{"id":"9be8f037-0cbe-4797-a172-57034cb943b4","arxiv_id":"1908.03018","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"UKRmol+ reengineers the UK molecular R-matrix codes with optional B-spline continuum functions, MPI parallelization, and photoionization and RMT interfaces, and demonstrates the new capabilities on electron, positron, and photoionization examples.","lead":"This paper presents UKRmol+, an open-source Fortran suite that models collisions of electrons and positrons with molecules and molecular photoionization using the R-matrix method. The release adds mixed Gaussian and B-spline continuum basis functions, parallel computing, and interfaces to time-dependent calculations.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"GBTOlib's mixed GTO/BTO two-electron integrals are the unverified foundation of the BTO continuum results; the paper's free-scattering check cannot validate them, and the library is cited only as 'In preparation' (Ref. [10]).","rationale":"The reader's CONDITIONAL verdict names GBTOlib correctness as the weakest assumption; I agree with that identification and sharpen it: the specifically unverified quantity is the mixed GTO/BTO two-electron integral evaluation, because the paper's own free-scattering test (Section 3.1.2) runs with H = -nabla^2/2 and therefore cannot detect errors in the two-electron classes, and because the test-suite benchmarks (Section 7) are regression outputs of the same code rather than independent reference values. Good faith balances the concern: the paper is unusually candid about its own limitations — Section 8.4 states the benzene calculation 'is not to present accurate observables,' demonstrates LLeg sensitivity above about 25 eV, and admits incomplete continuum-l convergence above about 50 eV; the footnote to Eq. (20) acknowledges the Szmytkowski–Hinze subtlety in the boundary expansion; Section 3.1.2 gives a quantitative free-scattering acceptance criterion (eigenphase sums below 10^-2 rad). Independent support is genuine: the BeH BTO application was published in a peer-reviewed journal (Ref. [38]); the thiophene excitation cross sections in Fig. 9 match unnormalized EELS data; the positron-H2 cross sections in Fig. 11 are compared with two experiments; and the suite ships a documented parallel test suite. Nevertheless, the central new capability — B-spline continuum with large inner regions and the RMT pathway — is built on a library with no archival description (Ref. [10], 'In preparation'), and the reader cannot audit its numerics from this paper. Secondary gaps (RMT also 'In preparation', Ref. [13]; the unquantified claims in Section 1 and Section 8.3 that old UKRmol results are reproduced; no DOI or checksum for the Zenodo release) reinforce but do not by themselves drive the verdict. This is a verification gap, not an identified error; I found no internal inconsistency. The proposed integral-level cross-check is the minimal decisive experiment: if an independent quadrature reproduces GBTOlib values to high precision, the main obstacle to ACCEPT is removed; if not, the BTO claims in Sections 8.2, 8.4, and Section 6 would require re-examination. The reader's CONDITIONAL verdict is therefore confirmed; no adjustment is needed.","tokens_in":42525,"tokens_out":17295,"duration_ms":172733,"concrete_test":"Recompute one representative mixed integral of the CC||TT class used in the benzene calculation (Section 8.4) — a B-spline continuum function with l = 2 and a diffuse target GTO, R-matrix radius a = 13 a0 — with an independent code using direct two-dimensional Gauss–Legendre quadrature (delta_r = 0.01 a0, LLeg = 60), and compare with the GBTOlib value produced by SCATCI_INTEGRALS for identical input. Require agreement to better than 10 significant digits, and additionally confirm that the GBTOlib value is stable when its own delta_r parameter is halved. Agreement and stability would validate the mixed-integral path underlying the BTO scattering, photoionization, and RMT-interface results; disagreement at the 10^-5 level or worse, or a material dependence on quadrature parameters, would show those results rest on an unvalidated integral evaluation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (Section 9) is that UKRmol+ provides a reengineered suite whose headline new capability is the mixed GTO/BTO continuum representation (BeH scattering at a = 35 a0, Section 8.2; stable benzene photoionization to 80 eV, Section 8.4). All BTO results flow through GBTOlib (Section 3.1). The load-bearing assumption is that GBTOlib evaluates the mixed one- and two-electron integrals accurately and stably. Three