{"id":"651a2ecd-0321-4101-b77e-ba7845d08310","arxiv_id":"2412.10688","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A new coupled-cluster method that includes four-hole-two-particle excitations and triple clusters gives near-exact double ionization potentials for small molecules.","lead":"This paper presents a new computational method for calculating how much energy it takes to remove two electrons from a molecule. In tests on small molecules, the method matches the best available reference values to within a few hundredths of an electronvolt, which could make it a useful standard for chemistry and spectroscopy.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Table III agreement of 0.00–0.03 eV with CIPSI is only as solid as the unreported CIPSI extrapolation uncertainty; without error bounds on the Ref. 58 references, the precision claim is not yet established.","rationale":"The reader's weakest assumption correctly identifies the CIPSI reference accuracy as the main load-bearing point: the paper claims sub-0.03 eV accuracy against references that carry no stated uncertainty. My stress test did not find a more fundamental flaw in the method itself. The equations are formulated explicitly, the implementation is in an open-source package, and the internal comparison between DIP-EOMCCSDT(4h-2p) and its (T)(a) approximation is self-consistent. The strongest concern is therefore evidential rather than formal: the benchmark values are treated as exact numbers, but they are products of a selected-CI extrapolation, whose uncertainty is not reported. If that uncertainty is small, the claim stands; if it is comparable to the claimed errors, the quantitative headline is not established. The exception-statement inconsistency in Table IV is real and should be corrected, but it concerns the secondary molecular set rather than the primary H2O/CH4/BN comparison. For these reasons the existing CONDITIONAL verdict should be retained, with the condition being a quantitative uncertainty estimate for the Ref. 58 CIPSI benchmarks and a cleanup of the inconsistent exception statements.","tokens_in":14094,"tokens_out":11972,"duration_ms":115935,"concrete_test":"Bound the CIPSI reference uncertainty for the six vertical DIPs of H2O, CH4, and BN in the aug-cc-pVTZ basis by comparing the spread of the final two extrapolation points or two independent extrapolation schemes from Ref. 58. If that spread exceeds about 0.03 eV, the paper must quote it, and the 0.00–0.03 eV agreement cannot be taken as exact. A complementary settled check is to compute one representative state, e.g., (H2O)2+ X3B1, with an independent high-level method (FCI quantum Monte Carlo or MRCI+Q) using the same basis, geometry, and frozen-core convention and verify that the deviation from the DIP-EOMCCSDT(4h-2p) value remains below 0.03 eV.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on Table III, where DIP-EOMCCSDT(4h-2p) errors against extrapolated CIPSI references for H2O, CH4, and BN are reported as 0.00–0.03 eV. Those references are quoted to 0.01 eV with no uncertainties, although they are selected-CI extrapolations to the full-CI limit, not exact FCI numbers. The manuscript never bounds the extrapolation error. If the CIPSI uncertainty for these dication states is comparable to or larger than 0.03 eV, the 'tiny' errors are within reference noise and the near-benchmark-quality conclusion is not supported. This is load-bearing because every error discussion in Section 4 and the abstract uses the CIPSI table entries as exact. A secondary issue is an internal inconsistency in the exception statements for Table IV: the results text names the c1Sigma-u state of Cl2 and three HBr states as exceptions, while the summary names the c1Sigma-u state of Br2. This does not overturn the Table III headline but indicates that the broader 'improves results' claim needs a corrected, consistent statement. The explicit factorized equations and the open-source CCpy implementation are positive evidence; no internal algebraic inconsistency was identified in Eqs. (8)–(10).","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":14310,"tokens_out":5657,"duration_ms":47687,"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":[{"comment":"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.","section":"Table III / Results discussion"},{"comment":"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.","section":"Results paragraph on exceptions / Summary"}],"minor_comments":[{"comment":"The text contains the typo 'DIP-EOMCSCD(3h-1p)' where 'DIP-EOMCCSD(3h-1p)' is clearly intended.","section":"Page 4, text after Table