{"id":"0c024d07-11f7-4e28-ab50-5d6b8e63ee9f","arxiv_id":"2505.16262","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A new ab initio potential energy surface for methanol, trained on 39,401 CCSD(T)-F12b/cc-pVTZ-F12 energies, yields variational vibrational band origins within about 5 cm-1 of experiment up to ~2500 cm-1.","lead":"This paper develops a new full-dimensional potential energy surface for methanol from about 39,000 high-level quantum chemistry calculations, and uses it to compute vibrational energy levels. The computed band origins match gas-phase experiments within about 5 cm-1 up to 2500 cm-1, an accuracy that could support methanol line lists for astronomy and precision tests.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Final fitted torsional barrier is 363.1 cm−1 vs 351.3 cm−1 ab initio (Fig. S13), an 11.8 cm−1 mismatch larger than the claimed sub-5 cm−1 accuracy; the reported VBO agreement may rest on cancellation.","rationale":"The reader's weakest assumption grouped electronic-structure accuracy and the experiment-informed stopping criterion. I find a more specific and more directly checkable weak point: the final fitted PES does not reproduce its own ab initio torsional barrier (363.1 vs 351.3 cm−1, Fig. S13). Because the paper's central novelty is the large-amplitude torsion/tunnelling dynamics and the sub-5 cm−1 VBO agreement, an 11.8 cm−1 error in the very coordinate that governs that physics is a red flag. The agreement in Table V could be the result of cancellation between a too-high fitted barrier and a too-low ab initio barrier, rather than a genuinely spectroscopic-quality PES. The authors themselves note the 'relatively large' torsional-path deviation, so this is not an artifact of my reading. The proposed test—sensitivity of the torsional VBOs to an 11.8 cm−1 barrier shift, plus a higher-level barrier calculation—would settle whether the result is robust. I do not think this overturns the paper; the methodology and data are valuable, and the concern is addressable. Hence the reader's CONDITIONAL verdict stands, and I mark no verdict change.","tokens_in":39973,"tokens_out":8428,"duration_ms":69996,"concrete_test":"Perform a controlled sensitivity test on the torsional barrier: refit PES25 or add a smooth corrective term to the torsional potential that lowers the PES25 barrier from 363.1 to the ab initio 351.3 cm−1 (e.g., by scaling the torsional Fourier components of the PES along the relaxed path), then recompute the variational torsional VBOs and tunnelling splittings in Table V/S7. If the MAE/MAX of the torsional states changes by more than ~1 cm−1, the reported experimental agreement depends on the fit's barrier error. Independently, compute the relaxed torsional barrier at CCSD(T)-F12b/cc-pVQZ-F12 (or with core-valence correlation) to determine whether 351.3 or 363.1 cm−1 is closer to the true barrier; if the higher-level value is ~363 cm−1, PES25's accuracy is accidental rather than ab initio.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline result is that PES25 reproduces experimental VBOs with MAE 0.9–1.5 cm−1 (Table V). A necessary condition is that the fitted PES faithfully represents the CCSD(T)-F12b/cc-pVTZ-F12 reference in the dynamically relevant region. That condition is demonstrably violated for the key large-amplitude coordinate: Fig. S13 of the Supplementary Material reports relaxed torsional barriers of 360.8, 367.4, 363.1, and 351.3 cm−1 for the 26 401, 30 401, 39 401 (PES25) fitting sets and the direct ab initio calculation, respectively. PES25 is thus 11.8 cm−1 higher than its own ab initio reference at the torsional barrier. This is more than twice the largest MAX error (4.0 cm−1) claimed in Table V, and it occurs in exactly the coordinate controlling the large-amplitude motion and tunnelling splittings that the paper emphasizes. The surrounding text in S3 acknowledges the 'relatively large' deviation but asserts that torsional levels still agree with experiment. That assertion, if true, implies error cancellation: the fitted barrier overshoots the ab initio value and the ab initio value undershoots the true barrier (or the levels are accidentally insensitive). Either way, the agreement in Table V cannot be attributed cleanly to an improved ab initio surface, and PES25 is not a faithful 'ab initio PES' in this region. This concern is not about the electronic-structure level per se; it is about the fitted PES not reproducing the electronic-structure data used to build it. The paper should either demonstrate that the 11.8 cm−1 barrier shift leaves all reported VBOs within stated errors, or provide a higher-level barrier calculation showing which value is correct.