1
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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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2
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Amblard D, Blase X, Duchemin I. Static versus dynamically polarizable environments within the many-body GW formalism. J Chem Phys 2024; 160:154104. [PMID: 38624115 DOI: 10.1063/5.0203637] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Accepted: 03/28/2024] [Indexed: 04/17/2024] Open
Abstract
Continuum- or discrete-polarizable models for the study of optoelectronic processes in embedded subsystems rely mostly on the restriction of the surrounding electronic dielectric response to its low frequency limit. Such a description hinges on the assumption that the electrons in the surrounding medium react instantaneously to any excitation in the central subsystem, thus treating the environment in the adiabatic limit. Exploiting a recently developed embedded GW formalism with an environment described at the fully ab initio level, we assess the merits of the adiabatic limit with respect to an environment where the full dynamics of the dielectric response are considered. Furthermore, we show how to properly take the static limit of the environment's susceptibility by introducing the so-called Coulomb-hole and screened-exchange contributions to the reaction field. As a first application, we consider a C60 molecule at the surface of a C60 crystal, namely, a case where the dynamics of the embedded and embedding subsystems are similar. The common adiabatic assumption, when properly treated, generates errors below 10% on the polarization energy associated with frontier energy levels and associated energy gaps. Finally, we consider a water molecule inside a metallic nanotube, the worst case for the environment's adiabatic limit. The error on the gap polarization energy remains below 10%, even though the error on the frontier orbital polarization energies can reach a few tenths of an electronvolt.
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Affiliation(s)
- David Amblard
- University Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
| | - Xavier Blase
- University Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
| | - Ivan Duchemin
- University Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054 Grenoble, France
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3
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Förster A, van Lenthe E, Spadetto E, Visscher L. Two-Component GW Calculations: Cubic Scaling Implementation and Comparison of Vertex-Corrected and Partially Self-Consistent GW Variants. J Chem Theory Comput 2023; 19:5958-5976. [PMID: 37594901 PMCID: PMC10501001 DOI: 10.1021/acs.jctc.3c00512] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Indexed: 08/20/2023]
Abstract
We report an all-electron, atomic orbital (AO)-based, two-component (2C) implementation of the GW approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation (AC) of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the GW self-energy at a quasi-one-component level, our 2C-GW algorithm is only about a factor of 2-3 slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened G3W2 correction. Comparison of first ionization potentials (IPs) of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations (MAD) of around 70 meV for G0W0@PBE and G0W0@PBE0. We check the accuracy of our AC treatment by comparison to full-frequency GW calculations, which shows that in the absence of multisolution cases, the errors due to AC are only minor. This implies that the main sources of the observed deviations between both implementations are the different single-particle bases and the pseudopotential approximation in the WEST code. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. G0W0@PBE0 (25% exact exchange) and G0W0@BHLYP (50% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Explicit treatment of spin-orbit effects at the 2C level is crucial for systematic agreement with experiment. On the other hand, eigenvalue-only self-consistent GW (evGW) and quasi-particle self-consistent GW (qsGW) significantly overestimate the IPs. Perturbative G3W2 corrections increase the IPs and therefore improve the agreement with experiment in cases where G0W0 alone underestimates the IPs. With a MAD of only 140 meV, 2C-G0W0@PBE0 + G3W2 is in best agreement with the experimental reference values.
