1
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Sorathia K, Frantzov D, Tew DP. Improved CPS and CBS Extrapolation of PNO-CCSD(T) Energies: The MOBH35 and ISOL24 Data Sets. J Chem Theory Comput 2024; 20:2740-2750. [PMID: 38513261 PMCID: PMC11008106 DOI: 10.1021/acs.jctc.3c00974] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Revised: 03/06/2024] [Accepted: 03/08/2024] [Indexed: 03/23/2024]
Abstract
Computation of heats of reaction of large molecules is now feasible using the domain-based pair natural orbital (PNO)-coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] theory. However, to obtain agreement within 1 kcal/mol of experiment, it is necessary to eliminate basis set incompleteness error, which comprises both the AO basis set error and the PNO truncation error. Our investigation into the convergence to the canonical limit of PNO-CCSD(T) energies with the PNO truncation threshold T shows that errors follow the model E ( T ) = E + A T 1 / 2 . Therefore, PNO truncation errors can be eliminated using a simple two-point CPS extrapolation to the canonical limit so that subsequent CBS extrapolation is not limited by the residual PNO truncation error. Using the ISOL24 and MOBH35 data sets, we find that PNO truncation errors are larger for molecules with significant static correlation and that it is necessary to use very tight thresholds of T = 10 - 8 to ensure that errors do not exceed 1 kcal/mol. We present a lower-cost extrapolation scheme that uses information from small basis sets to estimate the PNO truncation errors for larger basis sets. In this way, the canonical limit of CCSD(T) calculations on sizable molecules with large basis sets can be reliably estimated in a practical way. Using this approach, we report near complete basis set (CBS)-CCSD(T) reaction energies for the full ISOL24 and MOBH35 data sets.
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Affiliation(s)
- Kesha Sorathia
- University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K.
| | - Damyan Frantzov
- University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K.
| | - David P. Tew
- University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K.
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2
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Asadchev A, Valeev EF. Memory-Efficient Recursive Evaluation of 3-Center Gaussian Integrals. J Chem Theory Comput 2023; 19:1698-1710. [PMID: 36917186 DOI: 10.1021/acs.jctc.2c00995] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/16/2023]
Abstract
To improve the efficiency of Gaussian integral evaluation on modern accelerated architectures, FLOP-efficient Obara-Saika-based recursive evaluation schemes are optimized for the memory footprint. For the 3-center 2-particle integrals that are key for the evaluation of Coulomb and other 2-particle interactions in the density-fitting approximation, the use of multiquantal recurrences (in which multiple quanta are created or transferred at once) is shown to produce significant memory savings. Other innovations include leveraging register memory for reduced memory footprint and direct compile-time generation of optimized kernels (instead of custom code generation) with compile-time features of modern C++/CUDA. Performance of conventional and CUDA-based implementations of the proposed schemes is illustrated for both the individual batches of integrals involving up to Gaussians with low and high angular momenta (up to L = 6) and contraction degrees, as well as for the density-fitting-based evaluation of the Coulomb potential. The computer implementation is available in the open-source LibintX library.
