{"id":"77bf06e4-ff25-4ac3-8003-6daeffd798a5","arxiv_id":"2506.02201","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"The NEO-MRCI method reproduces fixed-geometry hydrogen and deuterium tunneling splittings for four test systems, though the agreement with the reference degrades at extended donor-acceptor distances.","lead":"This paper tests a new quantum chemistry method, NEO-MRCI, for computing hydrogen tunneling splittings in four small molecules and compares the results to a numerically exact grid calculation. The method gives tunneling splittings that agree with the reference for some systems and distances, but errors grow to tens of percent at larger donor-acceptor separations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Protonic basis set convergence is not established for OCHCO+ and malonaldehyde; reported 'quantitative' agreement may be fortuitous.","rationale":"The reader's verdict identifies the CCSD-optimized basis center placement as the weakest assumption. While that is a legitimate unvalidated protocol choice, the paper's own data point to a more immediate and falsifiable problem: the protonic basis set used for OCHCO+ and malonaldehyde is not demonstrated to be converged. Tables S3 and S4 show large differences between the 8s8p8d and 5s5p5d5f basis sets for these exact systems, yet the main text uses the smaller 5s5p5d5f basis and claims quantitative agreement. The convergence evidence provided (Table S5) is only for HeHHe+, and the FHF- data (Table S6) show that f functions change splittings by ~15%, so 8s8p8d is not a reliable proxy. This is load-bearing because the central claim is about accuracy; if the reported splittings are not converged with respect to the protonic basis, the agreement could be fortuitous and the method's predictive value is unestablished. The proposed test directly settles whether the basis is converged. If the test shows large shifts, the paper should either compute with larger basis sets or restrict its claims to converged systems; either way the verdict remains conditional pending this evidence.","tokens_in":15894,"tokens_out":10389,"duration_ms":85147,"concrete_test":"For OCHCO+ at C-C = 3.06 Å and malonaldehyde at O-O = 2.62 Å, recompute the NEO-MR-SD enCI tunneling splitting using the 8s8p8d8f protonic basis set (and ideally a 5s5p5d5f5g basis as well) with the same active space and electronic basis. Compare the resulting splittings to the 5s5p5d5f values and to the FGH benchmarks. If either splitting shifts by more than ~15% relative to the 5s5p5d5f value, the reported agreement is not basis-set converged and the central claim must be revised to exclude those systems or to use larger basis sets.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim that NEO-MRCI yields accurate tunneling splittings at fixed geometries is supported for OCHCO+ and malonaldehyde only with the 5s5p5d5f protonic basis, justified by a convergence test on HeHHe+ (Table S5). The paper's own SI data show that this basis is not converged for these systems. Table S3 (OCHCO+) lists 8s8p8d and 5s5p5d5f values that differ by 15-45% across the C-C range (e.g., at 2.90 Å: 196.4 vs 229.2 cm-1 vs FGH 224.3; at 3.10 Å: 3.9 vs 7.1 cm-1 vs FGH 5.6). Table S4 (malonaldehyde) shows 8s8p8d and 5s5p5d5f differ by ~35-50% (at 2.62 Å: 5.4 vs 10.3 cm-1 vs FGH 8.4). The paper does not report the 8s8p8d8f basis used for HeHHe+ and FHF- for these systems. Thus the favorable agreement of the 5s5p5d5f results with FGH at several distances is not demonstrably a property of the NEO-MRCI method rather than an artifact of basis incompleteness, and the 20-50% relative errors at extended distances may be dominated by this incompleteness.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper applies the recently developed NEO-MRCI method, specifically the NEO-MR-SD enCI variant, to compute hydrogen and deuterium tunneling splittings at fixed geometries for four systems: HeHHe+, FHF-, OCHCO+, and malonaldehyde. The results are benchmarked against three-dimensional Fourier Grid Hamiltonian (FGH) calculations whose potential energy surfaces are generated at the CCSD level. The authors report good qualitative agreement for the distance dependence of the splittings and conclude that NEO-MRCI can produce accurate tunneling splittings at fixed geometries, positioning the method as a parameter-free multicomponent wavefunction