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Affiliation(s)
- Arno Förster
- Theoretical
Chemistry, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Erik van Lenthe
- Software
for Chemistry and Materials NV, 1081 HV Amsterdam, The Netherlands
| | - Edoardo Spadetto
- Software
for Chemistry and Materials NV, 1081 HV Amsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical
Chemistry, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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4
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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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5
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Li J, Golze D, Yang W. Combining Renormalized Singles GW Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies. J Chem Theory Comput 2022; 18:6637-6645. [PMID: 36279250 PMCID: PMC9972216 DOI: 10.1021/acs.jctc.2c00686] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We apply the renormalized singles (RS) Green's function in the Bethe-Salpeter equation (BSE)/GW approach to predict accurate neutral excitation energies of molecular systems. The BSE calculations are performed on top of the GRSWRS method, which uses the RS Green's function also for the computation of the screened Coulomb interaction W. We show that the BSE/GRSWRS approach significantly outperforms BSE/G0W0 for predicting excitation energies of valence, Rydberg, and charge-transfer (CT) excitations by benchmarking the Truhlar-Gagliardi set, Stein CT set, and an atomic Rydberg test set. For the Truhlar-Gagliardi test set, BSE/GRSWRS provides comparable accuracy to time-dependent density functional theory (TDDFT) and is slightly better than BSE starting from eigenvalue self-consistent GW (evGW). For the Stein CT test set, BSE/GRSWRS significantly outperforms BSE/G0W0 and TDDFT with the accuracy comparable to BSE/evGW. We also show that BSE/GRSWRS predicts Rydberg excitation energies of atomic systems well. Besides the excellent accuracy, BSE/GRSWRS largely eliminates the dependence on the choice of the density functional approximation. This work demonstrates that the BSE/GRSWRS approach is accurate and efficient for predicting excitation energies for a broad range of systems, which expands the applicability of the BSE/GW approach.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Dorothea Golze
- Faculty of Chemistry and Food Chemistry, Technische Universität Dresden, 01062 Dresden, Germany
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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6
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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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7
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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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8
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Backhouse OJ, Santana-Bonilla A, Booth GH. Scalable and Predictive Spectra of Correlated Molecules with Moment Truncated Iterated Perturbation Theory. J Phys Chem Lett 2021; 12:7650-7658. [PMID: 34351782 DOI: 10.1021/acs.jpclett.1c02383] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
A reliable and efficient computation of the entire single-particle spectrum of correlated molecules is an outstanding challenge in the field of quantum chemistry, with standard density functional theory approaches often giving an inadequate description of excitation energies and gaps. In this work, we expand upon a recently introduced approach that relies on a fully self-consistent many-body perturbation theory coupled to a nonperturbative truncation of the effective dynamics at each step. We show that this yields a low-scaling and accurate method across a diverse benchmark test set that is capable of treating moderate levels of strong correlation effects, and we detail an efficient implementation for applications involving up to ∼1000 orbitals on parallel resources. We then use this method to characterize the spectral properties of the antimalarial drug molecule artemisinin, resolving discrepancies in previous works concerning the active sites of the lowest-energy fundamental excitations of the system.
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Affiliation(s)
- Oliver J Backhouse
- Department of Physics, King's College London, Strand, London WC2R 2LS, U.K
| | | | - George H Booth
- Department of Physics, King's College London, Strand, London WC2R 2LS, U.K
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9
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Yu JM, Nguyen BD, Tsai J, Hernandez DJ, Furche F. Selfconsistent random phase approximation methods. J Chem Phys 2021; 155:040902. [PMID: 34340391 DOI: 10.1063/5.0056565] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
This Perspective reviews recent efforts toward selfconsistent calculations of ground-state energies within the random phase approximation (RPA) in the (generalized) Kohn-Sham (KS) density functional theory context. Since the RPA correlation energy explicitly depends on the non-interacting KS potential, an additional condition to determine the energy as a functional of the density is necessary. This observation leads to the concept of functional selfconsistency (FSC), which requires that the KS density equals the interacting density defined as the functional derivative of the ground-state energy with respect to the external potential. While all existing selfconsistent RPA schemes violate FSC, the recent generalized KS semicanonical projected RPA (GKS-spRPA) method takes a step toward satisfying it. This leads to systematic improvements in densities, binding energy curves, reference state stability, and molecular properties compared to non-selfconsistent RPA as well as optimized effective potential RPA. GKS-spRPA orbital energies accurately approximate valence and core ionization potentials, and even electron affinities of non-valence bound anions. The computational cost and performance of GKS-spRPA are compared to those of related selfconsistent schemes, including GW and orbital optimization methods, and limitations are discussed. Large differences between KS and interacting densities observed in the absence of FSC and the well-rounded performance of GKS-spRPA suggest that the KS potential as a density functional should be defined via the FSC condition for explicitly potential-dependent density functionals.