facts make this the least secure link. (1) Reference [10], GBTOlib, is explicitly 'In preparation': no peer-reviewed description of its B-spline quadrature (delta_r = 0.25 a0), Legendre truncations max_l_legendre_1el/2el, or orthogonalization exists. (2) The paper's only in-suite check with an independent reference value, the free-scattering test (Section 3.1.2), solves a one-particle problem with H = -nabla^2/2; it exercises overlap, kinetic, and Bloch integrals plus basis completeness, but cannot detect errors in the mixed two-electron integral classes (CC||TT, CC||CT), which are precisely the numerically delicate parts. (3) The test-suite benchmark outputs (Section 7) are regression references generated by the same code, so agreement establishes reproducibility, not correctness. The only in-paper evidence that exercises mixed two-electron integrals is Fig. 12, whose authors state the calculation 'is not to present accurate observables' and admit incomplete continuum-l convergence above about 50 eV. Independent support is real — the BeH BTO application is published (Ref. [38]); thiophene EELS and positron-H2 comparisons match experiment (Figs. 9, 11) — but none of it audits the mixed-integral implementation. No internal inconsistency is apparent; the concern is an unverified foundation for the suite's central new capability, with secondary verifiability gaps (RMT, Ref. [13], also 'In preparation'; unquantified claims in Sections 1 and 8.3 of reproducing old UKRmol results).","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript describes UKRmol+, a Fortran 95/2003 suite for molecular R-matrix calculations of electron and positron scattering, molecular photoionization, and generation of input for the RMT time-dependent suite. The presentation covers the standard inner-/outer-region R-matrix formalism in Section 2, the individual programs and their namelists in Section 3, and the workflows for scattering, photoionization, and RMT input in Sections 4-6. A test suite is described in Section 7, and Section 8 presents illustrative applications: electron-impact excitation of thiophene compared with EELS data, electron scattering from BeH with a mixed GTO/BTO continuum at R = 35 a0, positron-H2 scattering with pseudostates, and photoionization of benzene comparing GTO-only and mixed GTO/BTO continuum bases.","tokens_in":42812,"tokens_out":4332,"duration_ms":45988,"significance":"If the central claims hold, UKRmol+ is a substantial community resource: it is open-source, distributed with a build system and test suite, supports MPI parallelization through MPI-SCATCI and MPI-RSOLVE, accepts target orbitals from external quantum chemistry packages, and extends the continuum representation to mixed Gaussian/B-spline bases. The Section 2.1 derivation is standard and correct, and the comparisons against independent experimental EELS and positron-beam data, together with reproduction of previously published BeH results, provide meaningful grounding. The authors are also candid about the limitations of the benzene demonstration. The main risk is that the new mixed GTO/BTO integral capability rests on GBTOlib, which is cited only as \"In preparation\", and the in-paper validation of that component is incomplete.","major_comments":[{"comment":"The free-scattering test (Section 3.1.2) checks overlap, kinetic-energy, and Bloch integrals in a one-electron problem with H = -nabla^2/2, but it cannot detect errors in the mixed two-electron integral classes <CC||TT> and <CC||CT>, which are precisely the numerically delicate classes needed for the BTO continuum capability. Since GBTOlib is described only as \"In preparation\" (Ref. [10]) and no independent analytical or numerical validation of these integral classes is reported, the headline BTO results rest on an unverified foundation. I recommend adding explicit convergence tests of these integral classes against known values, or against an independent implementation, and reporting the sensitivity to delta_r and the Legendre truncation parameters.","section":"Section 3.1.2 and Section 3.1.6"},{"comment":"The benzene photoionization example is the only in-paper molecular demonstration that exercises the mixed two-electron integrals, but the authors state that the calculation \"is not to present accurate observables\" and acknowledge that the results are not converged with respect to continuum angular momentum above about 50 eV. The visible differences between LLeg = 12 and LLeg = 24 in the 2E2g panel additionally show incomplete convergence in the Legendre truncation. As published evidence for the correctness of the mixed