1
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Duchemin I, Amblard D, Blase X. Polarizable Continuum Models and Green's Function GW Formalism: On the Dynamics of the Solvent Electrons. J Chem Theory Comput 2024. [PMID: 39226212 DOI: 10.1021/acs.jctc.4c00745] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/05/2024]
Abstract
The many-body GW formalism, for the calculation of ionization potentials or electronic affinities, relies on the frequency-dependent dielectric function built from the electronic degrees of freedom. Considering the case of water as a solvent treated within the polarizable continuum model, we explore the impact of restricting the full frequency-dependence of the solvent electronic dielectric response to a frequency-independent (ϵ∞) optical dielectric constant. For solutes presenting small to large highest-occupied to lowest-unoccupied molecular orbital energy gaps, we show that such a restriction induces errors no larger than a few percent on the energy level shifts from the gas to the solvated phase. We further introduce a remarkably accurate single-pole model for mimicking the effect of the full frequency dependence of the water dielectric function in the visible-UV range. This allows a fully dynamical embedded GW calculation with the only knowledge of the cavity reaction field calculated for the ϵ∞ optical dielectric constant.
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Affiliation(s)
- Ivan Duchemin
- CEA, IRIG-MEM-L_Sim, Université Grenoble Alpes, 38054 Grenoble, France
| | - David Amblard
- CNRS, Inst NEEL, Université Grenoble Alpes, F-38042 Grenoble, France
| | - Xavier Blase
- CNRS, Inst NEEL, Université Grenoble Alpes, F-38042 Grenoble, France
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2
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Alvertis AM, Williams-Young DB, Bruneval F, Neaton JB. Influence of Electronic Correlations on Electron-Phonon Interactions of Molecular Systems with the GW and Coupled Cluster Methods. J Chem Theory Comput 2024; 20:6175-6183. [PMID: 38954597 DOI: 10.1021/acs.jctc.4c00327] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/04/2024]
Abstract
Electron-phonon interactions are of great importance to a variety of physical phenomena, and their accurate description is an important goal for first-principles calculations. Isolated examples of materials and molecular systems have emerged where electron-phonon coupling is enhanced over density functional theory (DFT) when using the Green's-function-based ab initio GW method, which provides a more accurate description of electronic correlations. It is, however, unclear how general this enhancement is and how employing high-end quantum chemistry methods, which further improve the description of electronic correlations, might further alter electron-phonon interactions over GW or DFT. Here, we address these questions by computing the renormalization of the highest occupied molecular orbital energies of Thiel's set of organic molecules by harmonic vibrations using DFT, GW, and equation-of-motion coupled-cluster calculations. We find that, depending on the amount of exact exchange included in the DFT starting point, GW can increase the magnitude of the electron-phonon coupling across Thiel's set of molecules by an average factor of 1.1-1.8 compared to the underlying DFT, while equation-of-motion coupled-cluster leads to an increase of 1.4-2. The electron-phonon coupling predicted with the ab initio GW method is generally in much closer agreement to coupled cluster values compared to DFT, establishing GW as a promising route for accurately computing electron-phonon phenomena in molecules and beyond at a much lower computational cost than higher-end quantum chemistry techniques.
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Affiliation(s)
- Antonios M Alvertis
- KBR, Inc., NASA Ames Research Center, Moffett Field, California 94035, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David B Williams-Young
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Fabien Bruneval
- Université Paris-Saclay, CEA, Service de Corrosion et de Comportement des Matériaux, SRMP, 91191 Gif-sur-Yvette, France
| | - Jeffrey B Neaton
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Department of Physics, University of California Berkeley, Berkeley, California 94720, United States
- Kavli Energy NanoScience Institute at Berkeley, Berkeley, California 94720, United States
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3
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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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4
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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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5
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Reshetnyak I, Lorin A, Pasquarello A. Many-body screening effects in liquid water. Nat Commun 2023; 14:2705. [PMID: 37169764 PMCID: PMC10175292 DOI: 10.1038/s41467-023-38420-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2020] [Accepted: 04/27/2023] [Indexed: 05/13/2023] Open
Abstract
The screening arising from many-body excitations is a crucial quantity for describing absorption and inelastic X-ray scattering (IXS) of materials. Similarly, the electron screening plays a critical role in state-of-the-art approaches for determining the fundamental band gap. However, ab initio studies of the screening in liquid water have remained limited. Here, we use a combined analysis based on the Bethe-Salpeter equation and time-dependent density functional theory. We first show that absorption spectra at near-edge energies are insufficient to assess the accuracy by which the screening is described. Next, when the energy range under scrutiny is extended, we instead find that the IXS spectra are highly sensitive and allow for the selection of the optimal theoretical scheme. This leads to good agreement with experiment over a large range of transferred energies and momenta, and enables establishing the elusive fundamental band gap of liquid water at 9.3 eV.
