1
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Marie A, Loos PF. Reference Energies for Valence Ionizations and Satellite Transitions. J Chem Theory Comput 2024; 20:4751-4777. [PMID: 38776293 PMCID: PMC11171335 DOI: 10.1021/acs.jctc.4c00216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2024] [Revised: 04/10/2024] [Accepted: 04/11/2024] [Indexed: 05/24/2024]
Abstract
Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.
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Affiliation(s)
- Antoine Marie
- Laboratoire de Chimie et Physique
Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse 31062, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique
Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse 31062, France
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2
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Vacondio S, Varsano D, Ruini A, Ferretti A. Going Beyond the GW Approximation Using the Time-Dependent Hartree-Fock Vertex. J Chem Theory Comput 2024; 20:4718-4737. [PMID: 38772396 DOI: 10.1021/acs.jctc.4c00100] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/23/2024]
Abstract
The time-dependent Hartree-Fock (TDHF) vertex of many-body perturbation theory (MBPT) makes it possible to extend TDHF theory to charged excitations. Here we assess its performance by applying it to spherical atoms in their neutral electronic configuration. On a theoretical level, we recast the TDHF vertex as a reducible vertex, highlighting the emergence of a self-energy expansion purely in orders of the bare Coulomb interaction; then, on a numerical level, we present results for polarizabilities, ionization energies (IEs), and photoemission satellites. We confirm the superiority of THDF over simpler methods such as the random phase approximation for the prediction of atomic polarizabilities. We then find that the TDHF vertex reliably provides better IEs than GW and low-order self-energies do in the light-atom, few-electron regime; its performance degrades in heavier, many-electron atoms instead, where an expansion in orders of an unscreened Coulomb interaction becomes less justified. New relevant features are introduced in the satellite spectrum by the TDHF vertex, but the experimental spectra are not fully reproduced due to a missing account of nonlinear effects connected to hole relaxation. We also explore various truncations of the self-energy given by the TDHF vertex, but do not find them to be more convenient than low-order approximations such as GW and second Born (2B), suggesting that vertex corrections should be carried out consistently both in the self-energy and in the polarizability.
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Affiliation(s)
- Simone Vacondio
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia, Via G. Campi 213/a, 41125 Modena, Italy
- Centro S3, CNR-Istituto Nanoscienze, Via G. Campi 213/a, 41125 Modena, Italy
| | - Daniele Varsano
- Centro S3, CNR-Istituto Nanoscienze, Via G. Campi 213/a, 41125 Modena, Italy
| | - Alice Ruini
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia, Via G. Campi 213/a, 41125 Modena, Italy
- Centro S3, CNR-Istituto Nanoscienze, Via G. Campi 213/a, 41125 Modena, Italy
| | - Andrea Ferretti
- Centro S3, CNR-Istituto Nanoscienze, Via G. Campi 213/a, 41125 Modena, Italy
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3
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Bruneval F, Förster A. Fully Dynamic G3 W2 Self-Energy for Finite Systems: Formulas and Benchmark. J Chem Theory Comput 2024; 20:3218-3230. [PMID: 38603811 DOI: 10.1021/acs.jctc.4c00090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/13/2024]
Abstract
Over the years, Hedin's GW self-energy has been proven to be a rather accurate and simple approximation to evaluate electronic quasiparticle energies in solids and in molecules. Attempts to improve over the simple GW approximation, the so-called vertex corrections, have been constantly proposed in the literature. Here, we derive, analyze, and benchmark the complete second-order term in the screened Coulomb interaction W for finite systems. This self-energy named G3W2 contains all the possible time orderings that combine 3 Green's functions G and 2 dynamic W. We present the analytic formula and its imaginary frequency counterpart, with the latter allowing us to treat larger molecules. The accuracy of the G3W2 self-energy is evaluated on well-established benchmarks (GW100, Acceptor 24, and Core 65) for valence and core quasiparticle energies. Its link with the simpler static approximation, named SOSEX for static screened second-order exchange, is analyzed, which leads us to propose a more consistent approximation named 2SOSEX. In the end, we find that neither the G3W2 self-energy nor any of the investigated approximations to it improve over one-shot G0W0 with a good starting point. Only quasi-particle self-consistent GW HOMO energies are slightly improved by addition of the G3W2 self-energy correction. We show that this is due to the self-consistent update of the screened Coulomb interaction, leading to an overall sign change of the vertex correction to the frontier quasiparticle energies.
