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Yin C, Becker SB, Thorpe JH, Matthews DA. Spatial Signatures of Electron Correlation in Least-Squares Tensor Hypercontraction. J Phys Chem A 2025; 129:788-802. [PMID: 39784297 DOI: 10.1021/acs.jpca.4c06666] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2025]
Abstract
Least-squares tensor hypercontraction (LS-THC) has received some attention in recent years as an approach to reduce the significant computational costs of wave function-based methods in quantum chemistry. However, previous work has demonstrated that LS-THC factorization performs disproportionately worse in the description of wave function components (e.g., cluster amplitudes T̂2) than Hamiltonian components (e.g., electron repulsion integrals (pq|rs)). This work develops novel theoretical methods to study the source of these errors in the context of the real-space T̂2 kernel, and reports, for the first time, the existence of a "correlation feature" in the errors of the LS-THC representation of the "exchange-like" correlation energy EX and T̂2 that is remarkably consistent across ten molecular species, three correlated wave functions, and four basis sets. This correlation feature portends the existence of a "pair point kernel" missing in the usual LS-THC representation of the wave function, which critically depends upon pairs of grid points situated close to atoms and with interpair distances between one and two Bohr radii. These findings point the way for future LS-THC developments to address these shortcomings.
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Affiliation(s)
- Chao Yin
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Sara Beth Becker
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - James H Thorpe
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Devin A Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
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2
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Pokhilko P, Yeh CN, Morales MA, Zgid D. Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: Theory, implementation, and role of the Green's function second-order exchange for intermolecular interactions. J Chem Phys 2024; 161:084108. [PMID: 39185845 DOI: 10.1063/5.0215954] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2024] [Accepted: 08/05/2024] [Indexed: 08/27/2024] Open
Abstract
We present an efficient MPI-parallel algorithm and its implementation for evaluating the self-consistent correlated second-order exchange term (SOX), which is employed as a correction to the fully self-consistent GW scheme called scGWSOX (GW plus the SOX term iterated to achieve full Green's function self-consistency). Due to the application of the tensor hypercontraction (THC) in our computational procedure, the scaling of the evaluation of scGWSOX is reduced from O(nτnAO5) to O(nτN2nAO2). This fully MPI-parallel and THC-adapted approach enabled us to conduct the largest fully self-consistent scGWSOX calculations with over 1100 atomic orbitals with only negligible errors attributed to THC fitting. Utilizing our THC implementation for scGW, scGF2, and scGWSOX, we evaluated energies of intermolecular interactions. This approach allowed us to circumvent issues related to reference dependence and ambiguity in energy evaluation, which are common challenges in non-self-consistent calculations. We demonstrate that scGW exhibits a slight overbinding tendency for large systems, contrary to the underbinding observed with non-self-consistent RPA. Conversely, scGWSOX exhibits a slight underbinding tendency for such systems. This behavior is both physical and systematic and is caused by exclusion-principle violating diagrams or corresponding corrections. Our analysis elucidates the role played by these different diagrams, which is crucial for the construction of rigorous, accurate, and systematic methods. Finally, we explicitly show that all perturbative fully self-consistent Green's function methods are size-extensive and size-consistent.
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Affiliation(s)
- Pavel Pokhilko
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Chia-Nan Yeh
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Miguel A Morales
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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3
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Datar A, Matthews DA. Robust Tensor Hypercontraction of the Particle-Particle Ladder Term in Equation-of-Motion Coupled Cluster Theory. J Chem Theory Comput 2024; 20:708-720. [PMID: 38198505 DOI: 10.1021/acs.jctc.3c00892] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
One method of representing a high-rank tensor as a (hyper-)product of lower-rank tensors is the tensor hypercontraction (THC) method of Hohenstein et al. This strategy has been found to be useful for reducing the polynomial scaling of coupled-cluster methods by representation of a four-dimensional tensor of electron-repulsion integrals in terms of five two-dimensional matrices. Pierce et al. have already shown that the application of a robust form of THC to the particle-particle ladder (PPL) term reduces the cost of this term in couple-cluster singles and doubles (CCSD) from O ( N 6 ) to O ( N 5 ) with negligible errors in energy with respect to the density-fitted variant. In this work, we have implemented the least-squares variant of THC (LS-THC) which does not require a nonlinear tensor factorization, including the robust form (R-LS-THC), for the calculation of the excitation and electron attachment energies using equation-of-motion coupled cluster methods EOMEE-CCSD and EOMEA-CCSD, respectively. We have benchmarked the effect of the R-LS-THC-PPL approximation on excitation energies using the comprehensive QUEST database and the accuracy of electron attachment energies using the NAB22 database. We find that errors on the order of 1 meV are achievable with a reduction in total calculation time of approximately 5 ×.
