Spectroscopic photorelaxation signatures in pyrazine from nonadiabatic dynamics simulations with coupled cluster theory

Eirik F. Kj{\o}nstad; Henrik Koch; O. Jonathan Fajen; Sara Angelico; Todd J. Mart\'inez; Yi-Ping Chang

REVIEW 2 major objections 5 minor 15 references

Spectroscopic photorelaxation signatures in pyrazine from nonadiabatic dynamics simulations with coupled cluster theory

T0 review · 2 major / 5 minor · reviewed 2026-07-12 · grok-4.5

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Pith's one-line read High-level CCSD/SCCSD dynamics of pyrazine match the experimental B2u photoelectron decay and map ~34 fs B3u/Au beats to extractable spectral windows.

desk verdict Solid high-level AIMS/CCSD work that finally matches the experimental 1B2u PES decay without a strong revival and supplies a usable multistate SCCSD interface. read the letter →

arxiv 2607.03395 v2 pith:U6D53MAR submitted 2026-07-03 physics.chem-ph

Sara Angelico , Eirik F. Kj{o}nstad , Yi-Ping Chang , O. Jonathan Fajen , Todd J. Martínez , Henrik Koch This is my paper · ORCID

classification physics.chem-ph

keywords pyrazinenonadiabaticdynamicscoupledclustersimilarityconstrainedCCSDabinitiomultiplespawningtime-resolvedphotoelectronspectroscopyX-rayabsorptionconicalintersection

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Pyrazine after UV excitation has long been a benchmark for ultrafast nonadiabatic chemistry, yet theory and experiment have not fully agreed on the three-state decay path. This work runs ab initio multiple spawning on a new multistate similarity-constrained coupled-cluster (CCSD/SCCSD) surface for the first 200 fs and computes the time-resolved photoelectron spectrum plus nitrogen- and carbon-edge X-ray absorption spectra from the same trajectories. The simulated photoelectron signal of the bright 1B2u state decays with an ~11 fs constant and shows no strong revival, matching experiment; the 1B3u and 1Au populations then beat with a ~34 fs period that appears as clear oscillations in selected PES and N-edge energy windows. The beats are shown to be wave-packet motion on the adiabatic S1 surface between a B3u minimum and an Au transition state, not repeated nonadiabatic hops. The paper therefore supplies both a quantitative experimental benchmark and concrete spectroscopic fingerprints that higher-resolution experiments can test.

What carries the argument

Multistate similarity-constrained coupled cluster (SCCSD) with adaptive CCSD/SCCSD switching at a 0.01 eV gap threshold, interfaced to ab initio multiple spawning; the similarity constraints keep conical intersections real-valued so that three electronic states can be propagated on-the-fly and spectra can be built from the same trajectory ensemble.

What would settle it

A time- and energy-resolved photoelectron or N-edge X-ray absorption experiment that resolves the predicted ~30 fs oscillations in the 6.3–6.5 eV and 5.0–5.2 eV (PES) or 394.3–395.1 eV and 396.0–396.9 eV (N-edge) windows and either confirms or rules out the absence of a strong 1B2u revival after 50 fs.

Watch

Extended reading notes

Core claim

A multistate CCSD/SCCSD AIMS simulation of pyrazine produces a time-resolved photoelectron spectrum whose 1B2u feature decays with an exponential constant of 11 fs (6.9–7.4 eV window) and no strong later revival, in quantitative agreement with experiment, while the subsequent ~34 fs beats between the 1B3u and 1Au diabatic populations leave extractable oscillations in both PES and N-edge XAS windows and arise from nuclear motion on S1 between the B3u minimum and Au transition state.

Load-bearing premise

That twenty 0 K Wigner samples, an adaptive 0.01 eV CCSD/SCCSD switch, an incoherent trajectory-center approximation for spectra, and a transition-strength diabatization are enough to converge the populations, beat period and spectroscopic observables against experiment.

