Transient X‑ray Absorption Signatures of Photodissociation Pathways and Conical Intersection Dynamics in Phenol

Abstract

The UV photodissociation of phenol, a key nonradiative prototype, yields hydrogen atoms with a bimodal kinetic energy release (KER). While the high-KE component is often associated with direct dynamics, the mechanistic origin and branching of the low-KE component–spanning direct tunneling, statistical decay, and recrossing pathways–remain contested. To resolve this, we provide a definitive, atomically resolved roadmap by simulating oxygen K-edge transient X-ray absorption spectroscopy (TXAS) along the complete O–H dissociation coordinate. Our calculations predict distinct spectral fingerprints for the three branching pathways that pass through the second conical intersection: dissociation to electronically excited phenoxyl (Path 1), to ground-state phenoxyl (Path 2), and a nonadiabatic recrossing pathway (Path 3). Signatures are also assigned to predissociation dynamics upon UV excitation and to tunneling through the first conical intersection, as well as to both bound-side (Path 4) and dissociative-side (Path 3) channels of statistical ground-state decay. Systematic natural transition orbital (NTO) analysis along the reaction path decodes the evolving electronic character underlying these spectral features, delivering unprecedented orbital-resolved insight into the dissociation mechanism. This complete set of ab initio TXAS references establishes an unambiguous spectral framework, providing the essential theoretical foundation for future time-resolved X-ray experiments to disentangle these competing ultrafast bond-cleavage mechanisms.

Introduction

Phenol stands as the paradigmatic model for understanding ultrafast nonradiative dynamics and photostability in bioaromatic systems. Its fundamental photochemical processultrafast O–H bond fission following UV excitationhas been the focus of extensive experimental − and theoretical − study. As the simplest structural analogue of nucleobases, phenol exhibits a rich excited-state landscape orchestrated by its hydroxyl group, which mediates coupling across all principal orbital classes: the aromatic π/π*system, the O–H σ/σ*bond, the oxygen lone pair (n), and Rydberg orbitals. This comprehensive orbital interplay establishes phenol as a quintessential textbook model for photochemistry. Upon UV excitation to the bright ππ* state, the strongly coupled and energetically proximate πσ* state acts as the primary gateway for O–H bond fission. ,

Low-lying singlet excited states, especially the lowest three (S₀–S₂), ,,, are found essential in the O–H bond fission mechanisms. The O–H distance, R _OH, is unequivocally the only primary reaction coordinate that captures the essential dissociation chemistry via the potential energy curves (PECs), ,,, though other internal coordinates, such as the C–O bond length and the C–O–H angle, also modulate the process. , The photochemistry in the R _OH-dependent PECs involves two key conical intersections (CoIns) that funnel the excited-state population: the S₂/S₁ CoIn (CI ₁ ) and S₁/S₀ CoIn (CI ₂ ), as illustrated in Figure a (bottom), where adiabatic representations are used. Following initial relaxation through CI ₁ , the evolving wavepacket on the S₁ PEC bifurcates at CI ₂ , leading to three competing pathways:

• Path 1: Direct dissociation on the repulsive S₁ surface to yield H + PhO^•(Ã).

• Path 2: Nonadiabatic transition to S₀ followed by fast dissociation to H + PhO^•(X̃).

• Path 3: A recrossing channel where the wavepacket remains transiently trapped near CI ₂ .

1.

(a) Computed adiabatic PECs for S₀–S₂ and the lowest 10 O 1s excited states (e₁–e₁₀) along the reaction coordinate, R _OH (other coordinates fixed at S₀ geometry). Key geometries: I (scan start), II (S₀ minimum), III (CI ₁), IV (CI ₂), V (scan end). Wavepacket dynamics from the FC region show tunneling at CI ₁ (black wavy arrows) followed by three pathways (pink/orange/green arrows) at CI ₂. (b) Evolution of state characters while passing CI ₁ and CI ₂, illustrated by computed NTOs at selected R _OH values. Curves are part of S₀–S₂ PECs taken from (a), now recolored according to dominant state characters instead of energy orders: blue for ππ*, red for the π Ryd → πσ* → πn progression (where Ryd = Rydberg). For geometries at 0.96, 1.20, and 1.40 Å, NTOs were computed for the S₀ → S_1,2 transitions; at 3.00 Å, NTOs were computed for the S₁ → S₀ transition. Dominant NTO pairs (particle, top; hole, bottom) are displayed for each transition, with corresponding occupation numbers indicated. A color-aligned, grouped comparison is provided in Figure S2. More points are analyzed in Figure S3.

