1
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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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2
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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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3
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Graml M, Zollner K, Hernangómez-Pérez D, Faria Junior PE, Wilhelm J. Low-Scaling GW Algorithm Applied to Twisted Transition-Metal Dichalcogenide Heterobilayers. J Chem Theory Comput 2024; 20:2202-2208. [PMID: 38353944 PMCID: PMC10938508 DOI: 10.1021/acs.jctc.3c01230] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Revised: 12/30/2023] [Accepted: 01/08/2024] [Indexed: 03/13/2024]
Abstract
The GW method is widely used for calculating the electronic band structure of materials. The high computational cost of GW algorithms prohibits their application to many systems of interest. We present a periodic, low-scaling, and highly efficient GW algorithm that benefits from the locality of the Gaussian basis and the polarizability. The algorithm enables G0W0 calculations on a MoSe2/WS2 bilayer with 984 atoms per unit cell, in 42 h using 1536 cores. This is 4 orders of magnitude faster than a plane-wave G0W0 algorithm, allowing for unprecedented computational studies of electronic excitations at the nanoscale.
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Affiliation(s)
- Maximilian Graml
- Institute
of Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany
- Regensburg
Center for Ultrafast Nanoscopy (RUN), University
of Regensburg, 93053 Regensburg, Germany
| | - Klaus Zollner
- Institute
of Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany
| | - Daniel Hernangómez-Pérez
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Paulo E. Faria Junior
- Institute
of Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany
| | - Jan Wilhelm
- Institute
of Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany
- Regensburg
Center for Ultrafast Nanoscopy (RUN), University
of Regensburg, 93053 Regensburg, Germany
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4
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Lemke Y, Ochsenfeld C. Highly accurate σ- and τ-functionals for beyond-RPA methods with approximate exchange kernels. J Chem Phys 2023; 159:194104. [PMID: 37966000 DOI: 10.1063/5.0173042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2023] [Accepted: 10/12/2023] [Indexed: 11/16/2023] Open
Abstract
σ-Functionals are promising new developments for the Kohn-Sham correlation energy based upon the direct Random Phase Approximation (dRPA) within the adiabatic connection formalism, providing impressive improvements over dRPA for a broad range of benchmarks. However, σ-functionals exhibit a high amount of self-interaction inherited from the approximations made within dRPA. Inclusion of an exchange kernel in deriving the coupling-strength-dependent density-density response function leads to so-called τ-functionals, which - apart from a fourth-order Taylor series expansion - have only been realized in an approximate fashion so far to the best of our knowledge, most notably in the form of scaled σ-functionals. In this work, we derive, optimize, and benchmark three types of σ- and τ-functionals including approximate exchange effects in the form of an antisymmetrized Hartree kernel. These functionals, based on a second-order screened exchange type contribution in the adiabatic connection formalism, the electron-hole time-dependent Hartree-Fock kernel (eh-TDHF) otherwise known as RPA with exchange (RPAx), and an approximation thereof known as approximate exchange kernel (AXK), are optimized on the ASCDB database using two new parametrizations named A1 and A2. In addition, we report a first full evaluation of σ- and τ-functionals on the GMTKN55 database, revealing our exchange-including functionals to considerably outperform existing σ-functionals while being highly competitive with some of the best double-hybrid functionals of the original GMTKN55 publication. In particular, the σ-functionals based on AXK and τ-functionals based on RPAx with PBE0 reference stand out as highly accurate approaches for a wide variety of chemically relevant problems.
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Affiliation(s)
- Yannick Lemke
- Chair of Theoretical Chemistry, Department of Chemistry, Ludwig-Maximilians-Universität München (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, Ludwig-Maximilians-Universität München (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
- Max-Planck-Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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5
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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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6
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Graf D, Thom AJW. Corrected density functional theory and the random phase approximation: Improved accuracy at little extra cost. J Chem Phys 2023; 159:174106. [PMID: 37921249 DOI: 10.1063/5.0168569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Accepted: 10/16/2023] [Indexed: 11/04/2023] Open
Abstract
We recently introduced an efficient methodology to perform density-corrected Hartree-Fock density functional theory [DC(HF)-DFT] calculations and an extension to it we called "corrected" HF DFT [C(HF)-DFT] [Graf and Thom, J. Chem. Theory Comput. 19 5427-5438 (2023)]. In this work, we take a further step and combine C(HF)-DFT, augmented with a straightforward orbital energy correction, with the random phase approximation (RPA). We refer to the resulting methodology as corrected HF RPA [C(HF)-RPA]. We evaluate the proposed methodology across various RPA methods: direct RPA (dRPA), RPA with an approximate exchange kernel, and RPA with second-order screened exchange. C(HF)-dRPA demonstrates very promising performance; for RPA with exchange methods, on the other hand, we often find over-corrections.