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Affiliation(s)
- Fabien Bruneval
- Université Paris-Saclay, CEA, Service de recherche en Corrosion et Comportement des Matériaux, SRMP, 91191 Gif-sur-Yvette, France
| | - Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1108, 1081 HZ Amsterdam, The Netherlands
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4
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Wen M, Abraham V, Harsha G, Shee A, Whaley KB, Zgid D. Comparing Self-Consistent GW and Vertex-Corrected G0W0 ( G0W0Γ) Accuracy for Molecular Ionization Potentials. J Chem Theory Comput 2024; 20:3109-3120. [PMID: 38573104 DOI: 10.1021/acs.jctc.3c01279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/05/2024]
Abstract
We test the performance of self-consistent GW and several representative implementations of vertex-corrected G0W0 (G0W0Γ). These approaches are tested on benchmark data sets covering full valence spectra (first ionization potentials and some inner valence shell excitations). For small molecules, when comparing against state-of-the-art wave function techniques, our results show that full self-consistency in the GW scheme either systematically outperforms vertex-corrected G0W0 or gives results of at least comparative quality. Moreover, G0W0Γ results in additional computational cost when compared to G0W0 or self-consistent GW. The dependency of G0W0Γ on the starting mean-field solution is frequently more dominant than the magnitude of the vertex correction itself. Consequently, for molecular systems, self-consistent GW performed on the imaginary axis (and then followed by modern analytical continuation techniques) offers a more reliable approach to make predictions of ionization potentials.
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Affiliation(s)
- Ming Wen
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Gaurav Harsha
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Avijit Shee
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - K Birgitta Whaley
- Department of Chemistry, University of California, Berkeley, California 94720-1460, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
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5
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El-Sahili A, Sottile F, Reining L. Total Energy beyond GW: Exact Results and Guidelines for Approximations. J Chem Theory Comput 2024; 20:1972-1987. [PMID: 38324673 DOI: 10.1021/acs.jctc.3c01200] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2024]
Abstract
The total energy and electron addition and removal spectra can, in principle, be obtained exactly from the one-body Green's function (GF). In practice, the GF is obtained from an approximate self-energy. In the framework of many-body perturbation theory, we derive different expressions that are based on an approximate self-energy, but that yield nevertheless, in principle, the exact exchange-correlation contribution to the total energy for any interaction strength. Response functions play a crucial role, which explains why, for example, ingredients from time-dependent density functional theory can be used to build these approximate self-energies. We show that the key requirement for obtaining exact results is the consistent combination of ingredients. Also when further approximations are made, as it is necessary in practice, this consistency remains the key to obtain good results. All findings are illustrated using the exactly solvable symmetric Hubbard dimer.
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Affiliation(s)
- Abdallah El-Sahili
- LSI, CNRS, CEA/DRF/IRAMIS, École Polytechnique, Institut Polytechnique de Paris, Palaiseau F-91120, France
- European Theoretical Spectroscopy Facility (ETSF), https://www.etsf.eu/
| | - Francesco Sottile
- LSI, CNRS, CEA/DRF/IRAMIS, École Polytechnique, Institut Polytechnique de Paris, Palaiseau F-91120, France
- European Theoretical Spectroscopy Facility (ETSF), https://www.etsf.eu/
| | - Lucia Reining
- LSI, CNRS, CEA/DRF/IRAMIS, École Polytechnique, Institut Polytechnique de Paris, Palaiseau F-91120, France
- European Theoretical Spectroscopy Facility (ETSF), https://www.etsf.eu/
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6
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Orlando R, Romaniello P, Loos PF. The three channels of many-body perturbation theory: GW, particle-particle, and electron-hole T-matrix self-energies. J Chem Phys 2023; 159:184113. [PMID: 37962450 DOI: 10.1063/5.0176898] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 10/23/2023] [Indexed: 11/15/2023] Open
Abstract
We derive the explicit expression of the three self-energies that one encounters in many-body perturbation theory: the well-known GW self-energy, as well as the particle-particle and electron-hole T-matrix self-energies. Each of these can be easily computed via the eigenvalues and eigenvectors of a different random-phase approximation linear eigenvalue problem that completely defines their corresponding response function. For illustrative and comparative purposes, we report the principal ionization potentials of a set of small molecules computed at each level of theory. The performance of these schemes on strongly correlated systems (B2 and C2) is also discussed.