integral library this is weak; I ask for one converged benchmark, or a quantitative statement of the expected errors in the displayed curves.","section":"Section 8.4, Figure 12"},{"comment":"The claim that UKRmol+ \"should be able to reproduce virtually all the old results\" and that this \"has indeed been tested for a number of targets\" is not quantified, and the Section 7 test-suite benchmark outputs are generated by the same code, so they demonstrate reproducibility rather than correctness. A table comparing UKRmol and UKRmol+ results for at least one representative target, with stated tolerances, would make the backward-compatibility claim concrete and would strengthen the paper's central assertion.","section":"Section 1 and Section 7"}],"minor_comments":[{"comment":"The abstract contains the typo \"photionisation\" in place of \"photoionisation\".","section":"Abstract"},{"comment":"The text reads \"The next section shows shows how this leads\"; the duplicated word should be removed.","section":"Section 2.2"},{"comment":"There are several grammatical and typographical errors that should be corrected: \"all the orbitals used for m a single orthonormal set\" in Section 3.1.5, \"differnet\" in Section 3.2, \"quadropole\" in Section 3.4, \"This calculations was\" in Section 8.1, and \"Hamilonians\" in Section 8.2.","section":"Sections 3.1.5, 3.2, 3.4, 8.1, 8.2"},{"comment":"The caption ends with an incomplete phrase \"[72] and.\" which should be completed or removed.","section":"Figure 9"}],"recommendation":"major_revision","confidential_remarks":"The core reservation is the status of GBTOlib: the paper's principal new capability depends on an integral library that is cited only as \"In preparation\". The editor may wish to ask the authors for either independent validation of the mixed GTO/BTO integral classes or a companion report describing GBTOlib before acceptance. The extensive self-citation is mostly contextual, and the independent experimental benchmarks partially mitigate this concern."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a serious software paper, not a physics breakthrough, and it mostly delivers what it claims. The genuinely new stuff is engineering: UKRmol+ reworks the whole inner-region pipeline, lets users plug in Molpro/Psi4 orbitals, and adds a mixed Gaussian/B-spline continuum basis, MPI parallelization, photoionization dipole output, and an interface that feeds the RMT time-dependent code. That last set of capabilities did not exist in the old UKRmol suite. The code is open source, GPL, ships with CMake and a test suite, and the examples show real results: thiophene excitation cross sections match unnormalized EELS data, positron-H2 improves with pseudostates, and the BeH application with a 35 a0 box was already published. Credit where due: this is a reproducible artifact, not a set of slides.\n\nSoft spots: the main one is exactly where the stress-test points. The headline new capability is the BTO continuum, and all mixed Gaussian/B-spline integrals come from GBTOlib, cited as 'in preparation' with no numerical details. The free-scattering test in Section 3.1.2 only uses a one-electron Hamiltonian, so it cannot catch errors in the mixed two-electron integrals (CC||TT, CC||CT). The test suite's benchmark outputs are regression checks against the same code. That said, the concern is bigger in principle than it is in evidence: published BeH calculations in a peer-reviewed journal already exercised mixed BTO integrals, and the benzene comparison, while explicitly not meant to be final observables, does show the expected sensitivity to the Legendre truncation. So I would call this a documentation and validation gap, not a reason to believe the integrals are wrong. Minor gaps: the claim that UKRmol+ reproduces old UKRmol results is not quantified; the Zenodo artifact has no DOI or checksum in the paper; RMT is also 'in preparation'.\n\nBottom line: this paper deserves serious refereeing. It is the reference for a widely used code, and the experimental comparisons ground the workflow. Ask the authors to add a GBTOlib validation statement or an independent mixed-integral check, to quantify the old-code comparison for at least one target, and to put a DOI on the Zenodo release. None of that changes the verdict from conditional to reject.","headline":"A substantial open-source release that delivers real new capability; referees should focus on documenting the integral library that the headline B-spline results depend on.","tokens_in":43501,"tokens_out":2167,"would_cite":true,"duration_ms":23433,"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":"UKRmol+ reengineers the molecular R-matrix codes to model electron and positron scattering, photoionization, and time-dependent laser inputs with mixed Gaussian/B-spline continua.","keywords":["electron-molecule scattering","positron scattering","photoionization","R-matrix method","B-spline orbitals","Gaussian-type orbitals","quantum chemistry interface","MPI parallelization"],"falsifier":"Compare GBTOlib's mixed Gaussian/B-spline integrals with high-order numerical quadrature on a small molecule at the suite's stated R-matrix parameters, and run its free-scattering eigenphase test across a wide energy range; eigenphase sums consistently above the paper's $10^{-2}$ rad rule of thumb would falsify the continuum representation.","tokens_in":42305,"feed_emoji":"⚛️","tokens_out":8141,"duration_ms":78450,"temperature":0.7,"pith_summary":"This paper reports UKRmol+, a completely rewritten implementation of the UK polyatomic molecular R-matrix scattering codes. It claims that one suite can compute low-energy electron and positron scattering from molecules and clusters, photoionization cross sections, and input for time-dependent R-matrix (RMT) calculations. The key advance is an optional mixed Gaussian-type-orbital and B-spline continuum, which permits much larger R-matrix spheres and higher photoelectron energies than the previous GTO-only code. A sympathetic reader would care because this is the public, reproducible foundation for a widely used method in molecular collision and photoionization physics.","feed_headline":"Rebuilt R-matrix suite reaches diffuse molecules and higher energies","feed_subtitle":"Mixed Gaussian/B-spline bases let one code handle electron, positron, and photon-driven molecular processes.","key_machinery":"The central mechanism is the R-matrix division of space combined with the mixed Gaussian/B-spline continuum implemented in GBTOlib. BTOs, defined as radial B-splines multiplied by real spherical harmonics, represent the continuum at higher kinetic energies and support much larger R-matrix radii, while GTOs describe target and low-energy continuum regions. The load-bearing step is the construction and diagonalization of the energy-independent inner-region Hamiltonian: one diagonalization supplies all scattering energies, and subsequent outer-region propagation and matching produce the observables.","core_discovery":"On its own terms, the central assertion is that UKRmol+ is a completely reengineered and extended version of the previous UKRmol codes, not an incremental patch. It takes target molecular orbitals from external quantum chemistry packages, builds the inner-region Hamiltonian with the GBTOlib integral library, diagonalizes it serially or in parallel, and feeds the eigenpairs to outer-region modules that yield K-matrices, cross sections, eigenphase sums, resonance parameters, photoionization dipoles, or RMT input. The demonstration cases are electron-impact excitation of thiophene, electron scattering from BeH at an R-matrix radius of $35\\,a_0$ using a mixed GTO/BTO continuum, positron-H2 scattering with pseudostates, and photoionization of benzene. The paper argues that the suite reproduces earlier UKRmol results and that the BTO capability extends the reliable energy range beyond what double-precision GTO-only calculations allow.","pith_inferences":["Beyond the paper's examples, the BTO continuum could become a systematic convergence tool: varying the R-matrix radius and the B-spline grid start gives a direct route to checking continuum completeness rather than merely extending the energy range.","The benzene comparison suggests a cheap diagnostic: because the Legendre truncation parameters $L_{\\mathrm{Leg}}=12$ and $24$ visibly change results above 25 eV, one could monitor convergence of the free-scattering eigenphase sum while raising these parameters in any new calculation.","The phase-matching tools for geometry-dependent photoionization amplitudes imply a natural test: apply the suite to a molecule with a known conical intersection and verify that the matched dipoles vary smoothly along a closed loop around the intersection."],"forward_implications":["Diffuse targets with R-matrix radii of tens of bohr become practical, as demonstrated by the BeH calculation at $35\\,a_0$ with 50 target states.","Photoionization calculations reach higher photoelectron energies: the mixed GTO/BTO basis removes unphysical oscillations that break down the double-precision GTO-only benzene results near 50 eV.","Positron scattering with pseudostates improves the treatment of polarization and can be extended to larger targets through