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Affiliation(s)
- Daniel Graf
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, England
| | - Alex J W Thom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, England
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7
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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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8
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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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9
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Drontschenko V, Graf D, Laqua H, Ochsenfeld C. Efficient Method for the Computation of Frozen-Core Nuclear Gradients within the Random Phase Approximation. J Chem Theory Comput 2022; 18:7359-7372. [PMID: 36331398 DOI: 10.1021/acs.jctc.2c00774] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
A method for the evaluation of analytical frozen-core gradients within the random phase approximation is presented. We outline an efficient way to evaluate the response of the density of active electrons arising only when introducing the frozen-core approximation and constituting the main difficulty, together with the response of the standard Kohn-Sham density. The general framework allows to extend the outlined procedure to related electron correlation methods in the atomic orbital basis that require the evaluation of density responses, such as second-order Møller-Plesset perturbation theory or coupled cluster variants. By using Cholesky decomposed densities─which reintroduce the occupied index in the time-determining steps─we are able to achieve speedups of 20-30% (depending on the size of the basis set) by using the frozen-core approximation, which is of similar magnitude as for molecular orbital formulations. We further show that the errors introduced by the frozen-core approximation are practically insignificant for molecular geometries.
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Affiliation(s)
- Viktoria Drontschenko
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany
| | - Daniel Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany
| | - Henryk Laqua
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany.,Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
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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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Sacchetta F, Graf D, Laqua H, Ambroise MA, Kussmann J, Dreuw A, Ochsenfeld C. An effective sub-quadratic scaling atomic-orbital reformulation of the scaled opposite-spin RI-CC2 ground-state model using Cholesky-decomposed densities and an attenuated Coulomb metric. J Chem Phys 2022; 157:104104. [DOI: 10.1063/5.0098719] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An atomic-orbital reformulation of the Laplace-transformed scaled opposite-spin (SOS) coupled cluster singles and doubles (CC2) model within the resolution of the identity (RI) approximation (SOS-RI-CC2) is presented that extends its applicability to molecules with several hundreds of atoms and triple-zeta basis sets. We exploit sparse linear algebra and an attenuated Coulomb metric to decrease the disk space demands and the computational efforts. In this way, an effective sub-quadratic computational scaling is achieved with our ω-SOS-CDD-RI-CC2 model. Moreover, Cholesky decomposition of the ground-state one-electron density matrix reduces the prefactor, allowing for an early crossover with the molecular orbital formulation. The accuracy and performance of the presented method are investigated for various molecular systems.
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Affiliation(s)
- F. Sacchetta
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Munich, Germany
| | - D. Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Munich, Germany
| | - H. Laqua
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Munich, Germany
| | - M. A. Ambroise
- Chair of Theoretical and Computational Chemistry, Interdisciplinary Center for Scientific Computing, Heidelberg University, Heidelberg, Germany
| | - J. Kussmann
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Munich, Germany
| | - A. Dreuw
- Chair of Theoretical and Computational Chemistry, Interdisciplinary Center for Scientific Computing, Heidelberg University, Heidelberg, Germany
| | - C. Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Munich, Germany
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12
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Bangerter F, Glasbrenner M, Ochsenfeld C. Tensor-Hypercontracted MP2 First Derivatives: Runtime and Memory Efficient Computation of Hyperfine Coupling Constants. J Chem Theory Comput 2022; 18:5233-5245. [PMID: 35943450 PMCID: PMC9476664 DOI: 10.1021/acs.jctc.2c00118] [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: 01/05/2023]
Abstract
We employ our recently introduced tensor-hypercontracted (THC) second-order Møller-Plesset perturbation theory (MP2) method [Bangerter, F. H., Glasbrenner, M., Ochsenfeld, C. J. Chem. Theory Comput. 2021, 17, 211-221] for the computation of hyperfine coupling constants (HFCCs). The implementation leverages the tensor structure of the THC factorized electron repulsion integrals for an efficient formation of the integral-based intermediates. The computational complexity of the most expensive and formally quintic scaling exchange-like contribution is reduced to effectively subquadratic, by making use of the intrinsic, exponentially decaying coupling between tensor indices through screening based on natural blocking. Overall, this yields an effective subquadratic scaling with a low prefactor for the presented THC-based AO-MP2 method for the computation of isotropic HFCCs on DNA fragments with up to 500 atoms and 5000 basis functions. Furthermore, the implementation achieves considerable speedups with up to a factor of roughly 600-1000 compared to previous implementations [Vogler, S., Ludwig, M., Maurer, M., Ochsenfeld, C. J. Chem. Phys. 2017, 147, 024101] for medium-sized organic radicals, while also significantly reducing storage requirements.