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Affiliation(s)
- Igor Reshetnyak
- Chaire de Simulation à l'Echelle Atomique (CSEA), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland
| | - Arnaud Lorin
- Chaire de Simulation à l'Echelle Atomique (CSEA), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland
| | - Alfredo Pasquarello
- Chaire de Simulation à l'Echelle Atomique (CSEA), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland.
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6
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Förster A, Visscher L. Quasiparticle Self-Consistent GW-Bethe-Salpeter Equation Calculations for Large Chromophoric Systems. J Chem Theory Comput 2022; 18:6779-6793. [PMID: 36201788 PMCID: PMC9648197 DOI: 10.1021/acs.jctc.2c00531] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
The GW-Bethe–Salpeter equation
(BSE) method
is promising for calculating the low-lying excitonic states of molecular
systems. However, so far it has only been applied to rather small
molecules and in the commonly implemented diagonal approximations
to the electronic self-energy, it depends on a mean-field starting
point. We describe here an implementation of the self-consistent and
starting-point-independent quasiparticle self-consistent (qsGW)-BSE approach, which is suitable for calculations on
large molecules. We herein show that eigenvalue-only self-consistency
can lead to an unfaithful description of some excitonic states for
chlorophyll dimers while the qsGW-BSE vertical excitation
energies (VEEs) are in excellent agreement with spectroscopic experiments
for chlorophyll monomers and dimers measured in the gas phase. Furthermore,
VEEs from time-dependent density functional theory calculations tend
to disagree with experimental values and using different range-separated
hybrid (RSH) kernels does change the VEEs by up to 0.5 eV. We use
the new qsGW-BSE implementation to calculate the
lowest excitation energies of the six chromophores of the photosystem
II (PSII) reaction center (RC) with nearly 2000 correlated electrons.
Using more than 11,000 (6000) basis functions, the calculation could
be completed in less than 5 (2) days on a single modern compute node.
In agreement with previous TD-DFT calculations using RSH kernels on
models that also do not include environmental effects, our qsGW-BSE calculations only yield states with local characters
in the low-energy spectrum of the hexameric complex. Earlier works
with RSH kernels have demonstrated that the protein environment facilitates
the experimentally observed interchromophoric charge transfer. Therefore,
future research will need to combine correlation effects beyond TD-DFT
with an explicit treatment of environmental electrostatics.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
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7
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Monino E, Loos PF. Unphysical discontinuities, intruder states and regularization in GW methods. J Chem Phys 2022; 156:231101. [PMID: 35732525 DOI: 10.1063/5.0089317] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By recasting the non-linear frequency-dependent GW quasiparticle equation into a linear eigenvalue problem, we explain the appearance of multiple solutions and unphysical discontinuities in various physical quantities computed within the GW approximation. Considering the GW self-energy as an effective Hamiltonian, it is shown that these issues are key signatures of strong correlation in the (N ± 1)-electron states and can be directly related to the intruder state problem. A simple and efficient regularization procedure inspired by the similarity renormalization group is proposed to avoid such issues and speed up the convergence of partially self-consistent GW calculations.
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Affiliation(s)
- Enzo Monino
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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8
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Zhang L, Shu Y, Xing C, Chen X, Sun S, Huang Y, Truhlar DG. Recommendation of Orbitals for G0W0 Calculations on Molecules and Crystals. J Chem Theory Comput 2022; 18:3523-3537. [PMID: 35580263 DOI: 10.1021/acs.jctc.2c00242] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The many-body GW approximation, especially the G0W0 method, has been widely used for condensed matter and molecules to calculate quasiparticle energies for ionization, electron attachment, and band gaps. Because G0W0 calculations are well-known to have a strong dependence on the orbitals, the goal of the present work is to provide guidance on the choice of density functional used to generate orbitals and to recommend a choice that gives the most broadly accurate results. We have systematically investigated the dependence of G0W0 calculations on the orbitals for 100 molecules and 8 crystals by considering orbitals obtained with a diverse set of Kohn-Sham (KS) and generalized KS (GKS) functionals (63 functionals plus Hartree-Fock). The percentage of Hartree-Fock exchange employed in density functionals has been found to have strong influence on the predicted molecular ionization energy and crystal fundamental band gaps (with optimum values between 40 and 56%), but to have less effect on predicting molecular electron affinities. The low cost of the Gaussian implementation, even with hybrid functionals in periodic calculations, the better performance of global hybrids as compared to range-separated hybrids of either than screened exchange or long-range-corrected type, and the relatively low cost of global-hybrid-functional periodic calculations using Gaussians means that one can employ global-hybrid functionals at a very reasonable cost and obtain more accurate band gaps of semiconductors than are obtained by the methods currently widely employed, namely local gradient approximations. We single out three global-hybrid functionals that give especially good results for both molecules (100 in the test set) and crystals (8 in the test set, for all of which our benchmark data are the proper band gap rather than an optical band gap uncorrected for exciton effects).
