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arxiv: 2507.03496 · v1 · pith:MPKA4V7Knew · submitted 2025-07-04 · ⚛️ physics.chem-ph · cond-mat.mtrl-sci· cond-mat.str-el· nucl-th

Complex Absorbing Potential Green's Function Methods for Resonances

Loris Burth , F\'abris Kossoski , Pierre-Fran\c{c}ois Loos This is my paper

Pith reviewed 2026-05-22 00:35 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cond-mat.mtrl-scicond-mat.str-elnucl-th
keywords complex absorbing potentialGW approximationelectronic resonancesGreen's function methodsshape resonancesnon-Hermitian quantum chemistrymolecular anionsresonance lifetimes
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The pith

Integrating a complex absorbing potential into the GW approximation lets Green's function methods compute positions and lifetimes of electronic resonance states.

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

The paper shows how to embed the complex absorbing potential formalism inside the GW approximation so that resonances can be treated inside a Green's function framework. This requires allowing orbitals and quasiparticle energies to become fully complex and working with a non-Hermitian effective Hamiltonian. The resulting CAP-GW procedure is applied to shape resonances in N2^-, CO^-, CO2^-, C2H2^-, C2H4^-, and CH2O^-. It supplies both resonance positions and widths at a cost far below that of high-level wavefunction methods while reaching comparable numerical accuracy.

Core claim

We integrate the CAP formalism within the GW approximation, enabling the description of electronic resonances in a Green's function framework. This approach entails a fully complex treatment of orbitals and quasiparticle energies in a non-Hermitian setting. Validation on the prototypical shape resonances of N2^-, CO^-, CO2^-, C2H2^-, C2H4^-, and CH2O^- demonstrates that the method furnishes both positions and lifetimes with an accuracy comparable to state-of-the-art wavefunction-based techniques.

What carries the argument

The CAP-GW scheme, which augments the GW self-energy with a complex absorbing potential and solves the resulting non-Hermitian quasiparticle equations for complex orbitals and energies.

If this is right

  • Resonance lifetimes become directly accessible from the imaginary part of the complex quasiparticle energy.
  • The method supplies a practical route to resonances in molecules where full configuration-interaction or equation-of-motion coupled-cluster calculations remain prohibitive.
  • Green's function techniques, already standard for ionization potentials and electron affinities, can now address temporary negative ions on the same footing.
  • The fully complex orbital treatment opens a path to consistent inclusion of correlation and relaxation effects for resonances.

Where Pith is reading between the lines

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

  • The same CAP embedding could be tested inside other self-energy approximations such as second-order Green's function or vertex-corrected schemes to check transferability.
  • Because the approach is perturbative, it may combine naturally with embedding or fragmentation techniques for resonances in larger or solvated systems.
  • Extending the method to time-dependent perturbations could allow simulation of resonance-mediated electron scattering or photodetachment processes.

Load-bearing premise

Adding a complex absorbing potential to the GW equations will produce resonance energies and widths that remain physically meaningful without large artifacts or heavy system-by-system tuning.

What would settle it

A direct comparison showing that the computed position and width for the N2^- shape resonance differ by more than 0.5 eV or 0.1 eV from established experimental or high-level theoretical benchmarks would falsify the claim of comparable accuracy.

Figures

Figures reproduced from arXiv: 2507.03496 by F\'abris Kossoski, Loris Burth, Pierre-Fran\c{c}ois Loos.

Figure 1
Figure 1. Figure 1: FIG. 1. Trajectories of [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Trajectories of [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Trajectories of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Trajectories of [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Trajectories of [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
read the original abstract

The complex absorbing potential (CAP) formalism has been successfully employed in various wavefunction-based methods to study electronic resonance states. In contrast, Green's function-based methods are widely used to compute ionization potentials and electron affinities but have seen limited application to resonances. We integrate the CAP formalism within the $GW$ approximation, enabling the description of electronic resonances in a Green's function framework. This approach entails a fully complex treatment of orbitals and quasiparticle energies in a non-Hermitian setting. We validate our CAP-$GW$ implementation by applying it to the prototypical shape resonances of \ce{N2^-}, \ce{CO^-}, \ce{CO_2^-}, \ce{C2H2-}, \ce{C2H4-}, and \ce{CH2O-}. It offers a fast and practical route to approximate both the lifetimes and positions of resonance states, achieving an accuracy comparable to that of state-of-the-art wavefunction-based methods.

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 paper integrates the complex absorbing potential (CAP) formalism into the GW approximation to describe electronic resonance states within a Green's function framework. It employs a fully complex, non-Hermitian treatment of orbitals and quasiparticle energies, and validates the resulting CAP-GW method on the shape resonances of six molecular anions (N2^-, CO^-, CO2^-, C2H2^-, C2H4^-, CH2O^-), claiming accuracy for resonance positions and lifetimes comparable to state-of-the-art wavefunction-based methods.

Significance. If the central claims hold, the work is significant because it extends Green's function methods—widely used for ionization potentials and electron affinities—to metastable resonance states, offering a potentially faster and more scalable route than wavefunction approaches. The validation across six systems and the explicit handling of complex quantities in the non-Hermitian setting are strengths that could facilitate broader adoption in computational chemistry for temporary anions.

