{"id":"5a1e28a8-4d99-498b-b509-e38c2625fb96","arxiv_id":"2504.15490","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"New C6 and C9 dispersion coefficients are calculated for Cu and Ag with group I, II, and XII atoms and ions using relativistic sum-over-states polarizabilities.","lead":"This paper computes long-range van der Waals interaction coefficients for copper and silver atoms paired with alkali, alkaline-earth, and group XII atoms and ions. The reported C6 and C9 values are intended to support the design of cold-atom hybrid traps and quantum devices.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"C9 reliability rests on unvalidated partner dynamic polarizabilities; static-alpha and selective C6 checks do not certify the imaginary-frequency integrals, and Sr deviations already reach 18%.","rationale":"The reader's weakest assumption identifies the imported partner polarizabilities as the main risk, and I agree. The paper's validation chain is indirect: static polarizability comparisons test only the zero-frequency limit, while C6 comparisons test only a few species and, for Sr, already deviate by 14-18%. The C9 coefficients multiply three dynamic polarizabilities, so they inherit and combine any unquantified error in the imported partner data. The absence of uncertainty estimates and of public data makes it impossible to know whether the new C9 values are accurate to a few percent or to tens of percent. This does not make the calculation wrong; the methods are standard and the available comparisons are mostly consistent. It does mean the reported values should be labeled as provisional, which is exactly the reader's CONDITIONAL verdict. I therefore recommend no change to the reader's verdict, with the concrete test above available to upgrade or downgrade confidence once independent dynamic polarizabilities are checked.","tokens_in":11385,"tokens_out":7352,"duration_ms":72363,"concrete_test":"Select one partner with an unbenchmarked C6/C9, e.g., Hg, and one with a benchmarked case, e.g., Cs and Sr. Independently recompute the imaginary-frequency dynamic polarizabilities of Hg, Cs, and Sr from oscillator strengths or E1 matrix elements taken from a different high-precision source, such as NIST lifetimes or an independent all-order or CI calculation, and re-evaluate C6(Cu-Hg), C6(Cu-Sr), and C9(Cu-Cu-Hg) using Eqs. (2) and (4). If C6(Cu-Sr) shifts by more than about 5%, or C9(Cu-Cu-Hg) shifts by more than the sum of the relative errors of the three input polarizabilities, then the imported dynamic polarizabilities are the limiting error and the unbenchmarked C9 values require explicit uncertainty bounds before they can be treated as reference data.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the reported C6 and C9 coefficients are reliable. That claim is supported only by comparison of static dipole polarizabilities and of a subset of C6 values, but Eqs. (2) and (4) are integrals over imaginary frequency, so agreement at zero frequency does not constrain the dynamic polarizabilities at all contributing frequencies. The dynamic polarizabilities of all partner species are imported from earlier work [38,52,53] without being recomputed or assigned uncertainties. Because Eq. (4) multiplies three dynamic polarizabilities, a relative error in a partner polarizability propagates into roughly the same relative error in C9, on top of any Cu or Ag error. Table III already shows C6 deviations of 14.25% for Cu-Sr and 18.00% for Ag-Sr against [49], and group XII C6 values have no external comparison. All C9 values in Table IV are new and unbenchmarked. A C6 check for one species does not validate the dynamic polarizability of a different partner, so the paper's claim that the calculations can be considered reliable is not established for the unbenchmarked triple-dipole coefficients; at minimum, error estimates are needed.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports static dipole polarizabilities of Cu and Ag obtained from relativistic sum-over-states calculations and uses them, together with dynamic polarizabilities of partner atoms and ions taken from the authors' earlier work [38,52,53], to evaluate C6 two-body and C9 three-body van der Waals dispersion coefficients for Cu and Ag interacting with group I, II, and XII atoms and singly charged ions. Many of the reported C6 coefficients and all of the reported C9 coefficients are new. Validation consists of comparisons of Cu and Ag static polarizabilities and oscillator strengths with literature values, and comparisons of a subset of C6 coefficients with two earlier calculations. The authors conclude that the overall agreement establishes the reliability of the reported values.","tokens_in":11595,"tokens_out":4543,"duration_ms":44947,"significance":"If the tabulated coefficients are accurate, the paper would provide a useful data set for modeling ultracold collisions, hybrid atom-ion traps, and long-range interaction potentials involving Cu and Ag, especially for combinations that were previously unavailable. The methods are standard (Casimir-Polder integrals over imaginary-frequency polarizabilities) and the static polarizability comparisons are favorable for several test cases. However, the significance is limited by the absence of uncertainty estimates for