approach for tunneling problems.","tokens_in":16196,"tokens_out":5752,"duration_ms":48222,"significance":"If the central claim is upheld, NEO-MRCI would be a valuable addition to the toolbox for hydrogen tunneling because it treats the transferring proton and electrons on the same footing without a Born-Oppenheimer separation and does not rely on empirically fitted parameters. The paper provides a substantial amount of numerical data, including explicit coordinates, basis-set convergence tables, and timings, which is commendable for reproducibility. However, the reported agreement with the FGH reference is less quantitative than claimed in several cases, and the convergence of the protonic basis for two of the four systems is not demonstrated. These issues currently limit the strength of the conclusions, though they appear addressable with additional calculations and revised wording.","major_comments":[{"comment":"The abstract and the discussion of Fig. 2 state that the NEO-MR-SD enCI tunneling splittings 'agree quantitatively' and are in 'excellent agreement' with the FGH benchmarks. The tabulated data contradict this wording for extended donor-acceptor distances: Table S1 gives a relative error of about 53% at He-He = 2.40 Å (2.3 vs 4.9 cm-1), Table S3 gives a relative error of about 27% at C-C = 3.10 Å (7.1 vs 5.6 cm-1), and Table S4 gives a relative error of about 23% at O-O = 2.62 Å (10.3 vs 8.4 cm-1). These are systematic overestimates that grow with distance. The claim of quantitative agreement should be replaced with an explicit error analysis, or the calculations should be improved to support such a claim.","section":"Abstract and Fig. 2, Tables S1, S3, S4"},{"comment":"The 5s5p5d5f protonic basis used for OCHCO+ and malonaldehyde is justified by a convergence test on HeHHe+ (Table S5), but the same comparison is not reported for the two larger systems. Tables S3 and S4 show that 8s8p8d and 5s5p5d5f results differ by 15-45% for OCHCO+ and by 35-50% for malonaldehyde at the same geometries (e.g., OCHCO+ at 3.10 Å: 3.9 vs 7.1 cm-1; malonaldehyde at 2.62 Å: 5.4 vs 10.3 cm-1). Therefore the favorable agreement of the 5s5p5d5f results with FGH is not a demonstrated property of the NEO-MRCI method; it may reflect an accidental cancellation of basis-set incompleteness. The authors should either report 8s8p8d8f (or 5s5p5d5f5g) results for these systems at representative distances or explicitly state that the reported errors include an uncontrolled basis-set component.","section":"Computational Details and Tables S3-S5"},{"comment":"The proton basis-function center positions are determined by conventional CCSD geometry optimizations, as described in the Computational Details section. This is a free input to the NEO-MRCI calculation, and tunneling splittings are exponentially sensitive to the barrier and thus to the placement of these centers. The paper asserts that this CCSD-based procedure 'provides a reliable method' but reports no sensitivity tests, such as perturbing the centers or comparing with centers optimized at a different level. Consequently, the statement in the Conclusion that 'NEO-MRCI does not require any parameters' is overstated; the center positions are an external parameter of the protocol. The authors should either add a numerical test of the sensitivity to the center positions or qualify the 'parameter-free' claim to mean 'no empirically fitted parameters.'","section":"Computational Details and Conclusion"}],"minor_comments":[{"comment":"For the entry labeled 'He-He distance 2.4 Å', the He coordinates are listed as +/- 1.120 Å, which corresponds to a separation of 2.24 Å, not 2.40 Å. Please correct either the label or the coordinates, as this affects the reproducibility of the data point with the largest reported discrepancy.","section":"SI Section 8.1"},{"comment":"The word 'deterium' in the figure caption should be 'deuterium'.","section":"Fig. 5 caption"},{"comment":"The word 'inidcated' in the footnote should be 'indicated'.","section":"Table S1 footnote"},{"comment":"The SI headers contain 'V arying' and similar spacings; these should be cleaned up.","section":"SI table headers"},{"comment":"The statement 'We show that the same tunneling splitting is obtained for HeHHe+ using the 8s8p8d8f and 5s5p5d5f basis sets (Table S5)' is correct only for the single tested distance of 2.30 Å and should be phrased