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Affiliation(s)
- Roberto Orlando
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France
- European Theoretical Spectroscopy Facility (ETSF)
| | - Pina Romaniello
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France
- European Theoretical Spectroscopy Facility (ETSF)
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
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7
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Marie A, Loos PF. A Similarity Renormalization Group Approach to Green's Function Methods. J Chem Theory Comput 2023. [PMID: 37311565 DOI: 10.1021/acs.jctc.3c00281] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The family of Green's function methods based on the GW approximation has gained popularity in the electronic structure theory thanks to its accuracy in weakly correlated systems combined with its cost-effectiveness. Despite this, self-consistent versions still pose challenges in terms of convergence. A recent study [Monino and Loos J. Chem. Phys. 2022, 156, 231101.] has linked these convergence issues to the intruder-state problem. In this work, a perturbative analysis of the similarity renormalization group (SRG) approach is performed on Green's function methods. The SRG formalism enables us to derive, from first-principles, the expression of a naturally static and Hermitian form of the self-energy that can be employed in quasiparticle self-consistent GW (qsGW) calculations. The resulting SRG-based regularized self-energy significantly accelerates the convergence of qsGW calculations, slightly improves the overall accuracy, and is straightforward to implement in existing code.
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Affiliation(s)
- Antoine Marie
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31400 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31400 Toulouse, France
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8
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Weng G, Mallarapu R, Vlček V. Embedding vertex corrections in GW self-energy: Theory, implementation, and outlook. J Chem Phys 2023; 158:144105. [PMID: 37061461 DOI: 10.1063/5.0139117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2023] Open
Abstract
The vertex function (Γ) within the Green's function formalism encapsulates information about all higher-order electron-electron interaction beyond those mediated by density fluctuations. Herein, we present an efficient approach that embeds vertex corrections in the one-shot GW correlation self-energy for isolated and periodic systems. The vertex-corrected self-energy is constructed through the proposed separation-propagation-recombination procedure: the electronic Hilbert space is separated into an active space and its orthogonal complement denoted as the "rest;" the active component is propagated by a space-specific effective Hamiltonian different from the rest. The vertex corrections are introduced by a rescaled time-dependent nonlocal exchange interaction. The direct Γ correction to the self-energy is further updated by adjusting the rescaling factor in a self-consistent post-processing cycle. Our embedding method is tested mainly on donor-acceptor charge-transfer systems. The embedded vertex effects consistently and significantly correct the quasiparticle energies of the gap-edge states. The fundamental gap is generally improved by 1-3 eV upon the one-shot GW approximation. Furthermore, we provide an outlook for applications of (embedded) vertex corrections in calculations of extended solids.
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Affiliation(s)
- Guorong Weng
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, USA
| | - Rushil Mallarapu
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, USA
| | - Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, USA
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9
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Monzel L, Holzer C, Klopper W. Natural virtual orbitals for the GW method in the random-phase approximation and beyond. J Chem Phys 2023; 158:144102. [PMID: 37061489 DOI: 10.1063/5.0144469] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2023] Open
Abstract
The increasingly popular GW method is becoming a convenient tool to determine vertical ionization energies in molecular systems. However, depending on the formalism used and the range of orbitals investigated, it may be hampered by a steep computational scaling. To alleviate this issue, correlated natural virtual orbitals (NVOs) based on second-order Møller-Plesset (MP2) and direct MP2 correlation energies are implemented, and the resulting correlated NVOs are tested on GW quasiparticle energies. Test cases include the popular GW variants G0W0 and evGW0 as well as more elaborate vertex corrections. We find that for increasingly larger molecular systems and basis sets, NVOs considerably improve efficiency. Furthermore, we test the performance of the truncated (frozen) NVO ansatz on the GW100 test set. For the latter, it is demonstrated that, using a carefully chosen truncation threshold, NVOs lead to a negligible loss in accuracy while providing speedups of one order of magnitude. Furthermore, we compare the resulting quasiparticle energies to very accurate vertical ionization energies obtained from coupled-cluster theory with singles, doubles, and noniterative triples [CCSD(T)], confirming that the loss in accuracy introduced by truncating the NVOs is negligible compared to the methodical errors in the GW approximation. It is also demonstrated that the choice of basis set impacts results far more than using a suitably truncated NVO space. Therefore, at the same computational expense, more accurate results can be obtained using NVOs. Finally, we provide improved reference CCSD(T) values for the GW100 test set, which have been obtained using the def2-QZVPP basis set.