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a full-dimensional (12D) ab initio potential energy surface for methanol, PES25, obtained by fitting 39,401 CCSD(T)-F12b/cc-pVTZ-F12 energies with permutationally invariant polynomials using an active-learning (Robosurfer) procedure. The authors then solve the vibrational Schrödinger equation variationally with the GENIUSH-Smolyak approach and compare the computed vibrational band origins with gas-phase experimental data up to about 2500 cm−1. Table V reports mean absolute errors of 0.9, 1.5, and 1.5 cm−1 for the torsional, SAM-torsion, and combination-band ranges, respectively, with maximum errors below 4.1 cm−1. The paper also provides detailed state assignments, convergence tests, and a discussion of remaining sources of error.","tokens_in":40377,"tokens_out":4792,"duration_ms":42255,"significance":"If the reported accuracy is robust, this is a significant milestone: it would be the first full-dimensional ab initio surface for methanol that reproduces variational vibrational band origins to within a few cm−1 over a range including torsion-vibration couplings and combination bands. The work also demonstrates a carefully documented active-learning pipeline and a scalable variational approach for a 12-dimensional large-amplitude system, which is of broader methodological value. Strengths include the explicit convergence tests, the extensive supplementary state tables, and the fact that the PES coefficients are fitted to electronic-structure energies rather than directly to experimental band origins. However, the validation is weakened by two issues discussed below: a relatively large discrepancy between the fitted and ab initio torsional barrier, and the use of experimental data as a stopping criterion during PES development.","major_comments":[{"comment":"The final PES25 has a relaxed torsional barrier of 363.1 cm−1, whereas the CCSD(T)-F12b/cc-pVTZ-F12 reference value is 351.3 cm−1, a deviation of 11.8 cm−1. This is more than twice the largest MAX error reported in Table V (4.0 cm−1), and it occurs in the coordinate that controls the torsional and tunnelling motions emphasized in the paper. The paper acknowledges the deviation as relatively large but does not quantify its effect on the computed vibrational levels. As a result, the excellent agreement with experiment in Table V could arise from cancellation between the fitting error in the barrier and the electronic-structure error of the barrier, rather than from a faithful ab initio surface in this region. Please add a quantitative test, for example by recomputing the torsional and vibration-torsion states with the barrier shifted to the ab initio value, or by comparing the levels obtained with the intermediate fitting sets shown in Fig. S13, and report the resulting changes in the band origins. This is necessary to support the claim that PES25 is a reliable ab initio surface in the dynamically relevant region.","section":"Supplementary Material, Section S3 and Fig. S13"},{"comment":"The active-learning procedure used experimental band origins as a stopping criterion. At the 30,401-point stage, the paper states that the vibrational levels deviated more from experiment than the levels computed with PES13, which prompted continued sampling; the final 39,401-point set was then validated against the same experimental data in Table V. Thus the reported agreement is not a fully independent predictive test of the ab initio model. This usage of experimental data as a development checkpoint should be disclosed in the main text, along with the number of points added after the experimental comparison was first consulted and a discussion of whether the final agreement persists if the experimental comparison is withheld until the end. This does not invalidate the PES, but it changes the strength of the claim that the surface is a purely first-principles prediction.","section":"Supplementary Material, Section S1.3 and Table S2"},{"comment":"The total RMS fitting error of PES25 over the fitting set is 27.3 cm−1 (weighted RMS 17.3 cm−1), which is an order of magnitude larger than the mean absolute errors reported in Table V. The paper argues convincingly that fitting-set RMSE is not a direct measure of spectroscopic accuracy, but it does not provide a propagation-of-error estimate for the final band origins. A practical test would be to compare vibrational levels obtained with the DGELS and DGELSY variants given in Table S4, or with a refit to a random subset of the fitting points, so that the reader can see how much of the sub-cm−1 VBO agreement is robust to the fitting ambiguity. Without such a test, the relation between the large fitting RMSE and the claimed spectroscopic accuracy remains qualitative.","section":"Section II, Table II"}],"minor_comments":[{"comment":"The abstract says the computed band origins agree with experiment within 5 cm−1. This is technically consistent with Table V, but since the maximum deviations in the table are 2.1, 4.0, and 3.2 cm−1, the phrase 'within a few cm−1' or quoting the actual maxima would be