1
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Fauser S, Förster A, Redeker L, Neiss C, Erhard J, Trushin E, Görling A. Basis Set Requirements of σ-Functionals for Gaussian- and Slater-Type Basis Functions and Comparison with Range-Separated Hybrid and Double Hybrid Functionals. J Chem Theory Comput 2024; 20:2404-2422. [PMID: 38466924 DOI: 10.1021/acs.jctc.3c01132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/13/2024]
Abstract
σ-Functionals belong to the class of Kohn-Sham (KS) correlation functionals based on the adiabatic-connection fluctuation-dissipation theorem and are technically closely related to the random phase approximation (RPA). They have the same computational demand as the latter, with the computational effort of an energy evaluation for both methods being lower than that of a preceding hybrid DFT calculation for typical systems but yield much higher accuracy, reaching chemical accuracy of 1 kcal/mol for quantities such as reactions and transition energies in main group chemistry. In previous work on σ-functionals, rather large Gaussian basis sets have been used. Here, we investigate the actual basis set requirements of σ-functionals and present three setups that employ smaller Gaussian basis sets ranging from quadruple-ζ (QZ) to triple-ζ (TZ) quality and represent a good compromise between accuracy and computational efficiency. Furthermore, we introduce an implementation of σ-functionals based on Slater-type basis sets and present two setups of QZ and TZ quality for this implementation. We test the accuracy of these setups on a large database of various physical properties and types of reactions, as well as equilibrium geometries and vibrational frequencies. As expected, the accuracy of σ-functional calculations becomes somewhat lower with a decreasing basis set size. However, for all setups considered here, calculations with σ-functionals are clearly more accurate than those within the RPA and even more so than those of the conventional KS methods. For the smallest setup using Gaussian-type basis functions and Slater-type basis functions, we introduce a reparametrization that reduces the loss in accuracy due to the basis set error to some extent. A comparison with the range-separated hybrid ωB97X-V and the double hybrid DSD-BLYP-D3 shows that σ functionals outperform in accuracy both of these accurate and, for their class, representative functionals.
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Affiliation(s)
- Steffen Fauser
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands
| | - Leon Redeker
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Christian Neiss
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Jannis Erhard
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Egor Trushin
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
- Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
| | - Andreas Görling
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
- Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
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2
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Bradbury NC, Allen T, Nguyen M, Neuhauser D. Deterministic/Fragmented-Stochastic Exchange for Large-Scale Hybrid DFT Calculations. J Chem Theory Comput 2023; 19:9239-9247. [PMID: 38051791 DOI: 10.1021/acs.jctc.3c00987] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
We develop an efficient approach to evaluate range-separated exact exchange for grid- or plane-wave-based representations within the generalized Kohn-Sham-density functional theory (GKS-DFT) framework. The Coulomb kernel is fragmented in reciprocal space, and we employ a mixed deterministic-stochastic representation, retaining long-wavelength (low-k) contributions deterministically and using a sparse ("fragmented") stochastic basis for the high-k part. Coupled with a projection of the Hamiltonian onto a subspace of valence and conduction states from a prior local-DFT calculation, this method allows for the calculation of the long-range exchange of large molecular systems with hundreds and potentially thousands of coupled valence states delocalized over millions of grid points. We find that even a small number of valence and conduction states is sufficient for converging the HOMO and LUMO energies of the GKS-DFT. Excellent tuning of long-range separated hybrids (RSH) is easily obtained in the method for very large systems, as exemplified here for the chlorophyll hexamer of Photosystem II with 1320 electrons.
