{"id":"05237ea5-929c-465a-bf3c-f22bc964db52","arxiv_id":"2607.25247","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Vibronic transition calculations using standard TDDFT reproduce azulene's excited-state absorption band shapes and positions, enabling assignment of ESA peaks.","lead":"This paper shows that ordinary DFT/TDDFT calculations, combined with vibronic transition calculations, can reproduce the band shapes and peak positions of excited-state absorption spectra, demonstrated on azulene. The approach offers a practical way to assign transient-absorption bands without specialized quantum-chemistry methods.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The ad-hoc ESA energy correction σ_ESA = σ_S0→Sn' − σ_S0→Sn is the load-bearing assumption: if TDDFT excitation-energy errors do not cancel between state pairs, all predicted ESA positions shift and the central assignments fail.","rationale":"The reader's weakest assumption identifies precisely the σ_ESA = σ_S0→Sn' − σ_S0→Sn combination rule as the point where the central claim is least secure. I agree: the method's ability to reproduce ESA band positions depends on this correction transferring TDDFT's systematic errors between state pairs, and the azulene validation does not independently test that transfer because the σ values themselves are fitted to the experimental S0→Sn transitions. This is not a charge of circularity in the narrow sense — the ESA spectra involve different final/initial states than the calibration data — but it does mean the central claim rests on an unverified modeling rule rather than on a parameter-free prediction. I considered whether the acknowledged anharmonicity of the S4 state is the more load-bearing issue; it is serious for the 375 nm assignment, but the σ-transfer rule is broader, affecting all assigned ESA peaks, and is therefore the single most load-bearing concern. The paper's restriction to band shapes and positions, and its honest statement about the harmonic limitation, reduce the severity; the claim is plausible but conditional. Hence the reader's CONDITIONAL verdict stands without adjustment.","tokens_in":10990,"tokens_out":5076,"duration_ms":54448,"concrete_test":"Independently compute the adiabatic Sn→Sn' transition energies (S1→S3, S1→S4, S2→S8, S2→S9) using a high-level multireference or coupled-cluster method (e.g., CASPT2/NEVPT2 or EOM-CCSD) at the same APFD optimized geometries, then compare these to the σ-corrected APFD vibronic peak positions. If the deviations exceed ~0.05–0.1 eV (the width of the ESA features), the correction-transfer rule is invalid. A complementary check: for each pair, compare the raw APFD difference E(S0→Sn') − E(S0→Sn) against the experimental S0→Sn'−S0→Sn difference; if the residual is not equal to σ_ESA within the linewidth, the cancellation assumption fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The method's predicted ESA peak positions are obtained by applying the correction rule in Section 2 (after Eq. 5): the ESA shift σ_ESA for Sn→Sn' is set to σ_S0→Sn' − σ_S0→Sn, where each σ is fitted so that the calculated S0→Sn absorption/emission peaks match experiment (Table S1). This rule assumes that the TDDFT excitation-energy error for the S0→Sn' transition is identical to that for S0→Sn, so the errors cancel when taking the difference. That is not generally true: TDDFT errors vary systematically with state character — valence vs. Rydberg, single vs. double-excitation character, charge-transfer contributions — and are especially unpredictable for the high-lying states (S8, S9) invoked for the 575 nm feature. The azulene demonstration is therefore not an independent test of the method's predictive power for ESA positions: the S0→Sn peaks used to determine σ are the same experimental data used to calibrate the energy scale, and the ESA positions inherit the validity of an untested cancellation rule. If the cancellation fails by as little as ~0.1 eV, the reassignment of the 375 nm feature from S1→S7 to S1→S4 and the 575 nm feature from S2→S11 to S2→S8/S9 becomes unsupported. The authors acknowledge the harmonic approximation fails for the S4 state (Section 3.3), which further undermines one of the two main new assignments, but the correction rule is the more general load-bearing issue because it affects every reported ESA peak position.