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Affiliation(s)
- Felix
H. Bangerter
- Chair
of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Michael Glasbrenner
- 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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13
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Lemke Y, Graf D, Kussmann J, Ochsenfeld C. An assessment of orbital energy corrections for the direct random phase approximation and explicit σ-functionals. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2098862] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
Affiliation(s)
- Yannick Lemke
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Munich, Germany
| | - Daniel Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Munich, Germany
| | - Jörg Kussmann
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Munich, Germany
- Max Planck Institute for Solid State Research, Stuttgart, Germany
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14
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Lemke Y, Kussmann J, Ochsenfeld C. Efficient Integral-Direct Methods for Self-Consistent Reduced Density Matrix Functional Theory Calculations on Central and Graphics Processing Units. J Chem Theory Comput 2022; 18:4229-4244. [DOI: 10.1021/acs.jctc.2c00231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Y. Lemke
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 5−13, D-81377 Munich, Germany
| | - J. Kussmann
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 5−13, D-81377 Munich, Germany
| | - C. Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 5−13, D-81377 Munich, Germany
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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15
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Glasbrenner M, Vogler S, Ochsenfeld C. Efficient low-scaling computation of NMR shieldings at the second-order Møller-Plesset perturbation theory level with Cholesky-decomposed densities and an attenuated Coulomb metric. J Chem Phys 2021; 155:224107. [PMID: 34911319 DOI: 10.1063/5.0069956] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A method for the computation of nuclear magnetic resonance (NMR) shieldings with second-order Møller-Plesset perturbation theory (MP2) is presented which allows to efficiently compute the entire set of shieldings for a given molecular structure. The equations are derived using Laplace-transformed atomic orbital second-order Møller-Plesset perturbation theory as a starting point. The Z-vector approach is employed for minimizing the number of coupled-perturbed self-consistent-field equations that need to be solved. In addition, the method uses the resolution-of-the-identity approximation with an attenuated Coulomb metric and Cholesky decomposition of pseudo-density matrices. The sparsity in the three-center integrals is exploited with sparse linear algebra approaches, leading to reduced computational cost and memory demands. Test calculations show that the deviations from NMR shifts obtained with canonical MP2 are small if appropriate thresholds are used. The performance of the method is illustrated in calculations on DNA strands and on glycine chains with up to 283 atoms and 2864 basis functions.
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Affiliation(s)
- Michael Glasbrenner
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Sigurd Vogler
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
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16
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Glasbrenner M, Graf D, Ochsenfeld C. Benchmarking the Accuracy of the Direct Random Phase Approximation and σ-Functionals for NMR Shieldings. J Chem Theory Comput 2021; 18:192-205. [PMID: 34898213 DOI: 10.1021/acs.jctc.1c00866] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A method for computing NMR shieldings with the direct random phase approximation (RPA) and the closely related σ-functionals [Trushin, E.; Thierbach, A.; Görling, A. Toward chemical accuracy at low computational cost: density functional theory with σ-functionals for the correlation energy. J. Chem. Phys. 2021, 154, 014104] is presented, which is based on a finite-difference approach. The accuracy is evaluated in benchmark calculations using high-quality coupled cluster values as a reference. Our results show that the accuracy of the computed NMR shieldings using direct RPA is strongly dependent on the density functional theory reference orbitals and improves with increasing amounts of exact Hartree-Fock exchange in the functional. NMR shieldings computed with direct RPA using a Hartree-Fock reference are significantly more accurate than MP2 shieldings and comparable to CCSD shieldings. Also, the basis set convergence is analyzed and it is shown that at least triple-zeta basis sets are required for reliable results.