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Affiliation(s)
- Laurenz Monzel
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, 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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Vacondio S, Varsano D, Ruini A, Ferretti A. Numerically Precise Benchmark of Many-Body Self-Energies on Spherical Atoms. J Chem Theory Comput 2022; 18:3703-3717. [PMID: 35561415 PMCID: PMC9202310 DOI: 10.1021/acs.jctc.2c00048] [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
![]()
We investigate the
performance of beyond-GW approaches in many-body
perturbation theory by addressing atoms described within the spherical
approximation via a dedicated numerical treatment based on B-splines
and spherical harmonics. We consider the GW, second Born (2B), and
GW + second order screened exchange (GW+SOSEX) self-energies and use
them to obtain ionization potentials from the quasi-particle equation
(QPE) solved perturbatively on top of independent-particle calculations.
We also solve the linearized Sham–Schlüter equation
(LSSE) and compare the resulting xc potentials against exact data.
We find that the LSSE provides consistent starting points for the
QPE but does not present any practical advantage in the present context.
Still, the features of the xc potentials obtained with it shed light
on possible strategies for the inclusion of beyond-GW diagrams in
the many-body self-energy. Our findings show that solving the QPE
with the GW+SOSEX self-energy on top of a PBE or PBE0 solution is
a viable scheme to go beyond GW in finite systems, even in the atomic
limit. However, GW shows a comparable performance if one agrees to
use a hybrid starting point. We also obtain promising results with
the 2B self-energy on top of Hartree–Fock, suggesting that
the full time-dependent Hartree–Fock vertex may be another
viable beyond-GW scheme for finite systems.
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Affiliation(s)
- S Vacondio
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via G. Campi 213/a, Modena 41121, Italy.,Centro S3, CNR-Istituto Nanoscienze, 41125 Modena, Italy
| | - D Varsano
- Centro S3, CNR-Istituto Nanoscienze, 41125 Modena, Italy
| | - A Ruini
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via G. Campi 213/a, Modena 41121, Italy.,Centro S3, CNR-Istituto Nanoscienze, 41125 Modena, Italy
| | - A Ferretti
- Centro S3, CNR-Istituto Nanoscienze, 41125 Modena, Italy
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12
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Cho Y, Bintrim SJ, Berkelbach TC. Simplified GW/BSE Approach for Charged and Neutral Excitation Energies of Large Molecules and Nanomaterials. J Chem Theory Comput 2022; 18:3438-3446. [PMID: 35544591 DOI: 10.1021/acs.jctc.2c00087] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Inspired by Grimme's simplified Tamm-Dancoff density functional theory approach [Grimme, S. J. Chem. Phys. 2013, 138, 244104], we describe a simplified approach to excited-state calculations within the GW approximation to the self-energy and the Bethe-Salpeter equation (BSE), which we call sGW/sBSE. The primary simplification to the electron repulsion integrals yields the same structure as with tensor hypercontraction, such that our method has a storage requirement that grows quadratically with system size and computational timing that grows cubically with system size. The performance of sGW is tested on the ionization potential of the molecules in the GW100 test set, for which it differs from ab initio GW calculations by only 0.2 eV. The performance of sBSE (based on the sGW input) is tested on the excitation energies of molecules in Thiel's set, for which it differs from ab initio GW/BSE calculations by about 0.5 eV. As examples of the systems that can be routinely studied with sGW/sBSE, we calculate the band gap and excitation energy of hydrogen-passivated silicon nanocrystals with up to 2650 electrons in 4678 spatial orbitals and the absorption spectra of two large organic dye molecules with hundreds of atoms.