A cornerstone of mechanistic insight has been the measurement of kinetic energy release (KER) spectra, which exhibit a consistent bimodal profile for the hydrogen elimination channels, marked by well-separated high- and low-kinetic energy (KE) components. ,,,,,,, The assignment of these components, however, has been a subject of evolving interpretation. Ashfold et al. emphasized the significance of the dissociative πσ* state (see red curve in Figure b) in phenol photodissociation. They proposed two distinct pathways dependent on excitation energy: from higher S₁ (ππ*) vibrational levels, direct coupling to S₂ via CI ₁ yields the high-KE component; from the S₁ vibrational origin, internal conversion (IC) to vibrationally hot S₀ (S₀ ) provides access to CI ₂ . The latter route bifurcates into a direct fragmentation pathway and an indirect one involving partial recrossing to S₀ (see Path 3 in Figure a) and back, both accounting for features in the low-KE signal. A subsequent study refined this interpretation, explicitly assigning the high-KE component to direct coupling via CI ₁ , while further resolving the low-KE component into prompt and delayed dissociation pathways from S₀ , with the latter attributed to statistical decay after intramolecular vibrational energy redistribution (IVR). In contrast, based on dynamical simulations from different S₁ vibrational excitations, Xu et al. attributed the low-KE signal primarily to direct dissociation via tunneling on S₁ before CI ₁ (indicated by the wavy curve in Figure a), concluding that statistical decay via CI ₂ is minor for initial photodissociation. This view was challenged by Lin et al., who used time-resolved measurements to separate the statistical decay on S₀ . Their measurements at 213 and 193 nm showed this channel contributes 5–7% to the total OH bond fission yield, demonstrating it is a non-negligible source of the low-KE signal, a channel not accounted for in earlier simulations by Xu et al. The existence of this statistical ground-state dissociation channel is noted in a recent review, which explicitly attributes the slow H atom component to fragmentation after internal conversion to the electronic ground state via a πσ*/S₀ CoIn (our CI ₂ ), a description that aligns with the original assignment by Xu et al. Resolving the precise branching between all competing pathways, including branching at CI ₂ (Paths 1–3), and the statistical ground-state decay pathway following direct internal conversion from S₁, in real time requires a probe capable of distinguishing them with both electronic and atomic specificity.

Recent advancements in X-ray free electron lasers (XFELs) − and high harmonic generation (HHG) sources − now deliver intense, ultrashort (femto- to attosecond) pulses with atomic spatial resolution, enabling direct studies of ultrafast photochemistry. These include exciton localization, charge/proton transfer, , dissociation, ring-opening, internal conversion, intersystem crossing, and dynamics near CoIns, with supporting theoretical simulations developed for systems like uracil, malonaldehyde, and thiophenol.

Among ultrafast techniques, pump–probe transient X-ray absorption spectroscopy (TXAS) is particularly powerful for capturing the electronic and nuclear dynamics in light-induced processes. − Interpretation, however, requires robust theoretical support. Current strategies involve computing core-excited states either (1) along molecular dynamics (MD) trajectories or (2) along static potential energy surfaces (PESs). Strategy (1) faces scalability challenges. The nonadiabatic molecular dynamics (NAMD) method provides direct access to time-dependent density matrices but necessitates extensive trajectory sampling for reliable ensemble averaging. However, achieving statistical convergence for time-resolved spectra poses a core challenge for NAMD. While a few hundred trajectories may suffice for steady-state spectra (which sample a limited region around the Franck–Condon point), transient spectra usually demand many more trajectories. This is because, as the simulation time increases, the evolving wavepacket explores an expanding volume of configuration space. To maintain a compact representation of this increasingly dispersed ensemble, a proportionally larger number of trajectories is required for statistical averaging. Consequently, the computational cost of achieving converged transient spectra grows significantly with propagation time, restricting applications to small systems and short time scales. , Direct solution of the time-dependent Schrödinger equation avoids sampling (i.e., propagates on a single “trajectory”) but is computationally prohibitive. Intermediate solutions like ab initio multiple spawning (AIMS), multiconfigurational time-dependent Hartree (MCTDH), and direct dynamics variational multiconfigurational Gaussian (DD-vMCG) methods , have been applied to time-resolved X-ray spectra, ,,− but scalability issues persist. Alternatively, the static approach (Strategy 2) is more efficient, computing vertical core excitations along a reaction coordinate. It has successfully simulated TXAS for diverse systems, including uracil, malonaldehyde, azobenzene, molecular ions, and organic crystals, , often matching experiments and providing complementary insights. Notably, O 1s TXAS calculations on uracil identified a signature at 526–527 eV characteristic of the dark nπ* state, in good agreement with corresponding XFEL measurements on thymine.