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Affiliation(s)
- Linyao Zhang
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China.,School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, PR China
| | - Yinan Shu
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Chang Xing
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China.,School of Astronautics, Harbin Institute of Technology, Harbin 150001, PR China
| | - Xiye Chen
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China.,School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, PR China
| | - Shaozeng Sun
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China
| | - Yudong Huang
- School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, PR China
| | - Donald G Truhlar
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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9
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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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10
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Bruneval F, Dattani N, van Setten MJ. The GW Miracle in Many-Body Perturbation Theory for the Ionization Potential of Molecules. Front Chem 2022; 9:749779. [PMID: 35004607 PMCID: PMC8733722 DOI: 10.3389/fchem.2021.749779] [Citation(s) in RCA: 27] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Accepted: 09/14/2021] [Indexed: 11/30/2022] Open
Abstract
We use the GW100 benchmark set to systematically judge the quality of several perturbation theories against high-level quantum chemistry methods. First of all, we revisit the reference CCSD(T) ionization potentials for this popular benchmark set and establish a revised set of CCSD(T) results. Then, for all of these 100 molecules, we calculate the HOMO energy within second and third-order perturbation theory (PT2 and PT3), and, GW as post-Hartree-Fock methods. We found GW to be the most accurate of these three approximations for the ionization potential, by far. Going beyond GW by adding more diagrams is a tedious and dangerous activity: We tried to complement GW with second-order exchange (SOX), with second-order screened exchange (SOSEX), with interacting electron-hole pairs (WTDHF), and with a GW density-matrix (γGW). Only the γGW result has a positive impact. Finally using an improved hybrid functional for the non-interacting Green’s function, considering it as a cheap way to approximate self-consistency, the accuracy of the simplest GW approximation improves even more. We conclude that GW is a miracle: Its subtle balance makes GW both accurate and fast.
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Affiliation(s)
- Fabien Bruneval
- CEA, Service de Recherches de Métallurgie Physique, Direction des Energies, Université Paris-Saclay, Paris, France
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11
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Di Sabatino S, Loos PF, Romaniello P. Scrutinizing GW-Based Methods Using the Hubbard Dimer. Front Chem 2021; 9:751054. [PMID: 34778206 PMCID: PMC8586429 DOI: 10.3389/fchem.2021.751054] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Accepted: 09/28/2021] [Indexed: 12/03/2022] Open
Abstract
Using the simple (symmetric) Hubbard dimer, we analyze some important features of the GW approximation. We show that the problem of the existence of multiple quasiparticle solutions in the (perturbative) one-shot GW method and its partially self-consistent version is solved by full self-consistency. We also analyze the neutral excitation spectrum using the Bethe-Salpeter equation (BSE) formalism within the standard GW approximation and find, in particular, that 1) some neutral excitation energies become complex when the electron-electron interaction U increases, which can be traced back to the approximate nature of the GW quasiparticle energies; 2) the BSE formalism yields accurate correlation energies over a wide range of U when the trace (or plasmon) formula is employed; 3) the trace formula is sensitive to the occurrence of complex excitation energies (especially singlet), while the expression obtained from the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is more stable (yet less accurate); 4) the trace formula has the correct behavior for weak (i.e., small U) interaction, unlike the ACFDT expression.
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Affiliation(s)
- S. Di Sabatino
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS and ETSF, Toulouse, France
| | - P.-F. Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - P. Romaniello
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS and ETSF, Toulouse, France
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12
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Bruneval F, Rodriguez-Mayorga M, Rinke P, Dvorak M. Improved One-Shot Total Energies from the Linearized GW Density Matrix. J Chem Theory Comput 2021; 17:2126-2136. [PMID: 33705127 DOI: 10.1021/acs.jctc.0c01264] [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
The linearized GW density matrix (γGW) is an efficient method to improve the static portion of the self-energy compared to that of ordinary perturbative GW while keeping the single-shot simplicity of the calculation. Previous work has shown that γGW gives an improved Fock operator and total energy components that approach the self-consistent GW quality. Here, we test γGW for dimer dissociation for the first time by studying N2, LiH, and Be2. We also calculate a set of self-consistent GW results in identical basis sets for a direct and consistent comparison. γGW approaches self-consistent GW total energies for a starting point based on a high amount of exact exchange. We also compare the accuracy of different total energy functionals, which differ when evaluated with a non-self-consistent density or density matrix. While the errors in total energies among different functionals and starting points are small, the individual energy components show noticeable errors when compared to reference data. The energy component errors of γGW are smaller than functionals of the density and we suggest that the linearized GW density matrix is a route to improving total energy evaluations in the adiabatic connection framework.
