pith. sign in

arxiv: 2606.04285 · v1 · pith:RZ6P6OQInew · submitted 2026-06-02 · ⚛️ physics.chem-ph

An Algebraic-Diagrammatic Construction for Vertex Corrections to the GW Self-Energy

Antoine Marie , Johannes T\"olle , Pierre-Fran\c{c}ois Loos This is my paper

Pith reviewed 2026-06-28 07:40 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords GW approximationG3W2algebraic diagrammatic constructionself-energyvertex correctionspositive semi-definitenessquasiparticle energiesionization potentials
0
0 comments X

The pith

Embedding G3W2 inside the algebraic-diagrammatic construction enforces a sum-over-state self-energy that guarantees positive semi-definiteness.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The G3W2 approximation adds second-order vertex corrections to the GW self-energy but can produce negative spectral functions because it violates positive semi-definiteness. This work recasts G3W2 inside the algebraic-diagrammatic construction so the self-energy takes the exact analytic form of a sum over states. The resulting ADC-G3W2 schemes, including ADC-2SOSEX and ADC(3)-G3W2, generate Hermitian effective Hamiltonians whose diagonalization supplies quasiparticle and satellite energies. The construction also supplies a formal bridge between screened-interaction perturbation theory and conventional ADC schemes that use the bare Coulomb interaction. The methods are tested on valence ionization potentials against the parent G3W2 approximation.

Core claim

Reformulating the G3W2 approximation within the algebraic-diagrammatic construction produces expressions for the self-energy that match the exact sum-over-state representation, thereby guaranteeing positive semi-definiteness and enabling nonperturbative resummations of vertex corrections through Hermitian effective Hamiltonians.

What carries the argument

The algebraic-diagrammatic construction applied to the G3W2 self-energy (starting from GW), which converts the approximation into a sum-over-state form and yields a hierarchy of effective Hamiltonians.

If this is right

  • The ADC-based approximations produce spectral functions that remain non-negative by construction.
  • Quasiparticle and satellite energies are obtained directly from eigenvalues of Hermitian matrices.
  • The approach creates a formal connection between many-body perturbation theory formulated with the screened interaction W and standard ADC schemes that use the bare Coulomb interaction.
  • The hierarchy allows systematic inclusion of higher-order vertex corrections while retaining the required analytic properties.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same ADC embedding might be applied to other vertex-corrected self-energy approximations beyond G3W2 to restore analytic properties.
  • The effective-Hamiltonian form could simplify the inclusion of these corrections inside existing quantum-chemistry codes that already diagonalize ADC matrices.
  • Because the construction starts from GW, the resulting schemes might serve as a controlled way to add vertex effects without losing the starting point's computational advantages.

Load-bearing premise

The algebraic-diagrammatic construction can be applied to the G3W2 approximation while preserving its essential physical content and accuracy.

What would settle it

A computed spectral function from the ADC-G3W2 self-energy that takes a negative value at any frequency would show that positive semi-definiteness is not guaranteed.

Figures

Figures reproduced from arXiv: 2606.04285 by Antoine Marie, Johannes T\"olle, Pierre-Fran\c{c}ois Loos.

Figure 1
Figure 1. Figure 1: FIG. 1. Diagrammatic representation of the [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Histogram of the errors (with respect to the TBEs) for the inner- and outer-valence IPs computed with various self-energy schemes in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Histogram of the errors (with respect to the TBEs) for the inner- and outer-valence IPs computed with various ADC schemes in the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

The $G3W2$ approximation -- the second-order self-energy beyond $GW$ -- is known to violate some fundamental analytic properties of the self-energy. In particular, its lack of positive semi-definiteness leads to unphysical features such as negative spectral functions. In this work, we reformulate the $G3W2$ approximation within the algebraic-diagrammatic construction (ADC) framework. The resulting ADC-$G3W2$ formalism enforces the same analytic form as the exact self-energy, namely a sum-over-state representation, and, consequently, guarantees positive semi-definiteness. Starting from the $GW$ self-energy, we construct a hierarchy of ADC-based approximations of increasing sophistication, including ADC-2SOSEX, ADC(3)-$G3W2$, and a full ADC-$G3W2$ scheme. These methods can be interpreted as nonperturbative resummations of vertex corrections to the self-energy, yielding Hermitian effective Hamiltonians whose diagonalization provides quasiparticle and satellite energies. This establishes a formal bridge between many-body perturbation theory formulated in terms of the screened interaction $W$ and conventional ADC schemes based on the bare Coulomb interaction. The performance of these ADC-based approximations is gauged for valence ionization potentials and benchmarked against their parent method.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reformulates the G3W2 approximation (second-order self-energy beyond GW) inside the algebraic-diagrammatic construction (ADC) framework. The resulting ADC-G3W2, together with the intermediate schemes ADC-2SOSEX and ADC(3)-G3W2, is asserted to enforce the exact self-energy's sum-over-states analytic form via an effective Hermitian Hamiltonian, thereby guaranteeing positive semi-definiteness and eliminating unphysical negative spectral functions. The work presents these methods as nonperturbative resummations of vertex corrections and benchmarks them on valence ionization potentials against the parent perturbative G3W2.