Editorial extensions

If this is right

The experimental 1B2u decay constant near 11–13 fs and the lack of a strong revival can be taken as validated by high-level theory.
Energy-windowed integrations of PES and N-edge XAS can be used to track the separate 1B3u and 1Au beats once experimental time resolution reaches ~10 fs.
The ~34 fs beat period and the role of the totally symmetric ν8a mode become concrete spectroscopic targets rather than pure population plots.
The multistate SCCSD interface removes the two-state restriction that previously limited on-the-fly coupled-cluster nonadiabatic dynamics.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the same adaptive multistate SCCSD/AIMS protocol is applied to other azabenzenes, the relative importance of dark nπ* states versus bright ππ* revivals may prove transferable.
The residual mismatch in the 100–125 fs beat period may be a diagnostic of basis-set or triple-excitation effects that future CC3 or larger-basis dynamics could isolate.
Higher-resolution XAS at both edges could simultaneously map the B2u decay (C-edge) and the B3u/Au beats (N-edge), turning pyrazine into a multi-edge nonadiabatic benchmark.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This is the cleanest high-level simulation of the pyrazine three-state problem I have seen. The real advance is the adaptive multistate SCCSD interface that lets them run AIMS with more than two states at CCSD quality; everything else follows from that. They get a quantitative match to the experimental TR-PES 1B2u decay (11 fs fit in the 6.9–7.4 eV window versus 13±3 fs) and, crucially, no strong revival, which several earlier calculations had predicted. The ~34 fs 1B3u/1Au beats on S1 are internally consistent with the extracted PES and N-edge windows and map cleanly onto motion between the B3u minimum and Au TS along ν8a. Energy-conservation and adaptive-switch checks in the SI look fine; drifts are small.

What they do well: direct computation of the observables from the trajectories, multiple broadening widths and energy windows, static critical-point assignments, and honest comparison to the published PES and XAS data. The mechanistic picture is tighter than most previous work.

Soft spots are ordinary for the field and already flagged by the reader: only twenty 0 K Wigner ICs, empirical spectral shifts, post-hoc windows, incoherent TBF-center spectra, and a transition-strength diabatization. None of these overturn the central PES claim or the absence of a strong revival. Code and trajectories are not public, which is a practical nuisance but not a scientific flaw. Sampling is the only place I would push for more in revision.

This is for people who care about nonadiabatic benchmarks, XAS/PES interpretation, or CC methods for dynamics. It deserves a serious referee. I would accept it after ordinary polishing; the central result holds.

Referee Report

2 major / 5 minor

Summary. The manuscript reports an AIMS nonadiabatic dynamics simulation of pyrazine photorelaxation at the CCSD/SCCSD level (cc-pVDZ), enabled by a newly developed multistate adaptive similarity-constrained CC interface. From the trajectories the authors compute time-resolved photoelectron spectra and N- and C-edge X-ray absorption spectra and compare them to published experiments. The central claims are: (i) quantitative recovery of the experimental 1B2u decay signature in TR-PES (exponential fit ~11 fs in the 6.9–7.4 eV window, no strong revival), (ii) ~34 fs beats between diabatic 1B3u and 1Au populations that produce extractable oscillations in selected PES and N-edge windows, and (iii) a mechanistic picture in which, after the initial ultrafast 1B2u decay, the nuclear wave packet remains largely on S1 and oscillates between the B3u minimum and Au transition state along totally symmetric and B3g modes (especially ν8a).

Significance. Pyrazine is a long-standing benchmark for ultrafast nonadiabatic dynamics; theory and experiment have only partially converged on a three-state picture and on the spectroscopic visibility of 1B3u/1Au beats and 1B2u revivals. The work advances the field by (1) implementing multistate SCCSD so that more than two states can be treated at the CCSD/SCCSD level in AIMS, (2) computing the experimental observables (TR-PES, N/C-edge XAS) directly from the trajectories rather than only populations, and (3) providing falsifiable spectroscopic signatures and a concrete stationary-point/normal-mode mechanism. Energy-conservation and norm checks for the adaptive interface are reported (SI S11), multiple spectral broadenings and energy windows are tested, and the PES comparison is quantitative for the 1B2u decay. These strengths make the paper a useful high-level reference for both theory and future higher-resolution experiments.

major comments (2)

Methods and SI S8: only twenty 0 K Wigner initial conditions (selected by a 4.56–5.13 eV window and oscillator-strength weighting) are propagated, producing 445 TBFs. The reported 1B2u decay constant, absence of revival, and ~34 fs beat period are load-bearing for the central claim. The manuscript should either demonstrate that these quantities are stable under modest increases in sampling (or under a different energy window) or state more explicitly that residual sampling uncertainty remains, especially for the weaker late-time oscillations (100–125 fs) that already disagree with experiment.
SI S6 and Results (Figs. 1D, 2D–E, 4A): diabatic populations and spectral decompositions rest on an approximate orthogonalization of the square-root transition-strength matrix F(R). The assignment of the 5.0–5.2 eV / 6.3–6.5 eV PES windows and of the N-edge windows to 1Au / 1B3u is therefore only as reliable as this diabatization. A short validation (e.g., comparison to character from NTOs or to the known pure diabatic characters at the B3u minimum and Au TS) would strengthen the claim that the extracted oscillations track the diabatic beats rather than residual adiabatic mixing or window choice.

minor comments (5)

