1
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O’Neill N, Shi BX, Fong K, Michaelides A, Schran C. To Pair or not to Pair? Machine-Learned Explicitly-Correlated Electronic Structure for NaCl in Water. J Phys Chem Lett 2024; 15:6081-6091. [PMID: 38820256 PMCID: PMC11181334 DOI: 10.1021/acs.jpclett.4c01030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2024] [Revised: 05/23/2024] [Accepted: 05/24/2024] [Indexed: 06/02/2024]
Abstract
The extent of ion pairing in solution is an important phenomenon to rationalize transport and thermodynamic properties of electrolytes. A fundamental measure of this pairing is the potential of mean force (PMF) between solvated ions. The relative stabilities of the paired and solvent shared states in the PMF and the barrier between them are highly sensitive to the underlying potential energy surface. However, direct application of accurate electronic structure methods is challenging, since long simulations are required. We develop wave function based machine learning potentials with the random phase approximation (RPA) and second order Møller-Plesset (MP2) perturbation theory for the prototypical system of Na and Cl ions in water. We show both methods in agreement, predicting the paired and solvent shared states to have similar energies (within 0.2 kcal/mol). We also provide the same benchmarks for different DFT functionals as well as insight into the PMF based on simple analyses of the interactions in the system.
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Affiliation(s)
- Niamh O’Neill
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Cavendish
Laboratory, Department of Physics, University
of Cambridge, Cambridge CB3 0HE, United
Kingdom
- Lennard-Jones
Centre, University of Cambridge, Trinity Ln, Cambridge CB2 1TN, United Kingdom
| | - Benjamin X. Shi
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Lennard-Jones
Centre, University of Cambridge, Trinity Ln, Cambridge CB2 1TN, United Kingdom
| | - Kara Fong
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Lennard-Jones
Centre, University of Cambridge, Trinity Ln, Cambridge CB2 1TN, United Kingdom
| | - Angelos Michaelides
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Lennard-Jones
Centre, University of Cambridge, Trinity Ln, Cambridge CB2 1TN, United Kingdom
| | - Christoph Schran
- Cavendish
Laboratory, Department of Physics, University
of Cambridge, Cambridge CB3 0HE, United
Kingdom
- Lennard-Jones
Centre, University of Cambridge, Trinity Ln, Cambridge CB2 1TN, United Kingdom
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2
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Yeh CN, Morales MA. Low-Scaling Algorithms for GW and Constrained Random Phase Approximation Using Symmetry-Adapted Interpolative Separable Density Fitting. J Chem Theory Comput 2024; 20:3184-3198. [PMID: 38597496 DOI: 10.1021/acs.jctc.4c00085] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2024]
Abstract
We present low-scaling algorithms for GW and constrained random phase approximation based on a symmetry-adapted interpolative separable density fitting (ISDF) procedure that incorporates the space-group symmetries of crystalline systems. The resulting formulations scale cubically, with respect to system size, and linearly with the number of k-points, regardless of the choice of single-particle basis and whether a quasiparticle approximation is employed. We validate these methods through comparisons with published literature and demonstrate their efficiency in treating large-scale systems through the construction of downfolded many-body Hamiltonians for carbon dimer defects embedded in hexagonal boron nitride supercells. Our work highlights the efficiency and general applicability of ISDF in the context of large-scale many-body calculations with k-point sampling beyond density functional theory.
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Affiliation(s)
- Chia-Nan Yeh
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Miguel A Morales
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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3
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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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4
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Zhang Z, Yin X, Hu W, Yang J. Machine Learning K-Means Clustering of Interpolative Separable Density Fitting Algorithm for Accurate and Efficient Cubic-Scaling Exact Exchange Plus Random Phase Approximation within Plane Waves. J Chem Theory Comput 2024; 20:1944-1961. [PMID: 38361423 DOI: 10.1021/acs.jctc.3c01157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/17/2024]
Abstract
The exact-exchange plus random-phase approximation (EXX+RPA) method has emerged as a crucial tool for precisely characterizing electronic structures in molecular and solid systems. We present an accurate and efficient implementation of EXX+RPA calculations that scale cubically and are conducted within plane waves. Our approach incorporates the interpolative separable density fitting (ISDF) algorithm, effectively mitigating the computational challenges associated with the plane wave basis set. To overcome the constraints of the conventional ISDF algorithm, characterized by the exceptionally high prefactor in QR factorization for interpolation point selection, we introduce an enhanced machine learning K-means method. This method incorporates a novel empirical weight function called "SSM+" for more precise interpolation point selection, capturing physical information more accurately across diverse systems. Our machine learning approach offers a quasiquadratic scaling alternative, effectively replacing the computationally demanding cubic-scaling QRCP algorithm in plane-wave-based EXX+RPA calculations. Furthermore, we enhance the method's capabilities by optimizing GPU acceleration using MATLAB's integrated GPU toolkit. In particular, our approach reduces the computational scaling of χ0 from 3.80 to 2.13 and the overall computational scaling of EXX from 2.74 to 2.10. We achieve a remarkable GPU acceleration speedup of up to 35×. Regarding CPU computation time, the standard quartic-scaling method requires 22 h to compute Si128, while QRCP completes the calculation in only around 1 h, achieving a speedup up to 20×. However, the utilization of the K-means algorithm reduces the time to 800 s, a substantial improvement of 100× compared to the standard algorithm. By employing the K-means algorithm, the computational time for interpolative point calculation using QRCP decreases from 1 h to 1 min, resulting in a 55× speed increase. With this improved algorithm, we successfully computed the dissociation curve of H2 and the equilibrium polyynic geometry of C18 molecules.