every reported coefficient, by the fact that all C9 values are unbenchmarked products of imported dynamic polarizabilities, and by unexplained 14-18% deviations in two C6 comparisons.","major_comments":[{"comment":"The reliability claim in §IV.A ('can be considered reliable') is based on comparisons of static dipole polarizabilities and oscillator strengths. Static alpha(0) is a single point of the integrands in Eqs. (2) and (4); agreement at zero frequency does not validate the dynamic polarizabilities at all imaginary frequencies that contribute to the integrals. The partner-species dynamic polarizabilities are imported from Refs. [38,52,53] without being recomputed or assigned uncertainties. Since the paper presents no uncertainty for any C6 or C9 value and no propagation of input errors, the reliability claim for the tabulated coefficients is not quantitatively supported. Please provide uncertainty estimates propagated from the input polarizabilities or a sensitivity analysis showing how C6 and C9 change under plausible variations of the partner polarizabilities.","section":"§IV.A, Tables I-II"},{"comment":"The statement of 'good agreement' with earlier C6 results is weakened by the deviations in Table III for Cu-Sr (14.25%) and Ag-Sr (18.00%) with respect to Ref. [49]. These are considerably larger than the sub-percent to few-percent deviations quoted for lighter group I and II partners, and no specific explanation is offered for these two cases. In addition, all group XII C6 entries have no external comparison. The authors should either quantify and physically explain these outliers or temper the reliability claim so that it does not extend indiscriminately to every tabulated C6 value.","section":"§IV.B, Table III"},{"comment":"All C9 coefficients in Table IV are reported without any comparison to previously published three-body dispersion coefficients and without uncertainties. Equation (4) is a product of three dynamic polarizabilities, so relative errors in any partner species propagate directly into C9, on top of errors in the Cu or Ag polarizabilities. The existing checks on static polarizabilities and on selected C6 values do not certify these new C9 values. At minimum, the authors should provide an independent check for at least one C9 (for example against a known Axilrod-Teller-Muto coefficient for a well-studied triad), or clearly state in the abstract and conclusion that the C9 values are exploratory and should be used with caution until benchmarked.","section":"§IV.B, Table IV"}],"minor_comments":[{"comment":"The name 'Simalkowski' in the text should be 'Smialkowski', matching Ref. [49].","section":"§IV.B"},{"comment":"There is a typo on 'plarizabilities' that should read 'polarizabilities' in the discussion of the main contribution to the static polarizability.","section":"§IV.A"},{"comment":"Several entries are listed as '~ 0' rather than explicit numerical values; providing three significant digits (or a stated truncation threshold) would make the table more informative and reproducible.","section":"Table I"},{"comment":"The text refers to Cu and Ag as belonging to 'group XI', while the title and abstract use 'Group I, II, and XII'; please clarify the Roman-numeral group nomenclature so that Cu/Ag (group 11, formerly IB) are not confused with group XII (Zn, Cd, Hg).","section":"§IV.B"},{"comment":"No numerical details are given for the quadrature used to evaluate the integrals in Eqs. (2) and (4); specifying the frequency grid and convergence criteria would improve reproducibility.","section":"§II"},{"comment":"Since this is a data-oriented paper, the statement that data are not publicly available reduces its utility; consider depositing the dynamic polarizability tables and the final C6/C9 tables in a repository.","section":"Data Availability"}],"recommendation":"major_revision","confidential_remarks":"The paper depends heavily on dynamic polarizabilities imported from the same group's previous papers, and all C9 values are unvalidated. In my view the central claim of reliability needs either error bars or an explicitly reduced claim before publication. The fit with the journal's scope is otherwise appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, quick take on arXiv:2504.15490. The paper fills a real gap: C6 values for Cu and Ag with group XII atoms and ions, and essentially all C9 three-body coefficients, have not been reported before. It uses the standard Casimir-Polder integral over imaginary-frequency polarizabilities, with sum-over-states oscillator strengths and relativistic wavefunctions for Cu and Ag. That is the right framework, and the comparisons they do offer—static polarizabilities and several C6 coefficients—mostly look reasonable. So there is something here.\n\nThe soft spot is load-bearing. The C9 values rest on dynamic polarizabilities of partner atoms and ions imported from earlier papers [38,52,53], and those imported functions are never recomputed or assigned uncertainties. Agreement at zero frequency does not certify the integrand across imaginary frequency. And the checks that do exist are not reassuring across the whole table: Cu-Sr C6 is off by 14% from Smialkowski-Tomza, Ag-Sr by 18%, and the group XII C6 values have no external comparison at all. Since Eq. (4) multiplies three polarizabilities, any error in a partner function propagates roughly linearly into every new C9. Calling the whole set reliable in the conclusion is too strong without error bars or a benchmark for at least a few of the new coefficients.