Double Ionization Potential Equation-of-Motion Coupled-Cluster Approach with Full Inclusion of 4-Hole-2-Particle Excitations and Three-Body Clusters

Achintya Kumar Dutta; Karthik Gururangan; Piotr Piecuch

REVIEW 2 major objections 4 minor 1 cited by

Double Ionization Potential Equation-of-Motion Coupled-Cluster Approach with Full Inclusion of 4-Hole-2-Particle Excitations and Three-Body Clusters

T0 review · 2 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Adding triples to the neutral state fixes double-ionization energies to 0.03 eV.

desk verdict Solid new DIP-EOMCC method level with explicit factorized equations and open-source implementation; benchmark claims are plausible but the missing CIPSI uncertainty and a Cl2/Br2 inconsistency should be cleaned up. read the letter →

arxiv 2412.10688 v2 pith:K2NMJKRM submitted 2024-12-14 physics.chem-ph physics.comp-ph

Karthik Gururangan , Achintya Kumar Dutta , Piotr Piecuch This is my paper · ORCID

classification physics.chem-phphysics.comp-ph

keywords doubleionizationpotentialequation-of-motioncoupledcluster4-hole–2-particleexcitationstripleCCSDTperturbativetriplesCIPSIbenchmarkverticalenergies

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper establishes that a double ionization potential (DIP) equation-of-motion coupled-cluster method that includes 4-hole–2-particle excitations on top of a CCSDT ground state, called DIP-EOMCCSDT(4h-2p), reduces vertical DIP errors for H2O, CH4, and BN to 0.00–0.03 eV relative to extrapolated full-CI benchmarks. The same paper shows that a cheaper perturbative-triples variant, DIP-EOMCCSD(T)(a)(4h-2p), reproduces the full method to within 0.02 eV for these molecules and for Cl2, Br2, and HBr. The reason the improvement matters is that the earlier 4h-2p method built on CCSD was imbalanced, sometimes worsening the simpler 3h-1p results. If the claim holds, near-benchmark double ionization energies for small molecules become available without a full configuration-interaction calculation.

What carries the argument

The mechanism is diagonalization of the CCSDT similarity-transformed Hamiltonian in the (N−2)-electron Fock-space subspace spanned by 2-hole, 3-hole–1-particle, and 4-hole–2-particle basis states. Factorized programmable expressions for the projections are given as Eqs. (8)–(10), with intermediates in Tables I and II. The approximate variant replaces full CCSDT with CCSD plus a Møller–Plesset perturbative correction to T1, T2, and T3 (Eqs. (11)–(13)), so the most expensive steps scale as $n_o^4 n_u^4$ rather than $n_o^3 n_u^5$.

What would settle it

Compute a vertical double ionization potential for a small molecule whose true value is known from high-resolution experiment or an exact full-CI calculation to better than 0.01 eV, using the same aug-cc-pVTZ basis and frozen-core setup; if DIP-EOMCCSDT(4h-2p) deviates by more than about 0.03 eV, the claimed near-exactness would be refuted.

Watch

Extended reading notes

Core claim

The central claim is that the imbalance between a high-level 4h-2p treatment of the doubly ionized target and a low-level CCSD description of the neutral parent is removed by using CCSDT for the neutral species. Concretely, Table III shows DIP-EOMCCSDT(4h-2p) vertical DIPs for the lowest triplet and singlet states of (H2O)2+, (CH4)2+, and (BN)2+ at 40.27, 41.40, 38.27, 38.97, 33.74, and 34.98 eV, against CIPSI-extrapolated values 40.29, 41.43, 38.27, 38.98, 33.73, and 34.98 eV, giving errors of 0.02, 0.03, 0.00, 0.01, 0.01, and 0.00 eV. The approximate variant recovers the full-method DIPs for all six molecules to within 0.02 eV.

Load-bearing premise

The load-bearing premise is that the extrapolated CIPSI values from Ref. [58] are accurate enough to serve as exact benchmarks; if those numbers carry uncertainties larger than roughly 0.03 eV, the 0.00–0.03 eV agreement could be fortuitous.