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Affiliation(s)
- Nadine C Bradbury
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Tucker Allen
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Minh Nguyen
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
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3
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Belleflamme F, Hutter J. Radicals in aqueous solution: assessment of density-corrected SCAN functional. Phys Chem Chem Phys 2023; 25:20817-20836. [PMID: 37497572 DOI: 10.1039/d3cp02517a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/28/2023]
Abstract
We study self-interaction effects in solvated and strongly-correlated cationic molecular clusters, with a focus on the solvated hydroxyl radical. To address the self-interaction issue, we apply the DC-r2SCAN method, with the auxiliary density matrix approach. Validating our method through simulations of bulk liquid water, we demonstrate that DC-r2SCAN maintains the structural accuracy of r2SCAN while effectively addressing spin density localization issues. Extending our analysis to solvated cationic molecular clusters, we find that the hemibonded motif in the [CH3S∴CH3SH]+ cluster is disrupted in the DC-r2SCAN simulation, in contrast to r2SCAN that preserves the (three-electron-two-center)-bonded motif. Similarly, for the [SH∴SH2]+ cluster, r2SCAN restores the hemibonded motif through spin leakage, while DC-r2SCAN predicts a weaker hemibond formation influenced by solvent-solute interactions. Our findings demonstrate the potential of DC-r2SCAN combined with the auxiliary density matrix method to improve electronic structure calculations, providing insights into the properties of solvated cationic molecular clusters. This work contributes to the advancement of self-interaction corrected electronic structure theory and offers a computational framework for modeling condensed phase systems with intricate correlation effects.
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Affiliation(s)
| | - Jürg Hutter
- Department of Chemistry, University of Zurich, Zurich, Switzerland.
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4
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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] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [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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5
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Hehn AS, Sertcan B, Belleflamme F, Chulkov SK, Watkins MB, Hutter J. Excited-State Properties for Extended Systems: Efficient Hybrid Density Functional Methods. J Chem Theory Comput 2022; 18:4186-4202. [PMID: 35759470 PMCID: PMC9281608 DOI: 10.1021/acs.jctc.2c00144] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials because of its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg, and charge-transfer excitations. Several approaches for an efficient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational efficiency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.3 pm for excited-state bond lengths and in the range of 0.02-0.04 eV for vertical excitation, adiabatic excitation, and fluorescence energies. Computational timings for a series of covalent-organic frameworks demonstrate that a speed-up of at least 1 order of magnitude can be achieved for excited-state geometry optimizations in comparison to conventional hybrid functionals. The second method is to use a semiempirical tight binding approximation for both Coulomb and exchange contributions to the excited-state kernel. This simplified Tamm-Dancoff approximation (sTDA) achieves an accuracy comparable to approximated hybrid density functional theory when referring to highly accurate coupled-cluster reference data. We find that excited-state bond lengths deviate by 1.1 pm on average and mean absolute errors in vertical excitation, adiabatic excitation, and fluorescence energies are in the range of 0.2-0.5 eV. In comparison to ADMM-approximated hybrid functional theory, sTDA accelerates the computation of broad-band excitation spectra by 1 order of magnitude, suggesting its potential use for large-scale screening purposes.
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Affiliation(s)
- Anna-Sophia Hehn
- Department
of Chemistry, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Beliz Sertcan
- Department
of Chemistry, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Fabian Belleflamme
- Department
of Chemistry, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Sergey K. Chulkov
- School
of Mathematics and Physics, University of
Lincoln, Brayford Pool, Lincoln LN67TS, United Kingdom
| | - Matthew B. Watkins
- School
of Mathematics and Physics, University of
Lincoln, Brayford Pool, Lincoln LN67TS, United Kingdom
| | - Jürg Hutter
- Department
of Chemistry, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
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6
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Altun A, Neese F, Bistoni G. Open-Shell Variant of the London Dispersion-Corrected Hartree-Fock Method (HFLD) for the Quantification and Analysis of Noncovalent Interaction Energies. J Chem Theory Comput 2022; 18:2292-2307. [PMID: 35167304 PMCID: PMC9009084 DOI: 10.1021/acs.jctc.1c01295] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
The London dispersion
(LD)-corrected Hartree–Fock (HF) method
(HFLD) is an ab initio approach for the quantification
and analysis of noncovalent interactions (NCIs) in large systems that
is based on the domain-based local pair natural orbital coupled-cluster
(DLPNO-CC) theory. In the original HFLD paper, we discussed the implementation,
accuracy, and efficiency of its closed-shell variant. Herein, an extension
of this method to open-shell molecular systems is presented. Its accuracy
is tested on challenging benchmark sets for NCIs, using CCSD(T) energies
at the estimated complete basis set limit as reference. The HFLD scheme
was found to be as accurate as the best-performing dispersion-corrected
exchange-correlation functionals, while being nonempirical and equally
efficient. In addition, it can be combined with the well-established
local energy decomposition (LED) for the analysis of NCIs, thus yielding
additional physical insights.
