Hirakawa, Teppei Suzuki, David R Bowler, Tsuyoshi Miyazaki. Canonical-ensemble extended Lagrangian Born–Oppenheimer molecular dynamics for the linear scaling density functional theory. Journal of Physics: Condensed Matter 2017, 29 (40) , 405901. https://doi.org/10.1088/1361-648X/aa810d
- Kadir Akbudak, Oguz Selvitopi, Cevdet Aykanat. Partitioning Models for Scaling Parallel Sparse Matrix-Matrix Multiplication. ACM Transactions on Parallel Computing 2017, 4 (3) , 1-34. https://doi.org/10.1145/3155292
- Alessandro Genova, Davide Ceresoli, Alisa Krishtal, Oliviero Andreussi, Robert A. DiStasio, Michele Pavanello. eQE: An open‐source density functional embedding theory code for the condensed phase. International Journal of Quantum Chemistry 2017, 117 (16) https://doi.org/10.1002/qua.25401
- Anders M. N. Niklasson. Next generation extended Lagrangian first principles molecular dynamics. The Journal of Chemical Physics 2017, 147 (5) https://doi.org/10.1063/1.4985893
- Kadir Akbudak, Cevdet Aykanat. Exploiting Locality in Sparse Matrix-Matrix Multiplication on Many-Core Architectures. IEEE Transactions on Parallel and Distributed Systems 2017, 28 (8) , 2258-2271. https://doi.org/10.1109/TPDS.2017.2656893
- Md Salman Ahmed, Jennifer Houser, Mohammad A. Hoque, Rezaul Raju, Phil Pfeiffer. Reducing Inter-Process Communication Overhead in Parallel Sparse Matrix-Matrix Multiplication. International Journal of Grid and High Performance Computing 2017, 9 (3) , 46-59. https://doi.org/10.4018/IJGHPC.2017070104
- Alfio Lazzaro, Joost VandeVondele, Jürg Hutter, Ole Schütt. Increasing the Efficiency of Sparse Matrix-Matrix Multiplication with a 2.5D Algorithm and One-Sided MPI. 2017, 1-9. https://doi.org/10.1145/3093172.3093228
- Jon Paul Janet, Qing Zhao, Efthymios I. Ioannidis, Heather J. Kulik. Density functional theory for modelling large molecular adsorbate–surface interactions: a mini-review and worked example. Molecular Simulation 2017, 43 (5-6) , 327-345. https://doi.org/10.1080/08927022.2016.1258465
- Jolyon Aarons, Misbah Sarwar, David Thompsett, Chris-Kriton Skylaris. Perspective: Methods for large-scale density functional calculations on metallic systems. The Journal of Chemical Physics 2016, 145 (22) https://doi.org/10.1063/1.4972007
- A. Pozdneev, V. Weber, T. Laino, C. Bekas, A. Curioni. Enhanced MPSM3 for Applications to Quantum Biological Simulations. 2016, 96-106. https://doi.org/10.1109/SC.2016.8
- Alexander Heinecke, Greg Henry, Maxwell Hutchinson, Hans Pabst. LIBXSMM: Accelerating Small Matrix Multiplications by Runtime Code Generation. 2016, 981-991. https://doi.org/10.1109/SC.2016.83
- Jean-Luc Fattebert, Daniel Osei-Kuffuor, Erik W. Draeger, Tadashi Ogitsu, William D. Krauss. Modeling Dilute Solutions Using First-Principles Molecular Dynamics: Computing more than a Million Atoms with over a Million Cores. 2016, 12-22. https://doi.org/10.1109/SC.2016.88
- Amartya S. Banerjee, Lin Lin, Wei Hu, Chao Yang, John E. Pask. Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations. The Journal of Chemical Physics 2016, 145 (15) https://doi.org/10.1063/1.4964861
- Daniel J Cole, Nicholas D M Hine. Applications of large-scale density functional theory in biology. Journal of Physics: Condensed Matter 2016, 28 (39) , 393001. https://doi.org/10.1088/0953-8984/28/39/393001
- Emanuel H. Rubensson, Elias Rudberg. Locality-aware parallel block-sparse matrix-matrix multiplication using the Chunks and Tasks programming model. Parallel Computing 2016, 57 , 87-106. https://doi.org/10.1016/j.parco.2016.06.005
- Michael E. Wall. Quantum crystallographic charge density of urea. IUCrJ 2016, 3 (4) , 237-246. https://doi.org/10.1107/S2052252516006242
- Anders M. N. Niklasson, Susan M. Mniszewski, Christian F. A. Negre, Marc J. Cawkwell, Pieter J. Swart, Jamal Mohd-Yusof, Timothy C. Germann, Michael E. Wall, Nicolas Bock, Emanuel H. Rubensson, Hristo Djidjev. Graph-based linear scaling electronic structure theory. The Journal of Chemical Physics 2016, 144 (23) https://doi.org/10.1063/1.4952650
- Marie‐Pierre Gaigeot, Marialore Sulpizi. Mineral–Water Interaction. 2016, 271-309. https://doi.org/10.1002/9781118845226.ch8
- Ole Schütt, Peter Messmer, Jürg Hutter, Joost VandeVondele. GPU‐Accelerated Sparse Matrix–Matrix Multiplication for Linear Scaling Density Functional Theory. 2016, 173-190. https://doi.org/10.1002/9781118670712.ch8