1
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Williams-Young DB, Yuwono SH, DePrince III AE, Yang C. Approximate Exponential Integrators for Time-Dependent Equation-of-Motion Coupled Cluster Theory. J Chem Theory Comput 2023; 19:9177-9186. [PMID: 38086060 PMCID: PMC10753770 DOI: 10.1021/acs.jctc.3c00911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Revised: 10/09/2023] [Accepted: 10/16/2023] [Indexed: 12/27/2023]
Abstract
With a growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schrödinger equation is of keen interest in modern electronic structure theory. In this work, we present two approaches for the formation of the quantum propagator for time-dependent equation-of-motion coupled cluster theory based on the Chebyshev and Arnoldi expansions of the complex, nonhermitian matrix exponential, respectively. The proposed algorithms are compared with the short-iterative Lanczos method of Cooper et al. [J. Phys. Chem. A 2021 125, 5438-5447], the fourth-order Runge-Kutta method, and exact dynamics for a set of small but challenging test problems. For each of the cases studied, both of the proposed integration schemes demonstrate superior accuracy and efficiency relative to the reference simulations.
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Affiliation(s)
- David B. Williams-Young
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Stephen H. Yuwono
- Department
of Chemistry and Biochemistry, Florida State
University, Tallahassee, Florida 32306, United States
| | - A. Eugene DePrince III
- Department
of Chemistry and Biochemistry, Florida State
University, Tallahassee, Florida 32306, United States
| | - Chao Yang
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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2
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Di Felice R, Mayes ML, Richard RM, Williams-Young DB, Chan GKL, de Jong WA, Govind N, Head-Gordon M, Hermes MR, Kowalski K, Li X, Lischka H, Mueller KT, Mutlu E, Niklasson AMN, Pederson MR, Peng B, Shepard R, Valeev EF, van Schilfgaarde M, Vlaisavljevich B, Windus TL, Xantheas SS, Zhang X, Zimmerman PM. A Perspective on Sustainable Computational Chemistry Software Development and Integration. J Chem Theory Comput 2023; 19:7056-7076. [PMID: 37769271 PMCID: PMC10601486 DOI: 10.1021/acs.jctc.3c00419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Indexed: 09/30/2023]
Abstract
The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.
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Affiliation(s)
- Rosa Di Felice
- Departments
of Physics and Astronomy and Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, United States
- CNR-NANO
Modena, Modena 41125, Italy
| | - Maricris L. Mayes
- Department
of Chemistry and Biochemistry, University
of Massachusetts Dartmouth, North Dartmouth, Massachusetts 02747, United States
| | | | | | - Garnet Kin-Lic Chan
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Wibe A. de Jong
- Lawrence
Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Niranjan Govind
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Martin Head-Gordon
- Pitzer Center
for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Matthew R. Hermes
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Karol Kowalski
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hans Lischka
- Department
of Chemistry and Biochemistry, Texas Tech
University, Lubbock, Texas 79409, United States
| | - Karl T. Mueller
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Erdal Mutlu
- Advanced
Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Anders M. N. Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Mark R. Pederson
- Department
of Physics, The University of Texas at El
Paso, El Paso, Texas 79968, United States
| | - Bo Peng
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Ron Shepard
- Chemical
Sciences and Engineering Division, Argonne
National Laboratory, Lemont, Illinois 60439, United States
| | - Edward F. Valeev
- Department
of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | | | - Bess Vlaisavljevich
- Department
of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Theresa L. Windus
- Department
of Chemistry, Iowa State University and
Ames Laboratory, Ames, Iowa 50011, United States
| | - Sotiris S. Xantheas
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
- Advanced
Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Xing Zhang
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Paul M. Zimmerman
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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3
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Ko T, Heindel JP, Guan X, Head-Gordon T, Williams-Young DB, Yang C. Using Diffusion Maps to Analyze Reaction Dynamics for a Hydrogen Combustion Benchmark Dataset. J Chem Theory Comput 2023; 19:5872-5885. [PMID: 37585272 PMCID: PMC10500976 DOI: 10.1021/acs.jctc.3c00426] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Indexed: 08/18/2023]
Abstract
We use local diffusion maps to assess the quality of two types of collective variables (CVs) for a recently published hydrogen combustion benchmark dataset1 that contains ab initio molecular dynamics (MD) trajectories and normal modes along minimum energy paths. This approach was recently advocated in2 for assessing CVs and analyzing reactions modeled by classical MD simulations. We report the effectiveness of this approach to molecular systems modeled by quantum ab initio MD. In addition to assessing the quality of CVs, we also use global diffusion maps to perform committor analysis as proposed in.2 We show that the committor function obtained from the global diffusion map allows us to identify transition regions of interest in several hydrogen combustion reaction channels.
