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Park JW, Al-Saadon R, MacLeod MK, Shiozaki T, Vlaisavljevich B. Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces. Chem Rev 2020; 120:5878-5909. [PMID: 32239929 DOI: 10.1021/acs.chemrev.9b00496] [Citation(s) in RCA: 54] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.
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Affiliation(s)
- Jae Woo Park
- Department of Chemistry, Chungbuk National University, Chungdae-ro 1, Cheongju 28644, Korea
| | - Rachael Al-Saadon
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
| | - Matthew K MacLeod
- Workday, 4900 Pearl Circle East, Suite 100, Boulder, Colorado 80301, United States
| | - Toru Shiozaki
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States.,Quantum Simulation Technologies, Inc., 625 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Bess Vlaisavljevich
- Department of Chemistry, University of South Dakota, 414 East Clark Street, Vermillion, South Dakota 57069, United States
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Rolik Z, Kállay M. Novel strategy to implement active-space coupled-cluster methods. J Chem Phys 2018; 148:124108. [PMID: 29604813 DOI: 10.1063/1.5004971] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new approach is presented for the efficient implementation of coupled-cluster (CC) methods including higher excitations based on a molecular orbital space partitioned into active and inactive orbitals. In the new framework, the string representation of amplitudes and intermediates is used as long as it is beneficial, but the contractions are evaluated as matrix products. Using a new diagrammatic technique, the CC equations are represented in a compact form due to the string notations we introduced. As an application of these ideas, a new automated implementation of the single-reference-based multi-reference CC equations is presented for arbitrary excitation levels. The new program can be considered as an improvement over the previous implementations in many respects; e.g., diagram contributions are evaluated by efficient vectorized subroutines. Timings for test calculations for various complete active-space problems are presented. As an application of the new code, the weak interactions in the Be dimer were studied.
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Affiliation(s)
- Zoltán Rolik
- MTA-BME "Lendület" Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
| | - Mihály Kállay
- MTA-BME "Lendület" Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
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Lehtola S, Tubman NM, Whaley KB, Head-Gordon M. Cluster decomposition of full configuration interaction wave functions: A tool for chemical interpretation of systems with strong correlation. J Chem Phys 2017; 147:154105. [DOI: 10.1063/1.4996044] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Susi Lehtola
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Norm M. Tubman
- University of California, Berkeley, California 94720, USA
| | | | - Martin Head-Gordon
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- University of California, Berkeley, California 94720, USA
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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
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Manzer S, Epifanovsky E, Krylov AI, Head-Gordon M. A General Sparse Tensor Framework for Electronic Structure Theory. J Chem Theory Comput 2017; 13:1108-1116. [DOI: 10.1021/acs.jctc.6b00853] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Samuel Manzer
- Kenneth
S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California − Berkeley, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Evgeny Epifanovsky
- Q-Chem, Inc., 6601 Owens
Drive, Suite 105, Pleasanton, California 94588, United States
| | - Anna I. Krylov
- Department
of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | - Martin Head-Gordon
- Kenneth
S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California − Berkeley, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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Lehtola S, Parkhill J, Head-Gordon M. Cost-effective description of strong correlation: Efficient implementations of the perfect quadruples and perfect hextuples models. J Chem Phys 2016; 145:134110. [DOI: 10.1063/1.4964317] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Susi Lehtola
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - John Parkhill
- Department of Chemistry, University of Notre Dame, 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, USA
| | - Martin Head-Gordon
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Chemistry, University of California, Berkeley, California 94720, USA
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Yao K, Parkhill J. Kinetic Energy of Hydrocarbons as a Function of Electron Density and Convolutional Neural Networks. J Chem Theory Comput 2016; 12:1139-47. [PMID: 26812530 DOI: 10.1021/acs.jctc.5b01011] [Citation(s) in RCA: 73] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We demonstrate a convolutional neural network trained to reproduce the Kohn-Sham kinetic energy of hydrocarbons from an input electron density. The output of the network is used as a nonlocal correction to conventional local and semilocal kinetic functionals. We show that this approximation qualitatively reproduces Kohn-Sham potential energy surfaces when used with conventional exchange correlation functionals. The density which minimizes the total energy given by the functional is examined in detail. We identify several avenues to improve on this exploratory work, by reducing numerical noise and changing the structure of our functional. Finally we examine the features in the density learned by the neural network to anticipate the prospects of generalizing these models.
