{"id":"8081c672-a222-40db-86cc-9960f6d4dff6","arxiv_id":"2509.08245","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"CI on DFT molecular orbitals gives multi-reference-CI-level excitation energies for molecules with strong dynamic but weak static correlation, but fails for strongly multireference core states as in N2.","lead":"This paper tests configuration-interaction calculations that use density-functional-theory molecular orbitals instead of Hartree-Fock orbitals, applied to valence and core excited states of CH4, CO2, and N2. The DFT-orbital version matches multi-reference CI accuracy for CO2-like molecules with strong dynamic but weak static correlation, at lower computational cost.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"CO2 core-excitation claim rests on an unverified active-space plateau: if the 'Rydberg contamination' attribution is wrong, the reported 290.2 eV agreement is an artifact of truncation.","rationale":"The reader's weakest_assumption identifies exactly the same load-bearing concern: the CO2 core-excitation claim hinges on the plateau convention and the Rydberg-contamination attribution. My independent reading of the manuscript finds no more fundamental issue—the valence-state results for CO2 and N2 are solid and the method is clearly described. The N2 core-excitation failure is disclosed and does not by itself undermine the CO2 claim; the fractional-charge scan is a parameter but the +2 choice is physically motivated. The code is available, though without a commit hash or data files, which is a reproducibility limitation rather than a correctness flaw. The plateau selection, however, is critical: it is the difference between a 0.4 eV agreement with experiment and a 1.3 eV error, and it is supported only by a plausible but unverified explanation. A test that removes diffuse functions would distinguish a true physical plateau from a truncation artifact. Thus the verdict remains CONDITIONAL, requiring additional evidence to confirm the CO2 core-excitation claim.","tokens_in":18811,"tokens_out":3342,"duration_ms":42720,"concrete_test":"Recompute the CO2 C 1s→π* excitation energy using the same relaxed +1 fractional-charge orbital basis and RAS-CISD expansion, but with the non-augmented cc-pVTZ basis (i.e., removing diffuse functions) across the same active-space sizes. If the 1.3 eV rise above 40 eV disappears and the value converges monotonically to ≈290.2 eV, the plateau attribution to Rydberg contamination is confirmed. If the converged value is ≈291.9 eV, then the reported plateau is a truncation artifact. Additionally, compute ⟨r²⟩ of the excited-state natural orbitals at the 20 eV and 80 eV active spaces: the plateau state should be compact, while the larger-AS state should be diffuse (Rydberg). This test directly settles whether the physically meaningful excitation energy is the plateau value.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim that CI/DFT 'competes with' MRCI for core-excited CO2 (2σg→2πu) depends on selecting the first plateau in the active-space convergence (virtuals between 15 and 30 eV, Figure 7) and discarding the values at larger active spaces, which are ~1.3 eV higher (291.9 eV vs 290.2 eV). The paper attributes the rise to 'Rydberg-state contamination from states lying close in energy' but provides no diagnostic evidence—no expectation values of r², no natural orbital analysis, no oscillator strengths—that the plateau state is the target état and the larger-AS state is a Rydberg admixture. The same contamination argument is invoked for N2, yet there no plateau is found and the method fails by 2.3 eV, which suggests the explanation may be post hoc. If the plateau value is not the true vertical excitation energy, then the CO2 core-excitation agreement is an artifact of active-space truncation, and the headline claim loses its strongest quantitative support. This is the most load-bearing assumption for the paper's central conclusion.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a CI/DFT method in which configuration-interaction expansions are built from molecular orbitals generated by preliminary DFT calculations (BLYP, PBE0, B3LYP), using the full many-electron Hamiltonian and Slater–Condon matrix elements. After a LiH ground-state convergence test, the method is benchmarked on vertical excitation energies for CH4, CO2, and N2, covering both valence and core (C 1s, N 1s) excited states, with orbital relaxation modeled by fractional positive charges on core orbitals. The reported successes include valence states of CO2 (RAS-CISD/DFT: 8.31 eV vs MRCI 8.27–8.29 eV) and N2 (8.52 eV vs 8.45–8.48 eV), the CH4 core state with relaxed orbitals (287.04 eV vs 287.05–287.4 eV experiment), and the CO2 core state (290.22 eV vs 290.61–290.74 eV experiment, at a selected active-space plateau). The paper concludes that CI/DFT competes with MRCI/MCSCF for states with strong dynamic correlation but weak multireference character, while failing for the strongly multireference N2 core-hole state.","tokens_in":19069,"tokens_out":7365,"duration_ms":79403,"significance":"The valence-state benchmarks are a useful, reproducible demonstration that DFT orbitals can