Editorial extensions

If this is right

For small molecules with reliable benchmarks, DIP-EOMCCSDT(4h-2p) gives vertical double ionization potentials within 0.03 eV of full CI, so it can serve as a reference-quality method where full CI is impossible.
DIP-EOMCCSD(T)(a)(4h-2p) offers essentially the same DIPs as the full CCSDT-based method, to within 0.02 eV, at the cost of CCSD plus a perturbative triples correction.
The improvement documents that the earlier DIP-EOMCCSD(4h-2p) errors of 0.17–0.67 eV come mainly from the CCSD ground state, not from the 4h-2p operator itself.
The EOM diagonalization steps scale as $N^8$, the same as DIP-EOMCCSD(4h-2p); only the ground-state CCSDT step adds the $n_o^3 n_u^5$ cost.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural next test is to apply DIP-EOMCCSDT(4h-2p) to molecules where CIPSI extrapolation uncertainties are quantified; the sub-0.03 eV agreement may shrink or grow once benchmark error bars are included.
If the 0.02 eV fidelity of the approximate variant persists, it could become the practical default for larger dications, including Auger spectroscopy targets, where full CCSDT is too expensive.
The same CCSD/CCSDT imbalance likely affects other EOM-CC sectors, such as ionization potential and electron attachment methods with high-rank ionizing operators; the pattern found here suggests upgrading the ground state may be as important as adding higher-rank R operators.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The thing to know: this is a credible next rung on the DIP-EOMCC ladder, not a paradigm shift. The authors write down factorized, programmable equations for including 4h-2p ionizing correlations on top of CCSDT, implement both the full method and a (T)(a) approximation in the open-source CCpy code, and show on six small molecules that this cures the imbalance that made plain DIP-EOMCCSD(4h-2p) sometimes worse than DIP-EOMCCSD(3h-1p).

What is genuinely new is the algebraic content. Equations (8)-(10) are explicit and factorized, so the diagonalization step scales like the older 4h-2p method rather than something worse, with the extra cost pushed into the CCSDT ground state. The (T)(a) route, borrowing the Matthews-Stanton style perturbative T3, reproduces the full method to within 0.02 eV on these tests. That is a useful practical result. The open-source implementation is a real plus, and the citation pattern looks appropriate; the main self-reference is the (T)(a) recipe from Ref. 55, which is acknowledged.

On the numbers: the Table III agreement with extrapolated CIPSI is clean for the three molecules with near-exact references, with errors dropping from 0.17-0.67 eV at CCSD(4h-2p) to at most 0.03 eV. The stress-test point about missing CIPSI uncertainty is fair, but it should not be dialed up into fatal. Even if the extrapolated references carry a few hundredths of an eV of error, the improvement over the parent methods is far larger than that noise; only the claim of near-benchmark quality to 0.00-0.03 eV should be phrased more carefully. The authors could quote estimated uncertainties or compare against an independent reference for at least one state.

The soft spots are minor and fixable. The text and the summary disagree about which molecule has the exceptional c1Sigma-u state (Cl2 in the results, Br2 in the summary); that needs to be reconciled. The test set is small, so the method-level value is established, but broad statistical performance is not. No internal inconsistency in Eqs. (8)-(10) jumped out.

This paper is for methods developers and users who need DIPs for Auger spectroscopy, biradical gaps, or strong-field chemistry. It deserves a serious referee. A good referee will press on benchmark uncertainties and the exception statement, but the core contribution, a formulated, implemented, and tested new method level, is real.

Referee Report

2 major / 4 minor

Summary. The paper presents the formulation, implementation, and benchmark application of DIP-EOMCCSDT(4h-2p), a double-ionization-potential equation-of-motion coupled-cluster method with 4-hole-2-particle excitations on top of a CCSDT reference, together with the cheaper approximation DIP-EOMCCSD(T)(a)(4h-2p). The authors provide factorized programmable expressions in Eqs. (8)-(10) and Tables I-II, implement the methods in the open-source CCpy package, and test them on vertical DIPs of H2O, CH4, BN (against extrapolated CIPSI reference data) and Cl2, Br2, HBr (against experiment). The central numerical claim is that DIP-EOMCCSDT(4h-2p) reduces errors for H2O, CH4, and BN to 0.00-0.03 eV with respect to the CIPSI references, from errors of 0.17-0.67 eV for DIP-EOMCCSD(4h-2p), and that DIP-EOMCCSD(T)(a)(4h-2p) reproduces the full method to within 0.02 eV.

