{"id":"23ffcb40-4684-4183-8dd1-dbfaf274c911","arxiv_id":"2505.17299","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Nesting a small coupled cluster treatment inside a new Aufbau suppressed second-order perturbation theory reproduces about 0.1 eV charge transfer excitation accuracy at non-iterative N^5 plus iterative N^3 cost.","lead":"This paper derives a faster quantum chemistry method for charge transfer excitations, cutting formal cost from N^6 to non-iterative N^5 plus iterative N^3 while keeping errors near 0.1 eV. The approach enables accurate excited-state calculations on medium and large molecules in realistic environments, which matters for photovoltaics, photocatalysis, and photobiology.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The O(1) flagged-orbital premise is the load-bearing assumption; it is tested only on localized excitations and a saturated-bridge CT system, so the advertised cost scaling for delocalized CT and extended environments is not yet supported.","rationale":"Central claim has two legs: accuracy maintained and cost reduced. The accuracy leg is supported by benchmark comparisons and is honestly hedged (non-converged states flagged, threshold dependence in SI). The cost leg is where the argument is most exposed. The formal O(1)-active-space argument is internally plausible, and the delivered scaling measurements in Fig. 5 are consistent with it for the tested systems. But the generality of the premise is established only by three examples, one of which (Fig. 4C) shows the desired saturation on a saturated alkane bridge. Delocalized CT through a conjugated bridge is a common and chemically relevant class, and it is exactly the case where the number of orbitals 'strongly affected' may scale with system size. A failure there would not falsify the method for local excitations, but it would falsify the abstract's unqualified cost/scaling claim. The proposed test directly measures the active-set count as a function of system size for that class. Since the reader's weakest-assumption analysis already identified this premise, my stress-test agrees with the reader; the concern sharpens but does not overturn the conditional verdict, so I recommend no change.","tokens_in":20654,"tokens_out":5491,"duration_ms":72454,"concrete_test":"Repeat the Fig. 4C scaling experiment on a homologous donor-bridge-acceptor series with conjugated bridges (e.g., donor-(C≡C)n-acceptor or oligo-p-phenylene, n=1,2,4,8) in cc-pVDZ, using the same 0.005 eV nesting threshold and identical convergence criteria. Count the occupied and virtual orbitals flagged for CC refinement and fit the count versus bridge length; also record whether all states converge. If the flagged count grows linearly (or superlinearly) with n rather than saturating, the O(N^3) iterative cost claim fails for delocalized through-bridge CT, and the central cost claim must be restricted to localized CT cases.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central cost claim—non-iterative N^5 plus iterative N^3—depends on the assertion, made in the main text just before the nesting construction, that 'the number of individual orbitals that are directly involved in or strongly affected by the excitation is not likely to grow with system size.' This is the pivot on which both ingredients of the headline result rest: if the PT correlation analysis flags a growing number of orbitals, the nested CC active space grows, the O(1) residual argument collapses, and the iterative cost rises toward the full ASCC scaling. The evidence for the premise consists of three large-system examples. The only CT scaling test, the donor-bridge-acceptor chain in Fig. 4C, uses a saturated alkane bridge and shows saturation of the flagged set after three carbons; that is a favorable but narrow test. A conjugated bridge, a CT state delocalized over an extended chromophore, or a solvent response that polarizes many distant waters could behave differently. The screening is performed with a PT whose CT errors are ~0.5 eV, so the flagging criterion is itself built on a theory that misses a substantial part of the relaxation effect it is trying to localize; false negatives would silently degrade the accuracy claim. This is a generalization risk, not a demonstrated internal inconsistency, and the paper's own SI limitation statements are consistent with it.