{"id":"b9850f88-7dea-45e3-b97f-0954b6b50eea","arxiv_id":"2412.00368","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":2,"one_line_summary":"FN-DMC binding energies of non-covalent dimers have significant basis set incompleteness errors with small GTO basis sets; augmentation and counterpoise correction remove most of them.","lead":"This study measures how much the atomic basis set changes fixed-node diffusion Monte Carlo binding energies for 24 weakly bound dimers, and finds the error is not negligible with small basis sets. It shows that adding diffuse functions or applying counterpoise correction removes most of the error, giving practical guidance for DMC calculations.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's headline protocol 'cc-pVDZ is sufficient when CP correction is applied' is contradicted by its own Section 4, which requires cc-pVTZ or aug-cc-pVDZ with CP; the central recommendation is internally inconsistent.","rationale":"The reader's verdict CONDITIONAL flags the reference definition ('zero BSSE implies zero BSIE') as the weakest assumption. That is a legitimate concern, but the paper has a stronger internal check: the PW cross-check in QMCPACK, although using a different non-local scheme, provides independent evidence that aug-cc-pV6Z is near the CBS limit. The more immediately falsifiable and load-bearing problem is the contradiction between the abstract's protocol recommendation and Section 4's quantitative threshold. The paper's practical takeaway is part of the central claim ('cc-pVDZ is sufficient when CP correction is applied'); if that statement is wrong, users following the abstract will obtain errors outside the claimed sub-chemical accuracy. The test above settles it directly from the paper's own tables. I do not see a need to move the verdict: the paper's main empirical finding (BSIEs are significant in small basis sets and CP/augmentation mitigate them) is well supported by the LRDMC and QMCPACK data, and the inconsistency is fixable by aligning the abstract with Section 4. Hence CONDITIONAL/UNCHANGED remains appropriate.","tokens_in":21508,"tokens_out":12733,"duration_ms":109686,"concrete_test":"From Tables SII/SIII and the extrapolated BSSEs in Figure 1(a), compute the CP-corrected LRDMC binding energy for non-augmented cc-pVDZ for each of the 24 A24 dimers: E_b^CP = E_b(cc-pVDZ) - E_BSSE(cc-pVDZ) in the a→0 limit, and compare with the aug-cc-pV6Z reference values in Table 1. If any dimer's CP-corrected cc-pVDZ BSIE exceeds the paper's 3σ ≈ 0.25 kcal/mol threshold, the abstract's 'sufficient' claim is contradicted by the paper's own SI data. If all pass, the discrepancy is purely a wording error and Section 4 should be treated as authoritative.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract and Section 1 state as key conclusions that 'cc-pVDZ is sufficient when CP correction is applied' and 'aug-cc-pVTZ ... performs well without CP.' However, Section 4's analysis of Figure 3(a) states that for non-augmented cc basis sets 'one needs the cc-pVQZ without the CP corrections or the cc-pVTZ with the CP correction,' and for augmented sets 'one needs the aug-cc-pVTZ without the CP correction or the aug-cc-pVDZ basis with the CP correction.' Thus the paper's own data do not show non-augmented cc-pVDZ + CP reaching the CBS limit within the stated 3σ ≈ 0.25 kcal/mol threshold; the minimum CP-corrected non-augmented basis is cc-pVTZ. If the abstract is taken literally, practitioners would use a basis set that Section 4 indicates is insufficient, directly undermining the paper's practical recommendation. This is distinct from the reader's reference-bias concern: even taking aug-cc-pV6Z as the exact CBS reference, the internal contradiction stands. The likely fix is a typo (aug-cc-pVDZ or cc-pVTZ instead of cc-pVDZ), but as written the central claim's protocol is not self-consistent.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports a systematic fixed-node diffusion Monte Carlo (FN-DMC, specifically LRDMC) study of basis set incompleteness errors (BSIEs) and basis set superposition errors (BSSEs) in the binding energies of the 24 non-covalently bound dimers in the A24 benchmark set. Using cc-pVnZ and aug-cc-pVnZ basis sets with ccECP pseudopotentials, the authors extrapolate the LRDMC lattice-space bias to the a→0 limit, compute BSSEs and counterpoise (CP)-corrected binding energies, and define BSIEs relative to aug-cc-pV6Z reference values that are cross-checked against plane-wave DMC calculations. They find that BSIEs are significant for small basis sets such as cc-pVDZ, especially for hydrogen-bonded dimers, and that augmentation with diffuse functions and/or CP correction reduces BSIEs below