Significance. If the quantitative claims hold, the work is a valuable methodological advance: it provides a balanced treatment of the neutral parent and the doubly ionized target, resolves an imbalance identified in earlier DIP-EOMCCSD(4h-2p) work, and supplies explicit, programmable equations plus an open-source implementation. The methods contain no fitted parameters, and the approximate form offers a practical N^8-scaling route to near-CCSDT-quality DIPs. The main limitations are the small test set (six molecules), the absence of uncertainty estimates for the extrapolated CIPSI benchmarks used in the central comparison, and an internal inconsistency in the stated exceptions to the improvement claim.

major comments (2)

[Table III / Results discussion] Table III quotes the CIPSI reference values from Ref. 58 to 0.01 eV without any uncertainty estimate. The headline errors of 0.00-0.03 eV for DIP-EOMCCSDT(4h-2p) are only meaningful if the extrapolation error in the CIPSI full-CI limit is smaller than roughly 0.03 eV. The manuscript should state, or at least estimate, the expected uncertainty of the Ref. 58 extrapolations, or provide additional convergence evidence (e.g., a second basis set or a different extrapolation protocol), before the 'minuscule error' claim in the abstract and the discussion is accepted as quantitatively established.
[Results paragraph on exceptions / Summary] There is a direct inconsistency between the results text, which says 'The only exceptions are the c1Σ−u state of (Cl2)2+ and the three states of (HBr)2+', and the Summary, which says 'with the exception of the higher-lying c1Σ−u state of (Br2)2+'. Table IV shows the results-text version is the correct one. This misidentification matters because it affects the paper's general claim that DIP-EOMCCSDT(4h-2p) improves over DIP-EOMCCSD(4h-2p) for the heavier diatomics, and it must be corrected.

minor comments (4)

[Page 4, text after Table III] The text contains the typo 'DIP-EOMCSCD(3h-1p)' where 'DIP-EOMCCSD(3h-1p)' is clearly intended.
[Page 3, sentence defining n_o and n_u] The phrase 'where no (nu) is the number of occupied (unoccupied) orbitals' should be typeset as n_o and n_u; as written, 'no' reads as an English word rather than a symbol.
[Table III footnote e] Describing the CIPSI numbers as 'extrapolated to the exact, full CI, limit' overstates what an extrapolation provides; 'estimated full CI limit' would be more accurate and would appropriately flag the residual uncertainty discussed in the first major comment.
[Table IV] The experimental value for the c1Σ−u state of Br2 is given as 30.3 eV with only one decimal. The comparison for this state should acknowledge the reduced precision of this experimental datum.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the DIP-EOMCCSDT(4h-2p) working equations are parameter-free EOM-CC truncations validated against external CIPSI and experimental benchmarks; self-citations are routine and non-load-bearing.

full rationale

No circularity found. The DIP-EOMCCSDT(4h-2p) working equations, Eqs. (8)-(10), are derived from the standard DIP-EOMCC eigenvalue problem, Eq. (7), with no fitted parameters; the method's accuracy is assessed solely by comparing its outputs to external CIPSI full-CI-limit benchmarks (Ref. 58) and experimental data (Refs. 62-64). The DIP-EOMCCSD(T)(a)(4h-2p) approximation adopts the external CCSD(T)(a) recipe of Ref. 55, and its stated 0.02 eV agreement with the parent is a numerical validation, not an input to the parent method. The self-citations (Refs. 35,36,38,52) are routine and not load-bearing: the size-intensivity condition MR <= MT comes from prior parameter-free analysis, and CCpy is the openly available implementation, not a source of numerical predictions. The only flagged issues are correctness/consistency points, not circularity: (i) the CIPSI benchmarks in Table III are quoted without uncertainties, so the 0.00-0.03 eV agreement is only as strong as the unreported extrapolation error; and (ii) the exception statements for Table IV are internally inconsistent, with the results text naming "the c1Σ-u state of (Cl2)2+ and the three states of (HBr)2+" while the summary names "the higher-lying c1Σ-u state of (Br2)2+". Neither issue makes the derivation self-referential.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The method contains no fitted parameters and no new physical entities. It rests on standard coupled-cluster background, on a prior perturbative approximation, and on the reliability of external benchmark data.

assumptions (6)