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces a second-order Aufbau-suppressed perturbation theory (PT) derived from ASCC and uses its correlation contributions to identify orbitals that are strongly affected by an excitation. A small ASCC/PLASCC calculation is then nested inside the PT, with all other amplitudes frozen at the PT level. The authors report that on 130 QUEST valence/Rydberg states and 16 CT states, nested PLASCC matches full PLASCC accuracy (CT mean unsigned error near 0.1 eV, 0.25 eV better than EOM-CCSD), with formal cost reduced to non-iterative O(N^5) plus iterative O(N^3). Three larger tests (thiopropynal chains, solvated acetone, donor-bridge-acceptor) demonstrate physically intuitive orbital selection and wall-time scaling in an initial implementation.","tokens_in":20750,"tokens_out":6223,"duration_ms":47895,"significance":"If the cost and accuracy claims hold, this is a valuable step toward practical high-accuracy CT calculations with explicit environments: it preserves ASCC's orbital-relaxation capabilities while removing the iterative N^6 bottleneck. The benchmark references are independent (EOM-CCSDT/LR-CC3), the SI reports sensitivity to the nesting threshold, and the large-system tests are genuinely challenging. The main reservations concern the empirical basis for the O(1) flagged-orbital premise, the post-hoc threshold choice, and the undisclosed count of excluded states; these are load-bearing for the central scaling and accuracy claims.","major_comments":[{"comment":"The iterative O(N^3) cost claim is derived under the premise stated just before the nesting construction: 'the number of individual orbitals that are directly involved in or strongly affected by the excitation is not likely to grow with system size.' This premise is load-bearing: if the PT correlation screening flags a growing fraction of orbitals as system size increases, the nested CC active space grows, the O(1) residual argument collapses, and the iterative cost rises toward the full ASCCSD scaling. The evidence in Fig. 4 consists of only three large systems, and the only CT scaling test (Fig. 4C) uses a saturated alkane bridge that shows saturation of the flagged set after three carbons; conjugated bridges, delocalized CT states, or many explicitly correlated solvent molecules could behave differently. The authors should either prove a bound on the flagged set for a broader class of excitations or present scaling tests over a conjugated-bridge length series and over increasing solvent-shell size; without this, the advertised non-iterative N^5/iterative N^3 scaling is not yet supported for the full CT/environment domain claimed in the abstract.","section":"Main text, section introducing nesting; Fig. 4 and Fig. 5"},{"comment":"The 0.005 eV nesting threshold used for all main-text benchmark statistics was selected after examining the QUEST benchmark results (SI S4, Fig. S2). Because the same 130-state set is then used to report the accuracy improvements, the reported MUEs are in-sample estimates with no independent validation; the choice of threshold is a form of model selection on the evaluation set. The authors should report the selection procedure explicitly and provide either a held-out validation set or cross-validated accuracy, or at least quantify the sensitivity of the CT-state statistics separately from the QUEST statistics, to establish that the headline accuracy is not an artifact of threshold tuning.","section":"SI S4, Fig. S2; Computational Methods paragraph on thresholds"},{"comment":"The benchmark handling of non-converged states is not fully disclosed in the main text. SI S4 states that states were entirely removed if neither of the two ASCC solutions converged, and that some states are included with only one converged solution or with energies that stalled near the convergence criterion. The number and identity of removed states are not given, so it is impossible to assess whether the reported MUEs are biased by excluding difficult CT or valence cases. The authors should list all removed/reduced states, state how many there are per method, and show that the main conclusions are unchanged when including the stalled states or applying an alternative convergence criterion.","section":"SI S4"},{"comment":"The orbital flagging is based on PT correlation measures, yet the PT itself is substantially inaccurate for the target class: the text reports PT errors of ~0.5 eV for CT states and >1 eV outliers for aromatic valence states. If the PT misassigns correlation differences, it can silently fail to flag orbitals that genuinely need CC treatment, and the nested method would inherit PT-level errors without any diagnostic. The paper currently provides no validation that the PT-selected