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Affiliation(s)
- Avdhoot Datar
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Devin A Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
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4
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Cieśliński D, Tucholska AM, Modrzejewski M. Post-Kohn-Sham Random-Phase Approximation and Correction Terms in the Expectation-Value Coupled-Cluster Formulation. J Chem Theory Comput 2023; 19:6619-6631. [PMID: 37774375 PMCID: PMC10569055 DOI: 10.1021/acs.jctc.3c00496] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Indexed: 10/01/2023]
Abstract
Using expectation-value coupled-cluster theory and many-body perturbation theory (MBPT), we formulate a series of corrections to the post-Kohn-Sham (post-KS) random-phase approximation (RPA) energy. The beyond-RPA terms are of two types: those accounting for the non-Hartree-Fock reference and those introducing the coupled-cluster doubles non-ring contractions. The contributions of the former type, introduced via the semicanonical orbital basis, drastically reduce the binding strength in noncovalent systems. The good accuracy is recovered by the attractive third-order doubles correction referred to as Ec2g. The existing RPA approaches based on KS orbitals neglect most of the proposed corrections but can perform well thanks to error cancellation. The proposed method accounts for every contribution in the state-of-the-art renormalized second-order perturbation theory (rPT2) approach but adds additional terms which initially contribute in the third order of MBPT. The cost of energy evaluation scales as noniterative O ( N 4 ) in the implementation with low-rank tensor decomposition. The numerical tests of the proposed approach demonstrate accurate results for noncovalent dimers of polar molecules and for the challenging many-body noncovalent cluster of CH4···(H2O)20.
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Affiliation(s)
- Dominik Cieśliński
- Faculty
of Chemistry, University of Warsaw, Pasteura 1, Warsaw 02-093, Poland
| | | | - Marcin Modrzejewski
- Faculty
of Chemistry, University of Warsaw, Pasteura 1, Warsaw 02-093, Poland
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5
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Pierce K, Valeev EF. Efficient Construction of Canonical Polyadic Approximations of Tensor Networks. J Chem Theory Comput 2023; 19:71-81. [PMID: 36484711 DOI: 10.1021/acs.jctc.2c00861] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
We consider the problem of constructing a canonical polyadic (CP) decomposition for a tensor network, rather than a single tensor. We illustrate how it is possible to reduce the complexity of constructing an approximate CP representation of the network by leveraging its structure in the course of the CP factor optimization. The utility of this technique is demonstrated for the order-4 Coulomb interaction tensor approximated by two order-3 tensors via an approximate generalized square-root (SQ) factorization, such as density fitting or (pivoted) Cholesky. The complexity of constructing a four-way CP decomposition is reduced from O(n4RCP) (for the nonapproximated Coulomb tensor) to O(n3RCP) (for the SQ-factorized Coulomb tensor), where n and RCP are the basis and CP ranks, respectively. This reduces the cost of constructing the CP approximation of two-body interaction tensors of relevance to accurate many-body electronic structure by up to 2 orders of magnitude for systems with up to 36 atoms studied here. The full four-way CP approximation of the Coulomb interaction tensor is shown to be more accurate than the known approaches which utilize CP-factorizations of the SQ factors (which are also constructed with an O(n3RCP) cost), such as the algebraic pseudospectral and tensor hypercontraction approaches. The CP-decomposed SQ factors can also serve as a robust initial guess for the four-way CP factors.