major comments (2)
  1. [Results (validation on N2^-, CO^-, etc.)] Results section on validation for the six test anions: the manuscript provides no explicit stabilization plots or sensitivity analysis with respect to CAP strength and onset parameters. This is load-bearing for the central claim, as the non-Hermitian self-energy in the GW quasiparticle equation can shift the optimal CAP values relative to wavefunction methods, leaving open the possibility of unquantified CAP-induced artifacts in the reported resonance widths.
  2. [Methods (CAP integration in GW)] Method section describing the CAP-GW implementation: the treatment of the complex Dyson equation and self-energy consistency is not accompanied by quantitative checks on how the imaginary part of the self-energy remains faithful to the decay process after CAP addition, which is required to support the assertion of accuracy without extensive system-specific tuning.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'achieving an accuracy comparable to that of state-of-the-art wavefunction-based methods' would benefit from a brief parenthetical note on the specific error metrics (e.g., MAE in resonance position or width) used for the comparison.
  2. [Introduction/Methods] Notation: the distinction between the complex quasiparticle energies and the CAP-modified one-particle Hamiltonian could be clarified with an explicit equation reference in the introductory methods paragraph.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments on the validation and methodological details of the CAP-GW approach. We address each major comment below and will revise the manuscript to incorporate additional analyses that strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Results (validation on N2^-, CO^-, etc.)] Results section on validation for the six test anions: the manuscript provides no explicit stabilization plots or sensitivity analysis with respect to CAP strength and onset parameters. This is load-bearing for the central claim, as the non-Hermitian self-energy in the GW quasiparticle equation can shift the optimal CAP values relative to wavefunction methods, leaving open the possibility of unquantified CAP-induced artifacts in the reported resonance widths.

    Authors: We agree that explicit stabilization plots and sensitivity analysis are important to demonstrate robustness, particularly given the non-Hermitian nature of the GW self-energy. In the original manuscript, CAP parameters were optimized for each anion following established procedures from wavefunction-based CAP studies, with resonance positions and widths reported at the optimized values. To address the referee's concern and quantify any potential CAP-induced artifacts or shifts in optimal parameters, we will add stabilization plots (showing real and imaginary parts of the resonance energy versus CAP strength) for representative systems such as N2^- and CO^- in a revised Results section or as supplementary material. This will allow direct assessment of the sensitivity and support the central claims. revision: yes

  2. Referee: [Methods (CAP integration in GW)] Method section describing the CAP-GW implementation: the treatment of the complex Dyson equation and self-energy consistency is not accompanied by quantitative checks on how the imaginary part of the self-energy remains faithful to the decay process after CAP addition, which is required to support the assertion of accuracy without extensive system-specific tuning.

    Authors: We acknowledge the value of explicit quantitative checks on the imaginary part of the self-energy to confirm its fidelity to the resonance decay in the complex setting. Our implementation solves the fully complex Dyson equation iteratively with complex orbitals and quasiparticle energies, and the self-energy is constructed accordingly without additional approximations beyond the standard GW level. To provide the requested verification, we will expand the Methods section in the revision to include quantitative consistency checks—for example, comparing the imaginary component of the quasiparticle energies to the CAP-induced decay rates for the test systems and noting any observed consistency across the six anions. This will further support that the approach achieves the reported accuracy with standard parameter optimization. revision: yes

Circularity Check

0 steps flagged

CAP-GW integration is a direct non-Hermitian extension with external validation

full rationale

The paper defines the CAP-GW method by adding a complex absorbing potential to the one-particle Hamiltonian and solving the resulting non-Hermitian Dyson equation within the GW approximation, treating orbitals and quasiparticle energies as fully complex. This construction is presented as a straightforward methodological extension rather than a reparameterization of existing outputs. Validation proceeds by direct numerical comparison of resonance positions and widths to independent wavefunction-based calculations on the six listed molecular anions, without evidence that any central result is obtained by fitting to the target quantities or by self-referential definitions. No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work are invoked to close the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are detailed. The core assumption is that CAP can be integrated into GW without major modifications.

axioms (1)
  • domain assumption The CAP formalism can be integrated into the GW approximation using a fully complex treatment of orbitals and quasiparticle energies in a non-Hermitian setting.
    This integration is the central premise enabling resonance calculations within the Green's function framework.

pith-pipeline@v0.9.0 · 5714 in / 1178 out tokens · 45046 ms · 2026-05-22T00:35:47.969249+00:00 · methodology

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Works this paper leans on

227 extracted references · 227 canonical work pages

  1. [1]

    author author K. D. \ Jordan \ and\ author P. D. \ Burrow ,\ title title Temporary Anion States of Polyatomic Hydrocarbons , \ https://doi.org/10.1021/cr00079a005 journal journal Chem. Rev. \ volume 87 ,\ pages 557--588 ( year 1987 ) NoStop

    work page doi:10.1021/cr00079a005 1987

  2. [2]

    author author K. D. \ Jordan \ and\ author F. Wang ,\ title title Theory of Dipole-Bound Anions , \ https://doi.org/https://doi.org/10.1146/annurev.physchem.54.011002.103851 journal journal Annu. Rev. Phys. Chem. \ volume 54 ,\ pages 367--396 ( year 2003 ) NoStop

    work page doi:10.1146/annurev.physchem.54.011002.103851 2003

  3. [3]

    Simons ,\ title title Molecular Anions , \ https://doi.org/10.1021/jp711490b journal journal J

    author author J. Simons ,\ title title Molecular Anions , \ https://doi.org/10.1021/jp711490b journal journal J. Phys. Chem. A \ volume 112 ,\ pages 6401--6511 ( year 2008 ) NoStop

    work page doi:10.1021/jp711490b 2008

  4. [4]