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Affiliation(s)
- Zhenlin Zhang
- Key Laboratory of Precision and Intelligent Chemistry, Department of Chemical Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xilin Yin
- Key Laboratory of Precision and Intelligent Chemistry, Department of Chemical Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Wei Hu
- Key Laboratory of Precision and Intelligent Chemistry, Department of Chemical Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jinlong Yang
- Key Laboratory of Precision and Intelligent Chemistry, Department of Chemical Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
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5
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Delesma FA, Leucke M, Golze D, Rinke P. Benchmarking the accuracy of the separable resolution of the identity approach for correlated methods in the numeric atom-centered orbitals framework. J Chem Phys 2024; 160:024118. [PMID: 38205851 DOI: 10.1063/5.0184406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 12/19/2023] [Indexed: 01/12/2024] Open
Abstract
Four-center two-electron Coulomb integrals routinely appear in electronic structure algorithms. The resolution-of-the-identity (RI) is a popular technique to reduce the computational cost for the numerical evaluation of these integrals in localized basis-sets codes. Recently, Duchemin and Blase proposed a separable RI scheme [J. Chem. Phys. 150, 174120 (2019)], which preserves the accuracy of the standard global RI method with the Coulomb metric and permits the formulation of cubic-scaling random phase approximation (RPA) and GW approaches. Here, we present the implementation of a separable RI scheme within an all-electron numeric atom-centered orbital framework. We present comprehensive benchmark results using the Thiel and the GW100 test set. Our benchmarks include atomization energies from Hartree-Fock, second-order Møller-Plesset (MP2), coupled-cluster singles and doubles, RPA, and renormalized second-order perturbation theory, as well as quasiparticle energies from GW. We found that the separable RI approach reproduces RI-free HF calculations within 9 meV and MP2 calculations within 1 meV. We have confirmed that the separable RI error is independent of the system size by including disordered carbon clusters up to 116 atoms in our benchmarks.
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Affiliation(s)
| | - Moritz Leucke
- Faculty for Chemistry and Food Chemistry, Technische Universität Dresden, 01062 Dresden, Germany
| | - Dorothea Golze
- Faculty for Chemistry and Food Chemistry, Technische Universität Dresden, 01062 Dresden, Germany
| | - Patrick Rinke
- Department of Applied Physics, Aalto University, FI-02150 Espoo, Finland
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6
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Stein F, Hutter J. Massively parallel implementation of gradients within the random phase approximation: Application to the polymorphs of benzene. J Chem Phys 2024; 160:024120. [PMID: 38214385 DOI: 10.1063/5.0180704] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 12/15/2023] [Indexed: 01/13/2024] Open
Abstract
The Random-Phase approximation (RPA) provides an appealing framework for semi-local density functional theory. In its Resolution-of-the-Identity (RI) approach, it is a very accurate and more cost-effective method than most other wavefunction-based correlation methods. For widespread applications, efficient implementations of nuclear gradients for structure optimizations and data sampling of machine learning approaches are required. We report a well scaling implementation of RI-RPA nuclear gradients on massively parallel computers. The approach is applied to two polymorphs of the benzene crystal obtaining very good cohesive and relative energies. Different correction and extrapolation schemes are investigated for further improvement of the results and estimations of error bars.
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Affiliation(s)
- Frederick Stein
- Center for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden, Rossendorf (HZDR), Untermarkt 20, 02826 Görlitz, Germany
| | - Jürg Hutter
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
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7
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Drontschenko V, Bangerter FH, Ochsenfeld C. Analytical Second-Order Properties for the Random Phase Approximation: Nuclear Magnetic Resonance Shieldings. J Chem Theory Comput 2023; 19:7542-7554. [PMID: 37863033 DOI: 10.1021/acs.jctc.3c00542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2023]
Abstract
A method for the analytical computation of nuclear magnetic resonance (NMR) shieldings within the direct random phase approximation (RPA) is presented. As a starting point, we use the RPA ground-state energy expression within the resolution-of-the-identity approximation in the atomic-orbital formalism. As has been shown in a recent benchmark study using numerical second derivatives [Glasbrenner, M. J. Chem. Theory Comput. 2022, 18, 192], RPA based on a Hartree-Fock reference shows accuracies comparable to coupled cluster singles and doubles (CCSD) for NMR chemical shieldings. Together with the much lower computational cost of RPA, it has emerged as an accurate method for the computation of NMR shieldings. Therefore, we aim to extend the applicability of RPA NMR to larger systems by introducing analytical second-order derivatives, making it a viable method for the accurate and efficient computation of NMR chemical shieldings.
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Affiliation(s)
- Viktoria Drontschenko
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Felix H Bangerter
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
- Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
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8
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Yeh CN, Morales MA. Low-Scaling Algorithm for the Random Phase Approximation Using Tensor Hypercontraction with k-point Sampling. J Chem Theory Comput 2023; 19:6197-6207. [PMID: 37624575 DOI: 10.1021/acs.jctc.3c00615] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/26/2023]
Abstract
We present a low-scaling algorithm for the random phase approximation (RPA) with k-point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a revised interpolative separable density fitting (ISDF) procedure with a momentum-dependent auxiliary basis for generic single-particle Bloch orbitals. Our formulation does not require preoptimized interpolating points or auxiliary bases, and the accuracy is systematically controlled by the number of interpolating points. The resulting RPA algorithm scales linearly with the number of k-points and cubically with the system size without any assumption on sparsity or locality of orbitals. The errors of ERIs and RPA energy show rapid convergence with respect to the size of the THC auxiliary basis, suggesting a promising and robust direction to construct efficient algorithms of higher order many-body perturbation theories for large-scale systems.