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Affiliation(s)
- Jason M Yu
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Brian D Nguyen
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Jeffrey Tsai
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Devin J Hernandez
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Filipp Furche
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
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10
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Monino E, Loos PF. Spin-Conserved and Spin-Flip Optical Excitations from the Bethe-Salpeter Equation Formalism. J Chem Theory Comput 2021; 17:2852-2867. [PMID: 33724811 PMCID: PMC8154368 DOI: 10.1021/acs.jctc.1c00074] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
![]()
Like adiabatic time-dependent
density-functional theory (TD-DFT),
the Bethe–Salpeter equation (BSE) formalism of many-body perturbation
theory, in its static approximation, is “blind” to double
(and higher) excitations, which are ubiquitous, for example, in conjugated
molecules like polyenes. Here, we apply the spin-flip ansatz (which considers the lowest triplet state as the reference configuration
instead of the singlet ground state) to the BSE formalism in order
to access, in particular, double excitations. The present scheme is
based on a spin-unrestricted version of the GW approximation
employed to compute the charged excitations and screened Coulomb potential
required for the BSE calculations. Dynamical corrections to the static
BSE optical excitations are taken into account via an unrestricted
generalization of our recently developed (renormalized) perturbative
treatment. The performance of the present spin-flip BSE formalism
is illustrated by computing excited-state energies of the beryllium
atom, the hydrogen molecule at various bond lengths, and cyclobutadiene
in its rectangular and square-planar geometries.
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Affiliation(s)
- Enzo Monino
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Route de Narbonne, 31062 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Route de Narbonne, 31062 Toulouse, France
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11
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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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12
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Tölle J, Deilmann T, Rohlfing M, Neugebauer J. Subsystem-Based GW/Bethe-Salpeter Equation. J Chem Theory Comput 2021; 17:2186-2199. [PMID: 33683119 DOI: 10.1021/acs.jctc.0c01307] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Subsystem Density-Functional Theory and its extension to excited states, namely, subsystem Time-Dependent Density-Functional Theory, have been proven to be efficient and accurate fragmentation approaches for ground and excited states. In the present study we extend this approach to the subsystem-based description of total systems by means of GW and the Bethe-Salpeter equation (BSE). For this, we derive the working equations starting from a subsystem-based partitioning of the screened-Coulomb interaction for an arbitrary number of subsystems. Making use of certain approximations, we develop a parameter-free approach in which environmental screening contributions are effectively included for each subsystem. We demonstrate the applicability of these approximations by comparing quasi-particle energies and excitation energies from subsystem-based GW/BSE calculations to the supermolecular reference. Furthermore, we demonstrate the computational efficiency and the usefulness of this method for the description of photoinduced processes in complex chemical environments.