as a single-point comparison, not a general convergence statement.","section":"Main text"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and the method is interesting, but the central claim of 'quantitative' and 'excellent' agreement is not supported by the data at several of the reported points, especially the HeHHe+ 2.40 Å case with a relative error of about 53%. The basis-set convergence issue for OCHCO+ and malonaldehyde is the most serious technical concern; the authors should be asked to provide 8s8p8d8f (or better) results for these systems at least at a few representative distances. The SI coordinate error for HeHHe+ 2.40 Å should also be corrected before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper is worth a read, not because the headline holds but because it is the first application of NEO-MRCI to hydrogen tunneling splittings and it comes with enough data to see where it stands. The method itself is from ref. 51; the new part is the application to four fixed-geometry systems, the comparison to FGH benchmarks, and a specific protocol for placing proton basis centers via CCSD minimizations. That protocol is sensible and the paper is transparent about its choices. The SI tables are a real asset.\n\nThe problem is the \"quantitative agreement\" claim. For HeHHe+ at the longest distance, the NEO-MRCI splitting is 2.3 cm^-1 against FGH's 4.9 cm^-1, a 53% error. OCHCO+ at 3.10 Å is 7.1 versus 5.6, a 27% error, and malonaldehyde at 2.62 Å is 10.3 versus 8.4, 23% error. Those are not quantitative agreements in any normal sense, and the text should say so.\n\nMore importantly, the protonic basis is not converged for the larger systems. The paper uses a 5s5p5d5f basis for OCHCO+ and malonaldehyde, justified by a convergence check on HeHHe+ (Table S5). But Tables S3 and S4 show large differences between 8s8p8d and 5s5p5d5f for both molecules: at OCHCO+ 3.10 Å the two bases give 3.9 and 7.1 cm^-1; at malonaldehyde 2.62 Å they give 5.4 and 10.3 cm^-1. The 5s5p5d5f happens to sit closer to the FGH value at some distances, but that is not evidence of convergence. Without 8s8p8d8f or an equivalent check on these systems, the agreement could be partly a cancellation of errors. The stress-test note is right on this point.\n\nThere are smaller issues: the FGH benchmark is exact only for the CCSD surface, not for the real molecule, and the minimal (2e,2o) active space is not tested against larger spaces. Neither is fatal, but they should be acknowledged more carefully.\n\nWho should read this? Anyone working on non-Born-Oppenheimer treatments of proton transfer, and method developers who want a fixed-geometry benchmark for NEO methods. The data are reproducible and the protocol is described in enough detail to follow. The paper deserves a serious referee, but I would send it back for major revisions: temper the language, report relative errors, and ideally add a converged protonic basis calculation for at least one geometry of each larger system. The central idea is sound; the presentation oversells it.","headline":"First application of NEO-MRCI to tunneling splittings is credible and transparent, but 'quantitative agreement' is overstated and the protonic basis is demonstrably not converged for OCHCO+ and malonaldehyde.","tokens_in":16747,"tokens_out":4536,"would_cite":false,"duration_ms":38375,"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 claims that the nuclear-electronic orbital multireference configuration interaction method computes accurate hydrogen and deuterium tunneling splittings for fixed geometries, matching numerically exact grid benchmarks across…","keywords":["hydrogen tunneling","tunneling splitting","nuclear-electronic orbital","multireference configuration interaction","proton transfer","vibronic states","Fourier grid Hamiltonian","deuterium isotope effects"],"falsifier":"Run NEO-MRCI for a symmetric hydrogen-transfer system at a donor-acceptor distance where the CCSD-optimized proton center sits noticeably away from the maximum of the FGH ground-state proton density; if the computed tunneling splitting then deviates from the FGH benchmark by more than a few inverse centimeters, the center-placement assumption is falsified.","tokens_in":15633,"feed_emoji":"⚛️","tokens_out":6379,"duration_ms":57015,"temperature":0.7,"pith_summary":"This paper reports that the nuclear-electronic orbital multireference