Significance. If the mapping preserves the essential content of the original G3W2 diagrams, the construction supplies a systematic route to analyticity-preserving vertex corrections within the screened-interaction language and creates a concrete bridge to conventional ADC schemes based on the bare Coulomb interaction. The production of Hermitian effective Hamiltonians whose eigenvalues directly furnish quasiparticle and satellite energies is a clear technical advantage for practical calculations.

major comments (2)
  1. [Abstract / central construction] Abstract and the central construction section: the claim that ADC-G3W2 'enforces the same analytic form as the exact self-energy' and thereby guarantees positive semi-definiteness rests on the assertion that the ADC mapping is applied to G3W2 while 'preserving its essential physical content.' No explicit demonstration is given that the effective-Hamiltonian construction reproduces the original perturbative G3W2 poles and residues rather than generating a distinct resummation; this equivalence must be shown equation-by-equation for the claim to be load-bearing.
  2. [Hierarchy definition] Hierarchy definition: the paper introduces ADC-2SOSEX, ADC(3)-G3W2 and full ADC-G3W2 as successive approximations starting from the GW self-energy. It is unclear how the second-order vertex diagrams of G3W2 are partitioned among these levels and whether the truncation at each level remains consistent with the original perturbative ordering; an explicit diagram-to-ADC mapping table or set of equations is required.
minor comments (2)
  1. The benchmarking paragraph refers to 'valence ionization potentials' and 'the parent method' but does not specify the molecular test set, basis sets, or reference data; a table or figure caption should make these choices explicit.
  2. Notation for the screened interaction W and the effective ADC Hamiltonian should be introduced once with a clear distinction between the bare and screened quantities.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's detailed review and the opportunity to clarify the central aspects of our work. Below we address the major comments point by point, and we will revise the manuscript to incorporate the requested explicit demonstrations and mappings.

read point-by-point responses

  1. Referee: [Abstract / central construction] Abstract and the central construction section: the claim that ADC-G3W2 'enforces the same analytic form as the exact self-energy' and thereby guarantees positive semi-definiteness rests on the assertion that the ADC mapping is applied to G3W2 while 'preserving its essential physical content.' No explicit demonstration is given that the effective-Hamiltonian construction reproduces the original perturbative G3W2 poles and residues rather than generating a distinct resummation; this equivalence must be shown equation-by-equation for the claim to be load-bearing.

    Authors: We acknowledge that the manuscript would benefit from a more explicit equation-by-equation demonstration of how the ADC mapping preserves the poles and residues of the original G3W2 self-energy. In the revised version, we will add a dedicated subsection in the central construction section (or an appendix) that derives the effective Hamiltonian from the G3W2 diagrams and shows that, to second order in the screened interaction, the eigenvalues and residues match those of the perturbative G3W2 while the nonperturbative form ensures the sum-over-states representation. This will substantiate that the construction is a reformulation rather than an unrelated resummation. revision: yes

  2. Referee: [Hierarchy definition] Hierarchy definition: the paper introduces ADC-2SOSEX, ADC(3)-G3W2 and full ADC-G3W2 as successive approximations starting from the GW self-energy. It is unclear how the second-order vertex diagrams of G3W2 are partitioned among these levels and whether the truncation at each level remains consistent with the original perturbative ordering; an explicit diagram-to-ADC mapping table or set of equations is required.