domain assumption The CC/EOM-CC eigenvalue equation, Eq. (7), with the similarity-transformed Hamiltonian H_N = e^{-T} H_N e^T, correctly describes vertical double ionization energies.
This is the standard coupled-cluster EOM formalism, not derived in this paper. It is the foundation of the method.
domain assumption The size-intensivity condition MR <= MT from Refs. 35, 36, 38 applies to the DIP-EOMCCSDT(4h-2p) truncation (MR=2, MT=3).
The paper states that MR <= MT is a condition required for retaining size intensivity before imposing it on the method.
domain assumption The CCSD(T)(a) approximation of Matthews and Stanton (Ref. 55), using Moller-Plesset denominators in Eqs. (11)-(13), provides a reliable estimate of T3 effects for the tested molecules.
The approximate method DIP-EOMCCSD(T)(a)(4h-2p) adopts this recipe; its 0.02 eV agreement with full CCSDT is demonstrated empirically on only six small molecules.
domain assumption The CIPSI-extrapolated full-CI reference values from Ref. 58 are accurate benchmarks for H2O, CH4, and BN.
The central accuracy claim (errors of 0.00-0.03 eV) is measured against these values, which are treated as exact without quoted error bars.
domain assumption The experimental DIPs for Cl2, Br2, and HBr (Refs. 62-64) are reliable vertical ionization values for the assigned states.
The comparison in Table IV assumes the experimental peak assignments and vertical/adiabatic correspondence are correct.
domain assumption The frozen-core approximation and SFX2C-1e scalar-relativistic treatment (Ref. 71) do not introduce errors large enough to affect the conclusions.
The paper freezes core orbitals and uses spin-free scalar-relativistic Hamiltonians without detailed convergence checks.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Double Ionization Potential Equation-of-Motion Coupled-Cluster Approach with Full Inclusion of 4-Hole-2-Particle Excitations and Three-Body Clusters." pith.science (2026). https://pith.science/paper/K2NMJKRM

@misc{pith2026241210688,
  author       = {Pith},
  title        = {Pith review of: Double Ionization Potential Equation-of-Motion Coupled-Cluster Approach with Full Inclusion of 4-Hole-2-Particle Excitations and Three-Body Clusters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K2NMJKRM}},
  note         = {Machine review of arXiv:2412.10688}
}

abstract

The double ionization potential (DIP) equation-of-motion (EOM) coupled-cluster (CC) method with a full treatment of 4-hole-2-particle (4$h$-2$p$) correlations and triply excited clusters, abbreviated as DIP-EOMCCSDT(4$h$-2$p$), and its approximate form called DIP-EOMCCSD(T)(a)(4$h$-2$p$) have been formulated and implemented in the open-source CCpy package available on GitHub. The resulting codes work with both nonrelativistic and spin-free scalar-relativistic Hamiltonians. By examining the DIPs of a few small molecules, for which accurate reference data are available, we demonstrate that the DIP-EOMCCSDT(4$h$-2$p$) and DIP-EOMCCSD(T)(a)(4$h$-2$p$) approaches improve the results obtained using the DIP-EOMCC methods truncated at 3$h$-1$p$ or 4$h$-2$p$ excitations on top of the CC calculations with singles and doubles.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Anomalous propagators and the particle-particle channel: Bethe-Salpeter equation
physics.chem-ph 2024-11 conditional novelty 7.0 of 10

A new particle-particle Bethe-Salpeter kernel, expressed as a self-energy derivative, enables GW, T-matrix, and second-order approximations for double ionization potentials.

Reference graph

Works this paper leans on

75 extracted references · 72 canonical work pages · cited by 1 Pith paper

[1]

Coester ,\ @noop journal journal Nucl

author author F. Coester ,\ @noop journal journal Nucl. Phys. \ volume 7 ,\ pages 421 ( year 1958 ) NoStop

work page 1958
[2]

Coester \ and\ author H

author author F. Coester \ and\ author H. K \" u mmel ,\ @noop journal journal Nucl. Phys. \ volume 17 ,\ pages 477 ( year 1960 ) NoStop

work page 1960
[3]

C \' z ek ,\ @noop journal journal J

author author J. C \' z ek ,\ @noop journal journal J. Chem. Phys. \ volume 45 ,\ pages 4256 ( year 1966 ) NoStop

work page 1966
[4]

C \' z ek ,\ @noop journal journal Adv

author author J. C \' z ek ,\ @noop journal journal Adv. Chem. Phys. \ volume 14 ,\ pages 35 ( year 1969 ) NoStop

work page 1969
[5]

Paldus , author J

author author J. Paldus , author J. C \' z ek , \ and\ author I. Shavitt ,\ @noop journal journal Phys. Rev. A \ volume 5 ,\ pages 50 ( year 1972 ) NoStop

work page 1972
[6]

Emrich ,\ @noop journal journal Nucl

author author K. Emrich ,\ @noop journal journal Nucl. Phys. A \ volume 351 ,\ pages 379 ( year 1981 a ) NoStop

work page 1981
[7]

Emrich ,\ @noop journal journal Nucl

author author K. Emrich ,\ @noop journal journal Nucl. Phys. A \ volume 351 ,\ pages 397 ( year 1981 b ) NoStop

work page 1981
[8]