configuration interaction (NEO-MRCI) method, which treats the transferring proton as a quantum wavefunction together with the electrons, gives hydrogen and deuterium tunneling splittings that agree with numerically exact grid-based benchmarks at fixed geometries. The test set spans HeHHe+, OCHCO+, FHF–, and malonaldehyde, covering linear and non-linear tunneling paths over a range of donor-acceptor distances. The result is useful because tunneling splittings are extremely sensitive to the barrier and are usually hard to obtain without adjustable parameters. If the finding is correct, a parameter-free multicomponent quantum chemistry method can describe the vibronic states responsible for hydrogen tunneling.","feed_headline":"No free parameters in hydrogen tunneling splitting calculations.","feed_subtitle":"NEO-MRCI matches numerically exact grid benchmarks across four proton-transfer systems.","key_machinery":"The load-bearing object is the NEO-MRCI wavefunction, a linear combination of products of electronic and protonic Slater determinants built from orbitals optimized in a state-averaged NEO-MCSCF calculation that treats the lowest two vibronic states equally. Each tunneling proton is represented by two basis function centers, placed at the donor and acceptor minima of a conventional CCSD double-well surface, each carrying a protonic and an electronic basis set. The CI expansion includes single electron, single proton, and double electron-proton excitations (MR-SDenCI), along with a full protonic active space and, for FHF–, OCHCO+, and malonaldehyde, a minimal (2e,2o) electronic active space of in-phase sigma and sigma-star orbitals; HeHHe+ uses a single-reference NEO-CASSCF treatment. This structure supplies the electron-proton correlation and the balanced treatment across the barrier that make the tunneling splitting accurate.","core_discovery":"The central discovery is that NEO-MRCI, expanded as single electronic, single protonic, and double electron-proton excitations from a state-averaged NEO-MCSCF reference, reproduces tunneling splittings from three-dimensional Fourier grid Hamiltonian calculations at the same fixed heavy-atom geometries. The paper reports quantitative agreement for HeHHe+, FHF–, OCHCO+, and malonaldehyde, and for deuterium-substituted FDF– and malonaldehyde, with the protonic densities showing the expected bilobal shapes and nodal structures. Because electrons and the transferring proton are treated on the same footing, the calculation avoids a Born-Oppenheimer separation for the tunneling particle and captures both the static correlation of the double well and the electron-proton dynamic correlation needed for accurate splittings.","pith_inferences":["One consequence not tested here is that NEO-MRCI might serve as a benchmark generator for larger proton-transfer systems where the FGH grid calculation becomes too expensive; the current fixed-geometry benchmarks are the evidence that would justify that role.","The CCSD-based center placement means the method could be extended to non-symmetric systems by a second optimization near the acceptor, but the paper does not show how sensitive the splittings are to small displacements of those centers.","Because the wavefunction explicitly correlates the proton with electrons, the same machinery could in principle report excited protonic states beyond the lowest doublet, which would test the assumption that the (2e,2o) active space is sufficient for higher vibronic states."],"forward_implications":["Fixed-geometry tunneling splittings become accessible without tunable parameters in other electronically adiabatic hydrogen-transfer systems that share the two-center, double-well structure tested here.","Deuterium splittings follow from the same active spaces and basis sets, so kinetic isotope effects on tunneling are directly computable.","The method's excited vibronic states can be coupled to the other nuclear vibrations through vibronic coupling theory, a route the paper identifies toward comparing with experimental splittings such as malonaldehyde's 21.6 cm-1.","The small (2e,2o) electronic active space appears transferable across chemically different proton-bound systems, which keeps the cost of the NEO-MRCI step manageable despite the large protonic basis sets."],"supporting_citations":[{"why":"Introduces the NEO-MRCI method and its MR-SDenCI expansion