    Authors: We agree that an explicit mapping is needed for clarity. We will include a new table (or set of equations) that maps each second-order vertex diagram from G3W2 to the corresponding contributions in ADC-2SOSEX, ADC(3)-G3W2, and the full ADC-G3W2. This will illustrate the partitioning and confirm consistency with the perturbative ordering at each truncation level. revision: yes

Circularity Check

0 steps flagged

ADC reformulation of G3W2 is an explicit construction with no reduction to inputs by definition or self-citation

full rationale

The paper describes an explicit reformulation of the existing G3W2 approximation into the ADC framework to enforce a sum-over-states pole structure. This is presented as a deliberate mapping that alters the perturbative expression to guarantee positive semi-definiteness, rather than a derivation whose output equals its input by construction. No self-citations, fitted parameters renamed as predictions, or uniqueness theorems imported from prior author work appear in the abstract or described chain. The central claim rests on the known properties of ADC (sum-over-states form) applied to G3W2, which is independent of the target result. This is a standard non-circular reformulation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters or invented entities; the key domain assumption is the sum-over-states analytic form of the exact self-energy.

axioms (1)
  • domain assumption The exact self-energy admits a sum-over-state representation
    Invoked to justify that the ADC form matches the exact self-energy and thereby guarantees positive semi-definiteness.

pith-pipeline@v0.9.1-grok · 5777 in / 1270 out tokens · 26322 ms · 2026-06-28T07:40:43.585978+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

299 extracted references · 253 canonical work pages · 1 internal anchor

  1. [1]

    T. AB-. 2024 , bdsk-url-1 =. doi:10.1063/5.0195934 , journal =

    work page doi:10.1063/5.0195934 2024

  2. [2]

    Ammar, Abdallah and Marie, Antoine and. Can. J. Chem. Phys. , month = mar, number =. 2024 , bdsk-url-1 =. doi:10.1063/5.0196561 , issn =

    work page doi:10.1063/5.0196561 2024

  3. [3]

    Coveney, Christopher J. N. and Tew, David P. , date-added =. Non-Hermitian. Phys. Rev. Res. , month =. 2026 , bdsk-url-1 =. doi:10.1103/9vdr-vhxg , issue =

    work page doi:10.1103/9vdr-vhxg 2026

  4. [4]

    Fully Analytic

    T. Fully Analytic. 2025 , bdsk-url-1 =. doi:10.1021/acs.jpclett.5c00046 , journal =

    work page doi:10.1021/acs.jpclett.5c00046 2025

  5. [5]

    Fully Analytic Nuclear Gradients for the

    T. Fully Analytic Nuclear Gradients for the. 2025 , bdsk-url-1 =. doi:10.1021/acs.jpclett.5c02219 , journal =

    work page doi:10.1021/acs.jpclett.5c02219 2025

  6. [6]

    Analytic

    Kitsaras, Marios-Petros and T. Analytic. 2026 , bdsk-url-1 =. doi:10.1063/5.0309945 , journal =

    work page doi:10.1063/5.0309945 2026

  7. [7]

    2026 , bdsk-url-1 =

    Connection between. 2026 , bdsk-url-1 =. arXiv , author =:2602.10887 , primaryclass =

    Pith/arXiv arXiv 2026

  8. [8]

    2022 , bdsk-url-1 =

    Gabriele Riva and Timoth. 2022 , bdsk-url-1 =. doi:10.21468/SciPostPhys.12.3.093 , journal =

    work page doi:10.21468/scipostphys.12.3.093 2022

  9. [9]

    Arjan , date-added =

    Riva, Gabriele and Romaniello, Pina and Berger, J. Arjan , date-added =. Multichannel. 2023 , bdsk-url-1 =. doi:10.1103/PhysRevLett.131.216401 , journal =

    work page doi:10.1103/physrevlett.131.216401 2023

  10. [10]

    Arjan , date-added =

    Riva, Gabriele and Romaniello, Pina and Berger, J. Arjan , date-added =. Derivation and Analysis of the Multichannel. 2024 , bdsk-url-1 =. doi:10.1103/PhysRevB.110.115140 , journal =

    work page doi:10.1103/physrevb.110.115140 2024

  11. [11]

    arXiv , author =:2603.27329 , title =

    2026 , bdsk-url-1 =. arXiv , author =:2603.27329 , title =

    arXiv 2026

  12. [12]

    2026 , bdsk-url-1 =

    From Full Dynamic to Pure Static: A Family of. 2026 , bdsk-url-1 =. arXiv , author =:2604.08350 , primaryclass =

    Pith/arXiv arXiv 2026

  13. [13]

    and Liu, Junzi and Rehn, Dirk R

    Hodecker, Manuel and Thielen, Sebastian M. and Liu, Junzi and Rehn, Dirk R. and Dreuw, Andreas , date-added =. Third-Order Unitary Coupled Cluster. 2020 , bdsk-url-1 =. doi:10.1021/acs.jctc.0c00335 , journal =

    work page doi:10.1021/acs.jctc.0c00335 2020

  14. [14]

    Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications , volume =

    Liu, Junzi and Asthana, Ayush and Cheng, Lan and Mukherjee, Debashis , date-added =. Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications , volume =. 2018 , bdsk-url-1 =. doi:10.1063/1.5030344 , journal =

    work page doi:10.1063/1.5030344 2018

  15. [15]