    Simons ,\ title title Theoretical Study of Negative Molecular Ions , \ https://doi.org/10.1146/annurev-physchem-032210-103547 journal journal Annu

    author author J. Simons ,\ title title Theoretical Study of Negative Molecular Ions , \ https://doi.org/10.1146/annurev-physchem-032210-103547 journal journal Annu. Rev. Phys. Chem. \ volume 62 ,\ pages 107--128 ( year 2011 ) NoStop

    work page doi:10.1146/annurev-physchem-032210-103547 2011

  5. [5]

    author author K. D. \ Jordan , author V. K. \ Voora ,\ and\ author J. Simons ,\ title title Negative Electron Affinities From Conventional Electronic Structure Methods , \ https://doi.org/10.1007/s00214-014-1445-1 journal journal Theor. Chem. Acc. \ volume 133 ,\ pages 1445 ( year 2014 ) NoStop

    work page doi:10.1007/s00214-014-1445-1 2014

  6. [6]

    author author J. Simons ,\ title Detachment Processes For Molecular Anions , \ in\ https://doi.org/10.1142/9789812813473_0017 booktitle Advanced Series in Physical Chemistry: Photoionization and Photodetachment \ ( publisher World Scientific Publishing Co.: Singapore ,\ year 2000 )\ pp.\ pages 958--1010 NoStop

    work page doi:10.1142/9789812813473_0017 2000

  7. [7]

    Simons ,\ title title Molecular anions perspective , \ https://doi.org/10.1021/acs.jpca.3c01564 journal journal J

    author author J. Simons ,\ title title Molecular anions perspective , \ https://doi.org/10.1021/acs.jpca.3c01564 journal journal J. Phys. Chem. A \ volume 127 ,\ pages 3940--3957 ( year 2023 ) NoStop

    work page doi:10.1021/acs.jpca.3c01564 2023

  8. [8]

    Boudaiffa , author P

    author author B. Boudaiffa , author P. Cloutier , author D. Hunting , author M. A. \ Huels ,\ and\ author L. Sanche ,\ title title Resonant Formation of DNA Strand Breaks by Low-Energy (3 to 20 eV) Electrons , \ https://doi.org/10.1126/science.287.5458.1658 journal journal Science \ volume 287 ,\ pages 1658--1660 ( year 2000 ) NoStop

    work page doi:10.1126/science.287.5458.1658 2000

  9. [9]

    Martin , author P

    author author F. Martin , author P. D. \ Burrow , author Z. Cai , author P. Cloutier , author D. Hunting ,\ and\ author L. Sanche ,\ title title DNA Strand Breaks Induced by 0--4 eV Electrons: The Role of Shape Resonances , \ https://doi.org/10.1103/PhysRevLett.93.068101 journal journal Phys. Rev. Lett. \ volume 93 ,\ pages 068101 ( year 2004 ) NoStop

    work page doi:10.1103/physrevlett.93.068101 2004

  10. [10]

    Simons ,\ title title How Do Low-Energy (0.1--2 eV) Electrons Cause DNA-Strand Breaks? \ https://doi.org/10.1021/ar0680769 journal journal Acc

    author author J. Simons ,\ title title How Do Low-Energy (0.1--2 eV) Electrons Cause DNA-Strand Breaks? \ https://doi.org/10.1021/ar0680769 journal journal Acc. Chem. Res. \ volume 39 ,\ pages 772--779 ( year 2006 ) NoStop

    work page doi:10.1021/ar0680769 2006

  11. [11]

    Alizadeh , author T

    author author E. Alizadeh , author T. M. \ Orlando ,\ and\ author L. Sanche ,\ title title Biomolecular Damage Induced by Ionizing Radiation: The Direct and Indirect Effects of Low-Energy Electrons on DNA , \ https://doi.org/10.1146/annurev-physchem-040513-103605 journal journal Annu. Rev. Phys. Chem. \ ,\ pages 379--398 ( year 2015 ) NoStop

    work page doi:10.1146/annurev-physchem-040513-103605 2015

  12. [12]

    author author N. I. \ Hammer , author J.-W. \ Shin , author J. M. \ Headrick , author E. G. \ Diken , author J. R. \ Roscioli , author G. H. \ Weddle ,\ and\ author M. A. \ Johnson ,\ title title How Do Small Water Clusters Bind an Excess Electron? \ https://doi.org/10.1126/science.1102792 journal journal Science \ volume 306 ,\ pages 675--679 ( year 2004...

    work page doi:10.1126/science.1102792 2004

  13. [13]

    author author C. J. \ Clarke \ and\ author J. R. \ Verlet ,\ title title Dynamics of anions: From bound to unbound states and everything in between , \ https://doi.org/https://doi.org/10.1146/annurev-physchem-090722-125031 journal journal Annu. Rev. Phys. Chem. \ volume 75 ,\ pages 89--110 ( year 2024 ) NoStop

    work page doi:10.1146/annurev-physchem-090722-125031 2024

  14. [14]

    Zur quantentheorie des atomkernes

    author author G. Gamow ,\ title title Zur Quantentheorie des Atomkernes , \ https://doi.org/10.1007/BF01343196 journal journal Z. Phys. \ volume 51 ,\ pages 204--212 ( year 1928 ) NoStop

    work page doi:10.1007/bf01343196 1928

  15. [15]

    author author A. J. F. \ Siegert ,\ title title On the Derivation of the Dispersion Formula for Nuclear Reactions , \ https://doi.org/10.1103/PhysRev.56.750 journal journal Phys. Rev. \ volume 56 ,\ pages 750--752 ( year 1939 ) NoStop

    work page doi:10.1103/physrev.56.750 1939

  16. [16]

    Klaiman \ and\ author I

    author author S. Klaiman \ and\ author I. Gilary ,\ title title On Resonance: A First Glance into the Behavior of Unstable States , \ https://doi.org/10.1016/B978-0-12-397009-1.00001-1 journal journal Adv. Quantum Chem. \ volume 63 ,\ pages 1--31 ( year 2012 ) NoStop

    work page doi:10.1016/b978-0-12-397009-1.00001-1 2012

  17. [17]