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Affiliation(s)
- Ahmet Altun
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Giovanni Bistoni
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany.,Department of Chemistry, Biology and Biotechnology, University of Perugia, 06123 Perugia, Italy
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7
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Helmich-Paris B, de Souza B, Neese F, Izsák R. An improved chain of spheres for exchange algorithm. J Chem Phys 2021; 155:104109. [PMID: 34525816 DOI: 10.1063/5.0058766] [Citation(s) in RCA: 47] [Impact Index Per Article: 15.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
In the present work, we describe a more accurate and efficient variant of the chain-of-spheres algorithm (COSX) for exchange matrix computations. Higher accuracy for the numerical integration is obtained with new grids that were developed using global optimization techniques. With our new default grids, the average absolute energy errors are much lower than 0.1 kcal/mol, which is desirable to achieve "chemical accuracy." Although the size of the new grids is increased by roughly a factor of 2.5, the excellent efficiency of the original COSX implementation is still further improved in most cases. The evaluation of the analytic electrostatic potential integrals was significantly accelerated by a new implementation of rolled-out versions of the Dupuis-Rys-King and Head-Gordon-Pople algorithms. Compared to our earlier implementation, a twofold speedup is obtained for the frequently used triple-ζ basis sets, while up to a 16-fold speedup is observed for quadruple-ζ basis sets. These large gains are a consequence of both the more efficient integral evaluation and the intermediate exchange matrix computation in a partially contracted basis when generally contracted shells occur. With our new RIJCOSX implementation, we facilitate accurate self-consistent field (SCF) binding energy calculations on a large supra-molecular complex composed of 320 atoms. The binding-energy errors with respect to the fully analytic results are well below 0.1 kcal/mol for the cc-pV(T/Q)Z basis sets and even smaller than for RIJ with fully analytic exchange. At the same time, our RIJCOSX SCF calculation even with the cc-pVQZ basis and the finest grid is 21 times faster than the fully analytic calculation.
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Affiliation(s)
- Benjamin Helmich-Paris
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | | | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Róbert Izsák
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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8
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Duchemin I, Blase X. Cubic-Scaling All-Electron GW Calculations with a Separable Density-Fitting Space-Time Approach. J Chem Theory Comput 2021; 17:2383-2393. [PMID: 33797245 DOI: 10.1021/acs.jctc.1c00101] [Citation(s) in RCA: 35] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present an implementation of the GW space-time approach that allows cubic-scaling all-electron calculations with standard Gaussian basis sets without exploiting any localization or sparsity considerations. The independent-electron susceptibility is constructed in a time representation over a nonuniform distribution of real-space locations {rk} optimized within a separable resolution-of-the-identity framework to reproduce standard Coulomb-fitting calculations with meV accuracy. The compactness of the obtained {rk} distribution leads to a crossover with the standard Coulomb-fitting scheme for system sizes below a few hundred electrons. The needed analytic continuation follows a recent approach that requires the continuation of the screened Coulomb potential rather than the much more structured self-energy. The present scheme is benchmarked over large molecular sets, and scaling properties are demonstrated on a family of defected hexagonal boron-nitride flakes containing up to 6000 electrons.
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Affiliation(s)
- Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
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9
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Bussy A, Hutter J. Efficient and low-scaling linear-response time-dependent density functional theory implementation for core-level spectroscopy of large and periodic systems. Phys Chem Chem Phys 2021; 23:4736-4746. [PMID: 33598668 DOI: 10.1039/d0cp06164f] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We discuss our implementation of linear-response time-dependent density functional theory (LR-TDDFT) for core level near-edge absorption spectroscopy. The method is based on established LR-TDDFT approaches to X-ray absorption spectroscopy (XAS) with additional accurate approximations for increased efficiency. We validate our implementation by reproducing benchmark results at the K-edge and showing that spin-orbit coupling effects at the L2,3-edge are well described. We also demonstrate that the method is suitable for extended systems in periodic boundary conditions and measure a favorable sub-cubic scaling of the calculation cost with system size. We finally show that GPUs can be efficiently exploited and report speedups of up to a factor 2.