    Durga and Pal, Sourav and Mukherjee, Debashis , date-added =

    Prasad, M. Durga and Pal, Sourav and Mukherjee, Debashis , date-added =. Some aspects of self-consistent propagator theories , url =. Phys. Rev. A , month =. 1985 , bdsk-url-1 =. doi:10.1103/PhysRevA.31.1287 , issue =

    work page doi:10.1103/physreva.31.1287 1985

  16. [16]

    and Dreuw, Andreas , date-added =

    Hodecker, Manuel and Rehn, Dirk R. and Dreuw, Andreas , date-added =. Hermitian second-order methods for excited electronic states: Unitary coupled cluster in comparison with algebraic--diagrammatic construction schemes , volume =. 2020 , bdsk-url-1 =. doi:10.1063/1.5142354 , journal =

    work page doi:10.1063/1.5142354 2020

  17. [17]

    2026 , bdsk-url-1 =

    Multi-reference. 2026 , bdsk-url-1 =. arXiv , author =:2604.16013 , primaryclass =

    Pith/arXiv arXiv 2026

  18. [18]

    Improved density matrices for accurate molecular ionization potentials , volume =

    Bruneval, Fabien , date-added =. Improved density matrices for accurate molecular ionization potentials , volume =. 2019 , bdsk-url-1 =. doi:10.1103/PhysRevB.99.041118 , journal =

    work page doi:10.1103/physrevb.99.041118 2019

  19. [19]

    Assessment of the linearized

    Bruneval, Fabien , date-added =. Assessment of the linearized. 2019 , bdsk-url-1 =. doi:10.1021/acs.jctc.9b00333 , journal =

    work page doi:10.1021/acs.jctc.9b00333 2019

  20. [20]

    Improved one-shot total energies from the linearized

    Bruneval, Fabien and Rodriguez-Mayorga, Mauricio and Rinke, Patrick and Dvorak, Marc , date-added =. Improved one-shot total energies from the linearized. 2021 , bdsk-url-1 =. doi:10.1021/acs.jctc.0c01264 , journal =

    work page doi:10.1021/acs.jctc.0c01264 2021

  21. [21]

    and Angonoa, G

    Schirmer, J. and Angonoa, G. , doi =. On. J. Chem. Phys. , number =

  22. [22]

    Deleuze, Michael S. , doi =. Valence One-Electron and Shake-up Ionization Bands of Polycyclic Aromatic Hydrocarbons. J. Chem. Phys. , number =

  23. [23]

    and Trofimov, Alexander B

    Deleuze, Michael S. and Trofimov, Alexander B. and Cederbaum, Lorenz S. , doi =. Valence One-Electron and Shake-up Ionization Bands of Polycyclic Aromatic Hydrocarbons. J. Chem. Phys. , number =

  24. [24]

    Pernpointner, M. , doi =. The One-Particle. J. Chem. Phys. , number =

  25. [25]

    and Schneider, Matthias and Hodecker, Manuel and Dreuw, Andreas , doi =

    Dempwolff, Adrian L. and Schneider, Matthias and Hodecker, Manuel and Dreuw, Andreas , doi =. Efficient Implementation of the Non-. J. Chem. Phys. , number =

  26. [26]

    Parquet theory for molecular systems: Formalism and static kernel parquet approximation , volume =

    Marie, Antoine and Loos, Pierre-Fran. Parquet theory for molecular systems: Formalism and static kernel parquet approximation , volume =. 2025 , bdsk-url-1 =. doi:10.1063/5.0301331 , journal =

    work page doi:10.1063/5.0301331 2025

  27. [27]

    and Bogdanov, Nikolay A

    Sun, Qiming and Zhang, Xing and Banerjee, Samragni and Bao, Peng and Barbry, Marc and Blunt, Nick S. and Bogdanov, Nikolay A. and Booth, George H. and Chen, Jia and Cui, Zhi-Hao and Eriksen, Janus J. and Gao, Yang and Guo, Sheng and Hermann, Jan and Hermes, Matthew R. and Koh, Kevin and Koval, Peter and Lehtola, Susi and Li, Zhendong and Liu, Junzi and Ma...

    work page doi:10.1063/5.0006074 2020

  28. [28]

    and Blunt, Nick S

    Sun, Qiming and Berkelbach, Timothy C. and Blunt, Nick S. and Booth, George H. and Guo, Sheng and Li, Zhendong and Liu, Junzi and McClain, James D. and Sayfutyarova, Elvira R. and Sharma, Sandeep and Wouters, Sebastian and Chan, Garnet Kin-Lic , date-added =. PySCF: the Python-based simulations of chemistry framework , volume =. 2018 , bdsk-url-1 =. doi:h...