    Zuev , author K

    author author D. Zuev , author K. B. \ Bravaya , author T. D. \ Crawford , author R. Lindh ,\ and\ author A. I. \ Krylov ,\ title title Electronic structure of the two isomers of the anionic form of p-coumaric acid chromophore , \ https://doi.org/10.1063/1.3516211 journal journal J. Chem. Phys. \ volume 134 ,\ pages 034310 ( year 2011 ) NoStop

    work page doi:10.1063/1.3516211 2011

  18. [18]

    author author K. B. \ Bravaya , author D. Zuev , author E. Epifanovsky ,\ and\ author A. I. \ Krylov ,\ title title Complex-Scaled Equation-Of-Motion Coupled-Cluster Method with Single and Double Substitutions for Autoionizing Excited States: Theory, Implementation, and Examples , \ https://doi.org/10.1063/1.4795750 journal journal J. Chem. Phys. \ volume...

    work page doi:10.1063/1.4795750 2013

  19. [19]

    author author A. A. \ Kunitsa \ and\ author K. B. \ Bravaya ,\ title title First-Principles Calculations of the Energy and Width of the ^2A_u Shape Resonance in p-Benzoquinone: A Gateway State for Electron Transfer , \ https://doi.org/10.1021/acs.jpclett.5b00207 journal journal J. Phys. Chem. Lett. \ volume 6 ,\ pages 1053--1058 ( year 2015 ) NoStop

    work page doi:10.1021/acs.jpclett.5b00207 2015

  20. [20]

    Feshbach ,\ title title Unified Theory of Nuclear Reactions , \ https://doi.org/10.1016/0003-4916(58)90007-1 journal journal Ann

    author author H. Feshbach ,\ title title Unified Theory of Nuclear Reactions , \ https://doi.org/10.1016/0003-4916(58)90007-1 journal journal Ann. Phys. \ volume 5 ,\ pages 357--390 ( year 1958 ) NoStop

    work page doi:10.1016/0003-4916(58)90007-1 1958

  21. [21]

    Feshbach ,\ title title A Unified Theory of Nuclear Reactions

    author author H. Feshbach ,\ title title A Unified Theory of Nuclear Reactions. II , \ https://doi.org/10.1016/0003-4916(62)90221-X journal journal Ann. Phys. \ volume 19 ,\ pages 287--313 ( year 1962 ) NoStop

    work page doi:10.1016/0003-4916(62)90221-x 1962

  22. [22]

    author author W. Domcke ,\ title title Theory of resonance and threshold effects in electron-molecule collisions: The projection-operator approach , \ https://doi.org/https://doi.org/10.1016/0370-1573(91)90125-6 journal journal Phys. Rep. \ volume 208 ,\ pages 97--188 ( year 1991 ) NoStop

    work page doi:10.1016/0370-1573(91)90125-6 1991

  23. [23]

    Averbukh \ and\ author L

    author author V. Averbukh \ and\ author L. S. \ Cederbaum ,\ title title Ab initio calculation of interatomic decay rates by a combination of the fano ansatz, green's-function methods, and the stieltjes imaging technique , \ https://doi.org/10.1063/1.2126976 journal journal J. Chem. Phys. \ volume 123 ,\ pages 204107 ( year 2005 ) NoStop

    work page doi:10.1063/1.2126976 2005

  24. [24]

    Koloren c , author V

    author author P. Koloren c , author V. Averbukh , author K. Gokhberg ,\ and\ author L. S. \ Cederbaum ,\ title title Ab initio calculation of interatomic decay rates of excited doubly ionized states in clusters , \ https://doi.org/10.1063/1.3043437 journal journal J. Chem. Phys. \ volume 129 ,\ pages 244102 ( year 2008 ) NoStop

    work page doi:10.1063/1.3043437 2008

  25. [25]

    Kolorenc \ and\ author L

    author author J. Kolorenc \ and\ author L. Mitas ,\ title title Applications of quantum Monte Carlo methods in condensed systems , \ https://doi.org/10.1088/0034-4885/74/2/026502 journal journal Rep. Prog. Phys. \ volume 74 ,\ pages 026502 ( year 2011 ) NoStop

    work page doi:10.1088/0034-4885/74/2/026502 2011

  26. [26]

    Yabushita \ and\ author C

    author author S. Yabushita \ and\ author C. W. \ McCurdy ,\ title title Feshbach resonances in electron--molecule scattering by the complex multiconfiguration scf and configuration interaction procedures: The ^1 _g^+ autoionizing states of h2 , \ https://doi.org/10.1063/1.449160 journal journal J. Chem. Phys. \ volume 83 ,\ pages 3547--3559 ( year 1985 ) NoStop

    work page doi:10.1063/1.449160 1985

  27. [27]

    Sajeev , author V

    author author Y. Sajeev , author V. Vysotskiy , author L. S. \ Cederbaum ,\ and\ author N. Moiseyev ,\ title title Continuum remover-complex absorbing potential: Efficient removal of the nonphysical stabilization points , \ https://doi.org/10.1063/1.3271350 journal journal J. Chem. Phys. \ volume 131 ,\ pages 211102 ( year 2009 ) NoStop

    work page doi:10.1063/1.3271350 2009

  28. [28]

    Schiedt \ and\ author R

    author author J. Schiedt \ and\ author R. Weinkauf ,\ title title Resonant photodetachment via shape and feshbach resonances: p-benzoquinone anions as a model system , \ https://doi.org/10.1063/1.478066 journal journal J. Chem. Phys. \ volume 110 ,\ pages 304--314 ( year 1999 ) NoStop

    work page doi:10.1063/1.478066 1999

  29. [29]

    author author A. A. \ Kunitsa \ and\ author K. B. \ Bravaya ,\ title title Electronic structure of the para-benzoquinone radical anion revisited , \ https://doi.org/10.1039/C5CP06476G journal journal Phys. Chem. Chem. Phys. \ volume 18 ,\ pages 3454--3462 ( year 2016 ) NoStop

    work page doi:10.1039/c5cp06476g 2016

  30. [30]

    author author A. A. \ Kunitsa , author A. A. \ Granovsky ,\ and\ author K. B. \ Bravaya ,\ title title CAP-XMCQDPT2 Method for Molecular Electronic Resonances , \ https://doi.org/10.1063/1.4982950 journal journal J. Chem. Phys. \ volume 146 ,\ pages 184107 ( year 2017 ) NoStop

    work page doi:10.1063/1.4982950 2017

  31. [31]