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Affiliation(s)
- Michael Glasbrenner
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Daniel Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany.,Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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17
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Drontschenko V, Graf D, Laqua H, Ochsenfeld C. Lagrangian-Based Minimal-Overhead Batching Scheme for the Efficient Integral-Direct Evaluation of the RPA Correlation Energy. J Chem Theory Comput 2021; 17:5623-5634. [PMID: 34431662 DOI: 10.1021/acs.jctc.1c00494] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A highly memory-efficient integral-direct random phase approximation (RPA) method based on our ω-CDGD-RI-RPA method [Graf, D. J. Chem. Theory Comput. 2018, 14, 2505] is presented that completely alleviates the memory bottleneck of storing the multidimensional three-center integral tensor, which severely limited the tractable system sizes. Based on a Lagrangian formulation, we introduce an optimized batching scheme over the auxiliary and basis-function indices, which allows to compute the optimal number of batches for a given amount of system memory, while minimizing the batching overhead. Thus, our optimized batching constitutes the best tradeoff between program runtime and memory demand. Within this batching scheme, the half-transformed three-center integral tensor BiμM is recomputed for each batch of auxiliary and basis functions. This allows the computation of systems that were out of reach before. The largest system within this work consists of a DNA fragment comprising 1052 atoms and 11 230 basis functions calculated on a single node, which emphasizes the new possibilities of our integral-direct RPA method.
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Affiliation(s)
- Viktoria Drontschenko
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany
| | - Daniel Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany
| | - Henryk Laqua
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany.,Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
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18
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Yu JM, Nguyen BD, Tsai J, Hernandez DJ, Furche F. Selfconsistent random phase approximation methods. J Chem Phys 2021; 155:040902. [PMID: 34340391 DOI: 10.1063/5.0056565] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
This Perspective reviews recent efforts toward selfconsistent calculations of ground-state energies within the random phase approximation (RPA) in the (generalized) Kohn-Sham (KS) density functional theory context. Since the RPA correlation energy explicitly depends on the non-interacting KS potential, an additional condition to determine the energy as a functional of the density is necessary. This observation leads to the concept of functional selfconsistency (FSC), which requires that the KS density equals the interacting density defined as the functional derivative of the ground-state energy with respect to the external potential. While all existing selfconsistent RPA schemes violate FSC, the recent generalized KS semicanonical projected RPA (GKS-spRPA) method takes a step toward satisfying it. This leads to systematic improvements in densities, binding energy curves, reference state stability, and molecular properties compared to non-selfconsistent RPA as well as optimized effective potential RPA. GKS-spRPA orbital energies accurately approximate valence and core ionization potentials, and even electron affinities of non-valence bound anions. The computational cost and performance of GKS-spRPA are compared to those of related selfconsistent schemes, including GW and orbital optimization methods, and limitations are discussed. Large differences between KS and interacting densities observed in the absence of FSC and the well-rounded performance of GKS-spRPA suggest that the KS potential as a density functional should be defined via the FSC condition for explicitly potential-dependent density functionals.
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Affiliation(s)
- Jason M Yu
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Brian D Nguyen
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Jeffrey Tsai
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Devin J Hernandez
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Filipp Furche
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
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19
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Ye HZ, Berkelbach TC. Fast periodic Gaussian density fitting by range separation. J Chem Phys 2021; 154:131104. [PMID: 33832275 DOI: 10.1063/5.0046617] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present an efficient implementation of periodic Gaussian density fitting (GDF) using the Coulomb metric. The three-center integrals are divided into two parts by range-separating the Coulomb kernel, with the short-range part evaluated in real space and the long-range part in reciprocal space. With a few algorithmic optimizations, we show that this new method-which we call range-separated GDF (RSGDF)-scales sublinearly to linearly with the number of k-points for small to medium-sized k-point meshes that are commonly used in periodic calculations with electron correlation. Numerical results on a few three-dimensional solids show about ten-fold speedups over the previously developed GDF with little precision loss. The error introduced by RSGDF is about 10-5Eh in the converged Hartree-Fock energy with default auxiliary basis sets and can be systematically reduced by increasing the size of the auxiliary basis with little extra work.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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20
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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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21
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Low-Scaling Tensor Hypercontraction in the Cholesky Molecular Orbital Basis Applied to Second-Order Møller-Plesset Perturbation Theory. J Chem Theory Comput 2020; 17:211-221. [PMID: 33375790 DOI: 10.1021/acs.jctc.0c00934] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We employ various reduced scaling techniques to accelerate the recently developed least-squares tensor hypercontraction (LS-THC) approximation [Parrish, R. M., Hohenstein, E. G., Martínez, T. J., Sherrill, C. D. J. Chem. Phys. 137, 224106 (2012)] for electron repulsion integrals (ERIs) and apply it to second-order Møller-Plesset perturbation theory (MP2). The grid-projected ERI tensors are efficiently constructed using a localized Cholesky molecular orbital basis from density-fitted integrals with an attenuated Coulomb metric. Additionally, rigorous integral screening and the natural blocking matrix format are applied to reduce the complexity of this step. By recasting the equations to form the quantized representation of the 1/r operator Z into the form of a system of linear equations, the bottleneck of inverting the grid metric via pseudoinversion is removed. This leads to a reduced scaling THC algorithm and application to MP2 yields the (sub-)quadratically scaling THC-ω-RI-CDD-SOS-MP2 method. The efficiency of this method is assessed for various systems including DNA fragments with over 8000 basis functions and the subquadratic scaling is illustrated.