statistical error. The paper concludes with practical recommendations for choosing basis sets in DMC binding-energy calculations.","tokens_in":21841,"tokens_out":12746,"duration_ms":109475,"significance":"This work addresses a question of practical importance for the QMC community: whether FN-DMC binding energies of weakly bound dimers are significantly affected by basis set incompleteness and basis set superposition error. The study is careful in several respects: it uses the full A24 set, extrapolates the LRDMC lattice-space bias from four lattice spacings, reports statistical errors throughout, computes BSSE and CP corrections explicitly, and provides an independent plane-wave DMC cross-check. The central finding—that BSIEs can be significant for small localized basis sets and are mitigated by augmentation and/or CP correction—is likely to influence protocol choices in QMC calculations of non-covalent interactions, and the paper also offers a useful re-evaluation of earlier A24 benchmarks. No fitted parameters enter the physical claim; the BSIE estimates are simple differences against a converged reference, with lattice-space extrapolation coefficients serving as standard convergence parameters.","major_comments":[{"comment":"The paper's headline protocol is internally inconsistent. The abstract and Section 1 state that \"cc-pVDZ is sufficient when CP correction is applied,\" but Section 4's analysis of Figure 3(a) states that for non-augmented cc basis sets \"one needs the cc-pVQZ without the CP corrections or the cc-pVTZ with the CP correction,\" and Section 6 states \"with the CP correction, one can use a smaller basis, such as cc-pVTZ or aug-cc-pVDZ basis sets.\" These statements cannot all be true: the data do not show that cc-pVDZ with CP reaches the CBS limit within the stated 3σ ≈ 0.25 kcal/mol threshold. This contradiction directly affects the practical recommendation that is a central claim of the paper and must be resolved, for example by correcting what appears to be a typo in the abstract and introduction.","section":"Abstract and Section 1 vs Section 4 and Section 6"},{"comment":"The statement \"Since zero BSSE implies zero BSIE in binding energy calculation\" is not generally correct. Zero BSSE only tells one that the ghost functions of the partner monomer do not lower the monomer energies; it does not by itself establish that the monomer or dimer basis is at the CBS limit. A basis could be complete for each isolated monomer but still lack functions needed for the dimer, in which case BSSE would vanish while BSIE in E_b would not. This logical step is used to justify choosing aug-cc-pV6Z as the CBS reference in Eq. (2). The paper has independent support for that reference from the plane-wave QMCPACK cross-check in SI Table S1 and Figure S1, so the central estimates are not solely resting on the false implication, but the statement should be corrected or explicitly qualified and the reference validation presented as an empirical check rather than a logical consequence.","section":"Section 3"},{"comment":"The main-text BSIE estimates use TurboRVB LRDMC energies with the DTM localization, while the independent plane-wave cross-check is performed with QMCPACK using the T-move scheme, and the paper notes these are not equivalent. For some dimers the two codes give differences of order 0.1–0.2 kcal/mol (e.g., ammonia dimer: –3.10(6) in Table 1 vs –3.17(5) and –3.30(7) in SI Table S1). Since the BSIEs in Figures 2 and 3(a) are differences within TurboRVB, a DTM-specific offset would partly cancel, but the external validation of the aug-cc-pV6Z reference does not directly validate the DTM reference used in Eq. (2). The authors should either provide a DTM-based plane-wave check or explicitly discuss the transferability and show that the protocol conclusions are robust to the DTM/T-move difference, for example by reporting CP-corrected QMCPACK results that would confirm the cc-pVTZ and aug-cc-pVDZ recommendations.","section":"Section 3 and SI Section 1"}],"minor_comments":[{"comment":"Several dimer labels are duplicated or misspelled (e.g., \"methane--ethane\" appears twice, \"ethene dimer\" and \"ethyne dimer\" appear twice, and the SI has \"ammoniam--ethane\"); because the A24 set contains 24 distinct systems, these labels should be corrected.","section":"Table 1 and SI Tables SII/SIII"},{"comment":"The claim that Jastrow-factor optimization does not affect the extrapolated LRDMC energies under DTM would benefit from a one-sentence justification or citation, since DTM still uses the trial wavefunction in the nonlocal pseudopotential localization.","section":"Section 2"},{"comment":"The representative threshold \"3σ ≈ 0.25 kcal/mol\" should be