Geertsen , author M

author author J. Geertsen , author M. Rittby , \ and\ author R. J. \ Bartlett ,\ @noop journal journal Chem. Phys. Lett. \ volume 164 ,\ pages 57 ( year 1989 ) NoStop

work page 1989

Show all 75 references

[9]

author author D. C. \ Comeau \ and\ author R. J. \ Bartlett ,\ @noop journal journal Chem. Phys. Lett. \ volume 207 ,\ pages 414 ( year 1993 ) NoStop

1993
[10]

author author J. F. \ Stanton \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 98 ,\ pages 7029 ( year 1993 ) NoStop

1993
[11]

Nooijen \ and\ author R

author author M. Nooijen \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 102 ,\ pages 3629 ( year 1995 a ) NoStop

1995
[12]

Nooijen \ and\ author R

author author M. Nooijen \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 102 ,\ pages 6735 ( year 1995 b ) NoStop

1995
[13]

Hirata , author M

author author S. Hirata , author M. Nooijen , \ and\ author R. J. \ Bartlett ,\ @noop journal journal Chem. Phys. Lett. \ volume 328 ,\ pages 459 ( year 2000 ) NoStop

2000
[14]

Musia \ and\ author R

author author M. Musia \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 119 ,\ pages 1901 ( year 2003 ) NoStop

1901
[15]

author author J. R. \ Gour , author P. Piecuch , \ and\ author M. W och ,\ @noop journal journal J. Chem. Phys. \ volume 123 ,\ pages 134113 ( year 2005 ) NoStop

2005
[16]

author author J. R. \ Gour , author P. Piecuch , \ and\ author M. W och ,\ @noop journal journal Int. J. Quantum Chem. \ volume 106 ,\ pages 2854 ( year 2006 ) NoStop

2006
[17]

author author J. R. \ Gour \ and\ author P. Piecuch ,\ @noop journal journal J. Chem. Phys. \ volume 125 ,\ pages 234107 ( year 2006 ) NoStop

2006
[18]

Nooijen \ and\ author J

author author M. Nooijen \ and\ author J. G. \ Snijders ,\ @noop journal journal Int. J. Quantum Chem. Symp. \ volume 26 ,\ pages 55 ( year 1992 ) NoStop

1992
[19]

Nooijen \ and\ author J

author author M. Nooijen \ and\ author J. G. \ Snijders ,\ @noop journal journal Int. J. Quantum Chem. \ volume 48 ,\ pages 15 ( year 1993 ) NoStop

1993
[20]

author author J. F. \ Stanton \ and\ author J. Gauss ,\ @noop journal journal J. Chem. Phys. \ volume 101 ,\ pages 8938 ( year 1994 ) NoStop

1994
[21]

author author R. J. \ Bartlett \ and\ author J. F. \ Stanton ,\ in\ @noop booktitle Reviews in Computational Chemistry ,\ Vol. volume 5 ,\ editor edited by\ editor K. B. \ Lipkowitz \ and\ editor D. B. \ Boyd \ ( publisher VCH Publishers ,\ address New York ,\ year 1994 )\ pp....

1994
[22]

Musia , author S

author author M. Musia , author S. A. \ Kucharski , \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 118 ,\ pages 1128 ( year 2003 ) NoStop

2003
[23]

Musia \ and\ author R

author author M. Musia \ and\ author R. J. \ Bartlett ,\ @noop journal journal Chem. Phys. Lett. \ volume 384 ,\ pages 210 ( year 2004 ) NoStop

2004
[24]

author author Y. J. \ Bomble , author J. C. \ Saeh , author J. F. \ Stanton , author P. G. \ Szalay , author M. K \' a llay , \ and\ author J. Gauss ,\ @noop journal journal J. Chem. Phys. \ volume 122 ,\ pages 154107 ( year 2005 ) NoStop

2005
[25]

Kamiya \ and\ author S

author author M. Kamiya \ and\ author S. Hirata ,\ @noop journal journal J. Chem. Phys. \ volume 125 ,\ pages 074111 ( year 2006 ) NoStop

2006
[26]

Nooijen \ and\ author R

author author M. Nooijen \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 106 ,\ pages 6441 ( year 1997 a ) NoStop

1997
[27]

Nooijen \ and\ author R

author author M. Nooijen \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 107 ,\ pages 6812 ( year 1997 b ) NoStop

1997
[28]

Wladyslawski \ and\ author M

author author M. Wladyslawski \ and\ author M. Nooijen ,\ in\ @noop booktitle Low-Lying Potential Energy Surfaces ,\ series ACS Symposium Series , Vol.\ volume 828 ,\ editor edited by\ editor M. R. \ Hoffmann \ and\ editor K. G. \ Dyall \ ( publisher American Chemical Society ...