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Affiliation(s)
- Fabien Bruneval
- Université Paris-Saclay, CEA, Service de Recherches de Métallurgie Physique, 91191 Gif-sur-Yvette, France
| | - Mauricio Rodriguez-Mayorga
- Université Paris-Saclay, CEA, Service de Recherches de Métallurgie Physique, 91191 Gif-sur-Yvette, France
| | - Patrick Rinke
- Department of Applied Physics, Aalto University School of Science, 00076 Aalto, Finland
| | - Marc Dvorak
- Department of Applied Physics, Aalto University School of Science, 00076 Aalto, Finland
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13
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Akter S, Yamamoto Y, Diaz CM, Jackson KA, Zope RR, Baruah T. Study of self-interaction errors in density functional predictions of dipole polarizabilities and ionization energies of water clusters using Perdew–Zunger and locally scaled self-interaction corrected methods. J Chem Phys 2020; 153:164304. [DOI: 10.1063/5.0025601] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Sharmin Akter
- Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Carlos M. Diaz
- Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Koblar A. Jackson
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
| | - Rajendra R. Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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14
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Liu C, Kloppenburg J, Yao Y, Ren X, Appel H, Kanai Y, Blum V. All-electron ab initio Bethe-Salpeter equation approach to neutral excitations in molecules with numeric atom-centered orbitals. J Chem Phys 2020; 152:044105. [DOI: 10.1063/1.5123290] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chi Liu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Jan Kloppenburg
- Institute of Condensed Matter and Nanoscience, Université Catholique de Louvain, Louvain-la-Neuve 1348, Belgium
| | - Yi Yao
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, USA
- Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
| | - Xinguo Ren
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Heiko Appel
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany
| | - Yosuke Kanai
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, USA
| | - Volker Blum
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
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15
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Loos PF, Pradines B, Scemama A, Giner E, Toulouse J. Density-Based Basis-Set Incompleteness Correction for GW Methods. J Chem Theory Comput 2019; 16:1018-1028. [DOI: 10.1021/acs.jctc.9b01067] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Barthélémy Pradines
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
- Institut des Sciences du Calcul et des Données, Sorbonne Université, Paris, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Emmanuel Giner
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
- Institut Universitaire de France, Paris, France
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16
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Byun YM, Öğüt S. Practical GW scheme for electronic structure of 3d-transition-metal monoxide anions: ScO -, TiO -, CuO -, and ZnO . J Chem Phys 2019; 151:134305. [PMID: 31594362 DOI: 10.1063/1.5118671] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The GW approximation to many-body perturbation theory is a reliable tool for describing charged electronic excitations, and it has been successfully applied to a wide range of extended systems for several decades using a plane-wave basis. However, the GW approximation has been used to test limited spectral properties of a limited set of finite systems (e.g., frontier orbital energies of closed-shell sp molecules) only for about a decade using a local-orbital basis. Here, we calculate the quasiparticle spectra of closed- and open-shell molecular anions with partially and completely filled 3d shells (shallow and deep 3d states, respectively), ScO-, TiO-, CuO-, and ZnO-, using various levels of GW theory, and compare them to experiments to evaluate the performance of the GW approximation on the electronic structure of small molecules containing 3d transition metals. We find that the G-only eigenvalue self-consistent GW scheme with W fixed to the PBE level (GnW0@PBE), which gives the best compromise between accuracy and efficiency for solids, also gives good results for both localized (d) and delocalized (sp) states of 3d-transition-metal oxide molecules. The success of GnW0@PBE in predicting electronic excitations in these systems reasonably well is likely due to the fortuitous cancellation effect between the overscreening of the Coulomb interaction by PBE and the underscreening by the neglect of vertex corrections. Together with the absence of the self-consistent field convergence error (e.g., spin contamination in open-shell systems) and the GW multisolution issue, the GnW0@PBE scheme gives the possibility to predict the electronic structure of complex real systems (e.g., molecule-solid and sp-d hybrid systems) accurately and efficiently.
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Affiliation(s)
- Young-Moo Byun
- Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA
| | - Serdar Öğüt
- Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA
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17
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Zhang Y. Calculating spin crossover temperatures by a first-principles LDA+U scheme with parameter U evaluated from GW. J Chem Phys 2019; 151:134701. [PMID: 31594359 DOI: 10.1063/1.5124239] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
The prediction of spin crossover (SCO) temperatures (T1/2) depends sensitively on the description of local Coulomb correlation. Due to its balance between accuracy and computational cost, local density approximation combined with Hubbard U model (LDA+U) is an appealing tool for this purpose. Despite its accurate performance on energetic properties, such as spin adiabatic energy difference, it is well-known that the LDA+U approach would lose its predictive power if U is tuned to achieve close agreement with experiment for a certain property. On the other hand, a static U value cannot account for changes in the electronic structure. Here, we propose a framework to derive dynamical U (Udyn) values for iron(ii) complexes from the many-body GW calculations. By performing model calculations on a series of compounds with varying ligand fields, we show that the U values determined in this way are local environment dependent, and the resulting LDA+Udyn method could reproduce their experimental ground spin states. We present applications to selected SCO complexes illustrating that Udyn considerably overcomes some of the drawbacks of employing a constant U in the calculation of thermochemical quantities. Using the described calculation procedure, the T1/2 values are predicted with a small mean absolute error of 176 K with respect to experiment.