    Loupas \ and\ author J

    author author A. Loupas \ and\ author J. D. \ Gorfinkiel ,\ title title Resonances in low-energy electron scattering from para-benzoquinone , \ https://doi.org/10.1039/C7CP02916K journal journal Phys. Chem. Chem. Phys. \ volume 19 ,\ pages 18252--18261 ( year 2017 ) NoStop

    work page doi:10.1039/c7cp02916k 2017

  32. [32]

    author author R. F. \ da Costa , author J. C. \ Ruivo , author F. Kossoski , author M. T. d. N. \ Varella , author M. H. F. \ Bettega , author D. B. \ Jones , author M. J. \ Brunger ,\ and\ author M. A. P. \ Lima ,\ title title An ab initio investigation for elastic and electronically inelastic electron scattering from para-benzoquinone , \ https://doi.or...

    work page doi:10.1063/1.5050622 2018

  33. [33]

    Sedmidubsk a \' a \ and\ author J

    author author B. Sedmidubsk a \' a \ and\ author J. Ko c c i s s ek ,\ title title Interaction of low-energy electrons with radiosensitizers , \ https://doi.org/10.1039/D3CP06003A journal journal Phys. Chem. Chem. Phys. \ volume 26 ,\ pages 9112--9136 ( year 2024 ) NoStop

    work page doi:10.1039/d3cp06003a 2024

  34. [34]

    author author Q. T. \ Wu , author H. Anderson , author A. K. \ Watkins , author D. Arora , author K. Barnes , author M. Padovani , author C. N. \ Shingledecker , author C. R. \ Arumainayagam ,\ and\ author J. B. R. \ Battat ,\ title title Role of Low-Energy ( < 20 eV) Secondary Electrons in the Extraterrestrial Synthesis of Prebiotic Molecules , \ https:/...

    work page doi:10.1021/acsearthspacechem.3c00259 2024

  35. [35]

    author author C. R. \ Arumainayagam , author H.-L. \ Lee , author R. B. \ Nelson , author D. R. \ Haines ,\ and\ author R. P. \ Gunawardane ,\ title title Low-energy electron-induced reactions in condensed matter , \ https://doi.org/https://doi.org/10.1016/j.surfrep.2009.09.001 journal journal Surf. Sci. Rep. \ volume 65 ,\ pages 1--44 ( year 2010 ) NoStop

    work page doi:10.1016/j.surfrep.2009.09.001 2009

  36. [36]

    author author R. M. \ Thorman , author R. K. T. \ P. , author D. H. \ Fairbrother ,\ and\ author O. Ing \'o lfsson ,\ title title The role of low-energy electrons in focused electron beam induced deposition: four case studies of representative precursors , \ https://doi.org/10.3762/bjnano.6.194 journal journal Beilstein J. Nanotechnol. \ volume 6 ,\ pages...

    work page doi:10.3762/bjnano.6.194 1904

  37. [37]

    \ Jagau , author K

    author author T.-C. \ Jagau , author K. B. \ Bravaya ,\ and\ author A. I. \ Krylov ,\ title title Extending Quantum Chemistry of Bound States to Electronic Resonances , \ https://doi.org/10.1146/annurev-physchem-052516-050622 journal journal Annu. Rev. Phys. Chem. \ ,\ pages 525--553 ( year 2017 ) NoStop

    work page doi:10.1146/annurev-physchem-052516-050622 2017

  38. [38]

    \ Jagau ,\ title title Theory of electronic resonances: fundamental aspects and recent advances , \ https://doi.org/10.1039/D1CC07090H journal journal Chem

    author author T.-C. \ Jagau ,\ title title Theory of electronic resonances: fundamental aspects and recent advances , \ https://doi.org/10.1039/D1CC07090H journal journal Chem. Commun. \ volume 58 ,\ pages 5205--5224 ( year 2022 ) NoStop

    work page doi:10.1039/d1cc07090h 2022

  39. [39]

    Jolicard \ and\ author E

    author author G. Jolicard \ and\ author E. J. \ Austin ,\ title title Optical potential stabilisation method for predicting resonance levels , \ https://doi.org/10.1016/0009-2614(85)87164-5 journal journal Chem. Phys. Lett. \ volume 121 ,\ pages 106--110 ( year 1985 ) NoStop

    work page doi:10.1016/0009-2614(85)87164-5 1985

  40. [40]

    author author U. V. \ Riss \ and\ author H.-D. \ Meyer ,\ title title Calculation of resonance energies and widths using the complex absorbing potential method , \ https://doi.org/10.1088/0953-4075/26/23/021 journal journal J. Phys. B: At. Mol. Opt. Phys. \ volume 26 ,\ pages 4503 ( year 1993 ) NoStop

    work page doi:10.1088/0953-4075/26/23/021 1993

  41. [41]

    Sommerfeld , author U

    author author T. Sommerfeld , author U. V. \ Riss , author H.-D. \ Meyer , author L. S. \ Cederbaum , author B. Engels ,\ and\ author H. U. \ Suter ,\ title title Temporary anions - calculation of energy and lifetime by absorbing potentials: the resonance , \ https://doi.org/10.1088/0953-4075/31/18/009 journal journal J. Phys. B: At. Mol. Opt. Phys. \ vol...