Herein, we simulate the oxygen K-edge TXAS of photoexcited phenol using the static “snapshots along the PESs” approach, , focusing on its O–H dissociation dynamics. The TXAS spectrum is computed as a function of the reaction coordinate, R _OH, yielding

$$S_{\mathrm{TXAS}}(\omega ,R_{\mathrm{OH}})$$ 1

which provides a continuous map of the spectral evolution along the dissociation pathways. This theoretical spectral map can be directly correlated with future experimental spectra,

$$S_{\mathrm{TXAS}}(\omega ,\tau )$$ 2

corresponding to time delay τ, to build a comprehensive and well-resolved picture of the underlying ultrafast dynamics. Our goal is to provide definitive spectral signatures for all possible reaction pathways and to establish a clear mechanistic framework for future experiments. To decode the spectral evolution and connect it to changes in valence-state electronic structure, we employ natural transition orbital (NTO) analysis. ,

Results

Valence Potential Energy Curves and Nonadiabatic Pathways

Figure a (bottom) presents the computed state-averaged (SA) complete active space self-consistent field (CASSCF) PECs for S₀–S₂ states along R _OH (see Figure S1 for active space). The curves were generated by varying only R _OH, with all other internal coordinates fixed at their equilibrium values from the S₀ minimum (structure II). This constrained relaxation path facilitates convergence in multiconfigurational calculations, especially for subsequent core-level simulations, and spans geometries from a compressed bond (I, R _OH = 0.6 Å) to full dissociation (V, R _OH = 3.0 Å). The profiles reveal two key conical intersections CI ₁ (III, R _OH = 1.10 Å) and CI ₂ (IV, R _OH = 1.96 Å), and the overall topography is consistent with previously reported MRCISD PECs, validating our computational approach.

The evolution of the electronic state character passing the two conical intersections is elucidated by the NTO analysis in Figure b. At the Franck–Condon geometry, S₁ and S₂ exhibit ππ* and π-Rydberg character, respectively. Upon stretching the O–H bond and passing CI ₁ , the S₁ state acquires dominant σ* character, signaling the onset of the repulsive πσ* state that drives O–H bond cleavage. , After passing CI ₂ , this state–now becomes S₀–shows dominant oxygen lone pair (n) character, consistent with the expected electronic structure of the PhO^• radical product. Our NTO analysis thus provides a more complete, dynamic view of the “πσ*” gateway state central to the photodissociation mechanism. , Additional NTO analysis for more intermediate points is provided in Figure S3.

These distinct, configuration-dependent valence electronic structures are expected to produce unique transient X-ray absorption signatures. We decode these signatures in the following sections to establish a definitive spectral assignment of the dissociation dynamics.

O1s Potential Energy Curves

Figure a (top) displays the PECs for the lowest 10 O1s excited states (e₁–e₁₀), simulated by the state-averaged restricted-active-space SCF (SA-RASSCF) method. The core-excited state PECs exhibit markedly different evolution patterns compared to their valence counterparts. This demonstrates that the core-level manifold offers an independent, highly localized view of the dissociation process. While the valence states govern the nuclear dynamics, the O 1s core-excited states are exquisitely sensitive to the local electronic structure around the oxygen atom, making their spectral shifts a direct signature of the O–H bond cleavage. The smoothness of curves validates the appropriateness of our chosen active space. Notably, the lowest O1s excited state, e₁, exhibits a pronounced dissociative feature, approaching ca. 532 eV at long O–H distances. This state remains energetically well-separated from higher-lying core-excited states throughout the entire reaction coordinate, a behavior consistent with previous observations in uracil.