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Affiliation(s)
- Johannes Tölle
- Theoretische Organische Chemie Organisch-Chemisches Institut, Westfälische Wilhelms-Universität, Corrensstraße 40, Münster, 48149, Germany
| | | | | | - Johannes Neugebauer
- Theoretische Organische Chemie Organisch-Chemisches Institut, Westfälische Wilhelms-Universität, Corrensstraße 40, Münster, 48149, Germany
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13
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Berger JA, Loos PF, Romaniello P. Potential Energy Surfaces without Unphysical Discontinuities: The Coulomb Hole Plus Screened Exchange Approach. J Chem Theory Comput 2020; 17:191-200. [DOI: 10.1021/acs.jctc.0c00896] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- J. Arjan Berger
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, and European Theoretical Spectroscopy Facility (ETSF), Toulouse 31062, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse 31062, France
| | - Pina Romaniello
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, and European Theoretical Spectroscopy Facility (ETSF), Toulouse 31062, France
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14
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Abstract
We discuss the physical properties and accuracy of three distinct dynamical (i.e., frequency-dependent) kernels for the computation of optical excitations within linear response theory: (i) an a priori built kernel inspired by the dressed time-dependent density-functional theory kernel proposed by Maitra et al. [J. Chem. Phys. 120, 5932 (2004)], (ii) the dynamical kernel stemming from the Bethe-Salpeter equation (BSE) formalism derived originally by Strinati [Riv. Nuovo Cimento 11, 1-86 (1988)], and (iii) the second-order BSE kernel derived by Zhang et al. [J. Chem. Phys. 139, 154109 (2013)]. The principal take-home message of the present paper is that dynamical kernels can provide, thanks to their frequency-dependent nature, additional excitations that can be associated with higher-order excitations (such as the infamous double excitations), an unappreciated feature of dynamical quantities. We also analyze, for each kernel, the appearance of spurious excitations originating from the approximate nature of the kernels, as first evidenced by Romaniello et al. [J. Chem. Phys. 130, 044108 (2009)]. Using a simple two-level model, prototypical examples of valence, charge-transfer, and Rydberg excited states are considered.
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Affiliation(s)
- Juliette Authier
- 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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15
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Keller L, Blum V, Rinke P, Golze D. Relativistic correction scheme for core-level binding energies from GW. J Chem Phys 2020; 153:114110. [DOI: 10.1063/5.0018231] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Levi Keller
- Department of Applied Physics, Aalto University, Otakaari 1, FI-02150 Espoo, Finland
| | - Volker Blum
- Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708,
USA
| | - Patrick Rinke
- Department of Applied Physics, Aalto University, Otakaari 1, FI-02150 Espoo, Finland
| | - Dorothea Golze
- Department of Applied Physics, Aalto University, Otakaari 1, FI-02150 Espoo, Finland
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16
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Loos PF, Blase X. Dynamical correction to the Bethe-Salpeter equation beyond the plasmon-pole approximation. J Chem Phys 2020; 153:114120. [PMID: 32962392 DOI: 10.1063/5.0023168] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Bethe-Salpeter equation (BSE) formalism is a computationally affordable method for the calculation of accurate optical excitation energies in molecular systems. Similar to the ubiquitous adiabatic approximation of time-dependent density-functional theory, the static approximation, which substitutes a dynamical (i.e., frequency-dependent) kernel by its static limit, is usually enforced in most implementations of the BSE formalism. Here, going beyond the static approximation, we compute the dynamical correction of the electron-hole screening for molecular excitation energies, thanks to a renormalized first-order perturbative correction to the static BSE excitation energies. The present dynamical correction goes beyond the plasmon-pole approximation as the dynamical screening of the Coulomb interaction is computed exactly within the random-phase approximation. Our calculations are benchmarked against high-level (coupled-cluster) calculations, allowing one to assess the clear improvement brought by the dynamical correction for both singlet and triplet optical transitions.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France
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17
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Blase X, Duchemin I, Jacquemin D, Loos PF. The Bethe-Salpeter Equation Formalism: From Physics to Chemistry. J Phys Chem Lett 2020; 11:7371-7382. [PMID: 32787315 DOI: 10.1021/acs.jpclett.0c01875] [Citation(s) in RCA: 70] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The Bethe-Salpeter equation (BSE) formalism is steadily asserting itself as a new efficient and accurate tool in the ensemble of computational methods available to chemists in order to predict optical excitations in molecular systems. In particular, the combination of the so-called GW approximation, giving access to reliable ionization energies and electron affinities, and the BSE formalism, able to model UV/vis spectra, has shown to provide accurate singlet excitation energies with a typical error of 0.1-0.3 eV. With a similar computational cost as time-dependent density-functional theory (TD-DFT), BSE is able to provide an accuracy on par with the most accurate global and range-separated hybrid functionals without the unsettling choice of the exchange-correlation functional, resolving further known issues (e.g., charge-transfer excitations). In this Perspective, we provide a historical overview of BSE, with a particular focus on its condensed-matter roots. We also propose a critical review of its strengths and weaknesses in different chemical situations.