    work page doi:10.1088/0953-4075/31/18/009 1998

  42. [42]

    Ghosh , author N

    author author A. Ghosh , author N. Vaval ,\ and\ author S. Pal ,\ title title Equation-of-motion coupled-cluster method for the study of shape resonance , \ https://doi.org/10.1063/1.4729464 journal journal J. Chem. Phys. \ volume 136 ,\ pages 234110 ( year 2012 ) NoStop

    work page doi:10.1063/1.4729464 2012

  43. [43]

    Zuev , author T.-C

    author author D. Zuev , author T.-C. \ Jagau , author K. B. \ Bravaya , author E. Epifanovsky , author Y. Shao , author E. Sundstrom , author M. Head-Gordon ,\ and\ author A. I. \ Krylov ,\ title title Complex Absorbing Potentials Within EOM-CC Family of Methods: Theory, Implementation, and Benchmarks , \ https://doi.org/10.1063/1.4885056 journal journal ...

    work page doi:10.1063/1.4885056 2014

  44. [44]

    \ Jagau , author D

    author author T.-C. \ Jagau , author D. Zuev , author K. B. \ Bravaya , author E. Epifanovsky ,\ and\ author A. I. \ Krylov ,\ title title A Fresh Look at Resonances and Complex Absorbing Potentials: Density Matrix-Based Approach , \ https://doi.org/10.1021/jz402482a journal journal J. Phys. Chem. Lett. \ volume 5 ,\ pages 310--315 ( year 2014 ) NoStop

    work page doi:10.1021/jz402482a 2014

  45. [45]

    \ Jagau \ and\ author A

    author author T.-C. \ Jagau \ and\ author A. I. \ Krylov ,\ title title Complex Absorbing Potential Equation-of-Motion Coupled-Cluster Method Yields Smooth and Internally Consistent Potential Energy Surfaces and Lifetimes for Molecular Resonances , \ https://doi.org/10.1021/jz501515j journal journal J. Phys. Chem. Lett. \ volume 5 ,\ pages 3078--3085 ( ye...

    work page doi:10.1021/jz501515j 2014

  46. [46]

    Sommerfeld \ and\ author M

    author author T. Sommerfeld \ and\ author M. Ehara ,\ title title Complex absorbing potentials with voronoi isosurfaces wrapping perfectly around molecules , \ https://doi.org/10.1021/acs.jctc.5b00465 journal journal J. Chem. Theory Comput. \ volume 11 ,\ pages 4627--4633 ( year 2015 ) NoStop

    work page doi:10.1021/acs.jctc.5b00465 2015

  47. [47]

    author author J. A. \ Gyamfi \ and\ author T.-C. \ Jagau ,\ title title A New Strategy to Optimize Complex Absorbing Potentials for the Computation of Resonance Energies and Widths , \ https://doi.org/10.1021/acs.jctc.3c01039 journal journal J. Chem. Theory Comput. \ volume 20 ,\ pages 1096--1107 ( year 2024 ) NoStop

    work page doi:10.1021/acs.jctc.3c01039 2024

  48. [48]

    Balslev \ and\ author J

    author author E. Balslev \ and\ author J. M. \ Combes ,\ title title Spectral properties of many-body Schr o \" o dinger operators with dilatation-analytic interactions , \ https://doi.org/10.1007/BF01877511 journal journal Commun. Math. Phys. \ volume 22 ,\ pages 280--294 ( year 1971 ) NoStop

    work page doi:10.1007/bf01877511 1971

  49. [49]

    author author N. Moiseyev ,\ title title Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling , \ https://doi.org/10.1016/S0370-1573(98)00002-7 journal journal Phys. Rep. \ volume 302 ,\ pages 212--293 ( year 1998 ) NoStop

    work page doi:10.1016/s0370-1573(98)00002-7 1998

  50. [50]

    author author C. W. \ McCurdy \ and\ author T. N. \ Rescigno ,\ title title Extension of the method of complex basis functions to molecular resonances , \ https://doi.org/10.1103/PhysRevLett.41.1364 journal journal Phys. Rev. Lett. \ volume 41 ,\ pages 1364--1368 ( year 1978 ) NoStop

    work page doi:10.1103/physrevlett.41.1364 1978

  51. [51]

    author author A. F. \ White , author M. Head-Gordon ,\ and\ author C. W. \ McCurdy ,\ title title Complex basis functions revisited: Implementation with applications to carbon tetrafluoride and aromatic N-containing heterocycles within the static-exchange approximation , \ https://doi.org/10.1063/1.4906940 journal journal J. Chem. Phys. \ volume 142 ,\ pa...

    work page doi:10.1063/1.4906940 2015

  52. [52]

    author author N. Moiseyev ,\ https://doi.org/10.1017/CBO9780511976186 title Non-Hermitian Quantum Mechanics \ ( publisher Cambridge University Press ,\ address Cambridge, England, UK ,\ year 2011 ) NoStop

    work page doi:10.1017/cbo9780511976186 2011

  53. [53]

    Damour , author A

    author author Y. Damour , author A. Scemama , author F. Kossoski ,\ and\ author P.-F. \ Loos ,\ title title Selected Configuration Interaction for Resonances , \ https://doi.org/10.1021/acs.jpclett.4c02060 journal journal J. Phys. Chem. Lett. \ volume 15 ,\ pages 8296--8305 ( year 2024 ) NoStop

    work page doi:10.1021/acs.jpclett.4c02060 2024

  54. [54]