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Affiliation(s)
- Yachao Zhang
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Education University, Guiyang 550018, China
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18
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Bruneval F. Assessment of the Linearized GW Density Matrix for Molecules. J Chem Theory Comput 2019; 15:4069-4078. [DOI: 10.1021/acs.jctc.9b00333] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Fabien Bruneval
- DEN, Service de Recherches de Métallurgie Physique, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
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19
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Bouchafra Y, Shee A, Réal F, Vallet V, Severo Pereira Gomes A. Predictive Simulations of Ionization Energies of Solvated Halide Ions with Relativistic Embedded Equation of Motion Coupled Cluster Theory. PHYSICAL REVIEW LETTERS 2018; 121:266001. [PMID: 30636145 DOI: 10.1103/physrevlett.121.266001] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2018] [Indexed: 06/09/2023]
Abstract
A subsystem approach for obtaining electron binding energies in the valence region is presented and applied to the case of halide ions (X^{-},X=F-At) in water. This approach is based on electronic structure calculations combining the relativistic equation-of-motion coupled cluster method for electron detachment and density functional theory via the frozen density embedding approach, using structures from classical molecular dynamics with polarizable force fields for discrete systems (in our study, droplets containing the anion and 50 water molecules). Our results indicate that one can accurately capture both the large solvent effect observed for the halides and the splitting of their ionization signals due to the increasingly large spin-orbit coupling of the p_{3/2}-p_{1/2} manifold across the series, at an affordable computational cost. Furthermore, owing to the quantum mechanical treatment of both solute and solvent electron binding energies of semiquantitative quality are also obtained for (bulk) water as by-products of the calculations for the halogens (in droplets).
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Affiliation(s)
- Yassine Bouchafra
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, F-59000 Lille, France
| | - Avijit Shee
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, F-59000 Lille, France
| | - Florent Réal
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, F-59000 Lille, France
| | - Valérie Vallet
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, F-59000 Lille, France
| | - André Severo Pereira Gomes
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, F-59000 Lille, France
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20
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Wei M, Jin F, Chen T, Ma Y. Variation of optical spectra of water clusters with size from many-body Green's function theory. J Chem Phys 2018; 148:224302. [PMID: 29907027 DOI: 10.1063/1.5031083] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Water clusters are an important species in the environment and atmosphere and take part in various chemical and biological reactions. How their optical properties vary with size is still an open question. Using the GW method and Bethe-Salpeter equation within the ab initio many-body Green's function theory, we study the electronic excitations in a series of water clusters (H2O)n with n = 1-48. We find that their absorption peaks blueshift with increasing cluster size due to the reducing electron-hole binding energy which arises from the enhanced electronic screening and gradually delocalized excitonic spatial distribution. The position of the first absorption peak has a close relation to the average number of hydrogen bonds per molecule. Off-diagonal matrix elements of the self-energy operator have pronounced effects on the unoccupied electronic levels and optical absorption for small clusters with n ≤ 10 when using density functional theory as the starting point for GW calculations. Although the optical absorption is predominated by delocalized excitons, highly localized excitons on a single water molecule are always present on the cluster surface in the vicinity of the absorption edge. These localized excitons may facilitate the photodissociation of water molecules. This can provide inspiration on the excited-state dynamics and photolysis in water clusters.
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Affiliation(s)
- Min Wei
- School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, China
| | - Fan Jin
- School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, China
| | - Tingwei Chen
- School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, China
| | - Yuchen Ma
- School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, China
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21
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Loos PF, Romaniello P, Berger JA. Green Functions and Self-Consistency: Insights From the Spherium Model. J Chem Theory Comput 2018; 14:3071-3082. [PMID: 29746773 DOI: 10.1021/acs.jctc.8b00260] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We report an exhaustive study of the performance of different variants of Green function methods for the spherium model in which two electrons are confined to the surface of a sphere and interact via a genuine long-range Coulomb operator. We show that the spherium model provides a unique paradigm to study electronic correlation effects from the weakly correlated regime to the strongly correlated regime, since the mathematics are simple while the physics is rich. We compare perturbative GW, partially self-consistent GW and second-order Green function (GF2) methods for the computation of ionization potentials, electron affinities, energy gaps, correlation energies as well as singlet and triplet neutral excitations by solving the Bethe-Salpeter equation (BSE). We discuss the problem of self-screening in GW and show that it can be partially solved with a second-order screened exchange correction (SOSEX). We find that, in general, self-consistency deteriorates the results with respect to those obtained within perturbative approaches with a Hartree-Fock starting point. Finally, we unveil an important problem of partial self-consistency in GW: in the weakly correlated regime, it can produce artificial discontinuities in the self-energy caused by satellite resonances with large weights.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques , Université de Toulouse, CNRS, UPS , 31062 Toulouse , France