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Affiliation(s)
- Taehee Ko
- Department
of Mathematics, Penn State University, University Park, Pennsylvania 16802, United States
| | - Joseph P. Heindel
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Xingyi Guan
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Teresa Head-Gordon
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Departments
of Bioengineering and Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - David B. Williams-Young
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Chao Yang
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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4
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Williams-Young DB, Asadchev A, Popovici DT, Clark D, Waldrop J, Windus TL, Valeev EF, de Jong WA. Distributed memory, GPU accelerated Fock construction for hybrid, Gaussian basis density functional theory. J Chem Phys 2023; 158:234104. [PMID: 37326157 DOI: 10.1063/5.0151070] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2023] [Accepted: 05/26/2023] [Indexed: 06/17/2023] Open
Abstract
With the growing reliance of modern supercomputers on accelerator-based architecture such a graphics processing units (GPUs), the development and optimization of electronic structure methods to exploit these massively parallel resources has become a recent priority. While significant strides have been made in the development GPU accelerated, distributed memory algorithms for many modern electronic structure methods, the primary focus of GPU development for Gaussian basis atomic orbital methods has been for shared memory systems with only a handful of examples pursing massive parallelism. In the present work, we present a set of distributed memory algorithms for the evaluation of the Coulomb and exact exchange matrices for hybrid Kohn-Sham DFT with Gaussian basis sets via direct density-fitted (DF-J-Engine) and seminumerical (sn-K) methods, respectively. The absolute performance and strong scalability of the developed methods are demonstrated on systems ranging from a few hundred to over one thousand atoms using up to 128 NVIDIA A100 GPUs on the Perlmutter supercomputer.
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Affiliation(s)
- David B Williams-Young
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Andrey Asadchev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Doru Thom Popovici
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - David Clark
- NVIDIA Corporation, Santa Clara, California 95051, USA
| | - Jonathan Waldrop
- Chemical and Biological Sciences Division, Ames National Laboratory, Ames, Iowa 50011, USA
| | - Theresa L Windus
- Chemical and Biological Sciences Division, Ames National Laboratory, Ames, Iowa 50011, USA
- Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Wibe A de Jong
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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5
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Williams-Young DB, Tubman NM, Mejuto-Zaera C, de Jong WA. A parallel, distributed memory implementation of the adaptive sampling configuration interaction method. J Chem Phys 2023; 158:2893713. [PMID: 37259999 DOI: 10.1063/5.0148650] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Accepted: 05/10/2023] [Indexed: 06/02/2023] Open
Abstract
The many-body simulation of quantum systems is an active field of research that involves several different methods targeting various computing platforms. Many methods commonly employed, particularly coupled cluster methods, have been adapted to leverage the latest advances in modern high-performance computing. Selected configuration interaction (sCI) methods have seen extensive usage and development in recent years. However, the development of sCI methods targeting massively parallel resources has been explored only in a few research works. Here, we present a parallel, distributed memory implementation of the adaptive sampling configuration interaction approach (ASCI) for sCI. In particular, we will address the key concerns pertaining to the parallelization of the determinant search and selection, Hamiltonian formation, and the variational eigenvalue calculation for the ASCI method. Load balancing in the search step is achieved through the application of memory-efficient determinant constraints originally developed for the ASCI-PT2 method. The presented benchmarks demonstrate near optimal speedup for ASCI calculations of Cr2 (24e, 30o) with 106, 107, and 3 × 108 variational determinants on up to 16 384 CPUs. To the best of the authors' knowledge, this is the largest variational ASCI calculation to date.