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Affiliation(s)
- Karl Pierce
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia24061, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia24061, United States
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6
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Woo J, Kim WY, Choi S. System-Specific Separable Basis Based on Tucker Decomposition: Application to Density Functional Calculations. J Chem Theory Comput 2022; 18:2875-2884. [PMID: 35437014 PMCID: PMC9098162 DOI: 10.1021/acs.jctc.1c01263] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Indexed: 11/30/2022]
Abstract
For fast density functional calculations, a suitable basis that can accurately represent the orbitals within a reasonable number of dimensions is essential. Here, we propose a new type of basis constructed from Tucker decomposition of a finite-difference (FD) Hamiltonian matrix, which is intended to reflect the system information implied in the Hamiltonian matrix and satisfies orthonormality and separability conditions. By introducing the system-specific separable basis, the computation time for FD density functional calculations for seven two- and three-dimensional periodic systems was reduced by a factor of 2-71 times, while the errors in both the atomization energy per atom and the band gap were limited to less than 0.1 eV. The accuracy and speed of the density functional calculations with the proposed basis can be systematically controlled by adjusting the rank size of Tucker decomposition.
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Affiliation(s)
- Jeheon Woo
- Department
of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea
| | - Woo Youn Kim
- Department
of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea
| | - Sunghwan Choi
- National
Institute of Supercomputing and Networking, Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea
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7
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Lesiuk M. Quintic-scaling rank-reduced coupled cluster theory with single and double excitations. J Chem Phys 2022; 156:064103. [DOI: 10.1063/5.0071916] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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8
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Lesiuk M. Near-Exact CCSDT Energetics from Rank-Reduced Formalism Supplemented by Non-iterative Corrections. J Chem Theory Comput 2021; 17:7632-7647. [PMID: 34860018 DOI: 10.1021/acs.jctc.1c00933] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We introduce a non-iterative energy correction, added on top of the rank-reduced coupled-cluster method with single, double, and triple substitutions, that accounts for excitations excluded from the parent triple excitation subspace. The formula for the correction is derived by employing the coupled-cluster Lagrangian formalism, with an additional assumption that the parent excitation subspace is closed under the action of the Fock operator. Owing to the rank-reduced form of the triple excitation amplitudes tensor, the computational cost of evaluating the correction scales as N7, where N is the system size. The accuracy and computational efficiency of the proposed method is assessed for both total and relative correlation energies. We show that the non-iterative correction can fulfill two separate roles. If the accuracy level of a fraction of kJ/mol is sufficient for a given system, the correction significantly reduces the dimension of the parent triple excitation subspace needed in the iterative part of the calculations. Simultaneously, it enables reproducing the exact CCSDT results to an accuracy level below 0.1 kJ/mol, with a larger, yet still reasonable, dimension of the parent excitation subspace. This typically can be achieved at a computational cost only several times larger than required for the CCSD(T) method. The proposed method retains the black-box features of the single-reference coupled-cluster theory; the dimension of the parent excitation subspace remains the only additional parameter that has to be specified.
