{"id":"e4edf04f-5507-4aa0-841f-496826898e82","arxiv_id":"2411.11245","paper_version":2,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":4,"one_line_summary":"First excited-state application of active-orbital CC(t;3) and adaptive CC(P;Q) reproduces CCSDT/EOMCCSDT water potential cuts to within about 1-2 millihartree using 1-2% of triple excitations.","lead":"Scientists tested two cheaper coupled-cluster methods, CC(t;3) and adaptive CC(P;Q), on excited states of water breaking an O-H bond. The methods reproduce the expensive gold-standard CCSDT/EOMCCSDT potential curves within about one millihartree while using far fewer triple excitations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified; the water-benchmark claim is well supported, and the single-system limitation is acknowledged by the authors rather than a hidden flaw.","rationale":"The paper's central claim is specifically about water potential cuts, for which the evidence is strong and internally consistent. The reader's weakest_assumption concerns generalization of the moment-based adaptive selection beyond water/TZ, a limitation the authors explicitly acknowledge in Sec. 4; it does not undermine the demonstrated accuracy for the 12 water states. The only other caveat, missing wall-clock timings, affects the 'reduced cost' framing but not the accuracy benchmark. No load-bearing flaw was identified, so the verdict remains ACCEPT/UNCHANGED. A transferability check on a second system is the most informative next verification.","tokens_in":17864,"tokens_out":13093,"duration_ms":127025,"concrete_test":"Apply the adaptive CC(P;Q)[%T=2] algorithm to at least one additional small molecule with a challenging multi-reference excited state (e.g., CH+ or N2) in a double-zeta or TZ basis and compare against EOMCCSDT; if MUEs exceed about 2 mH, the transferability of the moment-based selection needs qualification.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that CC(t;3) and adaptive CC(P;Q) closely reproduce CCSDT/EOMCCSDT on the water O-H dissociation cuts is directly supported by Tables 2 and 3: all MUEs lie below 1 mH for CC(t;3) and adaptive CC(P;Q)[%T=2], with NPEs below 1.6 mH, and Table 1 confirms the CCSDT/EOMCCSDT parent is itself benchmarked against full CI. The adaptive selection heuristic (Eq. 4 moments) is validated only on this single molecule/basis, but the paper explicitly frames broader testing as future work. No internal inconsistency or unsupported numerical step was found. The absence of wall-clock timings weakens the 'reduced cost' phrasing but does not affect the accuracy claim, since the number of triples in the iterative P spaces is reported.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript extends the CC(P;Q) hierarchy to excited states by combining active-orbital-based CC(t;3) and adaptive CC(P;Q) with EOMCC, and benchmarks the resulting methods on the ground and 11 excited singlet/triplet A′/A′′ states of water along the O–H dissociation coordinate using the TZ basis. The parent CCSDT/EOMCCSDT potentials are first validated against full CI in Table 1 (MUEs 0.28–1.53 mH, NPEs 0.57–5.50 mH). The approximate methods are then compared with these parents in Tables 2 and 3, showing that CC(t;3) reproduces CCSDT/EOMCCSDT with MUEs below 1 mH and NPEs below 0.61 mH, while adaptive CC(P;Q) using 2% of triples in the iterative P spaces gives MUEs of 0.197–0.993 mH and NPEs of 0.133–1.572 mH, and both methods improve on CR-CC(2,3)/CR-EOMCC(2,3) in strongly stretched regions. The paper is framed as a single-molecule benchmark, with broader testing explicitly deferred to future work in Sec. 4.","tokens_in":18057,"tokens_out":6643,"duration_ms":67756,"significance":"The significance is incremental but real: it demonstrates that the adaptive, orbital-free variant of CC(P;Q), previously tested mainly on ground states, extends successfully to excited states, including states with strong multireference character such as 23A′′ and 33A′′ where CR-EOMCC(2,3) fails badly. Strengths of the paper include the deterministic and complete set of 12 states, the external full-CI grounding of the parent CCSDT/EOMCCSDT data, the clear reporting of MUE/NPE statistics with no post-hoc state exclusions, and the availability of total energies in Supplementary Data and of the CCpy code on GitHub. The main limitation—validation on a single molecule and one basis set—is acknowledged by the authors in Sec. 4 and does not undermine the stated water-benchmark claim.","major_comments":[],"minor_comments":[{"comment":"The abstract and Sec. 3.3 state that the adaptive calculations