defined more precisely; the statistical error differs from dimer to dimer, so the authors should state how this single value is obtained.","section":"Section 4"},{"comment":"The caption should clearly state that the PW BSIEs in the right panel are referenced to the QMCPACK plane-wave value, not to the TurboRVB aug-cc-pV6Z value used in the left and middle panels; as written this is ambiguous.","section":"Figure 3(a)"},{"comment":"The sentence \"the extrapolation is no longer needed when the CP correction is applied\" is too strong; the results show that CP correction reduces BSIEs to below the statistical threshold for sufficiently large basis sets, not that cardinal-number extrapolation is never useful.","section":"Section 4"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of a physical chemistry/chemical physics journal and is likely to be of interest to the QMC community. The abstract/introduction vs Section 4 contradiction is probably a typo, but it must be corrected before publication because the practical protocol is a central claim. The more substantive concern is the DTM/T-move gap in the reference validation; a targeted additional calculation or a clear robustness argument would strengthen the paper considerably."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear X,\n\nThe short version: this is a useful and mostly solid paper that quantifies basis-set incompleteness error (BSIE) in FN-DMC binding energies across the A24 set, and it deserves a proper referee. But the abstract's headline protocol is contradicted by the paper's own Section 4, and one of the logical justifications is wrong. Both are fixable.\n\nWhat's new: previous work looked at single systems (ammonia dimer, Li-thiophene, small clusters). Here they run the full A24 set with several cc basis sets, with and without counterpoise, using a consistent LRDMC setup and cross-checking against plane-wave DMC. That combination makes the central claim credible: tiny basis sets like cc-pVDZ do introduce significant BSIE in FN-DMC binding energies, especially for H-bonded systems, and diffuse functions plus CP correction mitigate. The plane-wave agreement supports their choice of aug-cc-pV6Z as the reference.\n\nSoft spots, in proportion: (1) The abstract and intro say 'cc-pVDZ is sufficient when CP correction is applied.' Section 4 says the opposite for non-augmented sets—the minimum is cc-pVTZ with CP. Either the abstract is a typo, or the protocol is internally inconsistent. Practitioners reading the abstract would use a basis that the paper's own data flags as insufficient. That has to be fixed. (2) Section 3 states 'zero BSSE implies zero BSIE in binding energy calculation.' That's not true in general—a basis can be free of superposition error while still being far from complete (e.g., plane waves with a small cutoff). The plane-wave check is what saves the reference, not the BSSE argument. (3) The lattice-space extrapolation coefficients (k2, k4) are not reported, which is a minor reproducibility gap. (4) Table 1/SI labels have duplicate entries (two 'methane–ethane' and two 'ethene dimer' rows) that need disambiguation.\n\nThe reader's concern about reference bias is reasonable but I think the PW cross-check covers it. The core finding is real and the systematic scan is a genuine step forward for DMC practice.\n\nVerdict: send to peer review. It's the kind of work a DMC practitioner needs: explicit guidance on which basis sets give CBS-limit binding energies and which don't. After the protocol inconsistency is cleaned up, it should be publishable and citable.\n\n— [no name]","headline":"Solid A24 scan showing FN-DMC binding energies need augmented or counterpoise-corrected basis sets, but the abstract's protocol contradicts Section 4 and the BSSE/BSIE claim is logically shaky.","tokens_in":22341,"tokens_out":3137,"would_cite":true,"duration_ms":26998,"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":"Basis set incompleteness shifts fixed-node DMC binding energies of weakly bound dimers by up to about 1 kcal/mol, with hydrogen-bonded complexes worst.","keywords":["fixed-node diffusion Monte Carlo","basis set incompleteness error","basis set superposition error","counterpoise correction","non-covalent interactions","A24 benchmark set","nodal surface","trial wavefunction"],"falsifier":"Compute the cc-pVDZ and aug-cc-pV6Z DMC binding energy of ammonia dimer, one of the largest-BSIE cases in the dataset, with a different pseudopotential or an all-electron treatment. If the gap between the two changes by more than the reported roughly 1.3 kcal/mol, the reference is not converged and every reported BSIE shifts.","tokens_in":21356,"feed_emoji":"🧪","tokens_out":9916,"duration_ms":84918,"temperature":0.7,"pith_summary":"Fixed-node