| | - Pina Romaniello
- Laboratoire de Physique Théorique , Université de Toulouse, CNRS, UPS , 31062 Toulouse , France.,European Theoretical Spectroscopy Facility (ETSF)
| | - J A Berger
- Laboratoire de Chimie et Physique Quantiques , Université de Toulouse, CNRS, UPS , 31062 Toulouse , France.,European Theoretical Spectroscopy Facility (ETSF)
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22
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Gui X, Holzer C, Klopper W. Accuracy Assessment of GW Starting Points for Calculating Molecular Excitation Energies Using the Bethe–Salpeter Formalism. J Chem Theory Comput 2018; 14:2127-2136. [DOI: 10.1021/acs.jctc.8b00014] [Citation(s) in RCA: 52] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Xin Gui
- Institute of Physical Chemistry, Theoretical Chemistry Group, Karlsruhe Institute of Technology (KIT), KIT Campus South, P.O. Box 6980, D-76049 Karlsruhe, Germany
| | - Christof Holzer
- Institute of Physical Chemistry, Theoretical Chemistry Group, Karlsruhe Institute of Technology (KIT), KIT Campus South, P.O. Box 6980, D-76049 Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Theoretical Chemistry Group, Karlsruhe Institute of Technology (KIT), KIT Campus South, P.O. Box 6980, D-76049 Karlsruhe, Germany
- Centre for Advanced Study (CAS) at The Norwegian Academy of Science and Letters, Drammensveien 78, N-0271 Oslo, Norway
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23
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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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24
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Reining L. The GW approximation: content, successes and limitations. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1344] [Citation(s) in RCA: 85] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Lucia Reining
- Laboratoire des Solides Irradiés, École Polytechnique, CNRS, CEAUniversité Paris‐Saclay Palaiseau France
- European Theoretical Spectroscopy Facility (ETSF), http:///www.etsf.eu
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25
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P SK, Genova A, Pavanello M. Cooperation and Environment Characterize the Low-Lying Optical Spectrum of Liquid Water. J Phys Chem Lett 2017; 8:5077-5083. [PMID: 28968128 DOI: 10.1021/acs.jpclett.7b02212] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The optical spectrum of liquid water is analyzed by subsystem time-dependent density functional theory. We provide simple explanations for several important (and so far elusive) features. Due to the disordered environment surrounding each water molecule, the joint density of states of the liquid is much broader than that of the vapor, thus explaining the red-shifted Urbach tail of the liquid compared to the gas phase. Confinement effects provided by the first solvation shell are responsible for the blue shift of the first absorption peak compared to the vapor. In addition, we also characterize many-body excitonic effects. These dramatically affect the spectral weights at low frequencies, contributing to the refractive index by a small but significant amount.
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Affiliation(s)
- Sudheer Kumar P
- Department of Chemistry, Rutgers University , Newark, New Jersey 07102, United States
| | - Alessandro Genova
- Department of Chemistry, Rutgers University , Newark, New Jersey 07102, United States
| | - Michele Pavanello
- Department of Chemistry, Rutgers University , Newark, New Jersey 07102, United States
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26
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Azarias C, Habert C, Budzák Š, Blase X, Duchemin I, Jacquemin D. Calculations of n→π* Transition Energies: Comparisons Between TD-DFT, ADC, CC, CASPT2, and BSE/GW Descriptions. J Phys Chem A 2017; 121:6122-6134. [DOI: 10.1021/acs.jpca.7b05222] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Cloé Azarias
- CEISAM,
BP 92208, UMR CNRS 6230, Université de Nantes, 2, Rue de
la Houssiniere, 44322 Nantes, Cedex 3, France
| | - Chloé Habert
- CEISAM,
BP 92208, UMR CNRS 6230, Université de Nantes, 2, Rue de
la Houssiniere, 44322 Nantes, Cedex 3, France
| | - Šimon Budzák
- Department
of Chemistry, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-97400 Banská Bystrica, Slovak Republic
| | - Xavier Blase
- CNRS, Inst NEEL, F-38042 Grenoble, France
- Univ.
Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France
| | - Ivan Duchemin
- Univ.
Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France
- Univ.
Grenobles Alpes, CEA, INAC-MEM, L_Sim, F-38000 Grenoble, France
| | - Denis Jacquemin
- CEISAM,
BP 92208, UMR CNRS 6230, Université de Nantes, 2, Rue de
la Houssiniere, 44322 Nantes, Cedex 3, France
- Institut Universitaire de France, 1, rue Descartes, F-75231 Paris Cedex 05, France
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27
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Bruneval F. Optimized virtual orbital subspace for faster GW calculations in localized basis. J Chem Phys 2017; 145:234110. [PMID: 28010103 DOI: 10.1063/1.4972003] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The popularity of the GW approximation to the self-energy to access the quasiparticle energies of molecules is constantly increasing. As the other methods addressing the electronic correlation, the GW self-energy unfortunately shows a very slow convergence with respect to the basis complexity, which precludes the calculation of accurate quasiparticle energies for large molecules. Here we propose a method to mitigate this issue that relies on two steps: (i) the definition of a reduced virtual orbital subspace, thanks to a much smaller basis set; (ii) the account of the remainder through the simpler one-ring approximation to the self-energy. We assess the quality of the corrected quasiparticle energies for simple molecules, and finally we show an application to large graphene chunks to demonstrate the numerical efficiency of the scheme.