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22
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Graf D, Ochsenfeld C. A range-separated generalized Kohn-Sham method including a long-range nonlocal random phase approximation correlation potential. J Chem Phys 2020; 153:244118. [PMID: 33380112 DOI: 10.1063/5.0031310] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
Based on our recently published range-separated random phase approximation (RPA) functional [Kreppel et al., "Range-separated density-functional theory in combination with the random phase approximation: An accuracy benchmark," J. Chem. Theory Comput. 16, 2985-2994 (2020)], we introduce self-consistent minimization with respect to the one-particle density matrix. In contrast to the range-separated RPA methods presented so far, the new method includes a long-range nonlocal RPA correlation potential in the orbital optimization process, making it a full-featured variational generalized Kohn-Sham (GKS) method. The new method not only improves upon all other tested RPA schemes including the standard post-GKS range-separated RPA for the investigated test cases covering general main group thermochemistry, kinetics, and noncovalent interactions but also significantly outperforms the popular G0W0 method in estimating the ionization potentials and fundamental gaps considered in this work using the eigenvalue spectra obtained from the GKS Hamiltonian.
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Affiliation(s)
- Daniel Graf
- 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
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23
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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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24
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Glasbrenner M, Graf D, Ochsenfeld C. Efficient Reduced-Scaling Second-Order Møller-Plesset Perturbation Theory with Cholesky-Decomposed Densities and an Attenuated Coulomb Metric. J Chem Theory Comput 2020; 16:6856-6868. [PMID: 33074664 DOI: 10.1021/acs.jctc.0c00600] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a novel, highly efficient method for the computation of second-order Møller-Plesset perturbation theory (MP2) correlation energies, which uses the resolution of the identity (RI) approximation and local molecular orbitals obtained from a Cholesky decomposition of pseudodensity matrices (CDD), as in the RI-CDD-MP2 method developed previously in our group [Maurer, S. A.; Clin, L.; Ochsenfeld, C. J. Chem. Phys. 2014, 140, 224112]. In addition, we introduce an attenuated Coulomb metric and subsequently redesign the RI-CDD-MP2 method in order to exploit the resulting sparsity in the three-center integrals. Coulomb and exchange energy contributions are computed separately using specialized algorithms. A simple, yet effective integral screening protocol based on Schwarz estimates is used for the MP2 exchange energy. The Coulomb energy computation and the preceding transformations of the three-center integrals are accelerated using a modified version of the natural blocking approach [Jung, Y.; Head-Gordon, M. Phys. Chem. Chem. Phys. 2006, 8, 2831-2840]. Effective subquadratic scaling for a wide range of molecule sizes is demonstrated in test calculations in conjunction with a low prefactor. The method is shown to enable cost-efficient MP2 calculations on large molecular systems with several thousand basis functions.