more informative.","section":"Abstract and Table V"},{"comment":"The corrupted symbol '⁄tildelow' appears in several places, for example in Section II.B and Section S1.3. It appears to be a LaTeX rendering error and should be replaced by the intended symbol, presumably 'approximately'.","section":"Throughout text and Supplementary Material"},{"comment":"The basis and grid parameters b = 7 and H = 21 are introduced without definitions in the main text; the authors refer to earlier papers, but a brief parenthetical explanation would improve readability, especially since these parameters are central to the reported convergence of 0.5–1.5 cm−1.","section":"Section III.A"},{"comment":"The caption of Figure 2 does not explain the colored bands or the legend entries 'TW' and 'Ref.' in sufficient detail; please add a sentence describing what the shaded region represents and how the reference values were obtained.","section":"Figure 2"}],"recommendation":"major_revision","confidential_remarks":"I recommend major revision. The central result is impressive and likely publishable after revision, but the torsional-barrier discrepancy and the experimental checkpoint during active learning are load-bearing for the paper's main claim of a purely ab initio spectroscopic-quality PES. These issues are addressable with additional computations and revised claims, so I do not see grounds for rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper delivers what it promises: a new full-dimensional ab initio PES for methanol, PES25, with variational vibrational states that match gas-phase band origins to within a few cm-1 up to ~2500 cm-1, a clear improvement over PES13. The 12D GENIUSH-Smolyak computations are carefully converged, the convergence tests are reported in detail, and the comparison against experiment is honest and thorough. The active-learning workflow with Robosurfer and the PIP fitting is a genuine technical contribution, even though each component existed before; the combination and the resulting surface are new.\n\nThe soft spots are real but not disqualifying. The biggest one is the torsional barrier: PES25 gives 363.1 cm-1 while the direct CCSD(T)-F12b/cc-pVTZ-F12 value is 351.3 cm-1, an 11.8 cm-1 discrepancy that is larger than the claimed sub-5 cm-1 VBO accuracy. The paper acknowledges the deviation in the supplementary material but does not explain why torsional levels still match experiment so well. That is exactly the kind of cancellation that needs to be addressed. It does not make the paper wrong, because the PES is a fitted surrogate and the absolute error of the fit at the barrier is within the overall fitting RMS, but it does mean the agreement with experiment cannot be cleanly attributed to the ab initio level. The paper should either show that the 11.8 cm-1 shift leaves all reported VBOs within stated errors or provide a higher-level barrier calculation to pin down which value is right.\n\nA smaller concern is the experiment-informed stopping criterion: the active learning was continued after early comparison with experiment showed deviations, so the final agreement is not a fully independent test of the ab initio model. That is a mild circularity, and the paper is reasonably transparent about it.\n\nOverall, the central claim—that the new PES improves the vibrational states by 10-20 cm-1 and reaches near-spectroscopic accuracy—holds up. The paper deserves a serious referee, and the torsional barrier issue is the thing the referee should press on. I would cite this work if I were working on methanol or on variational rovibrational methods.","headline":"A serious, high-quality methanol PES study whose headline agreement with experiment is real but partly propped up by an 11.8 cm-1 torsional barrier discrepancy that should be explained.","tokens_in":40987,"tokens_out":1269,"would_cite":true,"duration_ms":12524,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper reports a full-dimensional ab initio methanol potential energy surface on which variational vibrational band origins agree with gas-phase experiment within 5 cm-1 up to 2500 cm-1, including torsional tunnelling splittings.","keywords":["methanol","potential energy surface","variational vibrational computation","internal rotation","tunnelling splittings","permutationally invariant polynomials","active learning","coupled-cluster"],"falsifier":"Build a second full-dimensional surface at a higher electronic-structure level (for example quadruple-zeta basis or all-electron correlation) using the same active-learning and coordinate pipeline, and recompute the same band origins. If the mean absolute deviation from experiment does not fall below the current 0.9–1.5 cm$^{-1}$, or if the individual deviations scatter rather than shrink, the present agreement would be shown to rely partly on error cancellation.","tokens_in":39753,"feed_emoji":"🧪","tokens_out":15145,"duration_ms":115910,"temperature":0.7,"pith_summary":"The