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a practical methodology for predicting excited-state absorption (ESA) spectra by combining standard TDDFT geometry and frequency calculations with vibronic transition (Franck–Condon/Herzberg–Teller) calculations. Using azulene as a test system, the authors compute S1→Sn and S2→Sn vibronic band shapes and peak positions, compare them with transient absorption spectra, and reassign several ESA features (e.g., 375 nm to S1→S4, 575 nm to S2→S8/S9 instead of S2→S11). Absolute ESA intensities are not predicted; instead, a correction rule (σ_ESA = σ_S0→Sn' − σ_S0→Sn) and additive Gaussian widths are used, with the electronic transition moment taken from the corresponding S0→Sn' transition. The paper is explicitly framed as a practical, accessible alternative to specialized quadratic-response or real-time TDDFT methods.","tokens_in":11429,"tokens_out":2926,"duration_ms":36946,"significance":"If the central claim holds, the method would be valuable for interpreting transient-absorption and photoinduced-absorption spectra using only routine Gaussian 16 calculations, without requiring excited-to-excited transition moments. The paper is honest about its limitations: it acknowledges the harmonic approximation failure for the S4 state, the neglect of absolute intensities, and the approximate nature of the linewidth combination rule. The strengths are the transparency of the approach, the use of a well-studied molecule, and the direct identification of coupled normal modes. However, because the predicted ESA peak positions inherit a fitted correction that is not independently validated, and because one of the two main new assignments involves a state admitted to be anharmonic, the practical usefulness for band assignment is currently demonstrated only qualitatively and conditionally.","major_comments":[{"comment":"The comparison between calculated and experimental ESA spectra is entirely visual and uses an arbitrary scaling factor (1/13 in Figure 4b) for the key S1→S4 transition. Given that the central claim is that the method 'reproduces the vibrational band shapes and positions,' the absence of any quantitative metric (e.g., root-mean-square difference in peak positions, spectral overlap integral, or at least a table of calculated vs. experimental peak maxima for all assigned features) makes it impossible to judge how good the agreement actually is. The ω_FWHM values (800 cm⁻¹ in Figure 3, 2000 cm⁻¹ in Figure 4) are chosen ad hoc; their effect on the apparent agreement should be discussed, and the sensitivity of the assignments to these widths should be assessed.","section":"Section 3.3"}],"minor_comments":[{"comment":"The sentence 'Consequently, the present scheme does not provide absolute or relative ESA intensities' is repeated almost verbatim in Section 4; one occurrence could be removed. The notation in Eq. (5) is unclear: S is called 'the calculated spectrum' but is later convoluted with a Gaussian; it might be clearer to denote the stick spectrum explicitly.","section":"Section 2"},{"comment":"The caption says 'ω_FWHM = 2000 cm⁻¹ in (a) and (c)', but those panels are experimental spectra; presumably the experimental spectra are shown as measured and ω_FWHM applies to the calculated spectra in (b) and (d). This needs clarification.","section":"Figure 4 caption"},{"comment":"Reference 44 has a typo: 'ull. Korean Chem. Soc.' should be 'Bull. Korean Chem. Soc.' Also, reference 42 (Gaussian 16) is cited in a nonstandard format; consistent citation of the software manual would be preferable.","section":"References"},{"comment":"The sentence 'as can be evinced from the data reported in Figure 4(b)' appears twice in consecutive paragraphs; one can be removed. The phrase 'this does not imply that the S1→S5 and S2→S5 transitions are themselves forbidden' is good but could be accompanied by a short explanation of why the approximation fails for S5 rather than just stating it.","section":"Section 3.2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a practical application paper, and its central idea is plausible. The most serious concern is the energy correction rule in Section 2: it is the link between the raw vibronic calculations and the experimental peak positions, and it is fitted rather than derived or validated. The authors are refreshingly frank about limitations, but the S4 anharmonicity caveat in Section 3.3 cuts against one of the two main new assignments. I would ask for either a test of the σ cancellation rule or a clear statement that the assignments are tentative pending higher-level calculations."