orbital set coincides with the set that a full-CC sensitivity analysis would identify, e.g., by comparing flagged orbitals against those selected by comparing full ASCCSD amplitudes or by testing a case where PT is known to have a large error. A concrete diagnostic of flagging reliability would make the accuracy claim robust.","section":"Main text, paragraph introducing nesting; Figs. 1 and 2"}],"minor_comments":[{"comment":"The phrase 'typically below 0.1 eV on average' is imprecise; the underlying statistic is the mean unsigned error, so the wording should say, for example, 'a mean unsigned error below 0.1 eV'.","section":"Abstract"},{"comment":"The legend text runs together ('EOM-CCSDTDDFT/ωB97X-DNested PLASCC3') and the y-axis label in panel (b) is printed as 'potential energy (kcal/mol)excitation energy error (eV)' with no separator; these need typesetting fixes.","section":"Figure 3"},{"comment":"The statement that 'for all but two states, nested PLASCC closely maintains PLASCC's accuracy' should identify which two states and report their errors, since outliers are important for a benchmark claim.","section":"Results and discussion, CT benchmark paragraph"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is well within the journal's scope and the central idea is promising. The main risks are that the benchmark accuracy may be inflated by post-hoc threshold selection and by silent exclusion of non-converged states, and that the O(1) flagged-orbital premise underpinning the scaling claim is tested only on favorable examples. These issues are addressable within the manuscript's scope, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, this is a real method development paper: the Aufbau suppressed second-order PT is newly derived from the ASCC equations, and the nesting idea (use PT to flag strongly affected orbitals, then refine only those with CC) is new, with a careful cost analysis and formal properties for the screening. Second, the central accuracy claim holds up on the benchmarks. On 130 QUEST states and 16 CT states against EOM-CCSDT/LR-CC3 references, nested PLASCC keeps errors around 0.1–0.15 eV and beats EOM-CCSD by 0.25 eV on CT. The cost reduction from iterative N^6 to non-iterative N^5 plus iterative N^3 is plausible and is supported by wall-time fits on the alkane chain test.\n\nThe load-bearing assumption is that only O(1) orbitals are strongly affected by any given excitation, so the CC-refined set does not grow with system size. The evidence is three large-system tests, and the only CT scaling test uses a saturated alkane bridge that saturates after three carbons. A conjugated bridge, a delocalized CT state, or an extended solvent response could flag a growing number of orbitals. The screening is also done with a PT whose CT errors are roughly 0.5 eV, so it may miss orbitals that a better theory would flag. These are generalization risks, not demonstrated failures.\n\nMinor issues: the 0.005 eV nesting threshold was chosen after seeing benchmark results (SI S4, Figure S2), though the sensitivity is disclosed; non-converged states were excluded from the statistics; the abstract's “typically below 0.1 eV” is a bit optimistic relative to the 0.25 eV improvement figure; and no code or implementation artifact is released. None of these contradict the central claim, and the paper's own limitation statements align with my read.\n\nWho is this for? Practitioners needing correlated-level CT excitation energies for 100-atom systems with explicit environments, and method developers interested in state-specific perturbation theories. It deserves a serious referee: the derivation is checkable, the benchmarks are against independent references, and the generalization risk is clearly framed rather than hidden. I would accept it for peer review and would probably cite it in my own work.","headline":"Solid new excited-state method that delivers on its accuracy claims, with the O(1) flagged-orbital premise being the main generalization risk to watch.","tokens_in":21466,"tokens_out":1874,"would_cite":true,"duration_ms":20997,"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 establishes that nesting a small coupled cluster treatment inside a newly derived Aufbau-suppressed second-order perturbation theory matches the accuracy of full Aufbau-suppressed coupled cluster for charge transfer excitations…","keywords":["charge transfer excitations","Aufbau suppressed coupled cluster","excited-state perturbation theory","nested coupled cluster","orbital relaxation","excitation energies","size