PES and XAS figures: energy shifts (0.73 eV PES; –1.58 / –1.66 eV N/C-edge) and the precise FWHM used in each main-text panel should be stated once in the main text or figure captions, not only in the SI, so that the comparison protocol is self-contained.
Fig. 1E vs SI Fig. S2: the 6.9–7.4 eV window yields 11 fs while 6.9–7.9 eV yields 24 fs; a brief sentence in the main text on why the narrower window is preferred for the experimental comparison would help the reader.
Methods: the adaptive CCSD/SCCSD switch threshold τ = 0.01 eV is given; a one-line pointer to the SI S11 energy-drift and norm checks would reassure readers that the switch does not introduce artifacts.
SI S2.1 / S2.2: several figure captions still say “N-edge” when the panel is C-edge (e.g., S14–S16); correct for clarity.
Notation: Lord’s mode labels (ν8a, ν6a, ν8b, …) are used throughout; a short table or SI reference mapping them to the eT mode indices would aid reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: ab initio CCSD/SCCSD-AIMS dynamics and spectra are independent predictions compared to external experiments; shifts and windows are standard post-processing, not fits that force the claimed decay/beats.

full rationale

The central claims (1B2u decay constant ~11 fs from the 6.9-7.4 eV PES window with no strong revival; ~34 fs 1B3u/1Au population beats on S1 arising from wave-packet motion between the B3u minimum and Au TS; extractable oscillations in PES and N-edge XAS) are obtained from a first-principles nonadiabatic simulation (20 Wigner ICs, adaptive multistate SCCSD at 0.01 eV gap, AIMS propagation, incoherent TBF-center spectra, transition-strength diabatization) whose electronic-structure and nuclear-dynamics inputs do not include the experimental time constants or beat periods. Absolute energy shifts (0.73 eV PES; ~1.58/1.66 eV XAS) and energy-window choices are ordinary calibration/assignment steps justified by static critical-point calculations and diabatic decomposition (Figs. 1A, 2A, 3A; SI §§S1,S2,S6); they do not redefine or force the dynamical observables. Comparisons are to independent measurements (Suzuki PES, Wörner XAS). Methodological self-citations (SCCSD gradients/couplings, eT/FMS interface) supply the computational machinery but are not load-bearing uniqueness theorems that close the argument; energy-conservation and adaptive-switch checks (SI §S11) further corroborate numerical integrity. No equation or procedure reduces a claimed prediction to a fitted input or self-definition. Score 0 is therefore required.

Assumptions & free parameters 6 free parameters · 5 assumptions · 1 invented entities

The central claims rest on standard nonadiabatic-dynamics and coupled-cluster assumptions plus a handful of numerical thresholds and empirical spectral shifts. No new physical entities are postulated; the multistate SCCSD scheme is a methodological extension of prior two-state SCCSD work by the same group.

free parameters (6)

PES energy shift = 0.73 eV
Uniform +0.73 eV shift applied to all simulated binding energies to align the 1B2u feature with experiment (Fig. 1 caption).
N-edge / C-edge XAS shifts = −1.58 / −1.66 eV
Uniform shifts (−1.58 eV N-edge, −1.66 eV C-edge) to match experimental ground-state bleach (SI §§S2.1–S2.2).
Quasi-degeneracy threshold τ = 0.01 eV
Energy gap below which SCCSD constraints are activated (Methods; SI S10).
Spawning threshold and min population = 20 a.u. / 0.05
Norm of coupling vector >20 a.u. and population >0.05 required to spawn (Methods).
Spectral FWHM broadenings = various (5–30 fs, 0.1–0.4 eV)
Two-dimensional Gaussian widths chosen to approximate experimental resolution (13 fs/0.3 eV PES; 10 fs/0.3 eV XAS; additional widths tested in SI).
Initial-condition energy window = 4.56–5.13 eV
Only Wigner samples with vertical excitation 4.56–5.13 eV are propagated (Methods; SI S8).

assumptions (5)

domain assumption Ab initio multiple spawning with the independent-first-generation approximation adequately represents the nuclear quantum dynamics on the 200 fs timescale.
Standard AIMS premise; invoked throughout Methods and SI S8.
domain assumption CCSD (and SCCSD near intersections) with the cc-pVDZ basis is sufficiently accurate for the valence excited-state surfaces, gradients and couplings of pyrazine.
Core methodological choice; higher excitations are acknowledged to be missing for some XAS features (SI S2).
domain assumption The incoherent approximation (spectra evaluated only at TBF centers with amplitude >0.01) yields reliable time-resolved PES and XAS.
Stated in Methods; common but uncontrolled approximation.
ad hoc to paper Diabatic characters can be extracted from the square-root transition-strength matrix F(R) via the orthogonalization procedure of SI S6.
Specific diabatization recipe introduced for this work; used for all population and spectral decompositions.
domain assumption Three-state conical intersections are rare enough that pairwise adaptive SCCSD constraints remain valid.
Explicit assumption of the adaptive interface (SI S10).