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Affiliation(s)
- Augustin Bussy
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland.
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10
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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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11
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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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12
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Förster A, Visscher L. Double hybrid DFT calculations with Slater type orbitals. J Comput Chem 2020; 41:1660-1684. [PMID: 32297682 PMCID: PMC7317772 DOI: 10.1002/jcc.26209] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2020] [Revised: 03/31/2020] [Accepted: 04/01/2020] [Indexed: 12/14/2022]
Abstract
On a comprehensive database with 1,644 datapoints, covering several aspects of main-group as well as of transition metal chemistry, we assess the performance of 60 density functional approximations (DFA), among them 36 double hybrids (DH). All calculations are performed using a Slater type orbital (STO) basis set of triple-ζ (TZ) quality and the highly efficient pair atomic resolution of the identity approach for the exchange- and Coulomb-term of the KS matrix (PARI-K and PARI-J, respectively) and for the evaluation of the MP2 energy correction (PARI-MP2). Employing the quadratic scaling SOS-AO-PARI-MP2 algorithm, DHs based on the spin-opposite-scaled (SOS) MP2 approximation are benchmarked against a database of large molecules. We evaluate the accuracy of STO/PARI calculations for B3LYP as well as for the DH B2GP-PLYP and show that the combined basis set and PARI-error is comparable to the one obtained using the well-known def2-TZVPP Gaussian-type basis set in conjunction with global density fitting. While quadruple-ζ (QZ) calculations are currently not feasible for PARI-MP2 due to numerical issues, we show that, on the TZ level, Jacob's ladder for classifying DFAs is reproduced. However, while the best DHs are more accurate than the best hybrids, the improvements are less pronounced than the ones commonly found on the QZ level. For conformers of organic molecules and noncovalent interactions where very high accuracy is required for qualitatively correct results, DHs provide only small improvements over hybrids, while they still excel in thermochemistry, kinetics, transition metal chemistry and the description of strained organic systems.
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Affiliation(s)
- Arno Förster
- Theoretical ChemistryVrije UniversiteitAmsterdamThe Netherlands
| | - Lucas Visscher
- Theoretical ChemistryVrije UniversiteitAmsterdamThe Netherlands
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13
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Pausch A, Klopper W. Efficient evaluation of three-centre two-electron integrals over London orbitals. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1736675] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Ansgar Pausch
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
- Centre for Advanced Study (CAS), The Norwegian Academy of Science and Letters, Oslo, Norway
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14
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Förster A, Franchini M, van Lenthe E, Visscher L. A Quadratic Pair Atomic Resolution of the Identity Based SOS-AO-MP2 Algorithm Using Slater Type Orbitals. J Chem Theory Comput 2020; 16:875-891. [PMID: 31930915 PMCID: PMC7027358 DOI: 10.1021/acs.jctc.9b00854] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2019] [Indexed: 01/04/2023]
Abstract
We report a production level implementation of pair atomic resolution of the identity (PARI) based second-order Møller-Plesset perturbation theory (MP2) in the Slater type orbital (STO) based Amsterdam Density Functional (ADF) code. As demonstrated by systematic benchmarks, dimerization and isomerization energies obtained with our code using STO basis sets of triple-ζ-quality show mean absolute deviations from Gaussian type orbital, canonical, basis set limit extrapolated, global density fitting (DF)-MP2 results of less than 1 kcal/mol. Furthermore, we introduce a quadratic scaling atomic orbital based spin-opposite-scaled (SOS)-MP2 approach with a very small prefactor. Due to a worst-case scaling of [Formula: see text], our implementation is very fast already for small systems and shows an exceptionally early crossover to canonical SOS-PARI-MP2. We report computational wall time results for linear as well as for realistic three-dimensional molecules and show that triple-ζ quality calculations on molecules of several hundreds of atoms are only a matter of a few hours on a single compute node, the bottleneck of the computations being the SCF rather than the post-SCF energy correction.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije
Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The
Netherlands
| | - Mirko Franchini
- Theoretical Chemistry, Vrije
Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The
Netherlands
- Scientific Computing & Modelling
NV, De Boelelaan 1083, NL-1081 HV Amsterdam, The
Netherlands
| | - Erik van Lenthe
- Scientific Computing & Modelling
NV, 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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15
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Gould T, Vuckovic S. Range-separation and the multiple radii functional approximation inspired by the strongly interacting limit of density functional theory. J Chem Phys 2019; 151:184101. [DOI: 10.1063/1.5125692] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Tim Gould
- Qld Micro- and Nanotechnology Centre, Griffith University, Nathan, Qld 4111, Australia
| | - Stefan Vuckovic
- Department of Chemistry, University of California, Irvine, California 92697, USA
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16
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Pham BQ, Gordon MS. Compressing the Four-Index Two-Electron Repulsion Integral Matrix using the Resolution-of-the-Identity Approximation Combined with the Rank Factorization Approximation. J Chem Theory Comput 2019; 15:2254-2264. [DOI: 10.1021/acs.jctc.8b01256] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Buu Q. Pham
- Department of Chemistry, Iowa State University, Ames, Iowa 50011, United States
| | - Mark S. Gordon
- Department of Chemistry, Iowa State University, Ames, Iowa 50011, United States
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17
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Yang T, Berry JF. Numerical Nuclear Second Derivatives on a Computing Grid: Enabling and Accelerating Frequency Calculations on Complex Molecular Systems. J Chem Theory Comput 2018; 14:3459-3467. [DOI: 10.1021/acs.jctc.8b00120] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Tzuhsiung Yang
- Department of Chemistry, University of Wisconsin—Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - John F. Berry
- Department of Chemistry, University of Wisconsin—Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
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18
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Le HA, Shiozaki T. Occupied-Orbital Fast Multipole Method for Efficient Exact Exchange Evaluation. J Chem Theory Comput 2018; 14:1228-1234. [DOI: 10.1021/acs.jctc.7b00880] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hai-Anh Le
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
| | - Toru Shiozaki
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
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19
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Hu W, Lin L, Yang C. Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon. J Chem Theory Comput 2017; 13:5420-5431. [PMID: 28960982 DOI: 10.1021/acs.jctc.7b00807] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a new efficient way to perform hybrid density functional theory (DFT)-based electronic structure calculations. The new method uses an interpolative separable density fitting (ISDF) procedure to construct a set of numerical auxiliary basis vectors and a compact approximation of the matrix consisting of products of occupied orbitals represented in a large basis set such as the planewave basis. Such an approximation allows us to reduce the number of Poisson solves from [Formula: see text] to [Formula: see text] when we apply the exchange operator to occupied orbitals in an iterative method for solving the Kohn-Sham equations, where Ne is the number of electrons in the system to be studied. We show that the ISDF procedure can be carried out in [Formula: see text] operations, with a much smaller preconstant compared to methods used in existing approaches. When combined with the recently developed adaptively compressed exchange (ACE) operator formalism, which reduces the number of times the exchange operator needs to be updated, the resulting ACE-ISDF method significantly reduces the computational cost associated with the exchange operator by nearly 2 orders of magnitude compared to existing approaches for a large silicon system with 1000 atoms. We demonstrate that the ACE-ISDF method can produce accurate energies and forces for insulating and metallic systems and that it is possible to obtain converged hybrid functional calculation results for a 1000-atom bulk silicon within 10 min on 2000 computational cores. We also show that ACE-ISDF can scale to 8192 computational cores for a 4096-atom bulk silicon system. We use the ACE-ISDF method to geometrically optimize a 1000-atom silicon system with a vacancy defect using the HSE06 functional and computes its electronic structure. We find that that the computed energy gap from the HSE06 functional is much closer to the experimental value compared to that produced by semilocal functionals in the DFT calculations.