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Affiliation(s)
- Fabien Bruneval
- CEA, DEN, Service de Recherches de Métallurgie Physique, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
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28
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Hung L, Bruneval F, Baishya K, Öğüt S. Benchmarking the GW Approximation and Bethe–Salpeter Equation for Groups IB and IIB Atoms and Monoxides. J Chem Theory Comput 2017; 13:2135-2146. [DOI: 10.1021/acs.jctc.7b00123] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Linda Hung
- NIST
Center for Neutron Research, National Institute of Standard and Technology, Gaithersburg, Maryland 20899, United States
| | - Fabien Bruneval
- CEA,
DEN, Service de Recherches de Métallurgie Physique, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
| | - Kopinjol Baishya
- Department
of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, United States
| | - Serdar Öğüt
- Department
of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, United States
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29
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Jacquemin D, Duchemin I, Blase X. Is the Bethe-Salpeter Formalism Accurate for Excitation Energies? Comparisons with TD-DFT, CASPT2, and EOM-CCSD. J Phys Chem Lett 2017; 8:1524-1529. [PMID: 28301726 PMCID: PMC5385505 DOI: 10.1021/acs.jpclett.7b00381] [Citation(s) in RCA: 64] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2017] [Accepted: 03/16/2017] [Indexed: 05/25/2023]
Abstract
Developing ab initio approaches able to provide accurate excited-state energies at a reasonable computational cost is one of the biggest challenges in theoretical chemistry. In that framework, the Bethe-Salpeter equation approach, combined with the GW exchange-correlation self-energy, which maintains the same scaling with system size as TD-DFT, has recently been the focus of a rapidly increasing number of applications in molecular chemistry. Using a recently proposed set encompassing excitation energies of many kinds [J. Phys. Chem. Lett. 2016, 7, 586-591], we investigate here the performances of BSE/GW. We compare these results to CASPT2, EOM-CCSD, and TD-DFT data and show that BSE/GW provides an accuracy comparable to the two wave function methods. It is particularly remarkable that the BSE/GW is equally efficient for valence, Rydberg, and charge-transfer excitations. In contrast, it provides a poor description of triplet excited states, for which EOM-CCSD and CASPT2 clearly outperform BSE/GW. This contribution therefore supports the use of the Bethe-Salpeter approach for spin-conserving transitions.
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Affiliation(s)
- Denis Jacquemin
- Laboratoire
CEISAM - UMR CNRS 6230, Université
de Nantes, 2 Rue de la
Houssinière, BP 92208, 44322 Nantes Cedex 3, France
- Institut
Universitaire de France, 1 rue Descartes, 75231 Paris Cedex 5, France
| | - Ivan Duchemin
- Univ.
Grenobles Alpes, CEA, INAC-MEM, L_Sim, F-38000 Grenoble, France
- Univ.
Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France
| | - Xavier Blase
- Univ.
Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France
- CNRS, Inst
NEEL, F-38042 Grenoble, France
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30
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Jacquemin D, Duchemin I, Blondel A, Blase X. Benchmark of Bethe-Salpeter for Triplet Excited-States. J Chem Theory Comput 2017; 13:767-783. [PMID: 28107000 DOI: 10.1021/acs.jctc.6b01169] [Citation(s) in RCA: 51] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
We have evaluated the accuracy of the Bethe-Salpeter singlet-triplet transition energies as well as singlet-triplet and triplet-triplet splittings for 20 organic molecules, using as reference the CC3 values determined by Thiel and co-workers with both the TZVP and aug-cc-pVTZ atomic basis sets. Our excitation energies are obtained on the basis of GW quasiparticle energy levels that are self-consistently converged with respect to the starting DFT eigenvalues. In its current form, BSE/GW is often unable to provide a balanced description of both singlet and triplet excited-states. While the singlet-singlet and triplet-triplet energy separations are obtained accurately, triplets are located too close in energy from the ground-state, by typically -0.55 eV when using standard functionals to generate the starting eigenstates. Applying the Tamm-Dancoff approximation upshifts the BSE triplet energies and allows reducing this error to ca. -0.40 eV, while using M06-HF eigenstates allows a further increase and hence a reduction of the error for triplet states, but at the cost of larger errors for the singlet excited-states. At this stage, the most accurate TD-DFT estimates therefore remain competitive for computing singlet-triplet transition energies. Indeed, with M06-2X, irrespective of the application or not of the Tamm-Dancoff approximation and of the selected atomic basis set, the deviations obtained with TD-DFT are rather small.