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Affiliation(s)
- Michał Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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9
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Datta D, Gordon MS. A Massively Parallel Implementation of the CCSD(T) Method Using the Resolution-of-the-Identity Approximation and a Hybrid Distributed/Shared Memory Parallelization Model. J Chem Theory Comput 2021; 17:4799-4822. [PMID: 34279094 DOI: 10.1021/acs.jctc.1c00389] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A parallel algorithm is described for the coupled-cluster singles and doubles method augmented with a perturbative correction for triple excitations [CCSD(T)] using the resolution-of-the-identity (RI) approximation for two-electron repulsion integrals (ERIs). The algorithm bypasses the storage of four-center ERIs by adopting an integral-direct strategy. The CCSD amplitude equations are given in a compact quasi-linear form by factorizing them in terms of amplitude-dressed three-center intermediates. A hybrid MPI/OpenMP parallelization scheme is employed, which uses the OpenMP-based shared memory model for intranode parallelization and the MPI-based distributed memory model for internode parallelization. Parallel efficiency has been optimized for all terms in the CCSD amplitude equations. Two different algorithms have been implemented for the rate-limiting terms in the CCSD amplitude equations that entail O(NO2NV4) and O(NO3NV3)-scaling computational costs, where NO and NV denote the number of correlated occupied and virtual orbitals, respectively. One of the algorithms assembles the four-center ERIs requiring NV4 and NO2NV2-scaling memory costs in a distributed manner on a number of MPI ranks, while the other algorithm completely bypasses the assembling of quartic memory-scaling ERIs and thus largely reduces the memory demand. It is demonstrated that the former memory-expensive algorithm is faster on a few hundred cores, while the latter memory-economic algorithm shows a better strong scaling in the limit of a few thousand cores. The program is shown to exhibit a near-linear scaling, in particular for the compute-intensive triples correction step, on up to 8000 cores. The performance of the program is demonstrated via calculations involving molecules with 24-51 atoms and up to 1624 atomic basis functions. As the first application, the complete basis set (CBS) limit for the interaction energy of the π-stacked uracil dimer from the S66 data set has been investigated. This work reports the first calculation of the interaction energy at the CCSD(T)/aug-cc-pVQZ level without local orbital approximation. The CBS limit for the CCSD correlation contribution to the interaction energy was found to be -8.01 kcal/mol, which agrees very well with the value -7.99 kcal/mol reported by Schmitz, Hättig, and Tew [ Phys. Chem. Chem. Phys. 2014, 16, 22167-22178]. The CBS limit for the total interaction energy was estimated to be -9.64 kcal/mol.
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Affiliation(s)
- Dipayan Datta
- Department of Chemistry and Ames Laboratory, Iowa State University, 2416 Pammel Drive, Ames 50011-2416, Iowa United States of America
| | - Mark S Gordon
- Department of Chemistry and Ames Laboratory, Iowa State University, 2416 Pammel Drive, Ames 50011-2416, Iowa United States of America
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10
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Pierce K, Rishi V, Valeev EF. Robust Approximation of Tensor Networks: Application to Grid-Free Tensor Factorization of the Coulomb Interaction. J Chem Theory Comput 2021; 17:2217-2230. [PMID: 33780616 DOI: 10.1021/acs.jctc.0c01310] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Approximation of a tensor network by approximating (e.g., factorizing) one or more of its constituent tensors can be improved by canceling the leading-order error due to the constituents' approximation. The utility of such robust approximation is demonstrated for robust canonical polyadic (CP) approximation of a (density-fitting) factorized two-particle Coulomb interaction tensor. The resulting algebraic (grid-free) approximation for the Coulomb tensor, closely related to the factorization appearing in pseudospectral and tensor hypercontraction approaches, is efficient and accurate, with significantly reduced rank compared to the naive (nonrobust) approximation. Application of the robust approximation to the particle-particle ladder term in the coupled-cluster singles and doubles reduces the size complexity from O (N6) to O (N5) with robustness ensuring negligible errors in chemically relevant energy differences using CP ranks approximately equal to the size of the density-fitting basis.
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Affiliation(s)
- Karl Pierce
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Varun Rishi
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
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11
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Matthews DA. A critical analysis of least-squares tensor hypercontraction applied to MP3. J Chem Phys 2021; 154:134102. [PMID: 33832252 DOI: 10.1063/5.0038764] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The least-squares tensor hypercontraction (LS-THC) approach is a promising method of reducing the high polynomial scaling of wavefunction methods, for example, those based on many-body perturbation theory or coupled cluster. Here, we focus on LS-THC-MP3 and identify four variants with differing errors and efficiency characteristics. The performance of LS-THC-MP3 is analyzed for regular test systems with up to 40 first-row atoms. We also analyze the size-extensivity/size-consistency and grid- and basis set dependence of LS-THC-MP3. Overall, the errors observed are favorably small in comparison with standard density fitting, and a more streamlined method of generating grids via pruning is suggested. A practical crossover (the point at which LS-THC-MP3 is cheaper than the canonical method) is achieved around 240 correlated electrons. Despite several drawbacks of LS-THC that have been identified: an initial non-linearity of error when increasing system size, poor description of angular correlation, and a potentially large increase in error with the basis set size, the results show that LS-THC has significant potential for practical application to MP3 and other wavefunction methods.