TXAS Signatures of Early-Stage S₁ Dynamics (Min S ₀ → CI ₁ )

The early stage photodynamics of phenol along the S₁ PEC, spanning II → III → IV, are captured in the simulated TXAS spectrum shown in Figure (lower portion of panels a–c). In the initial II → III region (enlarged view at the bottom of Figure a), three distinct peaks (A–C) emerge, each exhibiting characteristic energy shifts. Peak B, which is the strongest among the three, experiences a pronounced ∼2 eV red shift (536 → 534 eV), while weaker peaks A and C display ∼1 eV blue shifts (533 → 534 eV and 538 → 539 eV, respectively). Consequently, peaks A and B become energetically closer as they approach CI ₁ at R _OH = 1.10 Å, signaling electronic reorganization at this critical geometry. Figure shows TXAS curves cut from the two-dimensional (2D) map, with accompanying NTO interpretations. The NTO analysis elucidates the electronic origins of these features. Peak A corresponds to two underlying O1s → π transitions. For peak B, the transition character evolves markedly with O–H elongation: the feature arises from O 1s → Rydberg excitations at shorter R _OH (near II), and as the bond extends, it progressively shifts to predominantly O 1s → σ* character (near III), accompanied by increasing electron localization on the dissociating O–H bond. Peak C is attributed to O 1s → π* transitions.

2.

Simulated O 1s TXAS spectra for early stage dynamics along the S₁ PEC, from min S ₀ until CI ₂ (II → III → IV; see the shaded curve in Figure a), followed by branching of three pathways: (a) Path 1, (b) Path 2, (c) Path 3. Bottom of (a) shows an enlarged view for the II → III region. White arrows are to guide eyes, indicating the direction of spectral evolution.

3.

Simulated O 1s TXAS spectra for early stage dynamics along the S₁ PEC, from the Franck–Condon region until CI ₂ (II → III → IV; see shaded curve in Figure a). Spectra curves represent cuts from the 2D maps of Figure (bottom part of each panel), with particle NTOs of dominant transitions (numbers represent final state indices) shown alongside and interpreted.

TXAS Signatures of Early-Stage S₁ Dynamics (CI ₁ → CI ₂ )

In the region between the two conical intersections, spanning III → IV (Figure a, middle), four new peaks (D–G) are identified. 2D curve cuts and their NTO interpretations are provided in Figure (top). Peak D is a prominent feature centered at 528–530 eV, which red-shifts and gains intensity; it is assigned to an O 1s → π transition. Peak E appears in the 532–534 eV range and corresponds to an O 1s → π* transition. Peak F emerges at 535–537 eV and exhibits characteristic π* character. Peak G is observed at 537–540 eV, assigned to an O 1s → σ* transition; both its energy and intensity decrease along the reaction coordinate. As the system approaches CI ₂ , peaks F and G merge into a single broad and weak absorption feature.

Our TXAS simulations capture the complete dynamical evolution along the S₁ PEC, including the vicinity of CI ₁ . Although the actual tunneling process may not precisely reach the CI ₁ geometry per the textbook picture (typically occurring slightly below it, as indicated by the wavy arrow in Figure a), our computed spectral signatures span the entire passage encompassing CI ₁ (from II to IV, see the shaded line in Figure a). The spectral changes proximate to CI ₁ can therefore serve as indicators for whether tunneling occurs relative to the O–H stretching coordinate. The fundamental nature of the tunneling process–whether it is time-dependent or instantaneous–remains actively debated. , While TXAS may lack the requisite time resolution to directly observe the tunneling event itself, characteristic spectral changes before and after this process provide sensitive indirect signatures of its occurrence.

TXAS Signatures of Post-CI ₂ Branching Pathways

The simulated O 1s TXAS spectra along the three post-CI ₂ pathways (Paths 1–3), presented in the top panels of Figure a–c, reveal distinct spectral signatures. Corresponding spectral cuts from the 2D map, supported by NTO assignments, are provided in Figure .

4.