diffusion Monte Carlo (FN-DMC) is often treated as nearly immune to basis set incompleteness because the fixed-node approximation depends only on the nodal surface of the trial wavefunction. This paper argues that this immunity fails for binding energies of weakly bound dimers: for the 24 complexes of the A24 set, a small localized basis such as cc-pVDZ introduces errors large enough to matter, and hydrogen-bonded systems suffer the most. The paper shows that adding diffuse functions, applying counterpoise (CP) correction, or both brings the binding energies to the complete-basis-set limit, so a modest basis set is enough if one of those measures is taken. If this is right, DMC benchmarks of non-covalent interactions need to state and control basis-set and counterpoise status, much as quantum chemistry already does.","feed_headline":"Small basis sets skew DMC binding energies by ~1 kcal/mol","feed_subtitle":"For H-bonded dimers, cc-pVDZ alone misses the complete-basis limit; diffuse functions or counterpoise correction close the gap.","key_machinery":"The central object is the nodal surface of the trial wavefunction, because fixed-node DMC inherits basis set incompleteness only through that surface. The determinant part of the trial wavefunction is expanded in correlation-consistent Gaussian bases of increasing cardinality, and the paper isolates the basis-set effect by computing lattice-regularized DMC (LRDMC), a lattice-discretized variant of DMC, at several lattice spacings and extrapolating to the continuum limit, with an augmented sextuple-zeta basis as the complete-basis reference. The second key piece is the counterpoise correction, defined by monomer calculations with ghost orbitals from the partner; the paper shows that ghost orbitals improve the monomer nodal surface and thereby reduce the BSIE. This is what makes the qualitative result believable: basis-set incompleteness affects DMC binding energies through the nodes, not through the projection step.","core_discovery":"The central claim is that basis set incompleteness errors (BSIEs) in fixed-node DMC binding energies are real and can be comparable in size to the benchmark accuracy being sought, contrary to the common assumption that projection methods wash out basis set bias. Working through all 24 dimers of the A24 set, the paper shows that with cc-pVDZ the BSIE can reach about a kilocalorie per mole for hydrogen-bonded systems, while dispersion-dominated dimers are affected less. The complete-basis-set reference is the aug-cc-pV6Z DMC binding energy, whose convergence the paper checks by showing that basis set superposition errors vanish at that size and by cross-checking against large-cutoff plane-wave DMC. The paper concludes that cc-pVDZ with counterpoise correction, or aug-cc-pVTZ without it, is sufficient to reach the CBS limit within statistical errors, and that no cardinal-number extrapolation is needed once either augmentation or CP correction is used.","pith_inferences":["The paper's hydrogen-bond versus dispersion trend suggests that interactions with long-range electrostatic tails, such as charged dimers or ionic clusters, will show larger BSIEs; a direct test would be to repeat the cc-pVDZ versus aug-cc-pV6Z comparison on a small set of charged or strongly dipolar dimers.","Because the nodal surface is the carrier, trial wavefunctions with better nodes, such as multideterminant or CASSCF expansions, may be less sensitive to basis size; this is testable by recomputing a few A24 dimers with correlated trial functions across cc-pVDZ and aug-cc-pVTZ.","A practical protocol for large systems follows implicitly: when aug-cc-pVTZ is unaffordable, cc-pVDZ with counterpoise correction is a validated route to CBS binding energies for non-covalent systems at a fraction of the cost.","The conclusions are tied to the specific ccECP pseudopotentials used, so transferring the protocol to other effective core potentials should be checked, since pseudopotentials alter the nodal surface and could change the BSIE magnitude."],"forward_implications":["FN-DMC binding energies from small localized basis sets such as cc-pVDZ should not be treated as complete-basis values; for hydrogen-bonded dimers the basis-set bias is on the order of 1 kcal/mol, comparable to the accuracy being targeted.","Adding diffuse functions changes the picture: aug-cc-pVTZ without counterpoise correction reaches the CBS limit within statistical error, making it a safe default for non-covalent DMC benchmarks.","Counterpoise correction is an alternative cure: CP-corrected cc-pVDZ or aug-cc-pVDZ recovers CBS binding energies, so smaller basis sets remain usable when