offer significantly reduced computational costs, but the manuscript reports only the fraction of triples in the iterative P spaces (1–2% versus the full CCSDT/EOMCCSDT triple manifolds), not wall-clock timings or operation counts for the excited-state implementation; since the noniterative Q-space correction still spans the remaining triples, a few timing data or an explicit complexity statement would make the cost claim easier to verify.","section":"Abstract and Sec. 3.3"},{"comment":"The adaptive algorithm parameters (1% growth rate and %T = 1 and 2% final spaces) are stated, but it is not specified whether %T refers to the final converged fraction after the growth process or to a target fraction imposed at each recursion step; a one-sentence definition would improve reproducibility.","section":"Sec. 3.1"},{"comment":"The manuscript does not describe how the individual EOMCC(P) roots are tracked through avoided crossings when constructing the state-specific P spaces; because the reported MUE/NPE values require consistent state labels along ROH, a sentence on root assignment would strengthen the comparisons.","section":"Sec. 3.1 and Fig. 1"},{"comment":"The footnotes define the active space for CCSDt/CC(t;3) only as the three highest occupied and two lowest unoccupied RHF orbitals; specifying whether this selection is by RHF orbital energy and collecting the symmetry labels already given in Sec. 3.1 in a single place would make the tables more self-contained.","section":"Tables 2 and 3"}],"recommendation":"minor_revision","confidential_remarks":"The paper is a good fit for Chemical Physics Letters. The single-system benchmark is narrow, but the title and conclusions are appropriately scoped, and the authors are transparent about the need for tests on other systems and larger basis sets."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know upfront. The paper does what it says: it is the first test of active-orbital CC(t;3) and the adaptive CC(P;Q) algorithm on excited states, and on the water O-H dissociation benchmark both closely follow CCSDT/EOMCCSDT. The 2% triple adaptive variant gives MUEs of 0.2-0.99 mH and NPEs up to 1.57 mH across all 12 states, which fixes the dramatic CR-EOMCC(2,3) failures on the 2 3A'' and 3 3A'' curves. That is a genuine practical result.\n\nWhat is well done: the parent CCSDT/EOMCCSDT data are benchmarked against full CI in Table 1, so the target is credible. The MUE/NPE tables are complete—no state exclusions, no post-hoc selection. The comparison with CR-EOMCC(2,3) is direct and the improvement is unambiguous. The authors also report the fraction of triples used (about 38% for CC(t;3), only 2% for adaptive), which is the relevant cost measure in the absence of wall-clock timings. The absence of explicit timings is a minor weakness, but the triple-count argument is enough to support the cost claim.\n\nSoft spots, in proportion. The benchmark is one molecule, one basis (water, TZ). The adaptive selection heuristic—using the moment contributions of Eq. (4) to pick the leading triples—is validated only on this system. The authors state this explicitly as future work, so it is not hidden. CC(t;3) requires a user-chosen active space, so it is not black-box; the adaptive variant is the one that claims black-box behavior. Both caveats are real but do not undermine the water results.\n\nOne more thing: the literature placement is fair. The paper cites its own prior CC(P;Q) work heavily, but that is appropriate because the methods are direct extensions. The novelty claim is accurate—earlier work tested only the semi-stochastic variant on excited states.\n\nWho should read this: anyone developing or applying cost-reduced CC methods for excited-state surfaces. It is a solid contribution for a specialized journal like Chemical Physics Letters. I would send it to peer review rather than desk reject. My own verdict is close to accept; the only thing I would ask for in revision is a brief statement about what could break the adaptive heuristic (e.g., a test with a larger basis or a different molecule), which they already gesture at.","headline":"A solid, well-benchmarked extension of CC(P;Q) to excited states; the accuracy on water holds, and the open question is transferability, not correctness.","tokens_in":18626,"tokens_out":1858,"would_cite":true,"duration_ms":17462,"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":"This paper shows that active-orbital and adaptive CC(P;Q) methods reproduce CCSDT/EOMCCSDT ground- and excited-state water potential cuts along O–H bond breaking.","keywords":["coupled-cluster