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Affiliation(s)
- Yeongsu Cho
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Sylvia J Bintrim
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States.,Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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13
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Wang Y, Rinke P, Ren X. Assessing the G0W0Γ 0(1) Approach: Beyond G0W0 with Hedin's Full Second-Order Self-Energy Contribution. J Chem Theory Comput 2021; 17:5140-5154. [PMID: 34319724 DOI: 10.1021/acs.jctc.1c00488] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present and benchmark a self-energy approach for quasiparticle energy calculations that goes beyond Hedin's GW approximation by adding the full second-order self-energy (FSOS-W) contribution. The FSOS-W diagram involves two screened Coulomb interaction (W) lines, and adding the FSOS-W to the GW self-energy can be interpreted as first-order vertex correction to GW (GWΓ(1)). Our FSOS-W implementation is based on the resolution-of-identity technique and exhibits better than O(N5) scaling with system size for small- to medium-sized molecules. We then present one-shot GWΓ(1) (G0W0Γ0(1)) benchmarks for the GW100 test set and a set of 24 acceptor molecules. For semilocal or hybrid density functional theory starting points, G0W0Γ0(1) systematically outperforms G0W0 for the first vertical ionization potentials and electron affinities of both test sets. Finally, we demonstrate that a static FSOS-W self-energy significantly underestimates the quasiparticle energies.
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Affiliation(s)
- Yanyong Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Patrick Rinke
- Department of Applied Physics, School of Science, Aalto University, 00076 Aalto, Finland
| | - Xinguo Ren
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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14
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Riemelmoser S, Kaltak M, Kresse G. Optimized effective potentials from the random-phase approximation: Accuracy of the quasiparticle approximation. J Chem Phys 2021; 154:154103. [PMID: 33887939 DOI: 10.1063/5.0045400] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
The optimized effective potential (OEP) method presents an unambiguous way to construct the Kohn-Sham potential corresponding to a given diagrammatic approximation for the exchange-correlation functional. The OEP from the random-phase approximation (RPA) has played an important role ever since the conception of the OEP formalism. However, the solution of the OEP equation is computationally fairly expensive and has to be done in a self-consistent way. So far, large scale solid state applications have, therefore, been performed only using the quasiparticle approximation (QPA), neglecting certain dynamical screening effects. We obtain the exact RPA-OEP for 15 semiconductors and insulators by direct solution of the linearized Sham-Schlüter equation. We investigate the accuracy of the QPA on Kohn-Sham bandgaps and dielectric constants, and comment on the issue of self-consistency.
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Affiliation(s)
- Stefan Riemelmoser
- Faculty of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
| | - Merzuk Kaltak
- VASP Software GmbH, Sensengasse 8/17, A-1090 Vienna, Austria
| | - Georg Kresse
- Faculty of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
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15
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Duchemin I, Blase X. Cubic-Scaling All-Electron GW Calculations with a Separable Density-Fitting Space-Time Approach. J Chem Theory Comput 2021; 17:2383-2393. [PMID: 33797245 DOI: 10.1021/acs.jctc.1c00101] [Citation(s) in RCA: 45] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present an implementation of the GW space-time approach that allows cubic-scaling all-electron calculations with standard Gaussian basis sets without exploiting any localization or sparsity considerations. The independent-electron susceptibility is constructed in a time representation over a nonuniform distribution of real-space locations {rk} optimized within a separable resolution-of-the-identity framework to reproduce standard Coulomb-fitting calculations with meV accuracy. The compactness of the obtained {rk} distribution leads to a crossover with the standard Coulomb-fitting scheme for system sizes below a few hundred electrons. The needed analytic continuation follows a recent approach that requires the continuation of the screened Coulomb potential rather than the much more structured self-energy. The present scheme is benchmarked over large molecular sets, and scaling properties are demonstrated on a family of defected hexagonal boron-nitride flakes containing up to 6000 electrons.