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Affiliation(s)
- Chia-Nan Yeh
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Miguel A Morales
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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9
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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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10
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Förster A. Assessment of the Second-Order Statically Screened Exchange Correction to the Random Phase Approximation for Correlation Energies. J Chem Theory Comput 2022; 18:5948-5965. [PMID: 36150190 PMCID: PMC9558381 DOI: 10.1021/acs.jctc.2c00366] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
With increasing interelectronic distance, the screening
of the
electron–electron interaction by the presence of other electrons
becomes the dominant source of electron correlation. This effect is
described by the random phase approximation (RPA) which is therefore
a promising method for the calculation of weak interactions. The success
of the RPA relies on the cancellation of errors, which can be traced
back to the violation of the crossing symmetry of the 4-point vertex,
leading to strongly overestimated total correlation energies. By the
addition of second-order screened exchange (SOSEX) to the correlation
energy, this issue is substantially reduced. In the adiabatic connection
(AC) SOSEX formalism, one of the two electron–electron interaction
lines in the second-order exchange term is dynamically screened (SOSEX(W, vc)). A
related SOSEX expression in which both electron–electron interaction
lines are statically screened (SOSEX(W(0), W(0))) is obtained from the G3W2 contribution to the electronic self-energy. In contrast to SOSEX(W, vc), the
evaluation of this correlation energy expression does not require
an expensive numerical frequency integration and is therefore advantageous
from a computational perspective. We compare the accuracy of the statically
screened variant to RPA and RPA+SOSEX(W, vc) for a wide range of chemical
reactions. While both methods fail for barrier heights, SOSEX(W(0), W(0)) agrees very well with SOSEX(W, vc) for
charged excitations and noncovalent interactions where they lead to
major improvements over RPA.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV, Amsterdam, The Netherlands
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11
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Stein F, Hutter J. Double-hybrid density functionals for the condensed phase: Gradients, stress tensor, and auxiliary-density matrix method acceleration. J Chem Phys 2022; 156:074107. [DOI: 10.1063/5.0082327] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Frederick Stein
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, Zurich 8057, Switzerland
| | - Jürg Hutter
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, Zurich 8057, Switzerland
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12
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Taherivardanjani S, Elfgen R, Reckien W, Suarez E, Perlt E, Kirchner B. Benchmarking the Computational Costs and Quality of Vibrational Spectra from Ab Initio Simulations. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202100293] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Shima Taherivardanjani
- Mulliken Center for Theoretical Chemistry Institute for Physical and Theoretical Chemistry Beringstr. 4 Bonn D‐53115 Germany
| | - Roman Elfgen
- Mulliken Center for Theoretical Chemistry Institute for Physical and Theoretical Chemistry Beringstr. 4 Bonn D‐53115 Germany
| | - Werner Reckien
- Mulliken Center for Theoretical Chemistry Institute for Physical and Theoretical Chemistry Beringstr. 4 Bonn D‐53115 Germany
| | - Estela Suarez
- Institute for Advanced Simulation Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH Wilhelm‐Johnen‐Straße Jülich D‐52425 Germany
| | - Eva Perlt
- Otto Schott Institute of Materials Research Faculty of Physics and Astronomy Friedrich‐Schiller‐Universität Jena Löbdergraben 32 Jena D‐07743 Germany
| | - Barbara Kirchner
- Mulliken Center for Theoretical Chemistry Institute for Physical and Theoretical Chemistry Beringstr. 4 Bonn D‐53115 Germany
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13
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Chedid J, Jocelyn N, Eshuis H. Energies, structures, and harmonic frequencies of small water clusters from the direct random phase approximation. J Chem Phys 2021; 155:084303. [PMID: 34470345 DOI: 10.1063/5.0059343] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
The binding energies, structures, and vibrational frequencies of water clusters up to 20 molecules are computed at the direct random phase approximation (RPA) level of theory and compared to theoretical benchmarks. Binding energies of the WATER27 set, which includes neutral and positively and negatively charged clusters, are predicted to be too low in the complete basis set limit by an average of 7 kcal/mol (9%) and are worse than the results from the best density functional theory methods or from the Møller-Plesset theory. The RPA shows significant basis set size dependence for binding energies. The order of the relative energies of the water hexamer and dodecamer isomers is predicted correctly by the RPA. The mean absolute deviation for angles and distances for neutral clusters up to the water hexamer are 0.2° and 0.6 pm, respectively, using quintuple-ζ basis sets. The relative energetic order of the hexamer isomers is preserved upon optimization. Vibrational frequencies for these systems are underestimated by several tens of wavenumbers for large basis sets, and deviations increase with the basis set size. Overall, the direct RPA method yields accurate structural parameters but systematically underestimates binding energies and shows strong basis set size dependence.
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Affiliation(s)
- Julianna Chedid
- Department of Chemistry and Biochemistry, Montclair State University, Montclair, New Jersey 07043, USA
| | - Nedjie Jocelyn
- Department of Chemistry and Biochemistry, Montclair State University, Montclair, New Jersey 07043, USA
| | - Henk Eshuis
- Department of Chemistry and Biochemistry, Montclair State University, Montclair, New Jersey 07043, USA
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14
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Rybkin VV. Formulation and Implementation of Density Functional Embedding Theory Using Products of Basis Functions. J Chem Theory Comput 2021; 17:3995-4005. [PMID: 34048247 DOI: 10.1021/acs.jctc.1c00175] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
The representation of embedding potential using products of atomic orbital basis functions has been developed in the context of density functional embedding theory. The formalism allows to treat pseudopotential and all-electron calculations on the same footing and enables simple transfer of the embedding potential in a compact matrix form. In addition, a cost-reduction procedure for the basis set and potential reduction based on population analysis has been proposed. Implemented for the condensed-phase and molecular systems within Gaussian and plane-waves and Gaussian and augmented plane-waves formalisms, the scheme has been tested for proton-transfer reactions in the cluster and the condensed phase and projected density of states of carbon monoxide adsorbed on platinum surface. With the computational scaling of the embedding potential optimization similar to that of hybrid density functional theory with a significantly reduced prefactor, the method allows for large-scale applications to extended systems.