    Ghosh , author A

    author author A. Ghosh , author A. Karne , author S. Pal ,\ and\ author N. Vaval ,\ title title CAP/EOM-CCSD method for the study of potential curves of resonant states , \ https://doi.org/10.1039/C3CP52552J journal journal Phys. Chem. Chem. Phys. \ volume 15 ,\ pages 17915--17921 ( year 2013 ) NoStop

    work page doi:10.1039/c3cp52552j 2013

  55. [55]

    Sajeev , author R

    author author Y. Sajeev , author R. Santra ,\ and\ author S. Pal ,\ title title Analytically continued Fock space multireference coupled-cluster theory: Application to the g2 shape resonance in e-N2 scattering , \ https://doi.org/10.1063/1.1938887 journal journal J. Chem. Phys. \ volume 122 ,\ pages 234320 ( year 2005 ) NoStop

    work page doi:10.1063/1.1938887 2005

  56. [56]

    Sajeev \ and\ author S

    author author Y. Sajeev \ and\ author S. Pal ,\ title title A general formalism of the Fock space multireference coupled cluster method for investigating molecular electronic resonances , \ https://www.tandfonline.com/doi/abs/10.1080/00268970500084158 journal journal Mol. Phys. \ volume 103 ,\ pages 2267--2275 ( year 2005 ) NoStop

    work page doi:10.1080/00268970500084158 2005

  57. [57]

    author author T.-C. \ Jagau ,\ title title Non-iterative triple excitations in equation-of-motion coupled-cluster theory for electron attachment with applications to bound and temporary anions , \ https://doi.org/10.1063/1.5006374 journal journal J. Chem. Phys. \ volume 148 ,\ pages 024104 ( year 2018 ) NoStop

    work page doi:10.1063/1.5006374 2018

  58. [58]

    Jana , author S

    author author I. Jana , author S. Basumallick , author S. Pal ,\ and\ author N. Vaval ,\ title title Resonance study: Effect of partial triples excitation using complex absorbing potential-based Fock-space multi-reference coupled cluster , \ https://doi.org/https://doi.org/10.1002/qua.26738 journal journal Int. J. Quantum Chem. \ volume 121 ,\ pages e2673...

    work page doi:10.1002/qua.26738 2021

  59. [59]

    Ehara \ and\ author T

    author author M. Ehara \ and\ author T. Sommerfeld ,\ title title CAP/SAC-CI method for calculating resonance states of metastable anions , \ https://doi.org/10.1016/j.cplett.2012.03.104 journal journal Chem. Phys. Lett. \ volume 537 ,\ pages 107--112 ( year 2012 ) NoStop

    work page doi:10.1016/j.cplett.2012.03.104 2012

  60. [60]

    author author Q. M. \ Phung , author Y. Komori , author T. Yanai , author T. Sommerfeld ,\ and\ author M. Ehara ,\ title title Combination of a Voronoi-Type Complex Absorbing Potential with the XMS-CASPT2 Method and Pilot Applications , \ https://doi.org/10.1021/acs.jctc.9b01032 journal journal J. Chem. Theory Comput. \ volume 16 ,\ pages 2606--2616 ( yea...

    work page doi:10.1021/acs.jctc.9b01032 2020

  61. [61]

    Sommerfeld \ and\ author R

    author author T. Sommerfeld \ and\ author R. Santra ,\ title title Efficient method to perform CAP/CI calculations for temporary anions , \ https://doi.org/10.1002/qua.1042 journal journal Int. J. Quantum Chem. \ volume 82 ,\ pages 218--226 ( year 2001 ) NoStop

    work page doi:10.1002/qua.1042 2001

  62. [62]

    Zhou \ and\ author M

    author author Y. Zhou \ and\ author M. Ernzerhof ,\ title title Calculating the lifetimes of metastable states with complex density functional theory , \ https://doi.org/10.1021/jz3006805 journal journal J. Phys. Chem. Lett. \ volume 3 ,\ pages 1916--1920 ( year 2012 ) NoStop

    work page doi:10.1021/jz3006805 1916

  63. [63]

    Santra \ and\ author L

    author author R. Santra \ and\ author L. S. \ Cederbaum ,\ title title Complex absorbing potentials in the framework of electron propagator theory. I. General formalism , \ https://doi.org/10.1063/1.1501903 journal journal J. Chem. Phys. \ volume 117 ,\ pages 5511--5521 ( year 2002 ) NoStop

    work page doi:10.1063/1.1501903 2002

  64. [64]

    Feuerbacher , author T

    author author S. Feuerbacher , author T. Sommerfeld , author R. Santra ,\ and\ author L. S. \ Cederbaum ,\ title title Complex absorbing potentials in the framework of electron propagator theory. II. Application to temporary anions , \ https://doi.org/10.1063/1.1557452 journal journal J. Chem. Phys. \ volume 118 ,\ pages 6188--6199 ( year 2003 ) NoStop

    work page doi:10.1063/1.1557452 2003

  65. [65]

    Feuerbacher \ and\ author R

    author author S. Feuerbacher \ and\ author R. Santra ,\ title title Calculating molecular Rydberg states using the one-particle Green's function: Application to HCO and C(NH2)3 , \ https://doi.org/10.1063/1.2122687 journal journal J. Chem. Phys. \ volume 123 ,\ pages 194310 ( year 2005 ) NoStop

    work page doi:10.1063/1.2122687 2005

  66. [66]

    author author A. M. \ Belogolova , author A. L. \ Dempwolff , author A. Dreuw ,\ and\ author A. B. \ Trofimov ,\ title title A complex absorbing potential electron propagator approach to resonance states of metastable anions , \ https://doi.org/10.1088/1742-6596/1847/1/012050 journal journal J. Phys. Conf. Ser. \ volume 1847 ,\ pages 012050 ( year 2021 ) NoStop

    work page doi:10.1088/1742-6596/1847/1/012050 2021

  67. [67]