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Affiliation(s)
- Xavier Blase
- Université Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France
| | - Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L Sim, 38054 Grenoble, France
| | - Denis Jacquemin
- Université de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
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Loos PF, Scemama A, Duchemin I, Jacquemin D, Blase X. Pros and Cons of the Bethe-Salpeter Formalism for Ground-State Energies. J Phys Chem Lett 2020; 11:3536-3545. [PMID: 32298578 DOI: 10.1021/acs.jpclett.0c00460] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The combination of the many-body Green's function GW approximation and the Bethe-Salpeter equation (BSE) formalism has shown to be a promising alternative to time-dependent density functional theory (TD-DFT) for computing vertical transition energies and oscillator strengths in molecular systems. The BSE formalism can also be employed to compute ground-state correlation energies thanks to the adiabatic-connection fluctuation-dissipation theorem (ACFDT). Here, we study the topology of the ground-state potential energy surfaces (PESs) of several diatomic molecules near their equilibrium bond length. Using comparisons with state-of-art computational approaches (CC3), we show that ACFDT@BSE is surprisingly accurate and can even compete with lower-order coupled cluster methods (CC2 and CCSD) in terms of total energies and equilibrium bond distances for the considered systems. However, we sometimes observe unphysical irregularities on the ground-state PES in relation with difficulties in the identification of a few GW quasiparticle energies.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31077 Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31077 Toulouse, France
| | - Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L Sim, 38054 Grenoble, France
| | - Denis Jacquemin
- Laboratoire CEISAM - UMR CNRS 6230, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France
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Golze D, Keller L, Rinke P. Accurate Absolute and Relative Core-Level Binding Energies from GW. J Phys Chem Lett 2020; 11:1840-1847. [PMID: 32043890 PMCID: PMC7735733 DOI: 10.1021/acs.jpclett.9b03423] [Citation(s) in RCA: 50] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Accepted: 02/11/2020] [Indexed: 05/13/2023]
Abstract
We present an accurate approach to compute X-ray photoelectron spectra based on the GW Green's function method that overcomes the shortcomings of common density functional theory approaches. GW has become a popular tool to compute valence excitations for a wide range of materials. However, core-level spectroscopy is thus far almost uncharted in GW. We show that single-shot perturbation calculations in the G0W0 approximation, which are routinely used for valence states, cannot be applied for core levels and suffer from an extreme, erroneous transfer of spectral weight to the satellite spectrum. The correct behavior can be restored by partial self-consistent GW schemes or by using hybrid functionals with almost 50% of exact exchange as a starting point for G0W0. We also include relativistic corrections and present a benchmark study for 65 molecular 1s excitations. Our absolute and relative GW core-level binding energies agree within 0.3 and 0.2 eV with experiment, respectively.