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12
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Calvin JA, Peng C, Rishi V, Kumar A, Valeev EF. Many-Body Quantum Chemistry on Massively Parallel Computers. Chem Rev 2020; 121:1203-1231. [DOI: 10.1021/acs.chemrev.0c00006] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Justus A. Calvin
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Varun Rishi
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Ashutosh Kumar
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
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13
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Lesiuk M. A straightforward a posteriori method for reduction of density-fitting error in coupled-cluster calculations. J Chem Phys 2020; 152:044104. [PMID: 32007079 DOI: 10.1063/1.5129883] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a simple method for a posteriori removal of a significant fraction of the density-fitting error from the calculated total coupled-cluster energies. The method treats the difference between the exact and density-fitted integrals as a perturbation, and simplified response-like equations allow us to calculate improved amplitudes and the corresponding energy correction. The proposed method is tested at the coupled-cluster singles and doubles level of theory for a diverse set of moderately-sized molecules. On average, error reductions by a factor of approximately 10 and 20 are observed in double-zeta and triple-zeta basis sets, respectively. Similar reductions are observed in calculations of interaction energies of several model complexes. The computational cost of the procedure is small in comparison with the preceding coupled-cluster iterations. The applicability of this method is not limited to the density-fitting approximation; in principle, it can be used in conjunction with an arbitrary decomposition scheme of the electron repulsion integrals.
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Affiliation(s)
- Michał Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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14
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Lesiuk M. Implementation of the Coupled-Cluster Method with Single, Double, and Triple Excitations using Tensor Decompositions. J Chem Theory Comput 2019; 16:453-467. [DOI: 10.1021/acs.jctc.9b00985] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Michał Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, Warsaw, 02-093, Poland
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15
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Motta M, Shee J, Zhang S, Chan GKL. Efficient Ab Initio Auxiliary-Field Quantum Monte Carlo Calculations in Gaussian Bases via Low-Rank Tensor Decomposition. J Chem Theory Comput 2019; 15:3510-3521. [DOI: 10.1021/acs.jctc.8b00996] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mario Motta
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - James Shee
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Shiwei Zhang
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23187-8795, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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16
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Parrish RM, Zhao Y, Hohenstein EG, Martínez TJ. Rank reduced coupled cluster theory. I. Ground state energies and wavefunctions. J Chem Phys 2019; 150:164118. [DOI: 10.1063/1.5092505] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Robert M. Parrish
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
| | - Yao Zhao
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
- Department of Chemistry and Biochemistry, The City College of New York, New York, New York 10031, USA
- Ph.D. Program in Chemistry, The Graduate Center, City University of New York, New York, New York 10016, USA
| | - Edward G. Hohenstein
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
- Department of Chemistry and Biochemistry, The City College of New York, New York, New York 10031, USA
- Ph.D. Program in Chemistry, The Graduate Center, City University of New York, New York, New York 10016, USA
| | - Todd J. Martínez
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
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17
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Lesiuk M. Efficient singular‐value decomposition of the coupled‐cluster triple excitation amplitudes. J Comput Chem 2019; 40:1319-1332. [DOI: 10.1002/jcc.25788] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2018] [Revised: 01/06/2019] [Accepted: 01/08/2019] [Indexed: 11/08/2022]
Affiliation(s)
- Michal Lesiuk
- Faculty of ChemistryUniversity of Warsaw Pasteura 1, 02‐093, Warsaw Poland
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18
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Schmitz G, Christiansen O. Assessment of the overlap metric in the context of RI-MP2 and atomic batched tensor decomposed MP2. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.04.014] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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19
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Madsen NK, Godtliebsen IH, Losilla SA, Christiansen O. Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations. J Chem Phys 2018; 148:024103. [DOI: 10.1063/1.5001569] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | | | | | - Ove Christiansen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
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20
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Schutski R, Zhao J, Henderson TM, Scuseria GE. Tensor-structured coupled cluster theory. J Chem Phys 2017; 147:184113. [DOI: 10.1063/1.4996988] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roman Schutski
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA
| | - Jinmo Zhao
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
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21
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Wirz LN, Reine SS, Pedersen TB. On Resolution-of-the-Identity Electron Repulsion Integral Approximations and Variational Stability. J Chem Theory Comput 2017; 13:4897-4906. [DOI: 10.1021/acs.jctc.7b00801] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Lukas N. Wirz
- Hylleraas Centre for Quantum
Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033