2002
[29]

Nooijen ,\ @noop journal journal Int

author author M. Nooijen ,\ @noop journal journal Int. J. Mol. Sci. \ volume 3 ,\ pages 656 ( year 2002 ) NoStop

2002
[30]

author author K. W. \ Sattelmeyer , author H. F. \ Schaefer , III , \ and\ author J. F. \ Stanton ,\ @noop journal journal Chem. Phys. Lett. \ volume 378 ,\ pages 42 ( year 2003 ) NoStop

2003
[31]

Musia , author A

author author M. Musia , author A. Perera , \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 134 ,\ pages 114108 ( year 2011 ) NoStop

2011
[32]

Musia , author S

author author M. Musia , author S. A. \ Kucharski , \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Theory Comput. \ volume 7 ,\ pages 3088 ( year 2011 ) NoStop

2011
[33]

Ku \' s \ and\ author A

author author T. Ku \' s \ and\ author A. I. \ Krylov ,\ @noop journal journal J. Chem. Phys. \ volume 135 ,\ pages 084109 ( year 2011 ) NoStop

2011
[34]

Ku \' s \ and\ author A

author author T. Ku \' s \ and\ author A. I. \ Krylov ,\ @noop journal journal J. Chem. Phys. \ volume 136 ,\ pages 244109 ( year 2012 ) NoStop

2012
[35]

Shen \ and\ author P

author author J. Shen \ and\ author P. Piecuch ,\ @noop journal journal J. Chem. Phys. \ volume 138 ,\ pages 194102 ( year 2013 ) NoStop

2013
[36]

Shen \ and\ author P

author author J. Shen \ and\ author P. Piecuch ,\ @noop journal journal Mol. Phys. \ volume 112 ,\ pages 868 ( year 2014 ) NoStop

2014
[37]

author author A. O. \ Ajala , author J. Shen , \ and\ author P. Piecuch ,\ @noop journal journal J. Phys. Chem. A \ volume 121 ,\ pages 3469 ( year 2017 ) NoStop

2017
[38]

Shen \ and\ author P

author author J. Shen \ and\ author P. Piecuch ,\ @noop journal journal Mol. Phys. \ volume 119 ,\ pages e1966534 ( year 2021 ) NoStop

2021
[39]

Gulania , author E

author author S. Gulania , author E. F. \ Kj nstad , author J. F. \ Stanton , author H. Koch , \ and\ author A. I. \ Krylov ,\ @noop journal journal J. Chem. Phys. \ volume 154 ,\ pages 114115 ( year 2021 ) NoStop

2021
[40]

Musia , author M

author author M. Musia , author M. Olsz \' o wka , author D. I. \ Lyakh , \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 137 ,\ pages 174102 ( year 2012 ) NoStop

2012
[41]

Ghosh , author N

author author A. Ghosh , author N. Vaval , \ and\ author S. Pal ,\ @noop journal journal Chem. Phys. \ volume 482 ,\ pages 160 ( year 2017 ) NoStop

2017
[42]

Skomorowski \ and\ author A

author author W. Skomorowski \ and\ author A. I. \ Krylov ,\ @noop journal journal J. Chem. Phys. \ volume 154 ,\ pages 084124 ( year 2021 a ) NoStop

2021
[43]

Skomorowski \ and\ author A

author author W. Skomorowski \ and\ author A. I. \ Krylov ,\ @noop journal journal J. Chem. Phys. \ volume 154 ,\ pages 084125 ( year 2021 b ) NoStop

2021
[44]

author author N. K. \ Jayadev , author A. Ferino-P \'e rez , author F. Matz , author A. I. \ Krylov , \ and\ author T.-C. \ Jagau ,\ @noop journal journal J. Chem. Phys. \ volume 158 ,\ pages 064109 ( year 2023 ) NoStop

2023
[45]

Stamm , author S

author author J. Stamm , author S. S. \ Priyadarsini , author S. Sandhu , author A. Chakraborty , author J. Shen , author S. Kwon , author J. Sandhu , author C. Wicka , author A. Mehmood , author B. G. \ Levine , author P. Piecuch , \ and\ author M. Dantus ,\ @noop journal jou...