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Affiliation(s)
- Andrey Asadchev
- 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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3
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Spadetto E, Philipsen PHT, Förster A, Visscher L. Toward Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy. J Chem Theory Comput 2023; 19:1499-1516. [PMID: 36787494 PMCID: PMC10018742 DOI: 10.1021/acs.jctc.2c01201] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Indexed: 02/16/2023]
Abstract
Pair atomic density fitting (PADF) has been identified as a promising strategy to reduce the scaling with system size of quantum chemical methods for the calculation of the correlation energy like the direct random-phase approximation (RPA) or second-order Møller-Plesset perturbation theory (MP2). PADF can however introduce large errors in correlation energies as the two-electron interaction energy is not guaranteed to be bounded from below. This issue can be partially alleviated by using very large fit sets, but this comes at the price of reduced efficiency and having to deal with near-linear dependencies in the fit set. One posibility is to use global density fitting (DF), but in this work, we introduce an alternative methodology to overcome this problem that preserves the intrinsically favorable scaling of PADF. We first regularize the Fock matrix by projecting out parts of the basis set which gives rise to orbital products that are hard to describe by PADF. After having thus obtained a reliable self-consistent field solution, we then also apply this projector to the orbital coefficient matrix to improve the precision of PADF-MP2 and PADF-RPA. We systematically assess the accuracy of this new approach in a numerical atomic orbital framework using Slater type orbitals (STO) and correlation consistent Gaussian type basis sets up to quintuple-ζ quality for systems with more than 200 atoms. For the small and medium systems in the S66 database we show the maximum deviation of PADF-MP2 and PADF-RPA relative correlation energies to DF-MP2 and DF-RPA reference results to be 0.07 and 0.14 kcal/mol, respectively. When the new projector method is used, the errors only slightly increase for large molecules and also when moderately sized fit sets are used the resulting errors are well under control. Finally, we demonstrate the computational efficiency of our algorithm by calculating the interaction energies of large, non-covalently bound complexes with more than 1000 atoms and 20000 atomic orbitals at the RPA@PBE/CC-pVTZ level of theory.
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Affiliation(s)
- Edoardo Spadetto
- Software
for Chemistry and Materials NV, NL-1081HV Amsterdam, The Netherlands
| | | | - Arno Förster
- Software
for Chemistry and Materials NV, NL-1081HV Amsterdam, The Netherlands
- Theoretical
Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical
Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands
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4
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Bintrim SJ, Berkelbach TC, Ye HZ. Integral-Direct Hartree-Fock and Møller-Plesset Perturbation Theory for Periodic Systems with Density Fitting: Application to the Benzene Crystal. J Chem Theory Comput 2022; 18:5374-5381. [PMID: 35969856 DOI: 10.1021/acs.jctc.2c00640] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present an algorithm and implementation of integral-direct, density-fitted Hartree-Fock (HF) and second-order Møller-Plesset perturbation theory (MP2) for periodic systems. The new code eliminates the formerly prohibitive storage requirements and allows us to study systems 1 order of magnitude larger than before at the periodic MP2 level. We demonstrate the significance of the development by studying the benzene crystal in both the thermodynamic limit and the complete basis set limit, for which we predict an MP2 cohesive energy of -72.8 kJ/mol, which is about 10-15 kJ/mol larger in magnitude than all previously reported MP2 calculations. Compared to the best theoretical estimate from literature, several modified MP2 models approach chemical accuracy in the predicted cohesive energy of the benzene crystal and hence may be promising cost-effective choices for future applications on molecular crystals.
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Affiliation(s)
- Sylvia J Bintrim
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States.,Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Hong-Zhou Ye
- Department of Chemistry, Columbia University, New York, New York 10027, United States
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5
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Dziedzic J, Womack JC, Ali R, Skylaris CK. Massively parallel linear-scaling Hartree-Fock exchange and hybrid exchange-correlation functionals with plane wave basis set accuracy. J Chem Phys 2021; 155:224106. [PMID: 34911310 DOI: 10.1063/5.0067781] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We extend our linear-scaling approach for the calculation of Hartree-Fock exchange energy using localized in situ optimized orbitals [Dziedzic et al., J. Chem. Phys. 139, 214103 (2013)] to leverage massive parallelism. Our approach has been implemented in the onetep (Order-N Electronic Total Energy Package) density functional theory framework, which employs a basis of non-orthogonal generalized Wannier functions (NGWFs) to achieve linear scaling with system size while retaining controllable near-complete-basis-set accuracy. For the calculation of Hartree-Fock exchange, we use a resolution-of-identity approach, where an auxiliary basis set of truncated spherical waves is used to fit products of NGWFs. The fact that the electrostatic potential of spherical waves (SWs) is known analytically, combined with the use of a distance-based cutoff for exchange interactions, leads to a calculation cost that scales linearly with the system size. Our new implementation, which we describe in detail, combines distributed memory parallelism (using the message passing interface) with shared memory parallelism (OpenMP threads) to efficiently utilize numbers of central processing unit cores comparable to, or exceeding, the number of atoms in the system. We show how the use of multiple time-memory trade-offs substantially increases performance, enabling our approach to achieve superlinear strong parallel scaling in many cases and excellent, although sublinear, parallel scaling otherwise. We demonstrate that in scenarios with low available memory, which preclude or limit the use of time-memory trade-offs, the performance degradation of our algorithm is graceful. We show that, crucially, linear scaling with system size is maintained in all cases. We demonstrate the practicability of our approach by performing a set of fully converged production calculations with a hybrid functional on large imogolite nanotubes up to over 1400 atoms. We finish with a brief study of how the employed approximations (exchange cutoff and the quality of the SW basis) affect the calculation walltime and the accuracy of the obtained results.