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Affiliation(s)
- Dorothea Golze
- Department of Applied Physics, Aalto University, Otakaari 1, FI-02150 Espoo, Finland
| | - Levi Keller
- Department of Applied Physics, Aalto University, Otakaari 1, FI-02150 Espoo, Finland
| | - Patrick Rinke
- Department of Applied Physics, Aalto University, Otakaari 1, FI-02150 Espoo, Finland
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Duchemin I, Blase X. Robust Analytic-Continuation Approach to Many-Body GW Calculations. J Chem Theory Comput 2020; 16:1742-1756. [DOI: 10.1021/acs.jctc.9b01235] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ivan Duchemin
- IRIG-MEM-L_Sim, Univ. Grenoble Alpes, CEA, F-38054 Grenoble, France
| | - Xavier Blase
- Inst NEEL, Univ. Grenoble Alpes, CNRS, F-38042 Grenoble, France
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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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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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Voora VK, Galhenage R, Hemminger JC, Furche F. Effective one-particle energies from generalized Kohn-Sham random phase approximation: A direct approach for computing and analyzing core ionization energies. J Chem Phys 2019; 151:134106. [PMID: 31594336 DOI: 10.1063/1.5116908] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Generalized-Kohn-Sham (GKS) orbital energies obtained self-consistently from the random phase approximation energy functional with a semicanonical projection (spRPA) were recently shown to rival the accuracy of GW quasiparticle energies for valence ionization potentials. Here, we extend the scope of GKS-spRPA correlated one-particle energies from frontier-orbital ionization to core orbital ionization energies, which are notoriously difficult for GW and other response methods due to strong orbital relaxation effects. For a benchmark consisting of 23 1s core electron binding energies (CEBEs) of second-row elements, chemical shifts estimated from GKS-spRPA one-particle energies yield mean absolute deviations from experiment of 0.2 eV, which are significantly more accurate than the standard GW and comparable to Δ self-consistent field theory without semiempirical adjustment of the energy functional. For small ammonia clusters and cytosine tautomers, GKS-spRPA based chemical shifts capture subtle variations in covalent and noncovalent bonding environments; GKS-spRPA 1s CEBEs for these systems agree with equation-of-motion coupled cluster singles and doubles and ADC(4) results within 0.2-0.3 eV. Two perturbative approximations to GKS-spRPA orbital energies, which reduce the scaling from O(N6) to O(N5) and O(N4), are introduced and tested. We illustrate the application of GKS-spRPA orbital energies to larger systems by using oxygen 1s CEBEs to probe solvation and packing effects in condensed phases of water. GKS-spRPA predicts a lowering of the oxygen 1s CEBE of approximately 1.6-1.7 eV in solid and liquid phases, consistent with liquid-jet X-ray photoelectron spectroscopy and gas phase cluster experiments. The results are rationalized by partitioning GKS-spRPA electron binding energies into static, relaxation, and correlation parts.
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Affiliation(s)
- Vamsee K Voora
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Randima Galhenage
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - John C Hemminger
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Filipp Furche
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
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Di Sabatino S, Berger JA, Romaniello P. Many-Body Effective Energy Theory: Photoemission at Strong Correlation. J Chem Theory Comput 2019; 15:5080-5086. [DOI: 10.1021/acs.jctc.9b00427] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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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: 153] [Impact Index Per Article: 30.6] [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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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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Garniron Y, Applencourt T, Gasperich K, Benali A, Ferté A, Paquier J, Pradines B, Assaraf R, Reinhardt P, Toulouse J, Barbaresco P, Renon N, David G, Malrieu JP, Véril M, Caffarel M, Loos PF, Giner E, Scemama A. Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs. J Chem Theory Comput 2019; 15:3591-3609. [DOI: 10.1021/acs.jctc.9b00176] [Citation(s) in RCA: 74] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Yann Garniron
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS,
UPS, Toulouse, France
| | - Thomas Applencourt
- Computational Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Kevin Gasperich
- Computational Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Anouar Benali
- Computational Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Anthony Ferté
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris, France
| | - Julien Paquier
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris, France
| | - Barthélémy Pradines
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris, France
- Institut des Sciences du Calcul et des Données, Sorbonne Université, F-75005 Paris, France
| | - Roland Assaraf
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris, France
| | - Peter Reinhardt
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris, France
| | - Pierrette Barbaresco
- CALMIP, Université de Toulouse, CNRS, INPT, INSA, UPS, UMS 3667, Toulouse, France
| | - Nicolas Renon
- CALMIP, Université de Toulouse, CNRS, INPT, INSA, UPS, UMS 3667, Toulouse, France
| | | | - Jean-Paul Malrieu
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS,
UPS, Toulouse, France
| | - Mickaël Véril
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS,
UPS, Toulouse, France
| | - Michel Caffarel
- 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
| | - Emmanuel Giner
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS,
UPS, Toulouse, France
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Burton HGA, Thom AJW, Loos PF. Complex adiabatic connection: A hidden non-Hermitian path from ground to excited states. J Chem Phys 2019; 150:041103. [DOI: 10.1063/1.5085121] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hugh G. A. Burton
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Alex J. W. Thom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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