Simulated O 1s TXAS spectra of phenol starting from CI ₂ which then separates along three possible Paths (a) 1, (b) 2, and (c) 3 (see Figure a). Spectra curves represent cuts from the 2D maps of Figure (top part of each panel), with particle NTOs of dominant transitions (numbers represent final state indices) shown alongside and interpreted.

Along Path 1 (Figure a), a very strong peak H (527–528 eV) originates from the S₁ → e₁ transition, exhibiting a slight red shift along the coordinate. It is characterized as evolving from O 1s → σ* to predominantly O 1s → n character as R _OH increases, reflecting the physical picture of a receding hydrogen atom leaving behind a localized hole on the oxygen lone pair orbital n. The large oscillator strength arises from the dipole-allowed nature of the oxygen-localized transitions (essentially O 1s → 2p). Notably, the energy position of peak H (527–528 eV) closely aligns with the strong absorption observed at 526–527 eV for the dark nπ* state in thymine and uracil in O 1s TXAS studies, owing to the same underlying electronic origin. Additionally, a weak transient feature I with π* character appears around 540–541 eV near CI ₂ but rapidly diminishes along this dissociation coordinate.

For Path 2 (Figure b), the spectrum exhibits three persistent features. A prominent peak J at 528–529 eV, assigned mainly to an O 1s → n transition (accounting for its large intensity) with also a few π feature mixing on adjacent atoms. Compared to Peak H in Path 1, J has approximately half the intensity and remains nearly constant in energy. Its reduced intensity stems from the mixed character of the final state, with only the n orbital portion localized on the oxygen atom being effective for O 1s overlap. In addition, a weaker peak K at 531–534 eV with π* character, and a further weaker peak L at 535–536 eV, primarily of π* character, with minor σ* mixing at shorter distance, both maintaining nearly constant energies and intensities along the reaction coordinate.

Path 3 (Figure c) displays the most dynamic spectral evolution. A strong peak M undergoes a significant blue shift of about 7 eV (from ∼529 eV at CI ₂ to ∼536 eV at min S ₀ ) accompanied by a decrease in intensity. It is assigned to the S₀ → e₁ resonance with predominant σ*character localized on the O–H bond. The decreased intensity comes from the more delocalized final-state orbital with the reaction coordinate, consistent with the radical feature and more delocalized electron distribution to the aromatic ring. Additionally, in the higher-energy region, two π* -mediated features emerge: peak N red-shifts from 541 eV, while the weaker peak O appears in the vicinity of min S ₀ .

All three pathways show distinct, strong features at the low-energy region (H, J, M), which are clean fingerprints for pathway identification. Although high-energy weak features are included for completeness, their utility is limited, particularly above the O 1s ionization potential (IP ∼ 539 eV). The consistently bright O 1s → e₁ transitions (for peaks H, J, M) across all pathways highlight the diagnostic value of the lowest core-excited state for monitoring excited-state absorption (ESA) dynamics. The characteristic spectral patterns enable unambiguous discrimination between dissociation channels. Especially, Path 3 is linked to the proposed “statistical dissociation” mechanism involving energy redistribution (thermalization) around CI ₂ . , A complete picture of statistical ground-state decay, however, also requires consideration of the complementary scenario: direct internal conversion from S₁ to the bound side of the S₀ potential.

TXAS Signatures of S₀ Photo-Decay Following Direct S₁ → S₀ Internal Conversion

To fully map the spectroscopic signatures of statistical decay, we therefore define Path 4, representing the direct internal conversion to a vibrationally hot ground state S₀ on the bound side of the potential, followed by vibrational relaxation (Figure a, golden arrows). , Paths 3 and 4 thus represent complementary initial conditions for the same underlying statistical process, distinguished by whether IVR and eventual dissociation occur from a predissociative or a bound configuration. This distinction addresses a key issue in the photodissociation literature regarding the mechanism and spectroscopic evidence for statistical decay from S₀ . ,,

5.