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First things first: the core idea is that vibronic band shapes for excited-state absorption can be computed from PESs alone, using ordinary TDDFT frequency calculations, without needing excited-to-excited transition moments. That is a useful and honest simplification. The authors apply it to azulene and obtain band shapes that resemble the experimental transient absorption, and they offer new assignments for the 375 nm and 575 nm ESA features. The writing is clear and the limitations are stated up front.\n\nWhat is genuinely new: Gierschner and co-workers had already demonstrated the vibronic approach with QR-TDDFT. This paper shows that routine TDDFT (APFD, etc.) may suffice, and it identifies specific coupled modes. The azulene absorption/emission benchmarks look good, giving some confidence that the PESs are reasonable.\n\nThe soft spot is the energy-scale correction. The authors fit a sigma to each S0→Sn transition to match experiment, then set the ESA shift to the difference of two sigmas. That assumes the TDDFT error for the initial and final excited states cancels. A careful reader will see this is load-bearing and unvalidated; if the cancellation fails by 0.1 eV, the reassignments become shaky. The paper does not discuss this transfer rule. The missing SI tables also prevent me from checking fitted values or doing replication.\n\nSecond, the S4 state is anharmonic (double well), and the harmonic adiabatic-Hessian treatment is acknowledged to be approximate. That is one of the two main new assignments (S1→S4), so the claim should be softer. The intensities are not predicted, and the 1/13 scaling is just for visualization; fine, but it means validation is by eye.\n\nThird, the abstract says the method 'reproduces the vibronic features and band positions.' That overstates it, since the band positions are adjusted by the fit. The band shapes are the genuine product.\n\nOverall: this is a serious, useful contribution for practitioners who want a quick way to assign ESA bands. It deserves a proper referee, but the authors should address the sigma transfer rule (e.g., test on a few molecules with known assignments or report sensitivity), include the SI data, and soften the position-claim. I would cite it if the SI and the revised argument hold up.\n\nRecommendation: send to peer review, with major revision.","headline":"Practical and honest for band shapes, but the fitted energy corrections mean the 'predicted' ESA positions are partly calibrated to the same data; the real product is a quick assignment tool, not independent prediction.","tokens_in":11930,"tokens_out":2703,"would_cite":true,"duration_ms":28310,"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":"Vibronic transition calculations reproduce azulene's excited-state absorption bands and reassign several peaks.","keywords":["excited-state absorption","vibronic transition","Franck-Condon","Herzberg-Teller","TDDFT","azulene","transient absorption","band assignment"],"falsifier":"Compute the S1→S4 transition energy of azulene with a wavefunction method that includes explicit excited-to-excited transition moments; if that energy lies outside the observed ESA band near 375 nm and its computed vibronic progression does not match the measured band shape, the central assignment fails.","tokens_in":10870,"feed_emoji":"🔬","tokens_out":6829,"duration_ms":64508,"temperature":0.7,"pith_summary":"The paper tries to establish that excited-state absorption (ESA) spectra can be predicted practically by combining vibronic (Franck-Condon) transition calculations with routine density functional theory, without needing excited-state-to-excited-state transition moments. Using azulene as a test case, the method reproduces the vibronic band shapes and peak positions of the experimental transient-absorption spectrum, and it reassigns several ESA peaks to different electronic transitions than earlier multireference calculations suggested. If true, this gives experimentalists a straightforward way to assign ESA bands in transient and photoinduced absorption spectra using standard quantum-chemistry packages.","feed_headline":"Vibronic shapes assign azulene's excited-state absorption peaks","feed_subtitle":"Franck-Condon factors, not transition moments, give band positions that reassign several peaks.","key_machinery":"The central object is the Franck-Condon–Herzberg-Teller vibronic transition calculation (adiabatic Hessian, time-independent framework at 298 K) between two electronic states, which yields the vibrational band shape from the overlap of harmonic vibrational wavefunctions. Its inputs are the pair of potential energy surfaces obtained