III"},{"comment":"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.","section":"Page 3, sentence defining n_o and n_u"},{"comment":"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.","section":"Table III footnote e"},{"comment":"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.","section":"Table IV"}],"recommendation":"major_revision","confidential_remarks":"I recommend major revision rather than rejection. The formal derivations and the open-source implementation appear sound, and no algebraic inconsistency was identified in Eqs. (8)-(10). The required revisions are focused: quantify or qualify the CIPSI reference uncertainty, and repair the exception-state inconsistency in the Summary. These are within the scope of the manuscript and do not require new methodology."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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).\n\nWhat 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.\n\nOn 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.\n\nThe 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.\n\nThis 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.","headline":"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.","tokens_in":14878,"tokens_out":3722,"would_cite":true,"duration_ms":32764,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Adding triples to the neutral state fixes double-ionization energies to 0.03 eV.","keywords":["double ionization potential","equation-of-motion coupled cluster","4-hole–2-particle excitations","triple excitations","CCSDT","perturbative triples","CIPSI benchmark","vertical ionization energies"],"falsifier":"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.","tokens_in":13858,"feed_emoji":"⚛️","tokens_out":7548,"duration_ms":58650,"temperature":0.7,"pith_summary":"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.","feed_headline":"Coupled-cluster method hits 0.00–0.03 eV double-ionization errors","feed_subtitle":"Restoring triples in the neutral ground state removes the imbalance behind 0.17–0.67 eV errors.","key_machinery":"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 $n_o^3 n_u^5$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the extrapolated CIPSI near-full-CI DIP benchmarks for H2O, CH4, and BN against which all errors are measured.","marker":"[58]"},{"why":"Defines the DIP-EOMCCSD(4h-2p) predecessor and the size-intensivity condition that the new method extends.","marker":"[35, 36]"},{"why":"Introduces the DIP-EOMCCSDT framework with 3h-1p correlations that the new method augments with 4h-2p.","marker":"[31]"},{"why":"Provides the Møller-Plesset perturbative triples correction used to build the approximate DIP-EOMCCSD(T)(a)(4h-2p) variant.","marker":"[55]"},{"why":"Defines the aug-cc-pVTZ basis set in which the benchmark comparisons are made.","marker":"[56, 57]"},{"why":"Supplies the CC3/aug-cc-pVTZ equilibrium geometries used for H2O, CH4, and BN.","marker":"[67]"}],"fun_headline_variants":["Double ionization to 0.03 eV with full 4h-2p coupled-cluster","Coupled-cluster upgrade nails double-ionization potentials to 0.03 eV","New EOM-CC method squeezes double-ionization errors below 0.03 eV","Full triples and 4h-2p shrink double-ionization errors to near zero","DIP-EOMCC with 4h-2p and triples: 0.00–0.03 eV accuracy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Double ionization to 0.03 eV with full 4h-2p coupled-cluster","Coupled-cluster upgrade nails double-ionization potentials to 0.03 eV","New EOM-CC method squeezes double-ionization errors below 0.03 eV","Full triples and 4h-2p shrink double-ionization errors to near zero","DIP-EOMCC with 4h-2p and triples: 0.00–0.03 eV accuracy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000942,"raw_usage":{"total_tokens":4056,"prompt_tokens":1004,"completion_tokens":3052,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":620,"completion_tokens_details":{"reasoning_tokens":2929}},"tokens_in":620,"tokens_out":3052,"duration_ms":18927,"temperature":1.0,"reasoning_tokens":2929,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T15:42:51.469646+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Musia , author A","cited_arxiv_id":null,"evidence_quote":"Introduces the DIP-EOMCCSDT framework with 3h-1p correlations that the new method augments with 4h-2p."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Møller-Plesset perturbative triples correction used to build the approximate DIP-EOMCCSD(T)(a)(4h-2p) variant."},{"cited_title":"Marie \\ and\\ author P.-F","cited_arxiv_id":null,"evidence_quote":"Supplies the CC3/aug-cc-pVTZ equilibrium geometries used for H2O, CH4, and BN."}],"review_version":1}