1
|
Hellmann L, Neugebauer J. Automatic Generation of Auxiliary Basis Sets in Spherical Representation Using the Cholesky Decomposition. J Phys Chem A 2023; 127:8698-8711. [PMID: 37801362 DOI: 10.1021/acs.jpca.3c04282] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/07/2023]
Abstract
Density fitting techniques that use automatically generated auxiliary basis sets generally rely on the formation of basis function products. Recently, Lehtola [ J. Chem. Theory Comput. 2021, 17, 6886-6900] presented a procedure making use of a purely spherical representation by adding auxiliary basis functions coupled to the required angular momentum quantum numbers for the product of spherical harmonics and then removing linear dependencies by means of a Cholesky decomposition. In this work, we extend this idea by making use of the explicit equations for the product of two spherical harmonics in the angular part of the basis function product. Some of the resulting terms are not directly accessible when popular standard integral libraries are used, which could prevent the widespread use of the exact product form. For these terms, we introduce four approximations of increasing sophistication that require integrals involving only standard Gaussian-type orbitals and thus can be computed with standard libraries. We assess the accuracy of the different schemes in the context of the aCD for the reconstruction of the electron repulsion integral matrix and absolute and relative single point energies and in the framework of optimally tuned range-separated hybrid functionals.
Collapse
Affiliation(s)
- Lars Hellmann
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Universität Münster, Corrensstraße 36, 48149 Münster, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Universität Münster, Corrensstraße 36, 48149 Münster, Germany
| |
Collapse
|
2
|
Wang Z, Aldossary A, Head-Gordon M. Sparsity of the electron repulsion integral tensor using different localized virtual orbital representations in local second-order Møller-Plesset theory. J Chem Phys 2023; 158:064105. [PMID: 36792513 DOI: 10.1063/5.0134764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree-Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller-Plesset theory (MP2), one of the simplest post-HF methods, only the (ia|jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the "ragged list") and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the "fixed sparsity pattern") for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising.
Collapse
Affiliation(s)
- Zhenling Wang
- Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Abdulrahman Aldossary
- Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Martin Head-Gordon
- Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| |
Collapse
|
3
|
Xu X, Xu B, Li P. An 𝒪( n) framework for internal coordinate molecular dynamics applicable to molecules with arbitrary constraints and geometries. MOLECULAR SIMULATION 2020. [DOI: 10.1080/08927022.2019.1706738] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Xiankun Xu
- Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ, USA
| | - Ben Xu
- Department of Mechanical Engineering, The University of Texas Rio Grande Valley, Edinburg, TX, USA
| | - Peiwen Li
- Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ, USA
| |
Collapse
|
4
|
Lambrecht DS. Generalizing energy decomposition analysis to response properties to inform expedited predictive models. COMPUT THEOR CHEM 2019. [DOI: 10.1016/j.comptc.2018.12.009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
5
|
Peng B, Kowalski K. Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations. J Chem Theory Comput 2017; 13:4179-4192. [DOI: 10.1021/acs.jctc.7b00605] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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
| | - 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
| |
Collapse
|
6
|
Negre CFA, Mniszewski SM, Cawkwell MJ, Bock N, Wall ME, Niklasson AMN. Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations. J Chem Theory Comput 2016; 12:3063-73. [DOI: 10.1021/acs.jctc.6b00154] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Christian F. A. Negre
- Theoretical Division and ‡Computer, Computational, and Statistical Sciences
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Susan M. Mniszewski
- Theoretical Division and ‡Computer, Computational, and Statistical Sciences
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Marc J. Cawkwell
- Theoretical Division and ‡Computer, Computational, and Statistical Sciences
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Nicolas Bock
- Theoretical Division and ‡Computer, Computational, and Statistical Sciences
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Michael E. Wall
- Theoretical Division and ‡Computer, Computational, and Statistical Sciences
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Anders M. N. Niklasson
- Theoretical Division and ‡Computer, Computational, and Statistical Sciences
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| |
Collapse
|
7
|
Hoy EP, Mazziotti DA. Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure. J Chem Phys 2015; 143:064103. [DOI: 10.1063/1.4928064] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Erik P. Hoy
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A. Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| |
Collapse
|
8
|
Osei-Kuffuor D, Fattebert JL. Accurate and scalable O(N) algorithm for first-principles molecular-dynamics computations on large parallel computers. PHYSICAL REVIEW LETTERS 2014; 112:046401. [PMID: 24580471 DOI: 10.1103/physrevlett.112.046401] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2013] [Indexed: 05/21/2023]
Abstract
We present the first truly scalable first-principles molecular dynamics algorithm with O(N) complexity and controllable accuracy, capable of simulating systems with finite band gaps of sizes that were previously impossible with this degree of accuracy. By avoiding global communications, we provide a practical computational scheme capable of extreme scalability. Accuracy is controlled by the mesh spacing of the finite difference discretization, the size of the localization regions in which the electronic wave functions are confined, and a cutoff beyond which the components of the overlap matrix can be omitted when computing selected elements of its inverse. We demonstrate the algorithm's excellent parallel scaling for up to 101,952 atoms on 23,328 processors, with a wall-clock time of the order of 1 min per molecular dynamics time step and numerical error on the forces of less than 7×10(-4) Ha/Bohr.
Collapse
Affiliation(s)
- Daniel Osei-Kuffuor
- Center for Applied Scientific Computing, L-561, Lawrence Livermore National Laboratory, Livermore, California 94551, USA
| | - Jean-Luc Fattebert
- Center for Applied Scientific Computing, L-561, Lawrence Livermore National Laboratory, Livermore, California 94551, USA
| |
Collapse
|
9
|
Guo Y, Li W, Li S. An efficient linear scaling procedure for constructing localized orbitals of large molecules based on the one-particle density matrix. J Chem Phys 2011; 135:134107. [DOI: 10.1063/1.3644893] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
10
|
Lambrecht DS, Brandhorst K, Miller WH, McCurdy CW, Head-Gordon M. A Kinetic Energy Fitting Metric for Resolution of the Identity Second-Order Møller−Plesset Perturbation Theory. J Phys Chem A 2011; 115:2794-801. [DOI: 10.1021/jp108218w] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Daniel S. Lambrecht
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Kai Brandhorst
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - William H. Miller
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - C. William McCurdy
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Department of Chemistry, University of California, Davis, California 95616, United States
| | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| |
Collapse
|