the parallel MPI-SCATCI diagonalizer.","The same inner-region data feed the RMT code, so intense-laser time-dependent studies share an identical molecular description with the scattering and photoionization calculations.","The distributed test suite covers all supported Abelian point groups, serial and parallel runs, and benchmark outputs for Hamiltonian eigenvalues, cross sections, and eigenphase sums."],"supporting_citations":[{"why":"In-preparation library that supplies the mixed GTO/BTO one- and two-electron integrals; the BTO continuum capability rests on it.","marker":"[10]"},{"why":"External quantum chemistry package that supplies the target molecular orbitals in Molden format used as the starting point of UKRmol+ calculations.","marker":"[9]"},{"why":"Describes the previous UKRmol suite that UKRmol+ reengineers and against which reproducing old results is tested.","marker":"[8]"},{"why":"Defines the fitting of continuum GTO exponents that provides the Gaussian part of the continuum basis.","marker":"[23]"},{"why":"Establishes the B-spline representation on which the BTO continuum functions are built.","marker":"[22]"},{"why":"BeH calculation with mixed GTO/BTO continuum that demonstrates the large-R-matrix-radius capability.","marker":"[38]"},{"why":"Thiophene calculation used to show that UKRmol+ reproduces measured electron-impact excitation cross sections and core-excited resonances.","marker":"[72]"},{"why":"Provides the positron-H2 pseudostate model that UKRmol+ reproduces and extends in the positron example.","marker":"[5]"},{"why":"Supplies the photoionization formalism, partial-wave dipoles, and cross-section framework implemented in RSOLVE and DIPELM.","marker":"[11]"},{"why":"Defines the RMT time-dependent suite for which UKRmol+ produces the molecular data input.","marker":"[13]"}],"fun_headline_variants":["Rebuilt R-matrix suite covers electrons, positrons, photons in one code","Mixed B-spline basis extends R-matrix to diffuse molecules and higher energies","UKRmol+ reengineers molecular scattering with quantum chemistry inputs","New R-matrix suite handles electron, positron, and photon interactions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"If the unpublished integral library used for the mixed Gaussian/B-spline basis has numerical errors, the B-spline continuum results collapse, since no independent published reference for those integrals yet exists.","fun_headline_variants_meta":{"raw":{"variants":["Rebuilt R-matrix suite covers electrons, positrons, photons in one code","Mixed B-spline basis extends R-matrix to diffuse molecules and higher energies","UKRmol+ reengineers molecular scattering with quantum chemistry inputs","New R-matrix suite handles electron, positron, and photon interactions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001268,"raw_usage":{"total_tokens":5131,"prompt_tokens":829,"completion_tokens":4302,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":445,"completion_tokens_details":{"reasoning_tokens":4221}},"tokens_in":445,"tokens_out":4302,"duration_ms":29817,"temperature":1.0,"reasoning_tokens":4221,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:27:15.884834+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare GBTOlib's mixed Gaussian/B-spline integrals with high-order numerical quadrature on a small molecule at the suite's stated R-matrix parameters, and run its free-scattering eigenphase test across a wide energy range; eigenphase sums consistently above the paper's $10^{-2}$ rad rule of thumb would falsify the continuum representation.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Describes the previous UKRmol suite that UKRmol+ reengineers and against which reproducing old results is tested."},{"cited_title":"Faure, J","cited_arxiv_id":null,"evidence_quote":"Defines the fitting of continuum GTO exponents that provides the Gaussian part of the continuum basis."},{"cited_title":"Bachau, E","cited_arxiv_id":null,"evidence_quote":"Establishes the B-spline representation on which the BTO continuum functions are built."},{"cited_title":"Darby-Lewis, Z","cited_arxiv_id":null,"evidence_quote":"BeH calculation with mixed GTO/BTO continuum that demonstrates the large-R-matrix-radius capability."},{"cited_title":"Loupas, K","cited_arxiv_id":null,"evidence_quote":"Thiophene calculation used to show that UKRmol+ reproduces measured electron-impact excitation cross sections and core-excited resonances."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the photoionization formalism, partial-wave dipoles, and cross-section framework implemented in RSOLVE and DIPELM."}],"review_version":1}