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Affiliation(s)
- Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
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Mejuto-Zaera C, Weng G, Romanova M, Cotton SJ, Whaley KB, Tubman NM, Vlček V. Are multi-quasiparticle interactions important in molecular ionization? J Chem Phys 2021; 154:121101. [DOI: 10.1063/5.0044060] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
| | - Guorong Weng
- University of California, Santa Barbara, California 93106, USA
| | - Mariya Romanova
- University of California, Santa Barbara, California 93106, USA
| | - Stephen J. Cotton
- Quantum Artificial Intelligence Laboratory (QuAIL), Exploration Technology Directorate, NASA Ames Research Center, Moffett Field, California 94035, USA
- KBR, 601 Jefferson St., Houston, Texas 77002, USA
| | | | - Norm M. Tubman
- Quantum Artificial Intelligence Laboratory (QuAIL), Exploration Technology Directorate, NASA Ames Research Center, Moffett Field, California 94035, USA
| | - Vojtěch Vlček
- University of California, Santa Barbara, California 93106, USA
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Wang K, Shao J, Paulus B. Electronic and optical properties of fluorinated graphene within many-body Green's function framework. J Chem Phys 2021; 154:104705. [PMID: 33722010 DOI: 10.1063/5.0042302] [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
In this article, a systematic examination of the electronic and optical properties of partially fluorinated graphene is presented. In order to capture a large variety of fluorination degrees and configurations, different sizes of the supercell combining with various degrees of fluorination are considered. On top of periodic density functional theory, the G0W0 method and the G0W0Γ method within many-body Green's function framework are employed. Including the description of electron-hole interactions, the optical spectra based on the Bethe-Salpeter equation are calculated. Two-sided fluorination with compact fluorination arrangements is energetically most favorable. The fluorination degree has a determined impact on the bandgap value in the system, while the fluorination pattern strongly influences the characteristics of the bands in the electronic structures. Depending on the polarization of the applied electromagnetic field, the optical absorption spectra of the same structure could vary significantly. These interesting results suggest the potential applications of partially fluorinated graphene as optoelectronic materials.
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Affiliation(s)
- Kangli Wang
- Institut für Chemie und Biochemie, Freie Universität Berlin, Arnimallee 22, 14195 Berlin, Germany
| | - Jingjing Shao
- Institut für Chemie und Biochemie, Freie Universität Berlin, Arnimallee 22, 14195 Berlin, Germany
| | - Beate Paulus
- Institut für Chemie und Biochemie, Freie Universität Berlin, Arnimallee 22, 14195 Berlin, Germany
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Advanced First-Principle Modeling of Relativistic Ruddlesden—Popper Strontium Iridates. APPLIED SCIENCES-BASEL 2021. [DOI: 10.3390/app11062527] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this review, we provide a survey of the application of advanced first-principle methods on the theoretical modeling and understanding of novel electronic, optical, and magnetic properties of the spin-orbit coupled Ruddlesden–Popper series of iridates Srn+1IrnO3n+1 (n = 1, 2, and ∞). After a brief description of the basic aspects of the adopted methods (noncollinear local spin density approximation plus an on-site Coulomb interaction (LSDA+U), constrained random phase approximation (cRPA), GW, and Bethe–Salpeter equation (BSE)), we present and discuss select results. We show that a detailed phase diagrams of the metal–insulator transition and magnetic phase transition can be constructed by inspecting the evolution of electronic and magnetic properties as a function of Hubbard U, spin–orbit coupling (SOC) strength, and dimensionality n, which provide clear evidence for the crucial role played by SOC and U in establishing a relativistic (Dirac) Mott–Hubbard insulating state in Sr2IrO4 and Sr3Ir2O7. To characterize the ground-state phases, we quantify the most relevant energy scales fully ab initio—crystal field energy, Hubbard U, and SOC constant of three compounds—and discuss the quasiparticle band structures in detail by comparing GW and LSDA+U data. We examine the different magnetic ground states of structurally similar n = 1 and n = 2 compounds and clarify that the origin of the in-plane canted antiferromagnetic (AFM) state of Sr2IrO4 arises from competition between isotropic exchange and Dzyaloshinskii–Moriya (DM) interactions whereas the collinear AFM state of Sr3Ir2O7 is due to strong interlayer magnetic coupling. Finally, we report the dimensionality controlled metal–insulator transition across the series by computing their optical transitions and conductivity spectra at the GW+BSE level from the the quasi two-dimensional insulating n = 1 and 2 phases to the three-dimensional metallic n=∞ phase.