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Affiliation(s)
- Vladimir V Rybkin
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, Zürich 8057, Switzerland
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15
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Sharma S, Beylkin G. Efficient Evaluation of Two-Center Gaussian Integrals in Periodic Systems. J Chem Theory Comput 2021; 17:3916-3922. [PMID: 34061523 DOI: 10.1021/acs.jctc.0c01195] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
By using Poisson's summation formula, we calculate periodic integrals over Gaussian basis functions by partitioning the lattice summations between the real and reciprocal space, where both sums converge exponentially fast with a large exponent. We demonstrate that the summation can be performed efficiently to calculate two-center Gaussian integrals over various kernels including overlap, kinetic, and Coulomb. The summation in real space is performed using an efficient flavor of the McMurchie-Davidson recurrence relation. The expressions for performing summation in the reciprocal space are also derived and implemented. The algorithm for reciprocal space summation allows us to reuse several terms and leads to a significant improvement in efficiency when highly contracted basis functions with large exponents are used. We find that the resulting algorithm is only between a factor of 5 and 15 slower than that for molecular integrals, indicating the very small number of terms needed in both the real and reciprocal space summations. An outline of the algorithm for calculating three-center Coulomb integrals is also provided.
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Affiliation(s)
- Sandeep Sharma
- Department of Chemistry, University of Colorado, Boulder, Boulder, Colorado 80302, United States
| | - Gregory Beylkin
- Department of Applied Mathematics, University of Colorado, Boulder, Boulder, Colorado 80309, United States
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16
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Wilhelm J, Seewald P, Golze D. Low-Scaling GW with Benchmark Accuracy and Application to Phosphorene Nanosheets. J Chem Theory Comput 2021; 17:1662-1677. [DOI: 10.1021/acs.jctc.0c01282] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- Jan Wilhelm
- Institute of Theoretical Physics, University of Regensburg, D-93053 Regensburg, Germany
| | - Patrick Seewald
- Department of Chemistry, University of Zurich, CH-8057 Zurich, Switzerland
| | - Dorothea Golze
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
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17
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Modrzejewski M, Yourdkhani S, Śmiga S, Klimeš J. Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage. J Chem Theory Comput 2021; 17:804-817. [PMID: 33445879 DOI: 10.1021/acs.jctc.0c00966] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH4···(H2O)20, is a stringent test for approximate methods, including density functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here, we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA), which uses approximate Kohn-Sham orbitals as its input. The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of the many-body expansion. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the many-body expansion. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.
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Affiliation(s)
- Marcin Modrzejewski
- Faculty of Chemistry, University of Warsaw, 02-093 Warsaw, Pasteura 1, Poland.,Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
| | - Sirous Yourdkhani
- Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
| | - Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5, 87-100 Toruń, Poland
| | - Jiří Klimeš
- Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
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18
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Abstract
The unprecedented ability of computations to probe atomic-level details of catalytic systems holds immense promise for the fundamentals-based bottom-up design of novel heterogeneous catalysts, which are at the heart of the chemical and energy sectors of industry. Here, we critically analyze recent advances in computational heterogeneous catalysis. First, we will survey the progress in electronic structure methods and atomistic catalyst models employed, which have enabled the catalysis community to build increasingly intricate, realistic, and accurate models of the active sites of supported transition-metal catalysts. We then review developments in microkinetic modeling, specifically mean-field microkinetic models and kinetic Monte Carlo simulations, which bridge the gap between nanoscale computational insights and macroscale experimental kinetics data with increasing fidelity. We finally review the advancements in theoretical methods for accelerating catalyst design and discovery. Throughout the review, we provide ample examples of applications, discuss remaining challenges, and provide our outlook for the near future.
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Affiliation(s)
- Benjamin W J Chen
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States
| | - Lang Xu
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States
| | - Manos Mavrikakis
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States
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19
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Rishi V, Perera A, Bartlett RJ. A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory. J Chem Phys 2020; 153:234101. [DOI: 10.1063/5.0023862] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Varun Rishi
- Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Ajith Perera
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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20
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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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21
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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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22
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Kühne TD, Iannuzzi M, Del Ben M, Rybkin VV, Seewald P, Stein F, Laino T, Khaliullin RZ, Schütt O, Schiffmann F, Golze D, Wilhelm J, Chulkov S, Bani-Hashemian MH, Weber V, Borštnik U, Taillefumier M, Jakobovits AS, Lazzaro A, Pabst H, Müller T, Schade R, Guidon M, Andermatt S, Holmberg N, Schenter GK, Hehn A, Bussy A, Belleflamme F, Tabacchi G, Glöß A, Lass M, Bethune I, Mundy CJ, Plessl C, Watkins M, VandeVondele J, Krack M, Hutter J. CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations. J Chem Phys 2020; 152:194103. [PMID: 33687235 DOI: 10.1063/5.0007045] [Citation(s) in RCA: 856] [Impact Index Per Article: 214.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.