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Affiliation(s)
- Kun Yao
- Department of Chemistry, University of Notre Dame , 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, United States
| | - John Parkhill
- Department of Chemistry, University of Notre Dame , 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, United States
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MacLeod MK, Shiozaki T. Communication: Automatic code generation enables nuclear gradient computations for fully internally contracted multireference theory. J Chem Phys 2015; 142:051103. [DOI: 10.1063/1.4907717] [Citation(s) in RCA: 78] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Affiliation(s)
- Matthew K. MacLeod
- Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA
| | - Toru Shiozaki
- Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA
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Rolik Z, Szegedy L, Ladjánszki I, Ladóczki B, Kállay M. An efficient linear-scaling CCSD(T) method based on local natural orbitals. J Chem Phys 2014; 139:094105. [PMID: 24028100 DOI: 10.1063/1.4819401] [Citation(s) in RCA: 288] [Impact Index Per Article: 28.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An improved version of our general-order local coupled-cluster (CC) approach [Z. Rolik and M. Kállay, J. Chem. Phys. 135, 104111 (2011)] and its efficient implementation at the CC singles and doubles with perturbative triples [CCSD(T)] level is presented. The method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with frozen natural orbital (NO) techniques. To break down the unfavorable fifth-power scaling of our original approach a two-level domain construction algorithm has been developed. First, an extended domain of localized molecular orbitals (LMOs) is assembled based on the spatial distance of the orbitals. The necessary integrals are evaluated and transformed in these domains invoking the density fitting approximation. In the second step, for each occupied LMO of the extended domain a local subspace of occupied and virtual orbitals is constructed including approximate second-order Mo̸ller-Plesset NOs. The CC equations are solved and the perturbative corrections are calculated in the local subspace for each occupied LMO using a highly-efficient CCSD(T) code, which was optimized for the typical sizes of the local subspaces. The total correlation energy is evaluated as the sum of the individual contributions. The computation time of our approach scales linearly with the system size, while its memory and disk space requirements are independent thereof. Test calculations demonstrate that currently our method is one of the most efficient local CCSD(T) approaches and can be routinely applied to molecules of up to 100 atoms with reasonable basis sets.
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Affiliation(s)
- Zoltán Rolik
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, P.O. Box 91, Hungary
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Kats D, Manby FR. Sparse tensor framework for implementation of general local correlation methods. J Chem Phys 2013; 138:144101. [DOI: 10.1063/1.4798940] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
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Parkhill JA, Markovich T, Tempel DG, Aspuru-Guzik A. A correlated-polaron electronic propagator: Open electronic dynamics beyond the Born-Oppenheimer approximation. J Chem Phys 2012; 137:22A547. [DOI: 10.1063/1.4762441] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Rolik Z, Kállay M. A general-order local coupled-cluster method based on the cluster-in-molecule approach. J Chem Phys 2011; 135:104111. [DOI: 10.1063/1.3632085] [Citation(s) in RCA: 162] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
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Parkhill JA, Azar J, Head-Gordon M. The formulation and performance of a perturbative correction to the perfect quadruples model. J Chem Phys 2011; 134:154112. [DOI: 10.1063/1.3582729] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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Thom AJW. Stochastic coupled cluster theory. PHYSICAL REVIEW LETTERS 2010; 105:263004. [PMID: 21231654 DOI: 10.1103/physrevlett.105.263004] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2010] [Indexed: 05/30/2023]
Abstract
We describe a stochastic coupled cluster theory which represents excitation amplitudes as discrete excitors in the space of excitation amplitudes. Reexpressing the coupled cluster (CC) equations as the dynamics of excitors in this space, we show that a simple set of rules suffices to evolve a distribution of excitors to sample the CC solution and correctly evaluate the CC energy. These rules are not truncation specific and this method can calculate CC solutions to an arbitrary level of truncation. We present results of calculation on the neon atom, and nitrogen and water molecules showing the ability to recover both truncated and full CC results.
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Affiliation(s)
- Alex J W Thom
- Department of Chemistry, Imperial College London, London, United Kingdom.
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Parkhill JA, Head-Gordon M. A truncation hierarchy of coupled cluster models of strongly correlated systems based on perfect-pairing references: The singles+doubles models. J Chem Phys 2010; 133:124102. [DOI: 10.1063/1.3483556] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Parkhill JA, Head-Gordon M. A tractable and accurate electronic structure method for static correlations: The perfect hextuples model. J Chem Phys 2010; 133:024103. [DOI: 10.1063/1.3456001] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
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