Blindern, N-0315 Oslo, Norway
| | - Simen S. Reine
- Hylleraas Centre for Quantum
Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033
Blindern, N-0315 Oslo, Norway
| | - Thomas Bondo Pedersen
- Hylleraas Centre for Quantum
Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033
Blindern, N-0315 Oslo, Norway
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22
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Mayhall NJ. Using Higher-Order Singular Value Decomposition To Define Weakly Coupled and Strongly Correlated Clusters: The n-Body Tucker Approximation. J Chem Theory Comput 2017; 13:4818-4828. [DOI: 10.1021/acs.jctc.7b00696] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Affiliation(s)
- Nicholas J. Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
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23
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Manthe U. Wavepacket dynamics and the multi-configurational time-dependent Hartree approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:253001. [PMID: 28430111 DOI: 10.1088/1361-648x/aa6e96] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.
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Affiliation(s)
- Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
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24
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Schmitz G, Madsen NK, Christiansen O. Atomic-batched tensor decomposed two-electron repulsion integrals. J Chem Phys 2017; 146:134112. [DOI: 10.1063/1.4979571] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gunnar Schmitz
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
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25
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Madsen NK, Godtliebsen IH, Christiansen O. Efficient algorithms for solving the non-linear vibrational coupled-cluster equations using full and decomposed tensors. J Chem Phys 2017; 146:134110. [DOI: 10.1063/1.4979498] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Niels K. Madsen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
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26
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Böhm KH, Auer AA, Espig M. Tensor representation techniques for full configuration interaction: A Fock space approach using the canonical product format. J Chem Phys 2016; 144:244102. [DOI: 10.1063/1.4953665] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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27
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Jones JR, Rouet FH, Lawler KV, Vecharynski E, Ibrahim KZ, Williams S, Abeln B, Yang C, McCurdy W, Haxton DJ, Li XS, Rescigno TN. An efficient basis set representation for calculating electrons in molecules. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1176262] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Jeremiah R. Jones
- Chemical Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | | | - Keith V. Lawler
- Department of Chemistry, University of Nevada-Las Vegas, Las Vegas, NV, USA
| | - Eugene Vecharynski
- Computing Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Khaled Z. Ibrahim
- Computing Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Samuel Williams
- Computing Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Brant Abeln
- Department of Chemistry, University of California, Davis, Davis, CA, USA
- Ultrafast X-Ray Science Laboratory, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Chemical Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Chao Yang
- Computing Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - William McCurdy
- Department of Chemistry, University of California, Davis, Davis, CA, USA
- Ultrafast X-Ray Science Laboratory, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Chemical Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Daniel J. Haxton
- Ultrafast X-Ray Science Laboratory, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Chemical Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Xiaoye S. Li
- Computing Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Thomas N. Rescigno
- Chemical Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
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28
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Lötstedt E, Kato T, Yamanouchi K. Decomposition of the configuration-interaction coefficients in the multiconfiguration time-dependent Hartree-Fock method. J Chem Phys 2016; 144:154111. [DOI: 10.1063/1.4947018] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Erik Lötstedt
- Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Tsuyoshi Kato
- Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Kaoru Yamanouchi
- Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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29
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Brabec J, Yang C, Epifanovsky E, Krylov AI, Ng E. Reduced‐cost sparsity‐exploiting algorithm for solving coupled‐cluster equations. J Comput Chem 2016; 37:1059-67. [DOI: 10.1002/jcc.24293] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Revised: 10/21/2015] [Accepted: 12/17/2015] [Indexed: 01/17/2023]
Affiliation(s)
- Jiri Brabec
- Computational Research DivisionLawrence Berkeley National LaboratoryBerkeley California94720
| | - Chao Yang
- Computational Research DivisionLawrence Berkeley National LaboratoryBerkeley California94720
| | - Evgeny Epifanovsky
- Department of ChemistryUniversity of Southern CaliforniaLos Angeles California90089‐0482
- Q‐Chem IncSuite 105 Pleasanton California94588
| | - Anna I. Krylov
- Department of ChemistryUniversity of Southern CaliforniaLos Angeles California90089‐0482
| | - Esmond Ng
- Computational Research DivisionLawrence Berkeley National LaboratoryBerkeley California94720
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30
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Kállay M. A systematic way for the cost reduction of density fitting methods. J Chem Phys 2015; 141:244113. [PMID: 25554139 DOI: 10.1063/1.4905005] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Abstract
We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of three-center two-electron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of the computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of three-center Coulomb integrals is a bottleneck.