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Affiliation(s)
- Michael Glasbrenner
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstrasse 7, 81377 Munich, Germany
| | - Daniel Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstrasse 7, 81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstrasse 7, 81377 Munich, Germany
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25
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Kreppel A, Graf D, Laqua H, Ochsenfeld C. Range-Separated Density-Functional Theory in Combination with the Random Phase Approximation: An Accuracy Benchmark. J Chem Theory Comput 2020; 16:2985-2994. [PMID: 32329618 DOI: 10.1021/acs.jctc.9b01294] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A formulation of range-separated random phase approximation (RPA) based on our efficient ω-CDGD-RI-RPA [J. Chem. Theory Comput. 2018, 14, 2505] method and a large scale benchmark study are presented. By application to the GMTKN55 data set, we obtain a comprehensive picture of the performance of range-separated RPA in general main group thermochemistry, kinetics, and noncovalent interactions. The results show that range-separated RPA performs stably over the broad range of molecular chemistry included in the GMTKN55 set. It improves significantly over semilocal DFT but it is still less accurate than modern dispersion corrected double-hybrid functionals. Furthermore, range-separated RPA shows a faster basis set convergence compared to standard full-range RPA making it a promising applicable approach with only one empirical parameter.
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Affiliation(s)
- Andrea Kreppel
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Daniel Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Henryk Laqua
- 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, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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26
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Nguyen BD, Chen GP, Agee MM, Burow AM, Tang MP, Furche F. Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules. J Chem Theory Comput 2020; 16:2258-2273. [DOI: 10.1021/acs.jctc.9b01176] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Brian D. Nguyen
- University of California, Irvine, Department of Chemistry, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Guo P. Chen
- University of California, Irvine, Department of Chemistry, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Matthew M. Agee
- University of California, Irvine, Department of Chemistry, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Asbjörn M. Burow
- University of California, Irvine, Department of Chemistry, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Matthew P. Tang
- University of California, Irvine, Department of Chemistry, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Filipp Furche
- University of California, Irvine, Department of Chemistry, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
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27
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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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28
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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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29
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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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30
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31
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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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32
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33
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Huang C. Embedded Cluster Density Approximation for Exchange–Correlation Energy: A Natural Extension of the Local Density Approximation. J Chem Theory Comput 2018; 14:6211-6225. [DOI: 10.1021/acs.jctc.8b00471] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Chen Huang
- Department of Scientific Computing and National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306, United States
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34
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Vogler S, Savasci G, Ludwig M, Ochsenfeld C. Selected-Nuclei Method for the Computation of Hyperfine Coupling Constants within Second-Order Møller-Plesset Perturbation Theory. J Chem Theory Comput 2018; 14:3014-3024. [PMID: 29762028 DOI: 10.1021/acs.jctc.8b00116] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
We introduce a new ansatz to compute hyperfine coupling constants of selected nuclei at the level of second-order Møller-Plesset perturbation (MP2) and double-hybrid density functional theory with reduced computational effort, opening the route to the analyis of hyperfine coupling constants of large molecular structures. Our approach is based on a reformulation of the canonical MP2 term in atomic orbitals, thus exploiting the locality of electron correlation. We show that a perturbation-including integral screening reduces the scaling behavior of the number of significant two-electron integrals to sublinear. This selected-nuclei approach allows for an efficient computation within scaled-opposite spin (SOS) RI-MP2 on massively parallelized architectures such as graphical processor units (GPUs), thus enabling studies on the influence of the environment on hyperfine coupling constants.
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Affiliation(s)
- Sigurd Vogler
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , Butenandtstrasse 7 , 81377 Munich , Germany
| | - Gökcen Savasci
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , Butenandtstrasse 7 , 81377 Munich , Germany.,Max Planck Institute for Solid State Research, Heisenbergstrasse 1 , 70569 Stuttgart , Germany
| | - Martin Ludwig
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , Butenandtstrasse 7 , 81377 Munich , Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , Butenandtstrasse 7 , 81377 Munich , Germany.,Max Planck Institute for Solid State Research, Heisenbergstrasse 1 , 70569 Stuttgart , Germany
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35
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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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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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Huang C, Chi YC. Directly patching high-level exchange-correlation potential based on fully determined optimized effective potentials. J Chem Phys 2017; 147:244111. [PMID: 29289130 DOI: 10.1063/1.5003663] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The key element in Kohn-Sham (KS) density functional theory is the exchange-correlation (XC) potential. We recently proposed the exchange-correlation potential patching (XCPP) method with the aim of directly constructing high-level XC potential in a large system by patching the locally computed, high-level XC potentials throughout the system. In this work, we investigate the patching of the exact exchange (EXX) and the random phase approximation (RPA) correlation potentials. A major challenge of XCPP is that a cluster's XC potential, obtained by solving the optimized effective potential equation, is only determined up to an unknown constant. Without fully determining the clusters' XC potentials, the patched system's XC potential is "uneven" in the real space and may cause non-physical results. Here, we developed a simple method to determine this unknown constant. The performance of XCPP-RPA is investigated on three one-dimensional systems: H20, H10Li8, and the stretching of the H19-H bond. We investigated two definitions of EXX: (i) the definition based on the adiabatic connection and fluctuation dissipation theorem (ACFDT) and (ii) the Hartree-Fock (HF) definition. With ACFDT-type EXX, effective error cancellations were observed between the patched EXX and the patched RPA correlation potentials. Such error cancellations were absent for the HF-type EXX, which was attributed to the fact that for systems with fractional occupation numbers, the integral of the HF-type EXX hole is not -1. The KS spectra and band gaps from XCPP agree reasonably well with the benchmarks as we make the clusters large.