from DFT/TDDFT frequency calculations. To compare with experiment, the calculation uses an empirical energy correction σ_ESA = σ(S0→Sn′) − σ(S0→Sn) and approximates the ESA line width as the sum of the two ground-state transition line widths.","core_discovery":"The paper shows that the vibronic band shapes and peak positions of ESA spectra can be obtained from Franck-Condon–Herzberg-Teller vibronic transition calculations between two electronic states, using only the potential energy surfaces (equilibrium geometry, vibrational frequencies, normal modes) that routine DFT/TDDFT provides. Because Franck-Condon factors depend only on the potential energy surfaces and not on the electronic transition moment between the two excited states, the method circumvents the need for excited-to-excited transition moments. For azulene, the calculated ESA bands reproduce the experimental transient-absorption spectrum and lead to different assignments than earlier m","pith_inferences":["If the empirical subtraction rule for the energy correction transfers TDDFT's systematic error, the approach should generalize to other π-conjugated molecules; a natural test is to apply it to molecules with known ESA spectra and compare the assigned transitions.","The azulene reassignments suggest some published ESA assignments based on vertical excitation energies alone may be worth revisiting with band-shape information.","The harmonic treatment of azulene's bent S4 state is explicitly approximate; for such double-well surfaces, an anharmonic or multireference treatment would be needed, and band-shape predictions there should be treated as qualitative.","Combining the calculated vibronic band shapes with measured ESA intensities could provide a route to estimate excited-to-excited transition moments by intensity fitting."],"forward_implications":["ESA bands in transient absorption and photoinduced absorption spectra of molecules with well-behaved excited-state potential energy surfaces can be assigned to specific electronic transitions using only standard DFT/TDDFT calculations.","Transitions whose surrogate S0→Sn′ transition has zero oscillator strength are invisible in this scheme even if the actual excited-state transition is allowed, as with S1→S5 in azulene.","Vibronic calculations identify the vibrational normal modes coupled to each electronic transition, directly pointing to the modes that drive excited-state structural changes.","The method is restricted to band positions and shapes; absolute ESA intensities still require quadratic-response or explicit excited-to-excited transition-moment evaluations.","The azulene reassignments imply that matching vibronic band shapes, not just vertical transition energies, is a useful criterion for assigning ESA bands."],"fun_headline_variants":["Franck-Condon factors, not transition moments, assign azulene ESA peaks","Vibronic calculations predict azulene's ESA band positions","Azulene's excited-state absorption reassigned via vibronics","ESA peaks from vibronic transitions, no excited-state moments"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The predicted ESA band positions rest on an empirical rule that sets the excited-state energy correction as the difference of two fitted ground-state corrections (σ_ESA = σ_S0→Sn′ − σ_S0→Sn); if the TDDFT systematic error does not cancel in that difference, every predicted ESA peak shifts coherently and the assignments fail.","fun_headline_variants_meta":{"raw":{"variants":["Franck-Condon factors, not transition moments, assign azulene ESA peaks","Vibronic calculations predict azulene's ESA band positions","Azulene's excited-state absorption reassigned via vibronics","ESA peaks from vibronic transitions, no excited-state moments"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000191,"raw_usage":{"total_tokens":1151,"prompt_tokens":684,"completion_tokens":467,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":428,"completion_tokens_details":{"reasoning_tokens":393}},"tokens_in":428,"tokens_out":467,"duration_ms":5414,"temperature":1.0,"reasoning_tokens":393,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T02:57:37.389937+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the S1→S4 transition energy of azulene with a wavefunction method that includes explicit excited-to-excited transition moments; if that energy lies outside the observed ESA band near 375 nm and its computed vibronic progression does not match the measured band shape, the central assignment fails.","supporting_citations":[],"review_version":1}