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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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Romanova M, Vlček V. Decomposition and embedding in the stochastic GW self-energy. J Chem Phys 2020; 153:134103. [DOI: 10.1063/5.0020430] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Mariya Romanova
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, USA
| | - Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, USA
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Vlček V. Stochastic Vertex Corrections: Linear Scaling Methods for Accurate Quasiparticle Energies. J Chem Theory Comput 2019; 15:6254-6266. [DOI: 10.1021/acs.jctc.9b00317] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, Santa Barbara, California 93106, United States
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Golze D, Dvorak M, Rinke P. The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy. Front Chem 2019; 7:377. [PMID: 31355177 PMCID: PMC6633269 DOI: 10.3389/fchem.2019.00377] [Citation(s) in RCA: 150] [Impact Index Per Article: 30.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Accepted: 05/08/2019] [Indexed: 12/22/2022] Open
Abstract
The GW approximation in electronic structure theory has become a widespread tool for predicting electronic excitations in chemical compounds and materials. In the realm of theoretical spectroscopy, the GW method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The number of GW calculations in the past two decades has exploded with increased computing power and modern codes. The success of GW can be attributed to many factors: favorable scaling with respect to system size, a formal interpretation for charged excitation energies, the importance of dynamical screening in real systems, and its practical combination with other theories. In this review, we provide an overview of these formal and practical considerations. We expand, in detail, on the choices presented to the scientist performing GW calculations for the first time. We also give an introduction to the many-body theory behind GW, a review of modern applications like molecules and surfaces, and a perspective on methods which go beyond conventional GW calculations. This review addresses chemists, physicists and material scientists with an interest in theoretical spectroscopy. It is intended for newcomers to GW calculations but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.
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Affiliation(s)
- Dorothea Golze
- Department of Applied Physics, Aalto University, School of Science, Espoo, Finland
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Lewis AM, Berkelbach TC. Vertex Corrections to the Polarizability Do Not Improve the GW Approximation for the Ionization Potential of Molecules. J Chem Theory Comput 2019; 15:2925-2932. [DOI: 10.1021/acs.jctc.8b00995] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alan M. Lewis
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States
| | - Timothy C. Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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Ma H, Govoni M, Gygi F, Galli G. A Finite-Field Approach for GW Calculations beyond the Random Phase Approximation. J Chem Theory Comput 2018; 15:154-164. [DOI: 10.1021/acs.jctc.8b00864] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- He Ma
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Marco Govoni
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Francois Gygi
- Department of Computer Science, University of California Davis, Davis, California 95616, United States
| | - Giulia Galli
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
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Ghosh S, Verma P, Cramer CJ, Gagliardi L, Truhlar DG. Combining Wave Function Methods with Density Functional Theory for Excited States. Chem Rev 2018; 118:7249-7292. [PMID: 30044618 DOI: 10.1021/acs.chemrev.8b00193] [Citation(s) in RCA: 128] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.
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Affiliation(s)
- Soumen Ghosh
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Pragya Verma
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Christopher J Cramer
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
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Govoni M, Galli G. GW100: Comparison of Methods and Accuracy of Results Obtained with the WEST Code. J Chem Theory Comput 2018; 14:1895-1909. [PMID: 29397712 DOI: 10.1021/acs.jctc.7b00952] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The reproducibility of calculations carried out within many-body perturbation theory at the G0 W0 level is assessed for 100 closed shell molecules and compared to that of density functional theory. We consider vertical ionization potentials (VIP) and electron affinities (VEA) obtained with five different codes: BerkeleyGW, FHI-aims, TURBOMOLE, VASP, and WEST. We review the approximations and parameters that control the accuracy of G0 W0 results in each code, and we discuss in detail the effect of extrapolation techniques for the parameters entering the WEST code. Differences between the VIP and VEA computed with the various codes are within ∼60 and ∼120 meV, respectively, which is up to four times larger than in the case of the best results obtained with DFT codes. Vertical ionization potentials are validated against experiment and CCSD(T) quantum chemistry results showing a mean absolute relative error of ∼4% for data obtained with WEST. Our analysis of the differences between localized orbitals and plane-wave implementations points out molecules containing Cu, I, Ga, and Xe as major sources of discrepancies, which call for a re-evaluation of the pseudopotentials used for these systems in G0 W0 calculations.