accelerate single-reference CI convergence: the CO2 and N2 valence results are within ~0.04–0.07 eV of high-level MRCI references, and the code is made available on GitHub. The core-excitation picture is more fragile. The paper's headline quantitative support for 'competing with MRCI' on core-excited CO2 rests on selecting a plateau in the active-space convergence (virtuals 15–30 eV) and discarding larger-active-space values that are ~1.3 eV higher. No diagnostic evidence is provided that the selected plateau state is the target 2σg→2πu state and that the discarded region is Rydberg-contaminated. The same Rydberg explanation is invoked for N2, where no plateau is found and the method fails by 2.3 eV. Without either diagnostics to confirm the plateau interpretation or a narrowing of the central claim, the core-excitation portion of the abstract is not yet established.","major_comments":[{"comment":"The reported CO2 core-excitation energy of 290.22 eV (RAS-CISD/DFT) is taken from the first active-space plateau (virtuals 15–30 eV). The largest-AS value is 291.92 eV, ~1.3 eV higher, and the paper rejects it as 'Rydberg-state contamination.' No diagnostic—⟨r²⟩, natural-orbital occupancies, state overlap, or oscillator strength—is provided to show the plateau state is the target 2σg→2πu state and the larger-AS state is a Rydberg admixture. Because the abstract's headline claim that CI/DFT 'competes with MRCI' for CO2 rests on this plateau value, the claim is currently an artifact of active-space truncation unless the attribution is substantiated. Please add diagnostics and, if they do not support the plateau, revise the claim.","section":"§4.2, Fig. 7, Table 2"},{"comment":"For N2 core excitation, the same Rydberg-mixing explanation is invoked after the energy rises with AS, but no plateau is selected and the best result is 2.3 eV above experiment. The different treatment of the two systems is not justified. In addition, the +2 fractional K-shell charge is selected as the minimum of a scan over +0 to +4; the physical one-hole state would be +1. This makes the N2 core result dependent on a target-informed parameter. Provide an a priori criterion for choosing the fractional charge and for identifying Rydberg contamination, or treat these results as indicative rather than benchmark.","section":"§4.3, Fig. 9, Table 3"},{"comment":"The functional dependence of the CO2 plateau is not addressed. Table 5 reports a plateau value for RAS-CISD/PBE0 (290.346 eV) while the text states the plateau is absent for PBE0; and it reports a plateau for RAS-CISDT/HF (290.819 eV) although the main text says no plateau is observed in any CI/HF calculation. These inconsistencies, plus the fact that only some functionals/excitation levels show the plateau, make 'Rydberg contamination' look like a post hoc selection rule rather than a physical diagnostic. Please reconcile and test the plateau with state-character diagnostics.","section":"Supporting Information, Table 5 and §4.2"}],"minor_comments":[{"comment":"The notation Vee(r−r′) should be Vee(|r−r′|) or the symbol should be defined; as written it is ambiguous.","section":"Eq. (6)"},{"comment":"References 35/36 and 38/39 are duplicate entries (Becke 1988; Lee–Yang–Parr 1988).","section":"References"},{"comment":"The acronym is written inconsistently as IS-GMPCT in the text and IS-GMCPT in the Fig. 9 caption.","section":"§4.3/Fig. 9"},{"comment":"There are several typographical and spacing errors ('Inquantumchemistry', 'eigen-value', 'electronelectron'); a language pass would help.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The SI/main-text inconsistency around the CO2 plateau (values reported for PBE0 and RAS-CISDT/HF despite statements to the contrary) should be resolved before further review. If the requested diagnostics fail to support the Rydberg-contamination interpretation, the abstract and conclusions need to be narrowed to the valence-state claims, which are well supported."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a genuinely careful methods paper. The valence-state benchmarks are the real contribution. For CO2, RAS-CISD/DFT gives 8.31 eV against 8.27–8.29 MRCI; for N2, 8.52 eV against 8.40–8.48. Those are hard to argue with. The CH4 core-excitation results with a relaxed orbital basis are also very good. The authors are honest about where the method fails, especially N2 core (2.3 eV off) and states with strong multireference character.\n\nWhat's new is not the general idea of CI on DFT orbitals—Grimme and Hermann are cited—but the specific non-empirical implementation: full Schrödinger Hamiltonian, explicit singles/doubles/triples, and systematic benchmarking against MRCI. The code is on GitHub, which is more than many papers in this area do.\n\nThe soft spot is the CO2 core-excitation claim. The paper reports 290.22 eV at an active-space plateau (virtuals 15–30 eV) and attributes the rise at larger active spaces to \"Rydberg-state contamination.