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Affiliation(s)
- Jacek Dziedzic
- School of Chemistry, Highfield, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - James C Womack
- School of Chemistry, Highfield, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Rozh Ali
- Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Gdańsk 80-233, Poland
| | - Chris-Kriton Skylaris
- School of Chemistry, Highfield, University of Southampton, Southampton SO17 1BJ, United Kingdom
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6
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Förster A, Visscher L. Low-Order Scaling G0W0 by Pair Atomic Density Fitting. J Chem Theory Comput 2020; 16:7381-7399. [PMID: 33174743 PMCID: PMC7726916 DOI: 10.1021/acs.jctc.0c00693] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Indexed: 12/18/2022]
Abstract
We derive a low-scaling G0W0 algorithm for molecules using pair atomic density fitting (PADF) and an imaginary time representation of the Green's function and describe its implementation in the Slater type orbital (STO)-based Amsterdam density functional (ADF) electronic structure code. We demonstrate the scalability of our algorithm on a series of water clusters with up to 432 atoms and 7776 basis functions and observe asymptotic quadratic scaling with realistic threshold qualities controlling distance effects and basis sets of triple-ζ (TZ) plus double polarization quality. Also owing to a very small prefactor, a G0W0 calculation for the largest of these clusters takes only 240 CPU hours with these settings. We assess the accuracy of our algorithm for HOMO and LUMO energies in the GW100 database. With errors of 0.24 eV for HOMO energies on the quadruple-ζ level, our implementation is less accurate than canonical all-electron implementations using the larger def2-QZVP GTO-type basis set. Apart from basis set errors, this is related to the well-known shortcomings of the GW space-time method using analytical continuation techniques as well as to numerical issues of the PADF approach of accurately representing diffuse atomic orbital (AO) products. We speculate that these difficulties might be overcome by using optimized auxiliary fit sets with more diffuse functions of higher angular momenta. Despite these shortcomings, for subsets of medium and large molecules from the GW5000 database, the error of our approach using basis sets of TZ and augmented double-ζ (DZ) quality is decreasing with system size. On the augmented DZ level, we reproduce canonical, complete basis set limit extrapolated reference values with an accuracy of 80 meV on average for a set of 20 large organic molecules. We anticipate our algorithm, in its current form, to be very useful in the study of single-particle properties of large organic systems such as chromophores and acceptor molecules.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands
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7
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Wang X, Lewis CA, Valeev EF. Efficient evaluation of exact exchange for periodic systems via concentric atomic density fitting. J Chem Phys 2020; 153:124116. [DOI: 10.1063/5.0016856] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xiao Wang
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Cannada A. Lewis
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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8
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Ye HZ, Tran HK, Van Voorhis T. Bootstrap Embedding For Large Molecular Systems. J Chem Theory Comput 2020; 16:5035-5046. [PMID: 32589842 DOI: 10.1021/acs.jctc.0c00438] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Recent developments in quantum embedding theories have provided attractive approaches to correlated calculations for large systems. In this work, we extend our previous work [J. Chem. Theory Comput. 2019, 15, 4497-4506; J. Phys. Chem. Lett. 2019, 10, 6368-6374] on bootstrap embedding (BE) to enable correlated ab initio calculations at the coupled cluster with singles and doubles (CCSD) level for large molecules. We introduce several new algorithmic developments that significantly reduce the computational cost of BE, while maintaining its accuracy. The resulting implementation scales as O(N3) for the integral transform and O(N) for the CCSD calculation. Numerical results on a series of conjugated molecules suggest that BE with reasonably sized fragments can recover more than 99.5% of the total correlation energy of a full CCSD calculation, while the required computational resources (time and storage) compare favorably to one popular local correlation scheme: domain localized pair natural orbital (DLPNO). The largest BE calculation in this work involves ∼2900 basis functions and can be performed on a single node with 16 CPU cores and 64 GB of memory in a few days. We anticipate that these developments represent an important step toward the application of BE to solve practical problems.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Henry K Tran