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Affiliation(s)
- Mihály Kállay
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
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31
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Kokkila Schumacher SIL, Hohenstein EG, Parrish RM, Wang LP, Martínez TJ. Tensor Hypercontraction Second-Order Møller–Plesset Perturbation Theory: Grid Optimization and Reaction Energies. J Chem Theory Comput 2015; 11:3042-52. [DOI: 10.1021/acs.jctc.5b00272] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Sara I. L. Kokkila Schumacher
- Department
of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
| | - Edward G. Hohenstein
- Department
of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
- Department
of Chemistry and Biochemistry, City College of New York, New York, New York 10031, United States
| | - Robert M. Parrish
- Center
for Computational Molecular Science and Technology, School of Chemistry
and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States
| | - Lee-Ping Wang
- Department
of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
| | - Todd J. Martínez
- Department
of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
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32
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First principles approach to the electronic structure, magnetic anisotropy and spin relaxation in mononuclear 3d-transition metal single molecule magnets. Coord Chem Rev 2015. [DOI: 10.1016/j.ccr.2014.10.015] [Citation(s) in RCA: 225] [Impact Index Per Article: 22.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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33
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Godtliebsen IH, Hansen MB, Christiansen O. Tensor decomposition techniques in the solution of vibrational coupled cluster response theory eigenvalue equations. J Chem Phys 2015; 142:024105. [DOI: 10.1063/1.4905160] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
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34
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Leclerc A, Carrington T. Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices. J Chem Phys 2014; 140:174111. [DOI: 10.1063/1.4871981] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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Benedikt U, Böhm KH, Auer AA. Tensor decomposition in post-Hartree–Fock methods. II. CCD implementation. J Chem Phys 2013; 139:224101. [DOI: 10.1063/1.4833565] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
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36
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Epifanovsky E, Zuev D, Feng X, Khistyaev K, Shao Y, Krylov AI. General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: Theory and benchmarks. J Chem Phys 2013; 139:134105. [DOI: 10.1063/1.4820484] [Citation(s) in RCA: 103] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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37
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Benedikt U, Auer H, Espig M, Hackbusch W, Auer AA. Tensor representation techniques in post-Hartree–Fock methods: matrix product state tensor format. Mol Phys 2013. [DOI: 10.1080/00268976.2013.798433] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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38
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Grasedyck L, Kressner D, Tobler C. A literature survey of low-rank tensor approximation techniques. ACTA ACUST UNITED AC 2013. [DOI: 10.1002/gamm.201310004] [Citation(s) in RCA: 343] [Impact Index Per Article: 28.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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39
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Hoy EP, Shenvi N, Mazziotti DA. Comparison of low-rank tensor expansions for the acceleration of quantum chemistry computations. J Chem Phys 2013; 139:034105. [DOI: 10.1063/1.4813495] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
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40
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Parker SM, Seideman T, Ratner MA, Shiozaki T. Communication: Active-space decomposition for molecular dimers. J Chem Phys 2013; 139:021108. [DOI: 10.1063/1.4813827] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
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41
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Yachmenev A, Klopper W. A composite ‘density fitting + numerical integration’ approximation for electron-repulsion integrals. Mol Phys 2013. [DOI: 10.1080/00268976.2013.800265] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Andrey Yachmenev
- a Karlsruhe Institute of Technology (KIT) , Institute of Physical Chemistry, Theoretical Chemistry Group , Karlsruhe , Germany
| | - Wim Klopper
- a Karlsruhe Institute of Technology (KIT) , Institute of Physical Chemistry, Theoretical Chemistry Group , Karlsruhe , Germany