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Affiliation(s)
- Thomas D Kühne
- Dynamics of Condensed Matter and Center for Sustainable Systems Design, Chair of Theoretical Chemistry, Paderborn University, Warburger Str. 100, D-33098 Paderborn, Germany
| | - Marcella Iannuzzi
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Mauro Del Ben
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Vladimir V Rybkin
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Patrick Seewald
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Frederick Stein
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Teodoro Laino
- IBM Research Europe, CH-8803 Rüschlikon, Switzerland
| | - Rustam Z Khaliullin
- Department of Chemistry, McGill University, CH-801 Sherbrooke St. West, Montreal, Quebec H3A 0B8, Canada
| | - Ole Schütt
- Department of Materials, ETH Zürich, CH-8092 Zürich, Switzerland
| | | | - Dorothea Golze
- Department of Applied Physics, Aalto University, Otakaari 1, FI-02150 Espoo, Finland
| | - Jan Wilhelm
- Institute of Theoretical Physics, University of Regensburg, Universitätsstraße 31, D-93053 Regensburg, Germany
| | - Sergey Chulkov
- School of Mathematics and Physics, University of Lincoln, Brayford Pool, Lincoln, United Kingdom
| | | | - Valéry Weber
- IBM Research Europe, CH-8803 Rüschlikon, Switzerland
| | | | | | | | | | - Hans Pabst
- Intel Extreme Computing, Software and Systems, Zürich, Switzerland
| | - Tiziano Müller
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Robert Schade
- Department of Computer Science and Paderborn Center for Parallel Computing, Paderborn University, Warburger Str. 100, D-33098 Paderborn, Germany
| | - Manuel Guidon
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Samuel Andermatt
- Integrated Systems Laboratory, ETH Zürich, CH-8092 Zürich, Switzerland
| | - Nico Holmberg
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, 00076 Aalto, Finland
| | - Gregory K Schenter
- Physical Science Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA
| | - Anna Hehn
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Augustin Bussy
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Fabian Belleflamme
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Gloria Tabacchi
- Department of Science and High Technology, University of Insubria and INSTM, via Valleggio 9, I-22100 Como, Italy
| | - Andreas Glöß
- BASF SE, Carl-Bosch-Straße 38, D-67056 Ludwigshafen am Rhein, Germany
| | - Michael Lass
- Department of Computer Science and Paderborn Center for Parallel Computing, Paderborn University, Warburger Str. 100, D-33098 Paderborn, Germany
| | - Iain Bethune
- Hartree Centre, Science and Technology Facilities Council, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
| | - Christopher J Mundy
- Physical Science Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA
| | - Christian Plessl
- Department of Computer Science and Paderborn Center for Parallel Computing, Paderborn University, Warburger Str. 100, D-33098 Paderborn, Germany
| | - Matt Watkins
- School of Mathematics and Physics, University of Lincoln, Brayford Pool, Lincoln, United Kingdom
| | - Joost VandeVondele
- Swiss National Supercomputing Centre (CSCS), ETH Zürich, Zürich, Switzerland
| | - Matthias Krack
- Laboratory for Scientific Computing and Modelling, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
| | - Jürg Hutter
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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23
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Gao W, Chelikowsky JR. Accelerating Time-Dependent Density Functional Theory and GW Calculations for Molecules and Nanoclusters with Symmetry Adapted Interpolative Separable Density Fitting. J Chem Theory Comput 2020; 16:2216-2223. [DOI: 10.1021/acs.jctc.9b01025] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Weiwei Gao
- Center for Computational Materials, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin Austin, Texas 78712, United States
| | - James R. Chelikowsky
- Center for Computational Materials, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin Austin, Texas 78712, United States
- Department of Physics, The University of Texas at Austin Austin, Texas 78712, United States
- Mcketta Department of Chemical Engineering, The University of Texas at Austin Austin, Texas 78712, United States
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24
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Ramberger B, Sukurma Z, Schäfer T, Kresse G. RPA natural orbitals and their application to post-Hartree-Fock electronic structure methods. J Chem Phys 2019; 151:214106. [DOI: 10.1063/1.5128415] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Benjamin Ramberger
- Faculty of Physics and Center for Computational Materials Sciences, University of Vienna, Sensengasse 8/12, 1090 Vienna, Austria
| | - Zoran Sukurma
- Faculty of Physics and Center for Computational Materials Sciences, University of Vienna, Sensengasse 8/12, 1090 Vienna, Austria
| | - Tobias Schäfer
- Institute for Theoretical Physics, Technical University of Vienna, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Georg Kresse
- Faculty of Physics and Center for Computational Materials Sciences, University of Vienna, Sensengasse 8/12, 1090 Vienna, Austria
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25
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Rybkin VV. Sampling Potential Energy Surfaces in the Condensed Phase with Many‐Body Electronic Structure Methods. Chemistry 2019; 26:362-368. [DOI: 10.1002/chem.201904012] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2019] [Indexed: 11/10/2022]
Affiliation(s)
- Vladimir V. Rybkin
- Department of ChemistryUniversity of Zurich Winterthurerstrasse 190 CH-8057 Zurich Switzerland
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26
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Modrzejewski M, Yourdkhani S, Klimeš J. Random Phase Approximation Applied to Many-Body Noncovalent Systems. J Chem Theory Comput 2019; 16:427-442. [DOI: 10.1021/acs.jctc.9b00979] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Marcin Modrzejewski
- Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Sirous Yourdkhani
- Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
| | - Jiří Klimeš
- Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
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27
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Graf D, Beuerle M, Ochsenfeld C. Low-Scaling Self-Consistent Minimization of a Density Matrix Based Random Phase Approximation Method in the Atomic Orbital Space. J Chem Theory Comput 2019; 15:4468-4477. [PMID: 31368702 DOI: 10.1021/acs.jctc.9b00444] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
An efficient minimization of the random phase approximation (RPA) energy with respect to the one-particle density matrix in the atomic orbital space is presented. The problem of imposing full self-consistency on functionals depending on the potential itself is bypassed by approximating the RPA Hamiltonian on the basis of the well-known Hartree-Fock Hamiltonian making our self-consistent RPA method completely parameter-free. It is shown that the new method not only outperforms post-Kohn-Sham RPA in describing noncovalent interactions but also gives accurate dipole moments demonstrating the high quality of the calculated densities. Furthermore, the main drawback of atomic orbital based methods, in increasing the prefactor as compared to their canonical counterparts, is overcome by introducing Cholesky decomposed projectors allowing the use of large basis sets. Exploiting the locality of atomic and/or Cholesky orbitals enables us to present a self-consistent RPA method which shows asymptotically quadratic scaling opening the door for calculations on large molecular systems.