    work page doi:10.1002/wcms.1340 2018

  29. [29]

    Cederbaum, L. S. , date-added =. Non-single-particle excitations in finite. 1975 , bdsk-url-1 =. doi:10.1063/1.430783 , journal =

    work page doi:10.1063/1.430783 1975

  30. [30]

    Winter , date-added =

    J. Winter , date-added =. Study of core excitations in one-particle and one-holf nuclei by means of the six-point. 1972 , bdsk-url-1 =. doi:10.1016/0375-9474(72)91000-7 , journal =

    work page doi:10.1016/0375-9474(72)91000-7 1972

  31. [31]

    and Stefanucci, G

    Uimonen, A.-M. and Stefanucci, G. and Pavlyukh, Y. and van Leeuwen, R. , date-added =. Diagrammatic expansion for positive density-response spectra: Application to the electron gas , url =. Phys. Rev. B , month =. 2015 , bdsk-url-1 =. doi:10.1103/PhysRevB.91.115104 , issue =

    work page doi:10.1103/physrevb.91.115104 2015

  32. [32]

    and Pavlyukh, Y

    Stefanucci, G. and Pavlyukh, Y. and Uimonen, A.-M. and van Leeuwen, R. , date-added =. Diagrammatic expansion for positive spectral functions beyond. 2014 , bdsk-url-1 =. doi:10.1103/physrevb.90.115134 , journal =

    work page doi:10.1103/physrevb.90.115134 2014

  33. [33]

    , date-added =

    Patterson, Charles H. , date-added =. Molecular Ionization Energies from. 2024 , bdsk-url-1 =. doi:10.1021/acs.jctc.4c00795 , journal =

    work page doi:10.1021/acs.jctc.4c00795 2024

  34. [34]

    Going Beyond the

    Vacondio, Simone and Varsano, Daniele and Ruini, Alice and Ferretti, Andrea , date-added =. Going Beyond the. 2024 , bdsk-url-1 =. doi:10.1021/acs.jctc.4c00100 , journal =

    work page doi:10.1021/acs.jctc.4c00100 2024

  35. [35]

    Kuwahara, Riichi and Noguchi, Yoshifumi and Ohno, Kaoru , date-added =. Phys. Rev. B , month =. 2016 , bdsk-url-1 =. doi:10.1103/PhysRevB.94.121116 , issue =

    work page doi:10.1103/physrevb.94.121116 2016

  36. [36]

    Approximate spatiotemporal structure of the vertex function

    Rohlfing, Michael , date-added =. Approximate spatiotemporal structure of the vertex function. Phys. Rev. B , month =. 2023 , bdsk-url-1 =. doi:10.1103/PhysRevB.108.195207 , issue =

    work page doi:10.1103/physrevb.108.195207 2023

  37. [37]

    Vertex function compliant with the Ward identity for quasiparticle self-consistent calculations beyond

    Tal, Alexey and Chen, Wei and Pasquarello, Alfredo , date-added =. Vertex function compliant with the Ward identity for quasiparticle self-consistent calculations beyond. Phys. Rev. B , month =. 2021 , bdsk-url-1 =. doi:10.1103/PhysRevB.103.L161104 , issue =

    work page doi:10.1103/physrevb.103.l161104 2021

  38. [38]

    A Finite-Field Approach for

    Ma, He and Govoni, Marco and Gygi, Francois and Galli, Giulia , date-added =. A Finite-Field Approach for. 2019 , bdsk-url-1 =. doi:10.1021/acs.jctc.8b00864 , journal =

    work page doi:10.1021/acs.jctc.8b00864 2019

  39. [39]

    and Stefanucci, G

    Pavlyukh, Y. and Stefanucci, G. and van Leeuwen, R. , date-added =. Dynamically screened vertex correction to. Phys. Rev. B , month =. 2020 , bdsk-url-1 =. doi:10.1103/PhysRevB.102.045121 , issue =

    work page doi:10.1103/physrevb.102.045121 2020

  40. [40]