\" But there is no diagnostic evidence for that attribution—no ⟨r²⟩, no natural orbital analysis, no oscillator strengths. And the supporting information shows the plateau is not even present for PBE0 orbitals, which is a red flag that the plateau may be an artifact of the functional rather than a physical separation. If the plateau is not the true vertical excitation energy, the agreement with experiment is a truncation effect, and the core-excitation claim weakens to \"still better than CI/HF but not MRCI-competitive.\" That is a real hole, but it is one that additional diagnostics or a test on another molecule could fill.\n\nThe N2 fractional charge is effectively fitted—scanning +0 to +4 and reporting the +2 minimum—but the authors disclose this clearly and the method still misses experiment by a wide margin, so it is not hidden.\n\nThe paper is worth a serious referee. The methods are sound, the valence results are solid, and the core-excitation issues are the kind of thing that peer review could push the authors to address. I would want the plateau attribution supported with actual wavefunction analysis before trusting the CO2 core number. That is a moderate revision, not a desk reject.\n\nWho this is for: people doing X-ray spectroscopy simulations or developing cheap CI variants. I'd bring it to a reading group focused on electronic structure methods, and I'd cite the valence benchmarks. Just don't cite the CO2 core plateau without a caveat.","headline":"Careful CI/DFT paper with solid valence benchmarks; the CO2 core-excitation win rests on an under-diagnosed active-space plateau.","tokens_in":19585,"tokens_out":1718,"would_cite":true,"duration_ms":19410,"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":"Configuration-interaction calculations built on DFT molecular orbitals rival multireference methods for core- and valence-excited states of molecules with strong dynamic electron correlation.","keywords":["configuration interaction","DFT orbitals","core-excited states","valence-excited states","dynamic electron correlation","restricted active space","orbital relaxation","CO2"],"falsifier":"Perform the CO2 carbon core-excitation calculation with an active space that explicitly includes the diffuse (Rydberg-like) orbitals but separates them, e.g., by projection or by a core-specific multireference method that treats them on equal footing. If the converged excitation energy is about 291.9 eV, the 290.2 eV plateau reading is an artifact of active-space truncation; if it stays near 290.2 eV, the plateau interpretation is correct.","tokens_in":18622,"feed_emoji":"⚛️","tokens_out":10413,"duration_ms":111923,"temperature":0.7,"pith_summary":"This paper tries to establish that configuration-interaction (CI) calculations built on molecular orbitals from a preliminary DFT calculation, called CI/DFT, can model valence- and core-excited states more reliably than standard CI on Hartree-Fock orbitals, at lower cost than multireference methods. The authors show that for molecules with strong electron correlation but limited multi-reference character, such as CO2, CI/DFT with double excitations comes within about 0.04 eV of multireference CI references for the valence state and within about 0.4 eV of experiment for the carbon K-edge core-excited state. For weakly correlated CH4 the orbital basis matters little once core-hole relaxation is accounted for, while for the strongly multi-reference N2 core-excited state CI/DFT stays about 2.3 eV above experiment, indicating the method's limit. The key moves are using DFT orbitals as the CI one-electron basis and modeling the core hole with fractionally charged relaxed orbitals. If right, the paper identifies a class of molecules where single-reference CI plus DFT orbitals can compete with far more expensive multireference calculations.","feed_headline":"DFT orbitals let cheap CI match multireference accuracy","feed_subtitle":"For CO2, CI on DFT orbitals lands core-excitation energies within 0.4 eV of experiment.","key_machinery":"The central object is the CI/DFT Hamiltonian: a configuration-interaction matrix built with Slater-Condon rules in a basis of molecular orbitals from a preliminary DFT calculation instead of Hartree-Fock orbitals. The DFT orbitals carry a portion of dynamic electron correlation into the reference space, so a truncated CI recovers more correlation energy per configuration. Two supporting devices carry the argument: restricted active spaces that control where singles, doubles, and triples are allowed, and a fractional-charge relaxation step that places a partial positive charge on core orbitals to mimic the core hole while preserving spin symmetry.","core_discovery":"The paper establishes that switching the CI one-electron basis from Hartree-Fock to DFT orbitals improves how much correlation a truncated CI expansion captures. For CO2, RAS-CISD/DFT gives a valence excitation of 8.31 eV versus MRCI references of 8.27–8.29 eV, and the carbon K-edge excitation reaches 290.22 eV at its first plateau against experimental values of 290.61–290.74 eV. For N2, the valence state agrees with MRCI and spectroscopy within 0.1 eV once doubles are included, but the 1σu→1πg core excitation stays 2.3 eV above experiment. Core-excited states require orbital relaxation (fractional positive charge on the core orbitals); without it, CH4 core energies miss by about 10 eV.","pith_inferences":["The