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Affiliation(s)
- David B Williams-Young
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Norm M Tubman
- NASA Ames Research Center, Moffett Field, California 94035, USA
| | - Carlos Mejuto-Zaera
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, TS, Italy
| | - Wibe A de Jong
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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6
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Gomes N, Williams-Young DB, de Jong WA. Computing the Many-Body Green's Function with Adaptive Variational Quantum Dynamics. J Chem Theory Comput 2023. [PMID: 37227367 DOI: 10.1021/acs.jctc.3c00150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We present a method to compute the many-body real-time Green's function using an adaptive variational quantum dynamics simulation approach. The real-time Green's function involves the time evolution of a quantum state with one additional electron with respect to the ground state wave function that is first expressed as a linear-linear combination of state vectors. The real-time evolution and the Green's function are obtained by combining the dynamics of the individual state vectors in a linear combination. The use of the adaptive protocol enables us to generate compact ansatzes on-the-fly while running the simulation. In order to improve the convergence of spectral features, Padé approximants are applied to obtain the Fourier transform of the Green's function. We demonstrate the evaluation of the Green's function on an IBM Q quantum computer. As a part of our error mitigation strategy, we develop a resolution-enhancing method that we successfully apply on the noisy data from the real-quantum hardware.
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Affiliation(s)
- Niladri Gomes
- Applied Mathematics and Computing Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David B Williams-Young
- Applied Mathematics and Computing Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Wibe A de Jong
- Applied Mathematics and Computing Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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7
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Kowalski K, Bair R, Bauman NP, Boschen JS, Bylaska EJ, Daily J, de Jong WA, Dunning T, Govind N, Harrison RJ, Keçeli M, Keipert K, Krishnamoorthy S, Kumar S, Mutlu E, Palmer B, Panyala A, Peng B, Richard RM, Straatsma TP, Sushko P, Valeev EF, Valiev M, van Dam HJJ, Waldrop JM, Williams-Young DB, Yang C, Zalewski M, Windus TL. From NWChem to NWChemEx: Evolving with the Computational Chemistry Landscape. Chem Rev 2021; 121:4962-4998. [PMID: 33788546 DOI: 10.1021/acs.chemrev.0c00998] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Since the advent of the first computers, chemists have been at the forefront of using computers to understand and solve complex chemical problems. As the hardware and software have evolved, so have the theoretical and computational chemistry methods and algorithms. Parallel computers clearly changed the common computing paradigm in the late 1970s and 80s, and the field has again seen a paradigm shift with the advent of graphical processing units. This review explores the challenges and some of the solutions in transforming software from the terascale to the petascale and now to the upcoming exascale computers. While discussing the field in general, NWChem and its redesign, NWChemEx, will be highlighted as one of the early codesign projects to take advantage of massively parallel computers and emerging software standards to enable large scientific challenges to be tackled.
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Affiliation(s)
- Karol Kowalski
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Raymond Bair
- Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Nicholas P Bauman
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | | | - Eric J Bylaska
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Jeff Daily
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Wibe A de Jong
- Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Thom Dunning
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Niranjan Govind
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Robert J Harrison
- Institute for Advanced Computational Science, Stony Brook University, Stony Brook, New York 11794, United States
| | - Murat Keçeli
- Argonne National Laboratory, Lemont, Illinois 60439, United States
| | | | | | - Suraj Kumar
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Erdal Mutlu
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Bruce Palmer
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Ajay Panyala
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Bo Peng
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | | | - T P Straatsma
- National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6373, United States
| | - Peter Sushko
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Marat Valiev
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | | | | | | | - Chao Yang
- Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Marcin Zalewski
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Theresa L Windus
- Department of Chemistry, Iowa State University and Ames Laboratory, Ames, Iowa 50011, United States
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8
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Yang C, Brabec J, Veis L, Williams-Young DB, Kowalski K. Solving Coupled Cluster Equations by the Newton Krylov Method. Front Chem 2020; 8:590184. [PMID: 33363108 PMCID: PMC7758425 DOI: 10.3389/fchem.2020.590184] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Accepted: 09/28/2020] [Indexed: 11/13/2022] Open
Abstract
We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples.