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Affiliation(s)
- Daniel Graf
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany
| | - Matthias Beuerle
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany
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28
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Duchemin I, Blase X. Separable resolution-of-the-identity with all-electron Gaussian bases: Application to cubic-scaling RPA. J Chem Phys 2019; 150:174120. [PMID: 31067912 DOI: 10.1063/1.5090605] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We explore a separable resolution-of-the-identity (RI) formalism built on quadratures over limited sets of real-space points designed for all-electron calculations. Our implementation preserves, in particular, the use of common atomic orbitals and their related auxiliary basis sets. The setup of the present density fitting scheme, i.e., the calculation of the system specific quadrature weights, scales cubically with respect to the system size. Extensive accuracy tests are presented for the Fock exchange and MP2 correlation energies. We finally demonstrate random phase approximation (RPA) correlation energy calculations with a scaling that is cubic in terms of operations, quadratic in memory, with a small crossover with respect to our standard RI-RPA implementation.
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Affiliation(s)
- Ivan Duchemin
- Laboratoire de Simulation Atomistique, Université Grenoble Alpes, CEA, 38054 Grenoble, France
| | - Xavier Blase
- Institut NEEL, Université Grenoble Alpes, CNRS, F-38042 Grenoble, France
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29
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Hummel F, Grüneis A, Kresse G, Ziesche P. Screened Exchange Corrections to the Random Phase Approximation from Many-Body Perturbation Theory. J Chem Theory Comput 2019; 15:3223-3236. [PMID: 30901204 DOI: 10.1021/acs.jctc.8b01247] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms that would otherwise cancel Pauli exclusion principle violating (EPV) contributions. The uncanceled EPV contributions also manifest themselves in form of an unphysical negative pair density of spin-parallel electrons close to electron-electron coalescence. We follow considerations of many-body perturbation theory to propose an exchange correction that corrects the largest set of EPV contributions, while having the lowest possible computational complexity. The proposed method exchanges adjacent particle/hole pairs in the RPA diagrams, considerably improving the pair density of spin-parallel electrons close to coalescence in the uniform electron gas (UEG). The accuracy of the correlation energy is comparable to other variants of second-order screened exchange (SOSEX) corrections although it is slightly more accurate for the spin-polarized UEG. Its computational complexity scales as [Formula: see text] or [Formula: see text] in orbital space or real space, respectively. Its memory requirement scales as [Formula: see text].
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Affiliation(s)
- Felix Hummel
- Institute for Theoretical Physics , Technische Universität Wien , Wiedner Hauptstraße 8-10/136 , 1040 Vienna , Austria
| | - Andreas Grüneis
- Institute for Theoretical Physics , Technische Universität Wien , Wiedner Hauptstraße 8-10/136 , 1040 Vienna , Austria
| | - Georg Kresse
- University of Vienna , Faculty of Physics and Center for Computational Materials Sciences , Sensengasse 8/12 , 1090 Vienna , Austria
| | - Paul Ziesche
- Max Planck Institute for the Physics of Complex Systems Nöthnitzer Straße 38 , 01187 Dresden , Germany
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30
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Ajala AO, Voora V, Mardirossian N, Furche F, Paesani F. Assessment of Density Functional Theory in Predicting Interaction Energies between Water and Polycyclic Aromatic Hydrocarbons: from Water on Benzene to Water on Graphene. J Chem Theory Comput 2019; 15:2359-2374. [PMID: 30860827 DOI: 10.1021/acs.jctc.9b00110] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
The interactions of water with polycyclic aromatic hydrocarbons, from benzene to graphene, are investigated using various exchange-correlation functionals selected across the hierarchy of density functional theory (DFT) approximations. The accuracy of the different functionals is assessed through comparisons with random phase approximation (RPA) and coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] calculations. Diffusion Monte Carlo (DMC) data reported in the literature are also used for comparison. Relatively large variations are found in interaction energies predicted by different DFT models, with GGA functionals underestimating the interaction strength for configurations with the water oxygen pointing toward the aromatic molecules. The meta-GGA B97M-rV and range-separated hybrid, meta-GGA ωB97M-V functionals provide nearly quantitative agreement with CCSD(T) values for the water-benzene, water-coronene, and water-circumcoronene dimers, while RPA and DMC predict interaction energies that differ by up to ∼1 kcal/mol and ∼0.4 kcal/mol from the corresponding CCSD(T) values, respectively. Similar trends among GGA, meta-GGA, and hybrid functionals are observed for larger polycyclic aromatic hydrocarbons. By performing absolutely localized molecular orbital energy decomposition analyses (ALMO-EDA), it is found that, independently of the number of carbon atoms and exchange-correlation functional, the dominant contributions to the interaction energies between water and polycyclic aromatic hydrocarbon molecules are the electrostatic and dispersion terms while polarization and charge transfer effects are negligibly small. Calculations carried out with GGA and meta-GGA functionals indicate that, as the number of carbon atoms increases, the interaction energies slowly converge to the corresponding values obtained for an infinite graphene sheet.