that this paper applies to tunneling systems.","marker":"[51]"},{"why":"Supplies the Fourier grid Hamiltonian approach used to generate the numerically exact reference tunneling splittings.","marker":"[61]"},{"why":"Extends FGH to multidimensional hydrogen vibrational wavefunctions, underpinning the three-dimensional proton benchmarks.","marker":"[62]"},{"why":"Earlier NEO-NOCI treatment of tunneling splittings that the paper contrasts as needing significant extension.","marker":"[45]"},{"why":"Provides the OCHCO+ geometry used here and the alternative NEO-MSDFT approach for tunneling systems.","marker":"[46]"},{"why":"Defines the aug-cc-pVTZ electronic basis set used for HeHHe+, FHF–, and OCHCO+ in both NEO and FGH calculations.","marker":"[63]"},{"why":"Defines the cc-pVTZ electronic basis set used for malonaldehyde.","marker":"[64]"},{"why":"Gives the even-tempered basis set formula used to build the protonic basis sets.","marker":"[66]"}],"fun_headline_variants":["NEO-MRCI matches exact grid benchmarks for four tunneling systems","NEO-MRCI computes tunneling splittings without Born-Oppenheimer","Exact splitting benchmarks met by NEO-MRCI","NEO-MRCI gives quantitative tunneling splits for H and D","NEO-MRCI matches numerically exact tunneling splits"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method's accuracy rests on the assumption that placing the two proton basis centers at the minima found by conventional CCSD optimizations reliably represents the proton's double-well density for every system and donor-acceptor distance studied.","fun_headline_variants_meta":{"raw":{"variants":["NEO-MRCI matches exact grid benchmarks for four tunneling systems","NEO-MRCI computes tunneling splittings without Born-Oppenheimer","Exact splitting benchmarks met by NEO-MRCI","NEO-MRCI gives quantitative tunneling splits for H and D","NEO-MRCI matches numerically exact tunneling splits"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001605,"raw_usage":{"total_tokens":6357,"prompt_tokens":875,"completion_tokens":5482,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":491,"completion_tokens_details":{"reasoning_tokens":5395}},"tokens_in":491,"tokens_out":5482,"duration_ms":34456,"temperature":1.0,"reasoning_tokens":5395,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:28:10.554633+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run NEO-MRCI for a symmetric hydrogen-transfer system at a donor-acceptor distance where the CCSD-optimized proton center sits noticeably away from the maximum of the FGH ground-state proton density; if the computed tunneling splitting then deviates from the FGH benchmark by more than a few inverse centimeters, the center-placement assumption is falsified.","supporting_citations":[{"cited_title":"L.; Hammes-Schiffer, S","cited_arxiv_id":null,"evidence_quote":"Introduces the NEO-MRCI method and its MR-SDenCI expansion that this paper applies to tunneling systems."},{"cited_title":"C.; Balint‐Kurti, G","cited_arxiv_id":null,"evidence_quote":"Supplies the Fourier grid Hamiltonian approach used to generate the numerically exact reference tunneling splittings."},{"cited_title":"P.; Hammes-Schiffer, S","cited_arxiv_id":null,"evidence_quote":"Extends FGH to multidimensional hydrogen vibrational wavefunctions, underpinning the three-dimensional proton benchmarks."},{"cited_title":"H.; Pak, M","cited_arxiv_id":null,"evidence_quote":"Earlier NEO-NOCI treatment of tunneling splittings that the paper contrasts as needing significant extension."},{"cited_title":"Nuclear-Electronic Orbital Multistate Density Functional Theory","cited_arxiv_id":null,"evidence_quote":"Provides the OCHCO+ geometry used here and the alternative NEO-MSDFT approach for tunneling systems."},{"cited_title":"A.; Dunning, J., Thom H.; Harrison, R","cited_arxiv_id":null,"evidence_quote":"Defines the aug-cc-pVTZ electronic basis set used for HeHHe+, FHF–, and OCHCO+ in both NEO and FGH calculations."},{"cited_title":"Gaussian basis sets for use in correlated molecular calculations","cited_arxiv_id":null,"evidence_quote":"Defines the cc-pVTZ electronic basis set used for malonaldehyde."},{"cited_title":"Molecular Electronic‐Structure Theory; John Wiley & Sons, Ltd, 2000; Chapter 8, pp 287--335","cited_arxiv_id":null,"evidence_quote":"Gives the even-tempered basis set formula used to build the protonic basis sets."}],"review_version":1}