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Affiliation(s)
- Chao Yang
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, United States
| | - Jiri Brabec
- J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences, Prague, Czechia
| | - Libor Veis
- J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences, Prague, Czechia
| | - David B Williams-Young
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, United States
| | - Karol Kowalski
- Pacific Northwest National Laboratory, Richland, WA, United States
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9
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Williams-Young DB, de Jong WA, van Dam HJJ, Yang C. On the Efficient Evaluation of the Exchange Correlation Potential on Graphics Processing Unit Clusters. Front Chem 2020; 8:581058. [PMID: 33363105 PMCID: PMC7758429 DOI: 10.3389/fchem.2020.581058] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Accepted: 09/14/2020] [Indexed: 11/20/2022] Open
Abstract
The predominance of Kohn–Sham density functional theory (KS-DFT) for the theoretical treatment of large experimentally relevant systems in molecular chemistry and materials science relies primarily on the existence of efficient software implementations which are capable of leveraging the latest advances in modern high-performance computing (HPC). With recent trends in HPC leading toward increasing reliance on heterogeneous accelerator-based architectures such as graphics processing units (GPU), existing code bases must embrace these architectural advances to maintain the high levels of performance that have come to be expected for these methods. In this work, we purpose a three-level parallelism scheme for the distributed numerical integration of the exchange-correlation (XC) potential in the Gaussian basis set discretization of the Kohn–Sham equations on large computing clusters consisting of multiple GPUs per compute node. In addition, we purpose and demonstrate the efficacy of the use of batched kernels, including batched level-3 BLAS operations, in achieving high levels of performance on the GPU. We demonstrate the performance and scalability of the implementation of the purposed method in the NWChemEx software package by comparing to the existing scalable CPU XC integration in NWChem.
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Affiliation(s)
- David B Williams-Young
- Lawrence Berkeley National Laboratory, Computational Research Division, Berkeley, CA, United States
| | - Wibe A de Jong
- Lawrence Berkeley National Laboratory, Computational Research Division, Berkeley, CA, United States
| | - Hubertus J J van Dam
- Brookhaven National Laboratory, Computational Science Initiative, Upton, NY, United States
| | - Chao Yang
- Lawrence Berkeley National Laboratory, Computational Research Division, Berkeley, CA, United States
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10
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Koulias LN, Williams-Young DB, Nascimento DR, DePrince AE, Li X. Relativistic Real-Time Time-Dependent Equation-of-Motion Coupled-Cluster. J Chem Theory Comput 2019; 15:6617-6624. [DOI: 10.1021/acs.jctc.9b00729] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Lauren N. Koulias
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - David B. Williams-Young
- Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road MS 50A-3111, Berkeley, California 94720, United States
| | - Daniel R. Nascimento
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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11
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Peng B, Van Beeumen R, Williams-Young DB, Kowalski K, Yang C. Approximate Green's Function Coupled Cluster Method Employing Effective Dimension Reduction. J Chem Theory Comput 2019; 15:3185-3196. [PMID: 30951302 DOI: 10.1021/acs.jctc.9b00172] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The Green's function coupled cluster (GFCC) method, originally proposed in the early 1990s, is a powerful many-body tool for computing and analyzing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, in order for the GFCC to become a method that may be routinely used in the electronic structure calculations, robust numerical techniques and approximations must be employed to reduce its extremely high computational overhead. In our recent studies, it has been demonstrated that the GFCC equations can be solved directly in the frequency domain using iterative linear solvers, which can be easily distributed in a massively parallel environment. In the present work, we demonstrate a successful application of model-order-reduction (MOR) techniques in the GFCC framework. Briefly speaking, for a frequency regime of interest that requires high-resolution descriptions of spectral function, instead of solving the GFCC linear equation of full dimension for every single frequency point of interest, an efficiently solvable linear system model of a reduced dimension may be built upon projecting the original GFCC linear system onto a subspace. From this reduced order model is obtained a reasonable approximation to the full dimensional GFCC linear equations in both interpolative and extrapolative spectral regions. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some selected frequencies within the spectral region of interest. During the iterations, the quality of the subspace, as well as the linear system model, can be systematically improved. The method is tested in this work in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems such as carbon monoxide, 1,3-butadiene, benzene, and adenine. To reach the same level of accuracy as that of the original GFCC method, the application of MOR in the GFCC method is able to significantly lower the original computational cost for the aforementioned molecules in designated frequency regimes. As a byproduct, the reduced order model obtained by this method is found to provide a high-quality initial guess, which improves the convergence rate for the existing iterative linear solver.