invented entities (1)

Adaptive multistate SCCSD interface
purpose: Allows an arbitrary number of electronic states in AIMS by switching between unconstrained CCSD and pairwise similarity-constrained CCSD when energy gaps fall below τ.
Methodological invention that enables the reported dynamics; independent evidence is the energy-conservation and norm checks in SI S11, but the scheme itself is new to this paper.

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Pith. "Pith review of Spectroscopic photorelaxation signatures in pyrazine from nonadiabatic dynamics simulations with coupled cluster theory." pith.science (2026). https://pith.science/paper/U6D53MAR

@misc{pith2026260703395,
  author       = {Pith},
  title        = {Pith review of: Spectroscopic photorelaxation signatures in pyrazine from nonadiabatic dynamics simulations with coupled cluster theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U6D53MAR}},
  note         = {Machine review of arXiv:2607.03395}
}

abstract

Despite extensive theoretical and experimental efforts, the mechanisms underlying the ultrafast relaxation of pyrazine after photoexcitation remain challenging to disentangle. Recently, theoretical investigations have been converging towards a three-state mechanism, with an ultrafast decay of the bright ${}^{1}B_{2u}$ state followed by beats in the populations of the low-lying ${}^{1}B_{3u}$ and ${}^{1}A_u$ states. However, a clear agreement between the experimental results and the corresponding theoretical predictions remains elusive. Here, we present a high-level simulation of the ultrafast excited states dynamics of pyrazine using coupled cluster theory with single and double excitations and ab initio multiple spawning, together with predictions of the time-resolved photoelectron spectrum and X-ray absorption spectra at the nitrogen and carbon edges. This is made possible by using a newly developed multistate implementation of similarity constrained coupled cluster theory. We find quantitative agreement with the experimental signature of the ${}^{1}B_{2u}$ decay in the photoelectron spectrum, and qualitative agreement with the available experimental X-ray absorption spectra. Moreover, we detail spectroscopic signatures that should be verifiable in experiments with sufficient resolution in the time and frequency domains. Compared to previous theoretical studies, we provide further detailed insight into the interplay of the states involved in the photorelaxation.

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Reference graph

Works this paper leans on

15 extracted references

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Pith tools

Reviewed July 12, 2026 · model on record in the stance chip above.

[1] [1]

Folkestad, S. D. et al. et 1.0: An open source electronic structure program with emphasis on coupled cluster and multilevel methods. The Journal of Chemical Physics 152 (2020)

2020

[2] [2]

C., Decleva, P., Koch, H

Moitra, T., Paul, A. C., Decleva, P., Koch, H. & Coriani, S. Multi-electron excitation contributions towards primary and satellite states in the photoelectron spectrum. Physical Chemistry Chemical Physics 24, 8329–8343 (2022)

2022

[3] [3]

Combined surface-hopping, dyson orbital, and b-spline approach for the computation of time-resolved photoelectron spectroscopy signals: The internal conversion in pyrazine

Piteˇ sa, T.et al. Combined surface-hopping, dyson orbital, and b-spline approach for the computation of time-resolved photoelectron spectroscopy signals: The internal conversion in pyrazine. Journal of chemical theory and computation 17, 5098–5109 (2021)

2021

[4] [4]

& Suzuki, T

Karashima, S., Humeniuk, A. & Suzuki, T. Vibrational motions in ultrafast electronic relaxation of pyrazine. Journal of the American Chemical Society 146, 11067–11071 (2024)

2024

[5] [5]

& Koch, H

Coriani, S. & Koch, H. Communication: X-ray absorption spectra and core- ionization potentials within a core-valence separated coupled cluster framework. The Journal of Chemical Physics 143 (2015)

2015

[6] [6]

Kjønstad, E. F. et al. Photoinduced hydrogen dissociation in thymine predicted by coupled cluster theory. Nature Communications 15, 10128 (2024)

2024

[7] [7]

Chang, Y.-P. et al. Electronic dynamics created at conical intersections and its dephasing in aqueous solution. Nature physics 21, 137–145 (2025)

2025

[8] [8]

& Moomaw, W

Innes, K., Ross, I. & Moomaw, W. R. Electronic states of azabenzenes and azanaphthalenes: A revised and extended critical review. Journal of Molecular Spectroscopy 132, 492–544 (1988)

1988