    Cunningham, Brian and Gr\"uning, Myrta and Pashov, Dimitar and van Schilfgaarde, Mark , date-added =. Phys. Rev. B , month =. 2023 , bdsk-url-1 =. doi:10.1103/PhysRevB.108.165104 , issue =

    work page doi:10.1103/physrevb.108.165104 2023

  41. [41]

    and Patrick, Christopher E

    Schmidt, Per S. and Patrick, Christopher E. and Thygesen, Kristian S. , date-added =. Simple vertex correction improves. Phys. Rev. B , month =. 2017 , bdsk-url-1 =. doi:10.1103/PhysRevB.96.205206 , issue =

    work page doi:10.1103/physrevb.96.205206 2017

  42. [42]

    Spatial non-locality of electronic correlations beyond

    Kutepov, A L , date-added =. Spatial non-locality of electronic correlations beyond. 2021 , bdsk-url-1 =. doi:10.1088/1361-648X/ac23fa , journal =

    work page doi:10.1088/1361-648x/ac23fa 2021

  43. [43]

    Many-Body Perturbation Theory Using the Density-Functional Concept: Beyond the

    Bruneval, Fabien and Sottile, Francesco and Olevano, Valerio and Del Sole, Rodolfo and Reining, Lucia , date-added =. Many-Body Perturbation Theory Using the Density-Functional Concept: Beyond the. Phys. Rev. Lett. , month =. 2005 , bdsk-url-1 =. doi:10.1103/PhysRevLett.94.186402 , issue =

    work page doi:10.1103/physrevlett.94.186402 2005

  44. [44]

    and Hybertsen, Mark S

    Northrup, John E. and Hybertsen, Mark S. and Louie, Steven G. , date-added =. Theory of quasiparticle energies in alkali metals , url =. Phys. Rev. Lett. , month =. 1987 , bdsk-url-1 =. doi:10.1103/PhysRevLett.59.819 , issue =

    work page doi:10.1103/physrevlett.59.819 1987

  45. [45]

    and van Schilfgaarde, M

    Tomczak, Jan M. and van Schilfgaarde, M. and Kotliar, G. , date-added =. Many-Body Effects in Iron Pnictides and Chalcogenides: Nonlocal Versus Dynamic Origin of Effective Masses , volume =. Phys. Rev. Lett. , month =. 2012 , bdsk-url-1 =. doi:10.1103/PhysRevLett.109.237010 , issue =

    work page doi:10.1103/physrevlett.109.237010 2012

  46. [46]

    Tomczak, J. M. and Liu, P. and Toschi, A. and Kresse, G. and Held, K. , date-added =. Merging. Eur. Phys. J. Spec. Top. , month = jul, number =. 2017 , bdsk-url-1 =. doi:10.1140/epjst/e2017-70053-1 , issn =

    work page doi:10.1140/epjst/e2017-70053-1 2017

  47. [47]

    and Koskelo, J

    Di Sabatino, S. and Koskelo, J. and Berger, J. A. and Romaniello, P. , date-added =. Introducing screening in one-body density matrix functionals: Impact on charged excitations of model systems via the extended. Phys. Rev. B , month =. 2022 , bdsk-url-1 =. doi:10.1103/PhysRevB.105.235123 , issue =

    work page doi:10.1103/physrevb.105.235123 2022

  48. [48]

    and Koskelo, J

    Di Sabatino, S. and Koskelo, J. and Berger, J. A. and Romaniello, P. , date-added =. Screened extended. Phys. Rev. B , month =. 2023 , bdsk-url-1 =. doi:10.1103/PhysRevB.107.035111 , issue =

    work page doi:10.1103/physrevb.107.035111 2023

  49. [49]

    and Barth, A

    Schirmer, J. and Barth, A. , date-added =. Higher-order approximations for the particle-particle propagator , volume =. 1984 , bdsk-url-1 =. doi:10.1007/bf01438358 , journal =

    work page doi:10.1007/bf01438358 1984

  50. [50]

    Block diagonalisation of Hermitian matrices , volume =

    Cederbaum, L S and Schirmer, J and Meyer, H -D , date-added =. Block diagonalisation of Hermitian matrices , volume =. 1989 , bdsk-url-1 =. doi:10.1088/0305-4470/22/13/035 , journal =

    work page doi:10.1088/0305-4470/22/13/035 1989

  51. [51]