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Affiliation(s)
- Bo Peng
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle , Pacific Northwest National Laboratory , K8-91, P.O. Box 999, Richland , Washington 99352 , United States
| | - Roel Van Beeumen
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | - David B Williams-Young
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle , Pacific Northwest National Laboratory , K8-91, P.O. Box 999, Richland , Washington 99352 , United States
| | - Chao Yang
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
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12
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Hoyer CE, Williams-Young DB, Huang C, Li X. Embedding non-collinear two-component electronic structure in a collinear quantum environment. J Chem Phys 2019; 150:174114. [DOI: 10.1063/1.5092628] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- Chad E. Hoyer
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | | | - Chen Huang
- Department of Scientific Computing, Materials Science and Engineering Program, and National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, USA
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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13
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Sun S, Williams-Young DB, Stetina TF, Li X. Generalized Hartree–Fock with Nonperturbative Treatment of Strong Magnetic Fields: Application to Molecular Spin Phase Transitions. J Chem Theory Comput 2018; 15:348-356. [DOI: 10.1021/acs.jctc.8b01140] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Shichao Sun
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - Torin F. Stetina
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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14
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Kasper JM, Williams-Young DB, Vecharynski E, Yang C, Li X. A Well-Tempered Hybrid Method for Solving Challenging Time-Dependent Density Functional Theory (TDDFT) Systems. J Chem Theory Comput 2018; 14:2034-2041. [DOI: 10.1021/acs.jctc.8b00141] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Joseph M. Kasper
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - Eugene Vecharynski
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Chao Yang
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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15
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Lestrange PJ, Williams-Young DB, Petrone A, Jiménez-Hoyos CA, Li X. Efficient Implementation of Variation after Projection Generalized Hartree–Fock. J Chem Theory Comput 2018; 14:588-596. [DOI: 10.1021/acs.jctc.7b00832] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Patrick J. Lestrange
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - Alessio Petrone
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
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16
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Van Beeumen R, Williams-Young DB, Kasper JM, Yang C, Ng EG, Li X. Model Order Reduction Algorithm for Estimating the Absorption Spectrum. J Chem Theory Comput 2017; 13:4950-4961. [PMID: 28862869 DOI: 10.1021/acs.jctc.7b00402] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator's eigenspectrum for medium-to-large sized systems, traditional approaches based on the partial diagonalization of the propagator often encounter oscillatory and stagnating convergence. Electronic structure methods which solve the molecular response problem through the solution of spectrally shifted linear systems, such as the complex polarization propagator, offer an alternative approach which is agnostic to the underlying spectral density or domain location. This generality comes at a seemingly high computational cost associated with solving a large linear system for each spectral shift in some discretization of the spectral domain of interest. In this work, we present a novel, adaptive solution to this high computational overhead based on model order reduction techniques via interpolation. Model order reduction reduces the computational complexity of mathematical models and is ubiquitous in the simulation of dynamical systems and control theory. The efficiency and effectiveness of the proposed algorithm in the ab initio prediction of X-ray absorption spectra is demonstrated using a test set of challenging water clusters which are spectrally dense in the neighborhood of the oxygen K-edge. On the basis of a single, user defined tolerance we automatically determine the order of the reduced models and approximate the absorption spectrum up to the given tolerance. We also illustrate that, for the systems studied, the automatically determined model order increases logarithmically with the problem dimension, compared to a linear increase of the number of eigenvalues within the energy window. Furthermore, we observed that the computational cost of the proposed algorithm only scales quadratically with respect to the problem dimension.