paper seeks to show that methanol's quantum vibrational dynamics can now be computed from first principles to near-spectroscopic accuracy. It builds a new full-dimensional potential energy surface, PES25, from about 39,400 explicitly correlated coupled-cluster energies selected by an active-learning procedure and fitted with permutationally invariant polynomials. Solving the 12-dimensional vibrational Schrödinger equation on this surface, the authors obtain vibrational band origins that agree with gas-phase experiment within 5 cm$^{-1}$ up to about 2500 cm$^{-1}$, with mean absolute errors around 1–1.5 cm$^{-1}$. This makes methanol a molecule in which large-amplitude internal rotation, tunnelling splittings, and small-amplitude vibrations are all described by a single ab initio surface, which is directly relevant to astronomical methanol spectra and precision tests of fundamental physics.","feed_headline":"Methanol's vibrations now match experiment within 5 cm-1","feed_subtitle":"A full-dimensional ab initio surface reproduces methanol's band origins up to 2500 cm-1 within a few cm-1.","key_machinery":"The load-bearing construct is PES25, a permutationally invariant polynomial (PIP) representation of the potential written in Morse variables, fitted to 39,401 explicitly correlated coupled-cluster energies chosen by an iterative active-learning loop that adds geometries where the current surface is most uncertain. The vibrational calculation uses a coordinate system whose large-amplitude part is the torsional angle $\\tau$, expressed as a symmetric combination of the three H-C-O-H dihedral angles, with 11 small-amplitude curvilinear normal coordinates built along the minimum-energy path in $\\tau$. A harmonic-oscillator basis for the small-amplitude modes times a Fourier basis for $\\tau$, combined with a Smolyak non-product grid and basis/grid pruning, keeps the 12D Hamiltonian matrix tractable. This machinery is what lets the torsional tunnelling splittings and anharmonic couplings be computed exactly rather than modeled.","core_discovery":"On the paper's own terms, PES25, a full-dimensional permutationally invariant polynomial fit to 39,401 CCSD(T)-F12b/cc-pVTZ-F12 energies, together with an exact variational solution of the 12D vibrational Schrödinger equation, reproduces the vibrational band origins of CH$_3$OH within 5 cm$^{-1}$ of gas-phase experiment. The improvement is concentrated in the vibration-torsion coupling and combination-band ranges, where the earlier PES13 deviated by 10–20 cm$^{-1}$; the maximum deviations with PES25 are 2.1, 4.0, and 3.2 cm$^{-1}$ in the torsional, coupling, and combination ranges, respectively. The paper argues that this makes PES25 the first full-dimensional ab initio surface for methanol to reach spectroscopic quality in variational vibrational computations, covering not only the small-amplitude fundamentals but also states in which torsional excitation is combined with CO-stretch overtones.","pith_inferences":["The agreement is not a fully blind test: the paper's supplement reports that the active-learning sampling was continued after an early comparison with experiment showed deviations, so experimental information influenced which fitting geometries were added. A strictly out-of-sample test would fix the sampling protocol before any experimental comparison.","The reported torsional barrier on PES25 (363.1 cm$^{-1}$) is about 12 cm$^{-1}$ above the direct ab initio value (351.3 cm$^{-1}$); since tunnelling splittings are exponentially sensitive to the barrier, a precise measurement of $A/E$ splittings in highly excited torsional states could help decide which value is correct.","The method should transfer to other molecules with internal rotation, such as acetaldehyde or methylamine, where a large-amplitude torsional mode also couples to small-amplitude vibrations; the methanol result suggests the active-learning plus polynomial-fitting pipeline can reach spectroscopic quality there too."],"forward_implications":["Methanol's unmeasured vibrational states up to about 2500 cm$^{-1}$ become concrete predictions with estimated accuracy of a few cm$^{-1}$, ready to be tested by high-resolution infrared spectroscopy.","Tunnelling splittings of torsion-vibration states can now be obtained from the PES wavefunctions rather than from effective models, so the splitting pattern as a function of vibrational excitation is a direct observable test of the surface.","The same surface can be combined with electric dipole and polarizability surfaces to simulate infrared and Raman spectra line by line for methanol and its isotopologues.","Because methanol's torsion-rotation levels are used as astrophysical probes of the proton-to-electron mass ratio, a validated ab initio surface gives those searches a firmer theoretical anchor.","The residual few-cm$^{-1}$ errors identify where electronic structure theory must improve next: core correlation, larger basis sets, and relativistic or quantum-electrodynamic corrections."],"supporting_citations":[{"why":"supplies the earlier full-dimensional PES (PES13) whose 10–20 cm-1 deviations are the baseline that PES25 must improve upon.","marker":"[59]"},{"why":"provides the earlier 12D variational energies on PES13 and the state assignment scheme used for comparing with PES25 and experiment.","marker":"[58]"},{"why":"provides the permutationally invariant polynomial fitting method used to represent PES25.","marker":"[61]"},{"why":"provides the automated active-learning PES development approach that selected the 39,401 fitting geometries.","marker":"[68]"},{"why":"defines the explicitly correlated coupled-cluster electronic structure method used for all potential energies.","marker":"[69]"},{"why":"defines the cc-pVTZ-F12 basis set used in the electronic structure computations.","marker":"[70]"},{"why":"supplies the exact vibrational kinetic energy operator formalism used in the variational solution.","marker":"[44]"},{"why":"supplies the Smolyak non-product grid and basis/grid pruning strategy that makes the 12D variational computation feasible.","marker":"[52]"},{"why":"provides the experimental methanol atlas of assigned lines used as gas-phase reference for the lowest torsional and vibrational band origins.","marker":"[94]"},{"why":"provides gas-phase experimental band origins in the 1034–2190 cm-1 region used in the comparison.","marker":"[22]"}],"fun_headline_variants":["Full-dimensional ab initio PES brings methanol vibrations to 5 cm-1","Exact 12D quantum dynamics: methanol vibrations match experiment","Methanol's full-dimensional PES achieves 5 cm-1 vibrational accuracy","Spectroscopic-quality methanol PES: variational states within 5 cm-1","Methanol's exact vibrations: ab initio surface hits band origins to 5 cm-1"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result depends on the assumption that the electronic-structure method used to generate the surface is accurate to roughly a few cm$^{-1}$ in the energy regions sampled by the vibrations; if errors in the torsional barrier or anharmonic coupling regions are larger and cancel against fitting errors, the agreement with experiment would be partly accidental.","fun_headline_variants_meta":{"raw":{"variants":["Full-dimensional ab initio PES brings methanol vibrations to 5 cm-1","Exact 12D quantum dynamics: methanol vibrations match experiment","Methanol's full-dimensional PES achieves 5 cm-1 vibrational accuracy","Spectroscopic-quality methanol PES: variational states within 5 cm-1","Methanol's exact vibrations: ab initio surface hits band origins to 5 cm-1"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000362,"raw_usage":{"total_tokens":1971,"prompt_tokens":981,"completion_tokens":990,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":597,"completion_tokens_details":{"reasoning_tokens":887}},"tokens_in":597,"tokens_out":990,"duration_ms":7293,"temperature":1.0,"reasoning_tokens":887,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T15:04:30.535969+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build a second full-dimensional surface at a higher electronic-structure level (for example quadruple-zeta basis or all-electron correlation) using the same active-learning and coordinate pipeline, and recompute the same band origins. If the mean absolute deviation from experiment does not fall below the current 0.9–1.5 cm$^{-1}$, or if the individual deviations scatter rather than shrink, the present agreement would be shown to rely partly on error cancellation.","supporting_citations":[{"cited_title":"Qu and J","cited_arxiv_id":null,"evidence_quote":"supplies the earlier full-dimensional PES (PES13) whose 10–20 cm-1 deviations are the baseline that PES25 must improve upon."},{"cited_title":"Sunaga, G","cited_arxiv_id":null,"evidence_quote":"provides the earlier 12D variational energies on PES13 and the state assignment scheme used for comparing with PES25 and experiment."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the permutationally invariant polynomial fitting method used to represent PES25."},{"cited_title":"Gy˝ ori and G","cited_arxiv_id":null,"evidence_quote":"provides the automated active-learning PES development approach that selected the 39,401 fitting geometries."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"defines the explicitly correlated coupled-cluster electronic structure method used for all potential energies."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"defines the cc-pVTZ-F12 basis set used in the electronic structure computations."},{"cited_title":"M´ atyus, A","cited_arxiv_id":null,"evidence_quote":"supplies the exact vibrational kinetic energy operator formalism used in the variational solution."}],"review_version":1}