theory","equation-of-motion coupled-cluster","CC(P;Q) methodology","CC(t;3)","adaptive selection of triples","excited states","potential energy surface","water dissociation"],"falsifier":"Run the adaptive CC(P;Q)[%T=2] protocol on a different stretched-bond system, such as ozone or N2, using a basis larger than TZ, and compare the resulting ground- and excited-state potentials against CCSDT/EOMCCSDT or full CI; if the mean unsigned error exceeds roughly 1–2 mH, or if more than 2% of triples is needed to remove the qualitative failures of CR-EOMCC(2,3), the selection assumption is falsified for that case.","tokens_in":17645,"feed_emoji":"⚛️","tokens_out":7962,"duration_ms":66574,"temperature":0.7,"pith_summary":"This paper is a first test of two cost-saving coupled-cluster strategies—active-orbital-based CC(t;3) and adaptive CC(P;Q)—on excited electronic states. The test case is water breaking one O–H bond, for which full CCSDT/EOMCCSDT potential cuts are known to be nearly exact. The paper shows that both methods reproduce those CCSDT/EOMCCSDT curves for 12 singlet and triplet states with mean unsigned errors of about 0.2–1.0 millihartree, while putting only a small fraction of the triple excitations into the iterative calculation. A sympathetic reader should care because excited-state potential surfaces at this accuracy normally cost far more, and the adaptive variant needs no user-chosen active orbitals.","feed_headline":"2% of triples reproduces full CCSDT across 12 water states","feed_subtitle":"Active-orbital and adaptive CC(P;Q) match full-triples energetics at a fraction of the cost.","key_machinery":"The object that carries the argument is the CC(P;Q) energy correction $\\delta_\\mu(P;Q)=\\sum_{|\\Phi_K\\rangle\\in\\mathcal H^{(Q)}} \\ell_{\\mu,K}(P) M_{\\mu,K}(P)$, in which the Hilbert space is split into an iterative P space and a noniterative Q space. $M_{\\mu,K}(P)$ are the generalized moments of the CC/EOMCC equations projected on Q-space determinants, and $\\ell_{\\mu,K}(P)$ are coefficients built from the left bra states with Epstein–Nesbet denominators. CC(t;3) chooses the P-space triples by active orbitals (here the three highest occupied and two lowest unoccupied RHF orbitals), while adaptive CC(P;Q) selects the leading 1–2% of triples by the size of their $\\ell_{\\mu,K}M_{\\mu,K}$ contributions, with no active-space input; the leftover Q-space triples enter through $\\delta_\\mu(P;Q)$. The method's power is that a tiny, selected subset of triples is treated iteratively and the rest perturbatively, so the expensive $N^8$ triple step of full CCSDT/EOMCCSDT is avoided.","core_discovery":"The central claim is that the CC(P;Q) moment-expansion hierarchy, in both its active-orbital CC(t;3) form and its black-box adaptive form, can converge ground- and excited-state potential cuts of water along the O–H dissociation coordinate to the parent CCSDT/EOMCCSDT results. Relative to CCSDT/EOMCCSDT, CC(t;3) has MUEs between 0.166 and 0.951 mH over 12 states, and adaptive CC(P;Q) with only 2% of the triples in the P space has MUEs between 0.197 and 0.993 mH and NPEs between 0.133 and 1.572 mH. The improvement is most dramatic for the 2 3A″ and 3 3A″ states, where the earlier CR-EOMCC(2,3) corrections produce errors of 13 and 42 mH in NPE and a spurious bump in the 3 3A″ curve; CC(t;3) removes the bump and reduces these NPEs to 0.255 and 0.608 mH. The paper also establishes that CCSDT/EOMCCSDT itself is an excellent benchmark here, with MUEs below 1.6 mH relative to full CI for all 12 states. This is the first use of these two CC(P;Q) variants for excited electronic states.","pith_inferences":["The 38%-vs-2% comparison implies that moment-based adaptive selection is more efficient than the active-space heuristic: the same accuracy is reached with far fewer iterative triples, so chemical-intuition active spaces may be over-inclusive.","The selection heuristic is not yet established for other molecules; a direct test would run the same 2% adaptive protocol on another multireference bond-breaking case, such as ozone or stretched N2, against CCSDT/EOMCCSDT or full CI.","If the heuristic transfers, this recipe could become a practical default for photochemical and spectroscopic studies, where many excited-state curves are needed and full CCSDT is feasible only for small molecules.","The remaining roughly 0.2 mH floor in the adaptive results suggests a possible refinement: using higher-rank moments or a second adaptive pass on the Q space to reduce that floor without admitting more triples into the iterative P space."],"forward_implications":["Excited-state