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Affiliation(s)
- Roel Van Beeumen
- Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States
| | - David B Williams-Young
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Joseph M Kasper
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Chao Yang
- Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States
| | - Esmond G Ng
- Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
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17
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Barclay MS, Quincy TJ, Williams-Young DB, Caricato M, Elles CG. Accurate Assignments of Excited-State Resonance Raman Spectra: A Benchmark Study Combining Experiment and Theory. J Phys Chem A 2017; 121:7937-7946. [DOI: 10.1021/acs.jpca.7b09467] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Matthew S. Barclay
- Department
of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - Timothy J. Quincy
- Department
of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | | | - Marco Caricato
- Department
of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - Christopher G. Elles
- Department
of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
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18
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Egidi F, Williams-Young DB, Baiardi A, Bloino J, Scalmani G, Frisch MJ, Li X, Barone V. Effective Inclusion of Mechanical and Electrical Anharmonicity in Excited Electronic States: VPT2-TDDFT Route. J Chem Theory Comput 2017; 13:2789-2803. [PMID: 28453287 DOI: 10.1021/acs.jctc.7b00218] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a reliable and cost-effective procedure for the inclusion of anharmonic effects in excited-state energies and spectroscopic intensities by means of second-order vibrational perturbation theory. This development is made possible thanks to a recent efficient implementation of excited-state analytic Hessians and properties within the time-dependent density functional theory framework. As illustrated in this work, by taking advantage of such algorithmic developments, it is possible to perform calculations of excited-state infrared spectra of medium-large isolated molecular systems, with anharmonicity effects included in both the energy and property surfaces. We also explore the use of this procedure for the inclusion of anharmonic effects in the simulation of vibronic bandshapes of electronic spectra and compare the results with previous, more approximate models.
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Affiliation(s)
- Franco Egidi
- Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - David B Williams-Young
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Alberto Baiardi
- Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Julien Bloino
- Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti OrganoMetallici (ICCOM-CNR) , UOS di Pisa, Area della Ricerca CNR, Via G. Moruzzi 1, Pisa 56124, Italy
| | - Giovanni Scalmani
- Gaussian, Inc. , 340 Quinnipiac St., Bldg. 40, Wallingford, Connecticut 06492, United States
| | - Michael J Frisch
- Gaussian, Inc. , 340 Quinnipiac St., Bldg. 40, Wallingford, Connecticut 06492, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Vincenzo Barone
- Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa, Italy
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19
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Affiliation(s)
- Alessio Petrone
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - David B. Lingerfelt
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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20
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Abstract
Pump probe spectroscopy techniques have enabled the direct observation of a variety of transient molecular species in both ground and excited electronic states. Time-resolved vibrational spectroscopy is becoming an indispensable tool for investigating photoinduced nuclear dynamics of chemical systems of all kinds. On the other hand, a complete picture of the chemical dynamics encoded in these spectra cannot be achieved without a full temporal description of the structural relaxation, including the explicit time-dependence of vibrational coordinates that are substantially displaced from equilibrium by electronic excitation. Here we present a transient vibrational analysis protocol combining ab initio direct molecular dynamics and time-integrated normal modes introduced in this work, relying on the recent development of analytic time-dependent density functional theory (TDDFT) second derivatives for excited states. Prototypical molecules will be used as test cases, showing the evolution of the vibrational signatures that follow electronic excitation. This protocol provides a direct route to assigning the vibrations implicated in the (photo)dynamics of several (photoactive) systems.
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Affiliation(s)
- Alessio Petrone
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - David B Lingerfelt
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - David B Williams-Young
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
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21
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Affiliation(s)
- David B. Lingerfelt
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - Alessio Petrone
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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