    A new approach to the random phase approximation , volume =

    Schirmer, J and Mertins, F , date-added =. A new approach to the random phase approximation , volume =. 1996 , bdsk-url-1 =. doi:10.1088/0953-4075/29/16/006 , journal =

    work page doi:10.1088/0953-4075/29/16/006 1996

  52. [52]

    and Schirmer, J

    Mertins, F. and Schirmer, J. and Tarantelli, A. , date-added =. Algebraic propagator approaches and intermediate-state representations. Phys. Rev. A , month =. 1996 , bdsk-url-1 =. doi:10.1103/PhysRevA.53.2153 , issue =

    work page doi:10.1103/physreva.53.2153 1996

  53. [53]

    and Schirmer, J

    Mertins, F. and Schirmer, J. , date-added =. Algebraic propagator approaches and intermediate-state representations. Phys. Rev. A , month =. 1996 , bdsk-url-1 =. doi:10.1103/PhysRevA.53.2140 , issue =

    work page doi:10.1103/physreva.53.2140 1996

  54. [54]

    and Trofimov, A

    Schirmer, J. and Trofimov, A. B. and Stelter, G. , date-added =. A non-. 1998 , bdsk-url-1 =. doi:10.1063/1.477085 , journal =

    work page doi:10.1063/1.477085 1998

  55. [55]

    Trofimov, A. B. and Stelter, G. and Schirmer, J. , date-added =. A consistent third-order propagator method for electronic excitation , volume =. 1999 , bdsk-url-1 =. doi:10.1063/1.480352 , journal =

    work page doi:10.1063/1.480352 1999

  56. [56]

    and Thiel, A

    Schirmer, J. and Thiel, A. , date-added =. An intermediate state representation approach to K-shell ionization in molecules. I. Theory , volume =. 2001 , bdsk-url-1 =. doi:10.1063/1.1418437 , journal =

    work page doi:10.1063/1.1418437 2001

  57. [57]

    Intermediate state representation approach to physical properties of dicationic states , volume =

    Velkov, Yasen and Miteva, Tsveta and Sisourat, Nicolas and Schirmer, Jochen , date-added =. Intermediate state representation approach to physical properties of dicationic states , volume =. 2011 , bdsk-url-1 =. doi:10.1063/1.3653229 , journal =

    work page doi:10.1063/1.3653229 2011

  58. [58]

    Many-Body Methods in Quantum Chemistry , year =

  59. [59]

    Hohlneicher and F

    G. Hohlneicher and F. Ecker and L. S. Cederbaum , date-added =. Electron Spectroscopy , year =

  60. [60]

    Cederbaum, L. S. , date-added =. On green's functions and their applications , volume =. 1990 , bdsk-url-1 =. doi:https://doi.org/10.1002/qua.560382439 , journal =

    work page doi:10.1002/qua.560382439 1990

  61. [61]

    and Schirmer, J

    von Niessen, W. and Schirmer, J. and Cederbaum, L.S. , date-added =. Computational methods for the one-particle Green's function , url =. Comput. Phys. Rep. , month = apr, number =. 1984 , bdsk-url-1 =. doi:10.1016/0167-7977(84)90002-9 , issn =

    work page doi:10.1016/0167-7977(84)90002-9 1984

  62. [62]

    , date-added =

    Dreuw, Andreas and Papapostolou, Antonia and Dempwolff, Adrian L. , date-added =. Algebraic Diagrammatic Construction Schemes Employing the Intermediate State Formalism: Theory, Capabilities, and Interpretation , volume =. 2023 , bdsk-url-1 =. doi:10.1021/acs.jpca.3c02761 , journal =

    work page doi:10.1021/acs.jpca.3c02761 2023

  63. [63]

    , date-added =

    Banerjee, Samragni and Sokolov, Alexander Yu. , date-added =. Efficient implementation of the single-reference algebraic diagrammatic construction theory for charged excitations: Applications to the TEMPO radical and DNA base pairs , volume =. 2021 , bdsk-url-1 =. doi:10.1063/5.0040317 , journal =

    work page doi:10.1063/5.0040317 2021

  64. [64]

    , date-added =

    Banerjee, Samragni and Sokolov, Alexander Yu. , date-added =. Non-. 2022 , bdsk-url-1 =. doi:10.1021/acs.jctc.2c00565 , journal =

    work page doi:10.1021/acs.jctc.2c00565 2022

  65. [65]

    Cumulant

    Loos, Pierre-Fran. Cumulant. Faraday Discuss. , pages =. 2024 , bdsk-url-1 =. doi:10.1039/D4FD00037D , issue =

    work page doi:10.1039/d4fd00037d 2024

  66. [66]

    2025 , bdsk-url-1 =

    Bruneval, Fabien and F. 2025 , bdsk-url-1 =. doi:10.1021/acs.jctc.5c01180 , journal =

    work page doi:10.1021/acs.jctc.5c01180 2025

  67. [67]

    Beyond Quasi-Particle Self-Consistent

    F. Beyond Quasi-Particle Self-Consistent. 2025 , bdsk-url-1 =. doi:10.1021/acs.jctc.4c01639 , journal =

    work page doi:10.1021/acs.jctc.4c01639 2025

  68. [68]