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Affiliation(s)
- Wei Hu
- Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States
| | - Lin Lin
- Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States.,Department of Mathematics, University of California , Berkeley, California 94720, United States
| | - Chao Yang
- Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States
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20
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Brémond É, Savarese M, Pérez-Jiménez ÁJ, Sancho-García JC, Adamo C. Speed-Up of the Excited-State Benchmarking: Double-Hybrid Density Functionals as Test Cases. J Chem Theory Comput 2017; 13:5539-5551. [DOI: 10.1021/acs.jctc.7b00627] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Éric Brémond
- CompuNet, Istituto
Italiano di Tecnologia, via Morego
30, I-16163 Genoa, Italy
| | - Marika Savarese
- CompuNet, Istituto
Italiano di Tecnologia, via Morego
30, I-16163 Genoa, Italy
| | | | | | - Carlo Adamo
- Chimie
ParisTech, PSL Research University, CNRS, Institut de Recherche de Chimie Paris IRCP, F-75005 Paris, France
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21
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Hollman DS, Schaefer HF, Valeev EF. Fast construction of the exchange operator in an atom-centred basis with concentric atomic density fitting. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1346312] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- David S. Hollman
- Center for Computing Research, Sandia National Laboratories, Livermore, CA, USA
- Center for Computational Quantum Chemistry, University of Georgia, Athens, GA, USA
- Department of Chemistry, Virginia Tech, Blacksburg, VA, USA
| | - Henry F. Schaefer
- Center for Computational Quantum Chemistry, University of Georgia, Athens, GA, USA
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22
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Jaoul A, Nocton G, Clavaguéra C. Assessment of Density Functionals for Computing Thermodynamic Properties of Lanthanide Complexes. Chemphyschem 2017; 18:2688-2696. [DOI: 10.1002/cphc.201700629] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2017] [Revised: 07/07/2017] [Indexed: 12/12/2022]
Affiliation(s)
- Arnaud Jaoul
- LCM, CNRS, Ecole polytechniqueUniversité Paris-Saclay Route de Saclay 91128 Palaiseau Cedex France
| | - Grégory Nocton
- LCM, CNRS, Ecole polytechniqueUniversité Paris-Saclay Route de Saclay 91128 Palaiseau Cedex France
| | - Carine Clavaguéra
- Laboratoire de Chimie PhysiqueCNRS Université Paris Sud, Université Paris-Saclay 15 avenue Jean Perrin 91405 Orsay Cedex France
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23
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Golze D, Iannuzzi M, Hutter J. Local Fitting of the Kohn–Sham Density in a Gaussian and Plane Waves Scheme for Large-Scale Density Functional Theory Simulations. J Chem Theory Comput 2017; 13:2202-2214. [DOI: 10.1021/acs.jctc.7b00148] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Dorothea Golze
- Department
of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
- COMP/Department
of Applied Physics, Aalto University, P.O. Box 11100, Aalto FI-00076, Finland
| | - Marcella Iannuzzi
- Department
of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Jürg Hutter
- Department
of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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24
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Aquilante F, Delcey MG, Pedersen TB, Fdez. Galván I, Lindh R. Inner projection techniques for the low-cost handling of two-electron integrals in quantum chemistry. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1284354] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Francesco Aquilante
- Dipartimento di Chimica “G. Ciamician”, Università di Bologna, Bologna, Italy
| | - Mickaël G. Delcey
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA, USA
| | - Thomas Bondo Pedersen
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, Blindern, Oslo, Norway
| | - Ignacio Fdez. Galván
- Department of Chemistry – Ångström, The Theoretical Chemistry Programme, Uppsala University, Uppsala, Sweden
- Uppsala Center for Computational Chemistry – UC3, Uppsala University, Uppsala, Sweden
| | - Roland Lindh
- Department of Chemistry – Ångström, The Theoretical Chemistry Programme, Uppsala University, Uppsala, Sweden
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25
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Wilhelm J, Seewald P, Del Ben M, Hutter J. Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis. J Chem Theory Comput 2016; 12:5851-5859. [DOI: 10.1021/acs.jctc.6b00840] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jan Wilhelm
- Department
of Chemistry and National Centre for Computational Design and Discovery
of Novel Materials (MARVEL), University of Zurich, 8057 Zurich, Switzerland
| | - Patrick Seewald
- Department
of Chemistry and National Centre for Computational Design and Discovery
of Novel Materials (MARVEL), University of Zurich, 8057 Zurich, Switzerland
| | - Mauro Del Ben
- Computational
Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Jürg Hutter
- Department
of Chemistry and National Centre for Computational Design and Discovery
of Novel Materials (MARVEL), University of Zurich, 8057 Zurich, Switzerland
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