\n\nMinor issues: no machine-readable public data despite the data-availability note; literature comparisons for one partner do not validate the others; and some of the language about good agreement glosses over the 14–18% cases.\n\nWould I cite it? Not as-is for the unbenchmarked coefficients. If the authors add uncertainties and validate a few C9s against independent methods, it becomes a standard reference for Cu/Ag interactions. Is this a serious thinker? Yes—the method is standard, the logic is coherent, and what is missing is diligence, not a broken framework.\n\nRecommendation: send to peer review, not desk reject. It is a useful data paper needing revision. Push the authors to quantify uncertainties, benchmark at least some dynamic polarizabilities and C9s, and put the tables in a repository.","headline":"Useful new tabulations of Cu/Ag dispersion coefficients, but the reliability claim outruns the evidence: no uncertainties and no benchmark for the partner dynamic polarizabilities that drive the new C9 values.","tokens_in":12125,"tokens_out":1824,"would_cite":false,"duration_ms":18334,"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":"The paper reports $C_6$ and $C_9$ van der Waals dispersion coefficients for copper and silver atoms with group I, II, and XII atoms and ions, many of them previously unavailable, and supports their reliability by comparing…","keywords":["van der Waals dispersion coefficients","C6 coefficient","C9 three-body coefficient","dynamic dipole polarizability","sum-over-states approach","relativistic many-body methods","copper atoms","silver atoms"],"falsifier":"An independent high-accuracy calculation of the three-body coefficient for Ag–Ag–Cs, predicted here to be 48,296 atomic units, that disagrees by more than the claimed few-percent accuracy of the inputs would show the imported partner polarizabilities are not reliable.","tokens_in":11191,"feed_emoji":"⚡️","tokens_out":15998,"duration_ms":121835,"temperature":0.7,"pith_summary":"This paper produces the long-range van der Waals dispersion coefficients $C_6$ and $C_9$ for copper and silver atoms interacting with atoms and singly charged ions of groups I, II, and XII. Many of these numbers, including every three-body $C_9$ value and most coefficients involving group XII partners, have not been reported before. The authors build them from dynamic dipole polarizabilities at imaginary frequencies, computed with relativistic wave functions and a sum over intermediate states, and they check their inputs by comparing oscillator strengths, static polarizabilities, and available $C_6$ values with earlier calculations. Agreement mostly within about ten percent, with larger deviations for some Sr and Ba cases, is the basis for the claim that the new coefficients, including the unbenchmarked $C_9$ tables, are reliable enough for cold-atom, hybrid trap, and van der Waals complex studies.","feed_headline":"First three-body van der Waals coefficients for Cu and Ag","feed_subtitle":"The C9 tables cover groups I, II, and XII atoms and ions, giving cold-atom and hybrid-trap models numbers they did not have.","key_machinery":"The load-bearing object is the imaginary-frequency dipole polarizability, written as a sum over intermediate states $$\\alpha_v(i\\omega)=\\sum_{k\\ne v}\\frac{f_{vk}}{(E_v-E_k)^2+\\$omega^{2}$},$$ where $f_{vk}$ is the oscillator strength of the dipole transition and the energies and matrix elements come from relativistic wave functions. Inserting these polarizabilities into the Casimir–Polder integrals turns every dispersion coefficient into a weighted product of the participating species' polarizabilities. This is what carries the argument: once the dynamic polarizabilities are accepted, the tabulated $C_6$ and $C_9$ values follow directly, with no additional fitted parameters.","core_discovery":"The paper's central claim is that the leading dispersion interactions of ground-state Cu ($4S_{1/2}$) and Ag ($5S_{1/2}$) with partners from groups I, II, and XII are accurately given by the two-body and three-body dipole dispersion coefficients $$C_6 = \\frac{3}{\\pi}\\int_0^\\infty \\alpha_A(i\\omega)\\alpha_B(i\\omega)\\,d\\omega \\quad\\text{and}\\quad C_9 = \\frac{3}{\\pi}\\int_0^\\infty \\alpha_A(i\\omega)\\alpha_B(i\\omega)\\alpha_C(i\\omega)\\,d\\omega,$$ evaluated with dynamic dipole polarizabilities from relativistic calculations. The polarizabilities themselves are sums over dipole transitions, with oscillator strengths computed by different many-body methods for different species: RMBPT for Cu and Ag, the multi-configuration Dirac-Fock method for group II and XII atoms, and the relativistic all-order method for monovalent partners. The reported $C_6$ values agree with earlier theoretical values mostly within about 1–10%, with the largest deviations (roughly 14–18%) for the Sr and Ba partners; the authors note that Ag–Cs has the largest $C_6$ and Cu–Be$^+$ the smallest in their set, and the $C_9$ values are all new.","pith_inferences":["Not stated in the paper, but the product structure of the Casimir–Polder