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Affiliation(s)
- Denis Jacquemin
- Laboratoire CEISAM - UMR CNR 6230, Université de Nantes , 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France.,Institut Universitaire de France , 103 bd St. Michel, 75005 Paris Cedex 5, France
| | - Ivan Duchemin
- INAC, SP2M/L_Sim, CEA/UJF Cedex 09, 38054 Grenoble, France.,Institut NEEL, Université Grenoble Alpes , F-38042 Grenoble, France
| | - Aymeric Blondel
- Laboratoire CEISAM - UMR CNR 6230, Université de Nantes , 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
| | - Xavier Blase
- Institut NEEL, Université Grenoble Alpes , F-38042 Grenoble, France.,CNRS, Institut NEEL, F-38042 Grenoble, France
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31
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Azarias C, Duchemin I, Blase X, Jacquemin D. Bethe-Salpeter study of cationic dyes: Comparisons with ADC(2) and TD-DFT. J Chem Phys 2017; 146:034301. [PMID: 28109224 DOI: 10.1063/1.4974097] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present a theoretical investigation of the excited-state properties of a large series of structurally diverse arylcarbonium derivatives that are known to be challenging for theoretical models. More specifically, we compare the pros and cons of TD-DFT (TD-M06-2X), ADC(2), and BSE/GW approaches for a large panel of compounds, using two different solvent models. Both 0-0 and vertical transition energies are considered and compared to the experimental values. All approaches reasonably reproduce the auxochromic and acidochromic shifts, although in most cases both TD-DFT and BSE/GW return larger correlation with experimental values than ADC(2) for these shifts. In contrast, the absolute transition energies obtained with ADC(2) tend to be closer to the measurements, TD-DFT using the M06-2X functional largely overestimating the experimental references (by ca. 0.5 eV), and BSE/GW providing intermediate values. In addition, we show that the selected solvent model has a significant impact on the results, the corrected linear-response approach providing larger transition energies than its linear-response counterpart.
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Affiliation(s)
- Cloé Azarias
- CEISAM, UMR CNRS 6230, BP 92208, Université de Nantes, 2, Rue de la Houssinière, 44322 Nantes Cedex 3, France
| | - Ivan Duchemin
- INAC, SP2M/L_Sim, CEA/UJF Cedex 09, 38054 Grenoble, France
| | - Xavier Blase
- Univ. Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France
| | - Denis Jacquemin
- CEISAM, UMR CNRS 6230, BP 92208, Université de Nantes, 2, Rue de la Houssinière, 44322 Nantes Cedex 3, France
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32
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Krause K, Klopper W. Implementation of the Bethe−Salpeter equation in the TURBOMOLE program. J Comput Chem 2016; 38:383-388. [DOI: 10.1002/jcc.24688] [Citation(s) in RCA: 57] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2016] [Revised: 11/15/2016] [Accepted: 11/17/2016] [Indexed: 11/06/2022]
Affiliation(s)
- Katharina Krause
- Karlsruhe Institute of Technology (KIT), Institute of Physical Chemistry; P.O. Box 6980 Karlsruhe D-76049 Germany
| | - Wim Klopper
- Karlsruhe Institute of Technology (KIT), Institute of Physical Chemistry; P.O. Box 6980 Karlsruhe D-76049 Germany
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33
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Ziaei V, Bredow T. GW-BSE approach on S1 vertical transition energy of large charge transfer compounds: A performance assessment. J Chem Phys 2016; 145:174305. [DOI: 10.1063/1.4966920] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Vafa Ziaei
- Mulliken Center for Theoretical Chemistry, University of Bonn, Bonn, Germany
| | - Thomas Bredow
- Mulliken Center for Theoretical Chemistry, University of Bonn, Bonn, Germany
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Blase X, Boulanger P, Bruneval F, Fernandez-Serra M, Duchemin I. Erratum: “GW and Bethe-Salpeter study of small water clusters” [J. Chem. Phys. 144, 034109 (2016)]. J Chem Phys 2016; 145:169901. [DOI: 10.1063/1.4965929] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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Hollas D, Muchová E, Slavíček P. Modeling Liquid Photoemission Spectra: Path-Integral Molecular Dynamics Combined with Tuned Range-Separated Hybrid Functionals. J Chem Theory Comput 2016; 12:5009-5017. [DOI: 10.1021/acs.jctc.6b00630] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel Hollas
- Department of Physical Chemistry, University of Chemistry and Technology Prague, Technická 5, 16628 Prague 6, Czech Republic
| | - Eva Muchová
- Department of Physical Chemistry, University of Chemistry and Technology Prague, Technická 5, 16628 Prague 6, Czech Republic
| | - Petr Slavíček
- Department of Physical Chemistry, University of Chemistry and Technology Prague, Technická 5, 16628 Prague 6, Czech Republic
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GW in the Gaussian and Plane Waves Scheme with Application to Linear Acenes. J Chem Theory Comput 2016; 12:3623-35. [DOI: 10.1021/acs.jctc.6b00380] [Citation(s) in RCA: 75] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
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