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Affiliation(s)
- Chen Huang
- Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306-4120, USA
| | - Yu-Chieh Chi
- Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306-4120, USA
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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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Helmich-Paris B, Knecht S. Laplace-transformed multi-reference second-order perturbation theories in the atomic and active molecular orbital basis. J Chem Phys 2017; 146:224101. [PMID: 29166042 PMCID: PMC5464961 DOI: 10.1063/1.4984591] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2017] [Accepted: 05/16/2017] [Indexed: 11/15/2022] Open
Abstract
In the present article, we show how to formulate the partially contracted n-electron valence second-order perturbation theory (NEVPT2) energies in the atomic and active molecular orbital basis by employing the Laplace transformation of orbital-energy denominators (OEDs). As atomic-orbital (AO) basis functions are inherently localized and the number of active orbitals is comparatively small, our formulation is particularly suited for a linearly scaling NEVPT2 implementation. In our formulation, there are two kinds of NEVPT2 energy contributions, which differ in the number of active orbitals in the two-electron integrals involved. Those involving integrals with either no or a single active orbital can be formulated completely in the AO basis as single-reference second-order Møller-Plesset perturbation theory and benefit from sparse active pseudo-density matrices-particularly if the active molecular orbitals are localized only in parts of a molecule. Conversely, energy contributions involving integrals with either two or three active orbitals can be obtained from Coulomb and exchange matrices generalized for pairs of active orbitals. Moreover, we demonstrate that Laplace-transformed partially contracted NEVPT2 is nothing less than time-dependent NEVPT2 [A. Y. Sokolov and G. K.-L. Chan, J. Chem. Phys. 144, 064102 (2016)] iff the all-active intermediates are computed with the internal-contraction approximation. Furthermore, we show that for multi-reference perturbation theories it is particularly challenging to find optimal parameters of the numerical Laplace transformation as the fit range may vary among the 8 different OEDs by many orders of magnitude. Selecting the number of quadrature points for each OED separately according to an accuracy-based criterion allows us to control the errors in the NEVPT2 energies reliably.
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Affiliation(s)
- Benjamin Helmich-Paris
- Section of Theoretical Chemistry, VU University Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Stefan Knecht
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich, Switzerland
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Schurkus HF, Luenser A, Ochsenfeld C. Communication: Almost error-free resolution-of-the-identity correlation methods by null space removal of the particle-hole interactions. J Chem Phys 2017; 146:211106. [PMID: 28595410 PMCID: PMC5462614 DOI: 10.1063/1.4985085] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2017] [Accepted: 05/24/2017] [Indexed: 11/14/2022] Open
Abstract
We present a method to improve upon the resolution-of-the-identity (RI) for correlation methods. While RI is known to allow for drastic speedups, it relies on a cancellation of errors. Our method eliminates the errors introduced by RI which are known to be problematic for absolute energies. In this way, independence of the error compensation assumption for relative energies is also achieved. The proposed method is based on the idea of starting with an oversized RI basis and projecting out all of its unphysical parts. The approach can be easily implemented into existing RI codes and results in an overhead of about 30%, while effectively removing the RI error. In passing, this process alleviates the problem that for many frequently employed basis sets no optimized RI basis sets have been constructed. In this paper, the theory is presented and results are discussed exemplarily for the random phase approximation and Møller-Plesset perturbation theory.
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Affiliation(s)
- Henry F Schurkus
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, 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), Butenandtstr. 7, 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), Butenandtstr. 7, D-81377 Munich, Germany
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