potential surfaces of near-EOMCCSDT quality become practical in the stretched-bond regions where EOMCCSD and CR-EOMCC(2,3) fail, because the leading triples enter the iterative wave function rather than only a correction.","The adaptive variant removes the need for an active-orbital choice, so the method can be applied as a black-box approximation to systems where full triples are too costly.","The largest CR-EOMCC(2,3) failures on water, the 2 3A″ and 3 3A″ curves, are repaired: their errors relative to EOMCCSDT drop from tens of millihartree to below one millihartree in CC(t;3) and to below one millihartree in most adaptive 2% calculations.","Only about 300 triply excited determinants per symmetry (2% of the total) suffice in this system to bring the MUE below about 1 mH, indicating the iterative cost can be far below the roughly 31,000 triples used by full EOMCCSDT.","Because CCSDT/EOMCCSDT is shown to be within about 1.6 mH of full CI for all 12 states, these low-cost approximations inherit a near-exact description of the same curves."],"supporting_citations":[{"why":"Supplies the 11 nuclear geometries, the TZ basis set, and the full CI and MRCC benchmark potentials used to validate CCSDT/EOMCCSDT as the reference.","marker":"[16]"},{"why":"Provides the earlier CR-CC(2,3)/CR-EOMCC(2,3) water potential cuts and full CI data that this work extends and improves on.","marker":"[13]"},{"why":"Defines the CC(P;Q) moment-expansion framework and the completely renormalized CC/EOMCC equations used throughout.","marker":"[29]"},{"why":"Introduces the active-orbital CC(t;3) method that corrects CCSDt/EOMCCSDt energies with moment expansions.","marker":"[36]"},{"why":"Introduces the adaptive CC(P;Q) algorithm that selects leading triples by their moment contributions without active orbitals.","marker":"[40]"},{"why":"Earlier semi-stochastic CC(P;Q) study of excited states that provides the precedent and benchmark for the present extension.","marker":"[37]"},{"why":"Defines the EOMCCSDt iterative excited-state method used as the P-space step in CC(t;3).","marker":"[11]"}],"fun_headline_variants":["CC(P;Q) matches full CCSDT for water states at low cost","First excited-state CC(P;Q): accurate water cuts, fewer triples","Adaptive CC(t;3) reproduces CCSDT on water potentials","Water O-H cuts: CC(P;Q) does CCSDT for 2% triples"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The weakest link is the assumption that a very small set of triple excitations, chosen by active orbitals or by moment-size ranking, captures almost all of the correlation that a full triples treatment would add; this has been demonstrated for one molecule, one basis set, and one active-space choice.","fun_headline_variants_meta":{"raw":{"variants":["CC(P;Q) matches full CCSDT for water states at low cost","First excited-state CC(P;Q): accurate water cuts, fewer triples","Adaptive CC(t;3) reproduces CCSDT on water potentials","Water O-H cuts: CC(P;Q) does CCSDT for 2% triples"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000256,"raw_usage":{"total_tokens":1610,"prompt_tokens":1016,"completion_tokens":594,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":632,"completion_tokens_details":{"reasoning_tokens":508}},"tokens_in":632,"tokens_out":594,"duration_ms":6434,"temperature":1.0,"reasoning_tokens":508,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T18:44:45.121251+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the adaptive CC(P;Q)[%T=2] protocol on a different stretched-bond system, such as ozone or N2, using a basis larger than TZ, and compare the resulting ground- and excited-state potentials against CCSDT/EOMCCSDT or full CI; if the mean unsigned error exceeds roughly 1–2 mH, or if more than 2% of triples is needed to remove the qualitative failures of CR-EOMCC(2,3), the selection assumption is falsified for that case.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the 11 nuclear geometries, the TZ basis set, and the full CI and MRCC benchmark potentials used to validate CCSDT/EOMCCSDT as the reference."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the earlier CR-CC(2,3)/CR-EOMCC(2,3) water potential cuts and full CI data that this work extends and improves on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the active-orbital CC(t;3) method that corrects CCSDt/EOMCCSDt energies with moment expansions."},{"cited_title":"Gururangan, P","cited_arxiv_id":null,"evidence_quote":"Introduces the adaptive CC(P;Q) algorithm that selects leading triples by their moment contributions without active orbitals."}],"review_version":1}