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Affiliation(s)
- Marco Govoni
- Institute for Molecular Engineering and Materials Science Division , Argonne National Laboratory , Lemont , Illinois 60439 , United States
| | - Giulia Galli
- Institute for Molecular Engineering and Materials Science Division , Argonne National Laboratory , Lemont , Illinois 60439 , United States
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Maggio E, Kresse G. Correction to GW Vertex Corrected Calculations for Molecular Systems. J Chem Theory Comput 2018; 14:1821. [DOI: 10.1021/acs.jctc.8b00129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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van Setten MJ, Costa R, Viñes F, Illas F. Assessing GW Approaches for Predicting Core Level Binding Energies. J Chem Theory Comput 2018; 14:877-883. [PMID: 29320628 DOI: 10.1021/acs.jctc.7b01192] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Here we present a systematic study on the performance of different GW approaches: G0W0, G0W0 with linearized quasiparticle equation (lin-G0W0), and quasiparticle self-consistent GW (qsGW), in predicting core level binding energies (CLBEs) on a series of representative molecules comparing to Kohn-Sham (KS) orbital energy-based results. KS orbital energies obtained using the PBE functional are 20-30 eV lower in energy than experimental values obtained from X-ray photoemission spectroscopy (XPS), showing that any Koopmans-like interpretation of KS core level orbitals fails dramatically. Results from qsGW lead to CLBEs that are closer to experimental values from XPS, yet too large. For the qsGW method, the mean absolute error is about 2 eV, an order of magnitude better than plain KS PBE orbital energies and quite close to predictions from ΔSCF calculations with the same functional, which are accurate within ∼1 eV. Smaller errors of ∼0.6 eV are found for qsGW CLBE shifts, again similar to those obtained using ΔSCF PBE. The computationally more affordable G0W0 approximation leads to results less accurate than qsGW, with an error of ∼9 eV for CLBEs and ∼0.9 eV for their shifts. Interestingly, starting G0W0 from PBE0 reduces this error to ∼4 eV with a slight improvement on the shifts as well (∼0.4 eV). The validity of the G0W0 results is however questionable since only linearized quasiparticle equation results can be obtained. The present results pave the way to estimate CLBEs in periodic systems where ΔSCF calculations are not straightforward although further improvement is clearly needed.
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Affiliation(s)
- Michiel J van Setten
- Nanoscopic Physics, Institute of Condensed Matter and Nanosciences, Université catholique de Louvain , 1348 Louvain-la-Neuve, Belgium
| | - Ramon Costa
- Departament de Química Inorgànica i Orgànica & Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona , Martí i Franqués 1, 08028 Barcelona, Spain
| | - Francesc Viñes
- Departament de Ciència de Materials i Química Fisica & Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona , Martí i Franqués 1, 08028 Barcelona, Spain
| | - Francesc Illas
- Departament de Ciència de Materials i Química Fisica & Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona , Martí i Franqués 1, 08028 Barcelona, Spain
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Blase X, Duchemin I, Jacquemin D. The Bethe–Salpeter equation in chemistry: relations with TD-DFT, applications and challenges. Chem Soc Rev 2018; 47:1022-1043. [DOI: 10.1039/c7cs00049a] [Citation(s) in RCA: 120] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
We review the Bethe–Salpeter formalism and analyze its performances for the calculation of the excited state properties of molecular systems.
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Affiliation(s)
- Xavier Blase
- Univ. Grenoble Alpes
- CNRS
- Inst NEEL
- F-38042 Grenoble
- France
| | - Ivan Duchemin
- Univ. Grenoble Alpes
- CEA
- INAC-MEM
- L-Sim
- F-38000 Grenoble
| | - Denis Jacquemin
- CEISAM UMR CNRS 6230
- Université de Nantes
- 44322 Nantes Cedex 3
- France
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