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Affiliation(s)
- Adeayo O Ajala
- Department of Chemistry and Biochemistry , University of California San Diego , La Jolla , California 92093 , United States
| | - Vamsee Voora
- Department of Chemistry , University of California Irvine , Irvine , California 92697 , United States
| | - Narbe Mardirossian
- Division of Chemistry and Chemical Engineering , California Institute of Technology , 1200 E. California Boulevard , Pasadena , California 91125 , United States
| | - Filipp Furche
- Department of Chemistry , University of California Irvine , Irvine , California 92697 , United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry , University of California San Diego , La Jolla , California 92093 , United States.,Materials Science and Engineering , University of California San Diego , La Jolla , California 92093 , United States.,San Diego Supercomputer Center , University of California San Diego , La Jolla , California 92093 , United States
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31
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Brandenburg JG, Zen A, Fitzner M, Ramberger B, Kresse G, Tsatsoulis T, Grüneis A, Michaelides A, Alfè D. Physisorption of Water on Graphene: Subchemical Accuracy from Many-Body Electronic Structure Methods. J Phys Chem Lett 2019; 10:358-368. [PMID: 30615460 DOI: 10.1021/acs.jpclett.8b03679] [Citation(s) in RCA: 64] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Wet carbon interfaces are ubiquitous in the natural world and exhibit anomalous properties, which could be exploited by emerging technologies. However, progress is limited by lack of understanding at the molecular level. Remarkably, even for the most fundamental system (a single water molecule interacting with graphene), there is no consensus on the nature of the interaction. We tackle this by performing an extensive set of complementary state-of-the-art computer simulations on some of the world's largest supercomputers. From this effort a consensus on the water-graphene interaction strength has been obtained. Our results have significant impact for the physical understanding, as they indicate that the interaction is weaker than predicted previously. They also pave the way for more accurate and reliable studies of liquid water at carbon interfaces.
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Affiliation(s)
- Jan Gerit Brandenburg
- Department of Physics and Astronomy , University College London , Gower Street , London WC1E 6BT , United Kingdom
- Thomas Young Centre and London Centre for Nanotechnology , 17-19 Gordon Street , London WC1H 0AH , United Kingdom
| | - Andrea Zen
- Department of Physics and Astronomy , University College London , Gower Street , London WC1E 6BT , United Kingdom
- Thomas Young Centre and London Centre for Nanotechnology , 17-19 Gordon Street , London WC1H 0AH , United Kingdom
| | - Martin Fitzner
- Department of Physics and Astronomy , University College London , Gower Street , London WC1E 6BT , United Kingdom
- Thomas Young Centre and London Centre for Nanotechnology , 17-19 Gordon Street , London WC1H 0AH , United Kingdom
| | - Benjamin Ramberger
- University of Vienna , Faculty of Physics and Center for Computational Materials Sciences , Sensengasse 8/12 , 1090 Wien , Austria
| | - Georg Kresse
- University of Vienna , Faculty of Physics and Center for Computational Materials Sciences , Sensengasse 8/12 , 1090 Wien , Austria
| | - Theodoros Tsatsoulis
- Institute for Theoretical Physics , Vienna University of Technology , Wiedner Hauptstrasse 8-10 , 1040 Vienna , Austria
- Max Planck Institute for Solid State Research , Heisenbergstrasse 1 , 70569 Stuttgart , Germany
| | - Andreas Grüneis
- Institute for Theoretical Physics , Vienna University of Technology , Wiedner Hauptstrasse 8-10 , 1040 Vienna , Austria
- Max Planck Institute for Solid State Research , Heisenbergstrasse 1 , 70569 Stuttgart , Germany
| | - Angelos Michaelides
- Department of Physics and Astronomy , University College London , Gower Street , London WC1E 6BT , United Kingdom
- Thomas Young Centre and London Centre for Nanotechnology , 17-19 Gordon Street , London WC1H 0AH , United Kingdom
| | - Dario Alfè
- Thomas Young Centre and London Centre for Nanotechnology , 17-19 Gordon Street , London WC1H 0AH , United Kingdom
- Department of Earth Sciences , University College London , Gower Street , London WC1E 6BT , United Kingdom
- Dipartimento di Fisica Ettore Pancini , Università di Napoli Federico II , Monte S. Angelo, I-80126 Napoli , Italy
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32
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Beuerle M, Ochsenfeld C. Low-scaling analytical gradients for the direct random phase approximation using an atomic orbital formalism. J Chem Phys 2018; 149:244111. [DOI: 10.1063/1.5052572] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Affiliation(s)
- Matthias Beuerle
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
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33
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Caldeweyher E, Brandenburg JG. Simplified DFT methods for consistent structures and energies of large systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:213001. [PMID: 29633964 DOI: 10.1088/1361-648x/aabcfb] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Kohn-Sham density functional theory (DFT) is routinely used for the fast electronic structure computation of large systems and will most likely continue to be the method of choice for the generation of reliable geometries in the foreseeable future. Here, we present a hierarchy of simplified DFT methods designed for consistent structures and non-covalent interactions of large systems with particular focus on molecular crystals. The covered methods are a minimal basis set Hartree-Fock (HF-3c), a small basis set screened exchange hybrid functional (HSE-3c), and a generalized gradient approximated functional evaluated in a medium-sized basis set (B97-3c), all augmented with semi-classical correction potentials. We give an overview on the methods design, a comprehensive evaluation on established benchmark sets for geometries and lattice energies of molecular crystals, and highlight some realistic applications on large organic crystals with several hundreds of atoms in the primitive unit cell.