the correction is applied.","The success of CP correction shows that ghost orbitals improve monomer nodal surfaces, confirming that basis-set superposition and incompleteness act through the trial wavefunction's nodes.","Earlier DMC benchmarks of the A24 set made with un-augmented triple-zeta basis sets carry a small BSIE contamination, so published reference values should come from augmented-basis or CP-corrected calculations."],"supporting_citations":[{"why":"Supplies the A24 benchmark set of 24 non-covalently bound dimers and the reference CCSD(T) binding energies used for comparison.","marker":"46"},{"why":"Defines basis set superposition error and the counterpoise correction that the paper tests and recommends.","marker":"44"},{"why":"Introduces the cc-pVnZ correlation-consistent basis set family whose incomplete members are the objects of the BSIE study.","marker":"43"},{"why":"Provides the ccECP effective core potentials paired with the basis sets in all DMC calculations.","marker":"47,48"},{"why":"Describes the lattice-regularized DMC algorithm whose lattice-space extrapolation yields the continuum binding energies.","marker":"49,50"},{"why":"Supplies the determinant locality T-move scheme used for the non-local pseudopotential in the main DMC results.","marker":"51"},{"why":"Prior ammonia-dimer DMC study showing diffuse functions are crucial, a specific result this paper generalizes.","marker":"30"},{"why":"Earlier A24 DMC benchmark with augmented basis sets whose RMSD the paper uses as the converged comparison.","marker":"31"},{"why":"Earlier A24 benchmark with cc-pVTZ whose larger RMSD the paper attributes to basis set incompleteness.","marker":"60"}],"fun_headline_variants":["Fixed-node DMC binding energies suffer basis set errors","Small basis sets skew DMC binding energies up to 1 kcal/mol","Basis set errors matter in DMC for H-bonded dimers","Diffuse functions or counterpoise correct DMC basis errors"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire error budget is measured against the paper's own aug-cc-pV6Z DMC binding energies, so the conclusions stand only if those values really are the complete-basis-set limit.","fun_headline_variants_meta":{"raw":{"variants":["Fixed-node DMC binding energies suffer basis set errors","Small basis sets skew DMC binding energies up to 1 kcal/mol","Basis set errors matter in DMC for H-bonded dimers","Diffuse functions or counterpoise correct DMC basis errors"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00024,"raw_usage":{"total_tokens":1539,"prompt_tokens":985,"completion_tokens":554,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":601,"completion_tokens_details":{"reasoning_tokens":481}},"tokens_in":601,"tokens_out":554,"duration_ms":4882,"temperature":1.0,"reasoning_tokens":481,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T05:28:02.011175+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the cc-pVDZ and aug-cc-pV6Z DMC binding energy of ammonia dimer, one of the largest-BSIE cases in the dataset, with a different pseudopotential or an all-electron treatment. If the gap between the two changes by more than the reported roughly 1.3 kcal/mol, the reference is not converged and every reported BSIE shifts.","supporting_citations":[{"cited_title":"gold standard,","cited_arxiv_id":null,"evidence_quote":"Supplies the A24 benchmark set of 24 non-covalently bound dimers and the reference CCSD(T) binding energies used for comparison."},{"cited_title":"The calculation of small molecular interactions by the differences of separate total energies","cited_arxiv_id":null,"evidence_quote":"Defines basis set superposition error and the counterpoise correction that the paper tests and recommends."},{"cited_title":"G.; Michaelides, A.; Alfè, D","cited_arxiv_id":null,"evidence_quote":"Supplies the determinant locality T-move scheme used for the non-local pseudopotential in the main DMC results."},{"cited_title":"Quantum Monte Carlo methods describe noncovalent interactions with subchemical accuracy","cited_arxiv_id":null,"evidence_quote":"Prior ammonia-dimer DMC study showing diffuse functions are crucial, a specific result this paper generalizes."},{"cited_title":"Quantum Monte Carlo for noncovalent interactions: an efficient protocol attaining benchmark accuracy","cited_arxiv_id":null,"evidence_quote":"Earlier A24 DMC benchmark with augmented basis sets whose RMSD the paper uses as the converged comparison."},{"cited_title":"TurboGenius: Python suite for high-throughput calculations of ab initio quantum Monte Carlo methods","cited_arxiv_id":null,"evidence_quote":"Earlier A24 benchmark with cc-pVTZ whose larger RMSD the paper attributes to basis set incompleteness."}],"review_version":1}