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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9
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Pedroza-Montero JN, Morales JL, Geudtner G, Álvarez-Ibarra A, Calaminici P, Köster AM. Variational Density Fitting with a Krylov Subspace Method. J Chem Theory Comput 2020; 16:2965-2974. [PMID: 32223134 DOI: 10.1021/acs.jctc.9b01212] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this work, we present the implementation of a variational density fitting methodology that uses iterative linear algebra for solving the associated system of linear equations. It is well known that most difficulties with this system arise from the fact that the coefficient matrix is in general ill-conditioned and, due to finite precision round-off errors, it may not be positive definite. The dimensionality, given by the number of auxiliary functions, also poses a challenge in terms of memory and time demand since the coefficient matrix is dense. The methodology presented is based on a preconditioned Krylov subspace method able to deal with indefinite ill-conditioned equation systems. To assess its potential, it has been combined with double asymptotic electron repulsion integral expansions as implemented in the deMon2k package. A numerical study on a set of problems with up to 130,000 auxiliary functions shows its effectiveness to alleviate the abovementioned problematic. A comparison with the default methodology used in deMon2k based on a truncated eigenvalue decomposition of the coefficient matrix indicates that the proposed method exhibits excellent robustness and scalability when implemented in a parallel setting.
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Affiliation(s)
- Jesús N Pedroza-Montero
- Programa de Doctorado de Nanociencias y Nanotecnologı́as, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
| | - José Luis Morales
- Departamento de Quı́mica, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
| | - Gerald Geudtner
- Departamento de Quı́mica, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
| | - Aurelio Álvarez-Ibarra
- Laboratoire de Chimie Physique, Université Paris Sud, CNRS, Université Paris Saclay. 15 avenue Jean Perrin, F91405 Orsay, France
| | - Patrizia Calaminici
- Programa de Doctorado de Nanociencias y Nanotecnologı́as, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico.,Departamento de Quı́mica, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
| | - Andreas M Köster
- Programa de Doctorado de Nanociencias y Nanotecnologı́as, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico.,Departamento de Quı́mica, CINVESTAV, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
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10
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Shaw RA, Hill JG. A Linear-Scaling Method for Noncovalent Interactions: An Efficient Combination of Absolutely Localized Molecular Orbitals and a Local Random Phase Approximation Approach. J Chem Theory Comput 2019; 15:5352-5369. [PMID: 31465215 DOI: 10.1021/acs.jctc.9b00615] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A novel method for the accurate and efficient calculation of interaction energies in weakly bound complexes composed of a large number of molecules is presented. The new ALMO+RPAd method circumvents the prohibitive scaling of coupled cluster singles and doubles while still providing similar accuracy across a diverse range of weakly bound chemical systems. Linear-scaling procedures for the Fock build are given utilizing absolutely localized molecular orbitals (ALMOs), resulting in the a priori exclusion of basis set superposition errors. A bespoke data structure and algorithm using density fitting are described, leading to linear scaling for the storage and computation of the two-electron integrals. Electron correlation is included through a new, linear-scaling pairwise local random phase approximation approach, including exchange interactions, and decomposed into purely dispersive excitations (RPAxd). Collectively, these allow meaningful decomposition of the interaction energy into physically distinct contributions: electrostatic, polarization, charge transfer, and dispersion. Comparison with symmetry-adapted perturbation theory shows good qualitative agreement. Tests on various dimers and the S66 benchmark set demonstrate results within 0.5 kcal mol-1 of coupled cluster singles and doubles results. On a large cluster of water molecules, we achieve calculations involving over 3500 orbital and 12,000 auxiliary basis functions in under 10 min on a single CPU core.