    Schirmer , author A

    author author J. Schirmer , author A. B. \ Trofimov ,\ and\ author G. Stelter ,\ title title A non-Dyson third-order approximation scheme for the electron propagator , \ https://doi.org/10.1063/1.477085 journal journal J. Chem. Phys. \ volume 109 ,\ pages 4734--4744 ( year 1998 ) NoStop

    work page doi:10.1063/1.477085 1998

  68. [68]

    Schirmer ,\ @noop title Many-Body Methods for Atoms, Molecules and Clusters \ ( publisher Springer ,\ year 2018 ) NoStop

    author author J. Schirmer ,\ @noop title Many-Body Methods for Atoms, Molecules and Clusters \ ( publisher Springer ,\ year 2018 ) NoStop

    work page 2018

  69. [69]

    author author R. M. \ Martin , author L. Reining ,\ and\ author D. M. \ Ceperley ,\ @noop title Interacting Electrons: Theory and Computational Approaches \ ( publisher Cambridge University Press ,\ year 2016 ) NoStop

    work page 2016

  70. [70]

    Csanak , author H

    author author G. Csanak , author H. Taylor ,\ and\ author R. Yaris ,\ title title Green's function technique in atomic and molecular physics , \ in\ @noop booktitle Advances in atomic and molecular physics ,\ Vol. volume 7 \ ( publisher Elsevier ,\ year 1971 )\ pp.\ pages 287--361 NoStop

    work page 1971

  71. [71]

    author author A. L. \ Fetter \ and\ author J. D. \ Waleck ,\ @noop title Quantum Theory of Many Particle Systems \ ( publisher McGraw Hill, San Francisco ,\ year 1971 ) NoStop

    work page 1971

  72. [72]

    author author L. Hedin ,\ title title New method for calculating the one-particle Green 's function with application to the electron-gas problem , \ https://doi.org/10.1103/PhysRev.139.A796 journal journal Phys. Rev. \ volume 139 ,\ pages A796 ( year 1965 ) NoStop

    work page doi:10.1103/physrev.139.a796 1965

  73. [73]

    The GW Compendium: A Practical Guide to Theoreti- cal Photoemission Spectroscopy.Frontiers in Chem- istry, 7, 2019

    author author D. Golze , author M. Dvorak ,\ and\ author P. Rinke ,\ title title The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy , \ https://doi.org/10.3389/fchem.2019.00377 journal journal Front. Chem. \ volume 7 ,\ pages 377 ( year 2019 ) NoStop

    work page doi:10.3389/fchem.2019.00377 2019

  74. [74]

    Marie , author A

    author author A. Marie , author A. Ammar ,\ and\ author P.-F. \ Loos ,\ title title The GW approximation: A quantum chemistry perspective , \ in\ https://doi.org/10.1016/bs.aiq.2024.04.001 booktitle Advances in Quantum Chemistry ,\ series Novel Treatments of Strong Correlations , Vol. volume 90 \ ( year 2024 )\ pp.\ pages 157--184 NoStop

    work page doi:10.1016/bs.aiq.2024.04.001 2024

  75. [75]

    author author M. F. \ Falcetta , author L. A. \ DiFalco , author D. S. \ Ackerman , author J. C. \ Barlow ,\ and\ author K. D. \ Jordan ,\ title title Assessment of various electronic structure methods for characterizing temporary anion states: Application to the ground state anions of n2, c2h2, c2h4, and c6h6 , \ https://doi.org/10.1021/jp5003287 journal...

    work page doi:10.1021/jp5003287 2014

  76. [76]

    author author M. J. \ van Setten , author F. Caruso , author S. Sharifzadeh , author X. Ren , author M. Scheffler , author F. Liu , author J. Lischner , author L. Lin , author J. R. \ Deslippe , author S. G. \ Louie , author C. Yang , author F. Weigend , author J. B. \ Neaton , author F. Evers ,\ and\ author P. Rinke ,\ title title GW 100: Benchmarking G ...

    work page doi:10.1021/acs.jctc.5b00453 2015

  77. [77]

    Caruso , author M

    author author F. Caruso , author M. Dauth , author M. J. \ van Setten ,\ and\ author P. Rinke ,\ title title Benchmark of GW Approaches for the GW100 Test Set , \ https://doi.org/10.1021/acs.jctc.6b00774 journal journal J. Chem. Theory Comput. \ volume 12 ,\ pages 5076 ( year 2016 ) NoStop

    work page doi:10.1021/acs.jctc.6b00774 2016

  78. [78]

    Krause \ and\ author W

    author author K. Krause \ and\ author W. Klopper ,\ title title Implementation of the bethe-salpeter equation in the turbomole program , \ https://doi.org/10.1002/jcc.24688 journal journal J. Comput. Chem. \ volume 38 ,\ pages 383--388 ( year 2017 ) NoStop

    work page doi:10.1002/jcc.24688 2017

  79. [79]

    author author A. M. \ Lewis \ and\ author T. C. \ Berkelbach ,\ title title Vertex corrections to the polarizability do not improve the gw approximation for the ionization potential of molecules , \ https://doi.org/10.1021/acs.jctc.8b00995 journal journal J. Chem. Theory Comput. \ volume 15 ,\ pages 2925 ( year 2019 ) NoStop

    work page doi:10.1021/acs.jctc.8b00995 2019

  80. [80]

    Bruneval, N

    author author F. Bruneval , author N. Dattani ,\ and\ author M. J. \ van Setten ,\ title title The GW Miracle in Many-Body Perturbation Theory for the Ionization Potential of Molecules , \ https://doi.org/10.3389/fchem.2021.749779 journal journal Front. Chem. \ volume 9 ,\ pages 749779 ( year 2021 ) NoStop

    work page doi:10.3389/fchem.2021.749779 2021

Showing first 80 references.