consistency","EOM-CCSD comparison"],"falsifier":"Take a donor-bridge-acceptor molecule with a conjugated bridge and increase the bridge length while recomputing which orbitals the 0.005 eV correlation analysis flags for CC refinement; if the flagged orbital count grows with bridge length, or if the measured wall-time exponent for the iterative step grows from 3 toward 6, the central locality premise fails.","tokens_in":20277,"feed_emoji":"⚛️","tokens_out":9969,"duration_ms":78752,"temperature":0.7,"pith_summary":"This paper shows that charge-transfer excitation energies, which require both orbital relaxation and electron correlation, can be computed accurately without paying the full coupled-cluster cost. The authors derive an excited-state-specific second-order perturbation theory whose bottleneck is a non-iterative $N^{5}$ integral transformation, then nest a small Aufbau-suppressed coupled cluster (ASCC/PLASCC) calculation inside it, keeping the coupled-cluster treatment only for orbitals whose correlation is strongly affected by the excitation. On 130 valence and Rydberg states and 16 charge-transfer states, the nested method keeps typical errors below 0.1 eV and beats $N^{6}$-cost EOM-CCSD by an average of 0.25 eV for charge transfer. Because the refined orbital set is assumed to stay fixed in size as the molecule grows, the formal cost becomes non-iterative $N^{5}$ plus iterative $N^{3}$, which the authors demonstrate is enough to handle roughly 100-atom systems with explicit solvent on a single compute node.","feed_headline":"Nested trick cuts charge-transfer cost from N^6 to N^5","feed_subtitle":"A small coupled cluster nested in cheap perturbation theory keeps ~0.1 eV CT accuracy and reaches 100-atom systems.","key_machinery":"The load-bearing object is the nested ASCC/PT construction. Aufbau suppressed coupled cluster is a state-specific coupled cluster method whose exponential ansatz includes a deexcitation operator that builds post-excitation orbital relaxation into the reference. The new Aufbau-suppressed second-order perturbation theory mirrors MP2: it uses a block-diagonal zeroth-order Hamiltonian that singles out the primary hole and particle orbitals, so the coupled amplitude equations form small blocks (at most six equations for single-CSF states) and can be solved non-iteratively at O($N^{4}$), with the O($N^{5}$) integral transformation as the bottleneck. A Foster-Boys localization and orbital-matching step places ground and excited orbitals in a common local basis, and per-orbital correlation differences flag the orbitals whose correlation is strongly changed by the excitation. The iterative part of the calculation then updates only those O(1) amplitudes, which, by the connectedness of the coupled-cluster equations, keeps the iterative cost at O($N^{3}$), followed by one whole-system energy evaluation at O($N^{4}$).","core_discovery":"The paper's central claim is that the accuracy of Aufbau suppressed coupled cluster for charge-transfer excitations does not require a full-system coupled-cluster treatment: a low-order perturbation theory can decide where the coupled-cluster refinement is needed. The new perturbation theory is derived from ASCC by order analysis, with a zeroth-order Hamiltonian that keeps the amplitude equations small-block block-diagonal and non-iteratively solvable. After localizing and matching ground and excited orbitals, per-orbital correlation measures built from the PT amplitudes identify the few orbitals whose correlation changes most under the excitation. Solving the coupled-cluster residual equations only for those flagged amplitudes, freezing the rest at their PT values, and performing one final whole-system energy evaluation preserves the parent method's ~0.1 eV accuracy, improves on full ASCC in some valence and Rydberg cases, and matches CC3-quality behavior on a hydrogen-bonding charge-transfer surface. The result is a method that is more accurate than EOM-CCSD on charge transfer by 0.25 eV while having a dramatically lower asymptotic cost.","pith_inferences":["Beyond the paper's tests, the same nesting pattern should transfer to core-excitation spectroscopy, where orbital relaxation is even stronger and system-size limits are severe.","The 0.005 eV screening threshold is an accuracy-cost dial; an adaptive threshold tied to the magnitude of the PT correlation correction would likely make the method more robust across different basis sets and state characters.","The per-orbital correlation-difference map could serve as a black-box diagnostic that