first-plateau criterion used for the CO2 core excitation suggests a practical protocol: scan the active-space size and read the core excitation at the plateau before high-lying virtuals mix in Rydberg-like states; if this protocol generalizes, it would give a cheaper route to core binding energies. (Our inference, not stated as a general rule in the paper.)","The near-equivalence of RAS-CISD/DFT and RAS-CISDT/HF for the CO2 valence state hints that a DFT basis may substitute for one excitation level in the CI hierarchy; a systematic test across more molecules would show how general this substitution is.","Because CI/DFT produces explicit wavefunctions, not just energies, the same orbitals and Hamiltonian could be carried into time-dependent simulations of core-hole dynamics; the paper does not explore this, but its implementation is compatible with such extensions.","For the N2 core state, the systematic overestimation may indicate that delocalized core orbitals plus DFT cannot reproduce the static correlation of the hole; a symmetry-broken fractional-charge localization might improve the energy without full CASSCF optimization, but this remains an untested variant."],"forward_implications":["RAS-CISD/DFT matches MRCI/MCSCF valence excitation energies within about 0.1 eV for CO2 and N2, suggesting a cheaper single-reference route to such states.","Core-excited states require orbital relaxation via a fractional core charge; without it even weakly correlated CH4 is off by about 10 eV.","Double excitations are essential for core-hole states in CO2 and N2; the DFT basis does not eliminate the need for doubles.","For states with strong multi-reference character, such as the N2 core excitation, CI/DFT stays about 2.3 eV above experiment, so the method's reach is limited to dynamic-correlation-dominated states.","In the full-CI limit, HF and DFT orbital bases produce identical energies, confirming that the advantage of CI/DFT is strictly a truncation effect."],"supporting_citations":[{"why":"Earlier DFT-based CI model with empirical scaling; this work uses the full Schrödinger Hamiltonian instead of empirical corrections.","marker":"22"},{"why":"Prior hybrid TDDFT/CIS framework that the present method contrasts with and extends to explicit higher excitations.","marker":"26"},{"why":"Quantum-chemistry package that supplies the SCF/DFT orbitals and one- and two-electron integrals from which the CI/DFT Hamiltonian is built.","marker":"27"},{"why":"Textbook Slater-Condon rules used to evaluate CI matrix elements and to validate the implementation against closed-form expressions.","marker":"29"},{"why":"Source of MRCISD, CASCI, and CASSCF benchmark excitation energies for CH4 used for comparison.","marker":"45"},{"why":"MRCI reference for the CO2 valence excited state used to assess accuracy.","marker":"48"},{"why":"MRCI on MCSCF orbitals for CO2; the accuracy level CI/DFT is claimed to compete with.","marker":"49"},{"why":"EELS experimental value for the CO2 carbon core excitation used as accuracy target.","marker":"50"},{"why":"MRCI and MR-AQCC calculations on CASSCF orbitals for N2 valence states used as benchmark.","marker":"52"},{"why":"IS-CASSCF and IS-GMPCT calculations for the N2 core-excited state, used to show the gap for strongly multi-reference states.","marker":"59"}],"fun_headline_variants":["DFT orbitals boost CI accuracy for core-excited states","Cheap CI on DFT orbitals rivals multireference for CO2","Core-excited states improved by CI with DFT orbitals","DFT orbitals in CI: better core-excitation energies","CO2 core excitations: CI/DFT matches MRCI"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The CO2 core-excitation conclusion rests on the assumption that high-lying virtual orbitals mix in diffuse Rydberg-like states, so that the physically meaningful excitation energy is the first flat region of the convergence curve rather than the largest-active-space value.","fun_headline_variants_meta":{"raw":{"variants":["DFT orbitals boost CI accuracy for core-excited states","Cheap CI on DFT orbitals rivals multireference for CO2","Core-excited states improved by CI with DFT orbitals","DFT orbitals in CI: better core-excitation energies","CO2 core excitations: CI/DFT matches MRCI"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000167,"raw_usage":{"total_tokens":1112,"prompt_tokens":782,"completion_tokens":330,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":526,"completion_tokens_details":{"reasoning_tokens":246}},"tokens_in":526,"tokens_out":330,"duration_ms":4607,"temperature":1.0,"reasoning_tokens":246,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T20:56:38.911462+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Perform the CO2 carbon core-excitation calculation with an active space that explicitly includes the diffuse (Rydberg-like) orbitals but separates them, e.g., by projection or by a core-specific multireference method that treats them on equal footing. If the converged excitation energy is about 291.9 eV, the 290.2 eV plateau reading is an artifact of active-space truncation; if it stays near 290.2 eV, the plateau interpretation is correct.","supporting_citations":[],"review_version":1}