    Why Does the

    F. Why Does the. 2024 , bdsk-url-1 =. doi:10.1021/acs.jpclett.4c03126 , journal =

    work page doi:10.1021/acs.jpclett.4c03126 2024

  69. [69]

    Fully Dynamic

    Bruneval, Fabien and F. Fully Dynamic. J. Chem. Theory Comput. , number =. 2024 , bdsk-url-1 =. doi:10.1021/acs.jctc.4c00090 , issn =

    work page doi:10.1021/acs.jctc.4c00090 2024

  70. [70]

    Birgitta and Zgid, Dominika , copyright =

    Wen, Ming and Abraham, Vibin and Harsha, Gaurav and Shee, Avijit and Whaley, K. Birgitta and Zgid, Dominika , copyright =. Comparing Self-Consistent. J. Chem. Theo. Comput. , number =. 2024 , bdsk-url-1 =. doi:10.1021/acs.jctc.3c01279 , issn =

    work page doi:10.1021/acs.jctc.3c01279 2024

  71. [71]

    Embedding Vertex Corrections in

    Weng, Guorong and Mallarapu, Rushil and Vl. Embedding Vertex Corrections in. Chem. Phys. , number =. 2023 , bdsk-url-1 =. doi:10.1063/5.0139117 , issn =

    work page doi:10.1063/5.0139117 2023

  72. [72]

    Exploring the Statically Screened

    F. Exploring the Statically Screened. 2022 , bdsk-url-1 =. doi:10.1103/PhysRevB.105.125121 , journal =

    work page doi:10.1103/physrevb.105.125121 2022

  73. [73]

    Assessing the

    Wang, Yanyong and Rinke, Patrick and Ren, Xinguo , date-added =. Assessing the. J. Chem. Theory Comput. , number =. 2021 , bdsk-url-1 =. doi:10.1021/acs.jctc.1c00488 , issn =

    work page doi:10.1021/acs.jctc.1c00488 2021

  74. [74]

    A thorough benchmark of density functional methods for general main group thermochemistry

    Goerigk, Lars and Grimme, Stefan , date-added =. A thorough benchmark of density functional methods for general main group thermochemistry. 2011 , bdsk-url-1 =. doi:10.1039/C0CP02984J , journal =

    work page doi:10.1039/c0cp02984j 2011

  75. [75]

    Goerigk, Lars and Grimme, Stefan , date-added =. Efficient and Accurate Double-Hybrid-Meta-GGA Density Functionals---Evaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions , volume =. J. Chem. Theory Comput. , note =. 2011 , bdsk-url-1 =. doi:10.1021/ct100466k , eprint =

    work page doi:10.1021/ct100466k 2011

  76. [76]

    A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry

    Goerigk, Lars and Hansen, Andreas and Bauer, Christoph and Ehrlich, Stephan and Najibi, Asim and Grimme, Stefan , date-added =. A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry. 2017 , bdsk-url-1 =. doi:10.1039/C7CP04913G , journal =

    work page doi:10.1039/c7cp04913g 2017

  77. [77]

    QUEST Database of Highly-Accurate Excitation Energies , volume =

    Loos, Pierre-Fran. QUEST Database of Highly-Accurate Excitation Energies , volume =. 2025 , bdsk-url-1 =. doi:10.1021/acs.jctc.5c00975 , journal =

    work page doi:10.1021/acs.jctc.5c00975 2025

  78. [78]

    Karton, Amir and Sylvetsky, Nitai and Martin, Jan M. L. , date-added =. W4-17: A diverse and high-confidence dataset of atomization energies for benchmarking high-level electronic structure methods , volume =. 2017 , bdsk-url-1 =. doi:https://doi.org/10.1002/jcc.24854 , journal =

    work page doi:10.1002/jcc.24854 2017

  79. [79]

    Karton, Amir and Rabinovich, Elena and Martin, Jan M. L. and Ruscic, Branko , date-added =. W4 theory for computational thermochemistry: In pursuit of confident sub-kJ/mol predictions , volume =. 2006 , bdsk-url-1 =. doi:10.1063/1.2348881 , journal =

    work page doi:10.1063/1.2348881 2006

  80. [80]

    Bomble,Yannick J. and V. High-accuracy extrapolated ab initio thermochemistry. II. Minor improvements to the protocol and a vital simplification , volume =. J. Chem. Phys. , pages =. 2006 , bdsk-url-1 =. doi:10.1063/1.2206789 , eprint =

    work page doi:10.1063/1.2206789 2006

Showing first 80 references.