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Affiliation(s)
- Eike Caldeweyher
- Mulliken Center for Theoretical Chemistry, Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, 53115 Bonn, Germany
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34
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Beuerle M, Graf D, Schurkus HF, Ochsenfeld C. Efficient calculation of beyond RPA correlation energies in the dielectric matrix formalism. J Chem Phys 2018; 148:204104. [DOI: 10.1063/1.5025938] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matthias Beuerle
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
| | - Daniel Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
| | - Henry F. Schurkus
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
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35
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Graf D, Beuerle M, Schurkus HF, Luenser A, Savasci G, Ochsenfeld C. Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method. J Chem Theory Comput 2018; 14:2505-2515. [PMID: 29658715 DOI: 10.1021/acs.jctc.8b00177] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.
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Affiliation(s)
- Daniel Graf
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany
| | - Matthias Beuerle
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany
| | - Henry F Schurkus
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany
| | - Arne Luenser
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany
| | - Gökcen Savasci
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany.,Max Planck Institute for Solid State Research , Heisenbergstraße 1 , 70569 Stuttgart , Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany.,Max Planck Institute for Solid State Research , Heisenbergstraße 1 , 70569 Stuttgart , Germany
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36
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Bates JE, Sengupta N, Sensenig J, Ruzsinszky A. Adiabatic Connection without Coupling Constant Integration. J Chem Theory Comput 2018; 14:2979-2990. [DOI: 10.1021/acs.jctc.8b00067] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jefferson E. Bates
- Department of Chemistry, Appalachian State University, Boone, North Carolina 28607, United States
| | - Niladri Sengupta
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Jonathon Sensenig
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, United States
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37
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Wilhelm J, Golze D, Talirz L, Hutter J, Pignedoli CA. Toward GW Calculations on Thousands of Atoms. J Phys Chem Lett 2018; 9:306-312. [PMID: 29280376 DOI: 10.1021/acs.jpclett.7b02740] [Citation(s) in RCA: 71] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
The GW approximation of many-body perturbation theory is an accurate method for computing electron addition and removal energies of molecules and solids. In a canonical implementation, however, its computational cost is [Formula: see text] in the system size N, which prohibits its application to many systems of interest. We present a full-frequency GW algorithm in a Gaussian-type basis, whose computational cost scales with N2 to N3. The implementation is optimized for massively parallel execution on state-of-the-art supercomputers and is suitable for nanostructures and molecules in the gas, liquid or condensed phase, using either pseudopotentials or all electrons. We validate the accuracy of the algorithm on the GW100 molecular test set, finding mean absolute deviations of 35 meV for ionization potentials and 27 meV for electron affinities. Furthermore, we study the length-dependence of quasiparticle energies in armchair graphene nanoribbons of up to 1734 atoms in size, and compute the local density of states across a nanoscale heterojunction.
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Affiliation(s)
- Jan Wilhelm
- Department of Chemistry, University of Zurich , Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Dorothea Golze
- COMP/Department of Applied Physics, Aalto University , P.O. Box 11100, FI-00076 Aalto, Finland
| | - Leopold Talirz
- Laboratory of Molecular Simulation, École Polytechnique Fédérale de Lausanne , Rue de l'Industrie 17, CH-1951 Sion, Switzerland
- Theory and Simulation of Materials, École Polytechnique Fédérale de Lausanne , Station 9, CH-1015 Lausanne, Switzerland
| | - Jürg Hutter
- Department of Chemistry, University of Zurich , Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Carlo A Pignedoli
- Swiss Federal Laboratories for Materials Science and Technology (Empa) , Überlandstrasse 129, CH-8600 Dübendorf, Switzerland
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38
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Beuerle M, Ochsenfeld C. Short-range second order screened exchange correction to RPA correlation energies. J Chem Phys 2017; 147:204107. [DOI: 10.1063/1.4998647] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Matthias Beuerle
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
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39
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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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40
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Luenser A, Schurkus HF, Ochsenfeld C. Vanishing-Overhead Linear-Scaling Random Phase Approximation by Cholesky Decomposition and an Attenuated Coulomb-Metric. J Chem Theory Comput 2017; 13:1647-1655. [DOI: 10.1021/acs.jctc.6b01235] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Arne Luenser
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstrasse
5-13, D-81377 Munich, Germany
- Center for Integrated Protein Science Munich (CIPSM), Butenandtstrasse
5-13, D-81377 Munich, Germany
| | - Henry F. Schurkus
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstrasse
5-13, D-81377 Munich, Germany
- Center for Integrated Protein Science Munich (CIPSM), Butenandtstrasse
5-13, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstrasse
5-13, D-81377 Munich, Germany
- Center for Integrated Protein Science Munich (CIPSM), Butenandtstrasse
5-13, D-81377 Munich, Germany
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41
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Grundei MMJ, Burow AM. Random Phase Approximation for Periodic Systems Employing Direct Coulomb Lattice Summation. J Chem Theory Comput 2017; 13:1159-1175. [DOI: 10.1021/acs.jctc.6b01146] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Martin M. J. Grundei
- Department of Chemistry, Ludwig-Maximilians-Universität (LMU) Munich, Butenandtstrasse 7, D-81377 Munich, Germany
| | - Asbjörn M. Burow
- Department of Chemistry, Ludwig-Maximilians-Universität (LMU) Munich, Butenandtstrasse 7, D-81377 Munich, Germany
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