- b Karlsruhe Institute of Technology (KIT) , Institute of Nanotechnology, Theoretical Chemistry Group , Karlsruhe , Germany
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42
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Godtliebsen IH, Thomsen B, Christiansen O. Tensor Decomposition and Vibrational Coupled Cluster Theory. J Phys Chem A 2013; 117:7267-79. [DOI: 10.1021/jp401153q] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Bo Thomsen
- Department of Chemistry, Aarhus University, Aarhus, Denmark
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43
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Peláez D, Meyer HD. The multigrid POTFIT (MGPF) method: Grid representations of potentials for quantum dynamics of large systems. J Chem Phys 2013; 138:014108. [DOI: 10.1063/1.4773021] [Citation(s) in RCA: 78] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
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44
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Schwerdtfeger CA, Mazziotti DA. Low-rank spectral expansions of two electron excitations for the acceleration of quantum chemistry calculations. J Chem Phys 2012; 137:244103. [DOI: 10.1063/1.4770278] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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45
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Uemura W, Sugino O. Symmetric tensor decomposition description of fermionic many-body wave functions. PHYSICAL REVIEW LETTERS 2012; 109:253001. [PMID: 23368456 DOI: 10.1103/physrevlett.109.253001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2012] [Indexed: 06/01/2023]
Abstract
The configuration interaction (CI) is a versatile wave function theory for interacting fermions, but it involves an extremely long CI series. Using a symmetric tensor decomposition method, we convert the CI series into a compact and numerically tractable form. The converted series encompasses the Hartree-Fock state in the first term and rapidly converges to the full-CI state, as numerically tested by using small molecules. Provided that the length of the symmetric tensor decomposition CI series grows only moderately with the increasing complexity of the system, the new method will serve as one of the alternative variational methods to achieve full CI with enhanced practicability.
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Affiliation(s)
- Wataru Uemura
- The Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan
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46
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Parrish RM, Hohenstein EG, Martínez TJ, Sherrill CD. Tensor hypercontraction. II. Least-squares renormalization. J Chem Phys 2012; 137:224106. [DOI: 10.1063/1.4768233] [Citation(s) in RCA: 159] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
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47
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Hohenstein EG, Parrish RM, Sherrill CD, Martínez TJ. Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions. J Chem Phys 2012; 137:221101. [DOI: 10.1063/1.4768241] [Citation(s) in RCA: 114] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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48
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Hohenstein EG, Parrish RM, Martínez TJ. Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory. J Chem Phys 2012; 137:044103. [DOI: 10.1063/1.4732310] [Citation(s) in RCA: 210] [Impact Index Per Article: 16.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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49
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Yang J, Chan GKL, Manby FR, Schütz M, Werner HJ. The orbital-specific-virtual local coupled cluster singles and doubles method. J Chem Phys 2012; 136:144105. [DOI: 10.1063/1.3696963] [Citation(s) in RCA: 150] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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50
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Limpanuparb T, Hollett JW, Gill PMW. Resolutions of the Coulomb operator. VI. Computation of auxiliary integrals. J Chem Phys 2012; 136:104102. [PMID: 22423823 DOI: 10.1063/1.3691829] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb operator [T. Limpanuparb, A. T. B. Gilbert, and P. M. W. Gill, J. Chem. Theory Comput. 7, 830 (2011)] and the long-range Ewald operator [T. Limpanuparb and P. M. W. Gill, J. Chem. Theory Comput. 7, 2353 (2011)]) are employed in quantum chemical calculations. We derive a recurrence relation that facilitates the generation of auxiliary integrals for Gaussian basis functions of arbitrary angular momentum and propose a near-optimal algorithm for its use.
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Affiliation(s)
- Taweetham Limpanuparb
- Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia.
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