2025
[46]

author author G. D. \ Purvis , III \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 76 ,\ pages 1910 ( year 1982 ) NoStop

1910
[47]

author author J. M. \ Cullen \ and\ author M. C. \ Zerner ,\ @noop journal journal J. Chem. Phys. \ volume 77 ,\ pages 4088 ( year 1982 ) NoStop

1982
[48]

author author G. E. \ Scuseria , author A. C. \ Scheiner , author T. J. \ Lee , author J. E. \ Rice , \ and\ author H. F. \ Schaefer , III ,\ @noop journal journal J. Chem. Phys. \ volume 86 ,\ pages 2881 ( year 1987 ) NoStop

1987
[49]

Piecuch \ and\ author J

author author P. Piecuch \ and\ author J. Paldus ,\ @noop journal journal Int. J. Quantum Chem. \ volume 36 ,\ pages 429 ( year 1989 ) NoStop

1989
[50]

Noga \ and\ author R

author author J. Noga \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 86 ,\ pages 7041 ( year 1987 ) ,\ note 89 , 3401 (1988) [Erratum] NoStop

1988
[51]

author author G. E. \ Scuseria \ and\ author H. F. \ Schaefer , III ,\ @noop journal journal Chem. Phys. Lett. \ volume 152 ,\ pages 382 ( year 1988 ) NoStop

1988
[52]

Gururangan and P

@noop note K. Gururangan and P. Piecuch, ``CCpy: A Coupled-Cluster Package Written in Python,'' see https://github.com/piecuch-group/ccpy NoStop
[53]

Hirao \ and\ author H

author author K. Hirao \ and\ author H. Nakatsuji ,\ @noop journal journal J. Comput. Phys. \ volume 45 ,\ pages 246 ( year 1982 ) NoStop

1982
[54]

author author E. R. \ Davidson ,\ @noop journal journal J. Comput. Phys. \ volume 17 ,\ pages 87 ( year 1975 ) NoStop

1975
[55]

author author D. A. \ Matthews \ and\ author J. F. \ Stanton ,\ @noop journal journal J. Chem. Phys. \ volume 145 ,\ pages 124102 ( year 2016 ) NoStop

2016
[56]

author author T. H. \ Dunning , Jr. ,\ @noop journal journal J. Chem. Phys. \ volume 90 ,\ pages 1007 ( year 1989 ) NoStop

1989
[57]

author author R. A. \ Kendall , author T. H. \ Dunning , Jr. , \ and\ author R. J. \ Harrison ,\ @noop journal journal J. Chem. Phys. \ volume 96 ,\ pages 6769 ( year 1992 ) NoStop

1992
[58]

Marie , author P

author author A. Marie , author P. Romaniello , author X. Blase , \ and\ author P.-F. \ Loos ,\ @noop title Anomalous propagators and the particle-particle channel: B ethe-- S alpeter equation , \ ( year 2024 ),\ http://arxiv.org/abs/2411.13167 arXiv:2411.13167 [physics.chem-p...

2024 arXiv
[59]

Huron , author J

author author B. Huron , author J. P. \ Malrieu , \ and\ author P. Rancurel ,\ @noop journal journal J. Chem. Phys. \ volume 58 ,\ pages 5745 ( year 1973 ) NoStop

1973
[60]

Garniron , author A

author author Y. Garniron , author A. Scemama , author P.-F. \ Loos , \ and\ author M. Caffarel ,\ @noop journal journal J. Chem. Phys. \ volume 147 ,\ pages 034101 ( year 2017 ) NoStop

2017
[61]

Garniron , author T

author author Y. Garniron , author T. Applencourt , author K. Gasperich , author A. Benali , author A. Ferte , author J. Paquier , author B. Pradines , author R. Assaraf , author P. Reinhardt , author J. Toulouse , author P. Barbaresco , author N. Renon , author G. David , aut...

2019
[62]

author author A. G. \ McConkey , author G. Dawber , author L. Avaldi , author M. A. \ MacDonald , author G. C. \ King , \ and\ author R. I. \ Hall ,\ @noop journal journal J. Phys. B: At. Mol. Opt. Phys. \ volume 27 ,\ pages 271 ( year 1994 ) NoStop

1994
[63]

Fleig , author D

author author T. Fleig , author D. Edvardsson , author S. T. \ Banks , \ and\ author J. H. \ Eland ,\ @noop journal journal Chem. Phys. \ volume 343 ,\ pages 270 ( year 2008 ) NoStop

2008
[64]

author author J. H. \ Eland ,\ @noop journal journal Chem. Phys. \ volume 294 ,\ pages 171 ( year 2003 ) NoStop

2003
[65]

author author D. E. \ Woon \ and\ author T. H. \ Dunning , Jr. ,\ @noop journal journal J. Chem. Phys. \ volume 98 ,\ pages 1358 ( year 1993 ) NoStop

1993
[66]

author author A. K. \ Wilson , author D. E. \ Woon , author K. A. \ Peterson , \ and\ author T. H. \ Dunning , Jr. ,\ @noop journal journal J. Chem. Phys. \ volume 110 ,\ pages 7667 ( year 1999 ) NoStop