reports where a given excitation changes electron correlation, useful not only for screening but for interpreting charge-transfer character.","Combining the nesting idea with local correlation or pair-natural-orbital techniques would likely cut the O(N^5) integral-transform prefactor and reduce memory further, extending the method to even larger systems."],"forward_implications":["Charge-transfer excitation energies in systems with around 100 atoms and explicit solvent can be computed on a single node with typical errors below 0.1 eV, a regime previously requiring much more expensive EOM-CCSD-level calculations.","Nested PLASCC produces excited-state potential energy surfaces for hydrogen-bonded charge-transfer systems within about 1 kcal/mol of CC3, while preserving the correct state character where EOM-CCSD and TD-DFT mix in spurious Rydberg character.","The orbital-selection procedure is automatic and physically interpretable: it flags donor and acceptor regions for charge transfer and hydrogen-bond-perturbed waters for solvated excitations, without user input about where the excitation is located.","Freezing the PT amplitudes preserves size consistency, extensivity, and intensivity, so the nested method can be applied to larger systems without introducing size-dependent errors.","The same nesting pattern should extend to higher-order non-iterative corrections to the ASCC energy, potentially improving accuracy further without returning to iterative N^6 cost."],"supporting_citations":[{"why":"Introduces Aufbau suppressed coupled cluster and its exponential deexcitation ansatz, the parent theory whose accuracy the nested method must preserve.","marker":"[20]"},{"why":"Introduces PLASCC and the perturbative analysis of ASCC that motivates the new second-order PT; establishes the ~0.1 eV accuracy baseline and the N^6 cost bottleneck.","marker":"[21]"},{"why":"Supplies the standard derivation of MP2 from CCSD by perturbative order, the template for deriving the Aufbau-suppressed PT.","marker":"[23]"},{"why":"Provides the benchmark of intermolecular charge-transfer states used to measure CT excitation energy errors.","marker":"[14]"},{"why":"Provides the QUEST reference excitation energies of at least EOM-CCSDT quality used for the 130 valence and Rydberg states.","marker":"[32,33]"},{"why":"Supplies reference energies for the intramolecular long-range CT states in the CT test set.","marker":"[34]"},{"why":"Supplies the Foster-Boys localization used to match ground and excited orbitals before the correlation analysis.","marker":"[37]"},{"why":"Supplies the excited state mean field method used to build the orbital-relaxed excited-state reference on which the PT and ASCC calculations stand.","marker":"[60]"},{"why":"Provides the displacement geometries for the water/hydrogen-bond CT surface used to show nested PLASCC's potential-energy-surface accuracy against CC3.","marker":"[52]"}],"fun_headline_variants":["Nested Aufbau trick cuts charge-transfer cost to N^5","Charge-transfer accuracy at N^5 cost via nested ASCC","0.1 eV CT errors with N^5 cost: nested ASCC trick","Fast CT excitations: nested CC in PT, N^5 scaling"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central assumption is that the number of orbitals whose correlation is strongly changed by a given excitation stays roughly constant as the molecule grows, so the coupled-cluster-refined orbital set does not scale with system size.","fun_headline_variants_meta":{"raw":{"variants":["Nested Aufbau trick cuts charge-transfer cost to N^5","Charge-transfer accuracy at N^5 cost via nested ASCC","0.1 eV CT errors with N^5 cost: nested ASCC trick","Fast CT excitations: nested CC in PT, N^5 scaling"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000235,"raw_usage":{"total_tokens":1495,"prompt_tokens":936,"completion_tokens":559,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":552,"completion_tokens_details":{"reasoning_tokens":481}},"tokens_in":552,"tokens_out":559,"duration_ms":5231,"temperature":1.0,"reasoning_tokens":481,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:49:22.791376+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a donor-bridge-acceptor molecule with a conjugated bridge and increase the bridge length while recomputing which orbitals the 0.005 eV correlation analysis flags for CC refinement; if the flagged orbital count grows with bridge length, or if the measured wall-time exponent for the iterative step grows from 3 toward 6, the central locality premise fails.","supporting_citations":[],"review_version":1}