integrals implies that if a partner's dynamic polarizability is later improved, every coefficient involving that partner can be rescaled without recalculating the Cu or Ag side of the integrand.","Ratios such as $C_9$(Cu–Cu–X)/$C_6$(Cu–X) may be more stable against systematic errors than the absolute values because some errors would partially cancel; this is a testable cross-check the paper does not perform.","A natural next check is to measure trap-loss or photoassociation spectra for one of the predicted pairs, for example Ag–Cs or Cu–Hg, and invert the data for $C_6$; that would provide the first experimental benchmark for these tables."],"forward_implications":["Cold-atom and hybrid atom–ion experiments involving Cu or Ag now have the leading two-body interaction strengths needed to estimate whether atom–atom or atom–ion pairs remain bound at ultracold temperatures.","The three-body coefficients allow estimates of non-additive contributions to the interaction potential, which matter for three-body recombination and for the stability of mixed-species traps.","The reported hierarchy—Ag–Cs largest $C_6$, Ag–Ag–Cs largest $C_9$, Cu–Be$^+$ and Cu–Zn$^+$ smallest—gives a quick guide to which combinations will interact most strongly.","Because most group XII values and all $C_9$ values were previously missing, the tables fill a specific gap in inputs for modeling van der Waals complexes and lattice or surface traps involving metallic atoms."],"supporting_citations":[{"why":"The authors' earlier papers that supply the dynamic dipole polarizabilities of the group I, II, and XII atoms and ions used in Eqs. (2) and (4).","marker":"[38, 52, 53]"},{"why":"Provides the main comparison $C_6$ values for Cu and Ag with group I and II atoms; agreement with these values is the paper's stated accuracy check.","marker":"[49]"},{"why":"Supplies the TDDFT $C_6$ values and static polarizabilities used as secondary comparisons for Cu and Ag dimers.","marker":"[48]"},{"why":"Defines the relativistic all-order single-double with partial triples wave functions used for monovalent partners.","marker":"[40]"},{"why":"Gives the multi-configuration Dirac-Fock code used to obtain wave functions and matrix elements for the divalent group II and XII atoms.","marker":"[51]"},{"why":"Provides semiempirical static dipole polarizabilities of Cu and Ag used to benchmark the new polarizability values.","marker":"[47]"},{"why":"Gives coupled-cluster static polarizabilities of Cu and Ag that serve as an additional benchmark for the new polarizability values.","marker":"[46]"}],"fun_headline_variants":["First C9 coefficients for Cu and Ag with groups I, II, XII","Cu and Ag vdW: new three-body dispersion coefficients","C6 and C9 tables for Cu-Ag with 18 elements and ions","Two- and three-body dispersion for Cu and Ag atoms"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole table trusts the dynamic polarizabilities of the partner atoms and ions that are imported from the authors' earlier papers without being recomputed here, so a systematic error in those inputs would shift every $C_6$ and $C_9$ value.","fun_headline_variants_meta":{"raw":{"variants":["First C9 coefficients for Cu and Ag with groups I, II, XII","Cu and Ag vdW: new three-body dispersion coefficients","C6 and C9 tables for Cu-Ag with 18 elements and ions","Two- and three-body dispersion for Cu and Ag atoms"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000235,"raw_usage":{"total_tokens":1575,"prompt_tokens":1093,"completion_tokens":482,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":709,"completion_tokens_details":{"reasoning_tokens":405}},"tokens_in":709,"tokens_out":482,"duration_ms":4598,"temperature":1.0,"reasoning_tokens":405,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:25:00.441161+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"An independent high-accuracy calculation of the three-body coefficient for Ag–Ag–Cs, predicted here to be 48,296 atomic units, that disagrees by more than the claimed few-percent accuracy of the inputs would show the imported partner polarizabilities are not reliable.","supporting_citations":[{"cited_title":"´Smia lkowski and M","cited_arxiv_id":null,"evidence_quote":"Provides the main comparison $C_6$ values for Cu and Ag with group I and II atoms; agreement with these values is the paper's stated accuracy check."},{"cited_title":"Gould and T","cited_arxiv_id":null,"evidence_quote":"Supplies the TDDFT $C_6$ values and static polarizabilities used as secondary comparisons for Cu and Ag dimers."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the relativistic all-order single-double with partial triples wave functions used for monovalent partners."},{"cited_title":"J¨ onsson, G","cited_arxiv_id":null,"evidence_quote":"Gives the multi-configuration Dirac-Fock code used to obtain wave functions and matrix elements for the divalent group II and XII atoms."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides semiempirical static dipole polarizabilities of Cu and Ag used to benchmark the new polarizability values."},{"cited_title":"Neogr´ ady, V","cited_arxiv_id":null,"evidence_quote":"Gives coupled-cluster static polarizabilities of Cu and Ag that serve as an additional benchmark for the new polarizability values."}],"review_version":1}