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Affiliation(s)
- Robert A Shaw
- Department of Chemistry , University of Sheffield , Sheffield S3 7HF , United Kingdom
| | - J Grant Hill
- Department of Chemistry , University of Sheffield , Sheffield S3 7HF , United Kingdom
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11
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Chen GP, Agee MM, Furche F. Performance and Scope of Perturbative Corrections to Random-Phase Approximation Energies. J Chem Theory Comput 2018; 14:5701-5714. [PMID: 30240213 DOI: 10.1021/acs.jctc.8b00777] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
It has been suspected since the early days of the random-phase approximation (RPA) that corrections to RPA correlation energies result mostly from short-range correlation effects and are thus amenable to perturbation theory. Here we test this hypothesis by analyzing formal and numerical results for the most common beyond-RPA perturbative corrections, including the bare second-order exchange (SOX), second-order screened exchange (SOSEX), and approximate exchange kernel (AXK) methods. Our analysis is facilitated by efficient and robust algorithms based on the resolution-of-the-identity (RI) approximation and numerical frequency integration, which enable benchmark beyond-RPA calculations on medium- and large-size molecules with size-independent accuracy. The AXK method systematically improves upon RPA, SOX, and SOSEX for reaction barrier heights, reaction energies, and noncovalent interaction energies of main-group compounds. The improved accuracy of AXK compared with SOX and SOSEX is attributed to stronger screening of bare SOX in AXK. For reactions involving transition-metal compounds, particularly 3d transition-metal dimers, the AXK correction is too small and can even have the wrong sign. These observations are rationalized by a measure α̅ of the effective coupling strength for beyond-RPA correlation. When the effective coupling strength increases beyond a critical α̅ value of approximately 0.5, the RPA errors increase rapidly and perturbative corrections become unreliable. Thus, perturbation theory can systematically correct RPA but only for systems and properties qualitatively well captured by RPA, as indicated by small α̅ values.
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Affiliation(s)
- Guo P Chen
- University of California, Irvine , Department of Chemistry , 1102 Natural Sciences II , Irvine , California 92697-2025 , United States
| | - Matthew M Agee
- University of California, Irvine , Department of Chemistry , 1102 Natural Sciences II , Irvine , California 92697-2025 , United States
| | - Filipp Furche
- University of California, Irvine , Department of Chemistry , 1102 Natural Sciences II , Irvine , California 92697-2025 , United States
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12
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Khire SS, Bartolotti LJ, Gadre SR. Harmonizing accuracy and efficiency: A pragmatic approach to fragmentation of large molecules. J Chem Phys 2018; 149:064112. [PMID: 30111143 DOI: 10.1063/1.5036595] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
Fragmentation methods offer an attractive alternative for ab initio treatment of large molecules and molecular clusters. However, balancing the accuracy and efficiency of these methods is a tight-rope-act. With this in view, we present an algorithm for automatic molecular fragmentation within Molecular Tailoring Approach (MTA) achieving this delicate balance. The automated code is tested out on a variety of molecules and clusters at the Hartree-Fock (HF)- and Møller-Plesset second order perturbation theory as well as density functional theory employing augmented Dunning basis sets. The results show remarkable accuracy and efficiency vis-à-vis the respective full calculations. Thus the present work forms an important step toward the development of an MTA-based black box code for implementation of HF as well as correlated quantum chemical calculations on large molecular systems.
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Affiliation(s)
- Subodh S Khire
- Interdisciplinary School of Scientific Computing, Savitribai Phule Pune University, Pune 411007, India
| | - Libero J Bartolotti
- Department of Physical and Computational Chemistry, East Carolina University, Greenville, North Carolina 27858, USA
| | - Shridhar R Gadre
- Interdisciplinary School of Scientific Computing, Savitribai Phule Pune University, Pune 411007, India
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13
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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: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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