1999
[67]

Marie \ and\ author P.-F

author author A. Marie \ and\ author P.-F. \ Loos ,\ @noop journal journal J. Chem. Theory Comput. \ volume 20 ,\ pages 4751 ( year 2024 ) NoStop

2024
[68]

author author K. P. \ Huber \ and\ author G. Herzberg ,\ @noop title Molecular Spectra and Molecular Structure: Constants of Diatomic Molecules \ ( publisher Van Nostrand Reinhold ,\ address New York ,\ year 1979 ) NoStop

1979
[69]

Sun , author T

author author Q. Sun , author T. C. \ Berkelbach , author N. S. \ Blunt , author G. H. \ Booth , author S. Guo , author Z. Li , author J. Liu , author J. D. \ McClain , author E. R. \ Sayfutyarova , author S. Sharma , author S. Wouters , \ and\ author G. K.-L. \ Chan ,\ @noop ...

2018
[70]

Sun , author X

author author Q. Sun , author X. Zhang , author S. Banerjee , author P. Bao , author M. Barbry , author N. S. \ Blunt , author N. A. \ Bogdanov , author G. H. \ Booth , author J. Chen , author Z.-H. \ Cui , author J. J. \ Eriksen , author Y. Gao , author S. Guo , author J. Her...

2020
[71]

Cheng \ and\ author J

author author L. Cheng \ and\ author J. Gauss ,\ @noop journal journal J. Chem. Phys. \ volume 135 ,\ pages 084114 ( year 2011 ) NoStop

2011
[72]

Oliphant \ and\ author L

author author N. Oliphant \ and\ author L. Adamowicz ,\ @noop journal journal J. Chem. Phys. \ volume 96 ,\ pages 3739 ( year 1992 ) NoStop

1992
[73]

Piecuch , author N

author author P. Piecuch , author N. Oliphant , \ and\ author L. Adamowicz ,\ @noop journal journal J. Chem. Phys. \ volume 99 ,\ pages 1875 ( year 1993 ) NoStop

1993
[74]

Piecuch , author S

author author P. Piecuch , author S. A. \ Kucharski , \ and\ author R. J. \ Bartlett ,\ @noop journal journal J. Chem. Phys. \ volume 110 ,\ pages 6103 ( year 1999 ) NoStop

1999
[75]

Surjuse , author S

author author K. Surjuse , author S. Chamoli , author M. K. \ Nayak , \ and\ author A. K. \ Dutta ,\ @noop journal journal J. Chem. Phys. \ volume 157 ,\ pages 204106 ( year 2022 ) NoStop

2022

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

Coester ,\ @noop journal journal Nucl

author author F. Coester ,\ @noop journal journal Nucl. Phys. \ volume 7 ,\ pages 421 ( year 1958 ) NoStop

work page 1958

[2] [2]

Coester \ and\ author H

author author F. Coester \ and\ author H. K \" u mmel ,\ @noop journal journal Nucl. Phys. \ volume 17 ,\ pages 477 ( year 1960 ) NoStop

work page 1960

[3] [3]

C \' z ek ,\ @noop journal journal J

author author J. C \' z ek ,\ @noop journal journal J. Chem. Phys. \ volume 45 ,\ pages 4256 ( year 1966 ) NoStop

work page 1966

[4] [4]

C \' z ek ,\ @noop journal journal Adv

author author J. C \' z ek ,\ @noop journal journal Adv. Chem. Phys. \ volume 14 ,\ pages 35 ( year 1969 ) NoStop

work page 1969

[5] [5]

Paldus , author J

author author J. Paldus , author J. C \' z ek , \ and\ author I. Shavitt ,\ @noop journal journal Phys. Rev. A \ volume 5 ,\ pages 50 ( year 1972 ) NoStop

work page 1972

[6] [6]

Emrich ,\ @noop journal journal Nucl

author author K. Emrich ,\ @noop journal journal Nucl. Phys. A \ volume 351 ,\ pages 379 ( year 1981 a ) NoStop

work page 1981

[7] [7]

Emrich ,\ @noop journal journal Nucl

author author K. Emrich ,\ @noop journal journal Nucl. Phys. A \ volume 351 ,\ pages 397 ( year 1981 b ) NoStop

work page 1981

[8] [8]

Geertsen , author M

author author J. Geertsen , author M. Rittby , \ and\ author R. J. \ Bartlett ,\ @noop journal journal Chem. Phys. Lett. \ volume 164 ,\ pages 57 ( year 1989 ) NoStop

work page 1989