(a) Computed S₀–S₂ PECs (reproduced from Figure a). Golden arrows depict internal conversion from S₁ to a vibrationally hot ground state S₀ , followed by vibrational relaxation on the S₀ surface. Path 4 (thick black line) and Path 3 (green arrow) illustrate the bound-side and dissociative-side channels of statistical ground-state decay, respectively, of statistical ground-state decay. (b) Simulated O 1s TXAS spectra along Path 4, tracking relaxation from structure I to II. White arrows indicate the evolution direction of dominant peaks. (c) Spectral cuts from the 2D map in (b), with particle NTOs and state assignments for key transitions (numbers denote final-state indices).

The simulated TXAS spectra along Path 4 are shown in Figure b, tracking the vibrational relaxation from a highly contracted O–H distance (R _OH = 0.6 Å) back to the equilibrium geometry (0.96 Å) (see shaded black line in Figure a). Corresponding spectral cuts from the 2D map and their NTO analysis are provided in Figure c. Four peaks (P–S) are identified, with P and Q being the most intense. Given the consistent intensity scale used across all 2D maps in this work, the signals along Path 4 are notably weaker than those along Path 3. The most prominent spectral evolution is the splitting of a broad feature at 535–537 eV into two distinct peaks (P and Q), which shift slightly in opposite directions with increasing R _OH. Stick spectra reveal the splitting arises from the growing energy separation between the S₀ → e₁ (mixed σ*/Rydberg) and S₀ → e₂ (π*) transitions, accentuated by the S₀ → e₁ intensity first decreasing then increasing while the S₀ → e₂ intensity remains nearly constant. The overlap of multiple transitions within a single broad feature underscores the importance of theoretical simulations for interpreting complex TXAS data. Two additional weak π* peaks, R (∼541 eV) and S (545–547 eV), are observed at higher energies.

Discussion

Distinctness and Experimental Resolvability of Spectral Fingerprints

The diagnostic power of the identified spectral fingerprints is supported by their substantial energy separations, which far exceed typical broadening effects. Peak M (Path 3) undergoes a blue shift from 529 to 536 eV, resulting in a final separation of about 7 eV from the characteristic peaks of Paths 1 and 2 (Peak H and J, both around 528–529 eV). Even the closer-lying Peaks H and J are separated by ∼1 eV and exhibit markedly different intensities. These separations far exceed the sub-eV shifts typically induced by vibrational broadening or nonequilibrium nuclear motions for core-level excitations. Given that modern X-ray free-electron lasers (XFELs) routinely achieve resolutions better than 0.5 eV at the O K-edge, these substantial energy separations ensure that the spectral features will remain clearly distinguishable in time-resolved experiments, unaffected by dynamical broadening. This conclusion is further strengthened by independent validation from other aromatic systems, as discussed in the Introduction: the calculated RASSCF signature for the dark S₁ state of uracil (526–527 eV) is in excellent agreement with XFEL measurements on thymine.

Influence of Additional Nuclear Coordinates

The calculations presented thus far have focused on the one-dimensional O–H dissociation coordinate R _OH with all other internal coordinates fixed. While this constrained approach effectively captures the essential electronic evolution and is uniquely practical for constructing smooth core-excited state PECs, we performed additional calculations to assess the influence of other nuclear degrees of freedom. Specifically, valence-state PECs were computed along a more physically representative pathway featuring relaxed molecular geometries.

The conical intersections III and IV were fully optimized to yield structures III′ and IV′. The initial (I) and final (V) points were optimized with constrained O–H distances of 0.6 and 3.0 Å, yielding I′ and V′. Valence-excited-state PECs were then computed along the linearly interpolated path connecting I′, II, III′, IV′, and V′.

Geometric analysis reveals systematic structural adjustments upon relaxation. At III′ (Figure S4c, inset), the O–H bond shortens to 1.01 Å (from 1.10 Å in III), the C–O bond contracts to 1.27 Å (from 1.38 Å), and the ∠COH increases to 113.92° (from 108.61°). Similarly, IV′ (Figure d, inset) exhibits a shorter O–H distance (1.73 vs 1.96 Å in IV), a contracted C–O bond (1.27 vs 1.38 Å), and an increased ∠COH (113.22° vs 108.61°). These observed structural adjustments are consistent with previous calculations.

6.

(a) Computed S₀–S₂ PECs along R _OH with all other coordinates relaxed (vibrant lines). Key geometries are denoted with primes: I′ (I optimized with R _OH = 0.60 Å), III′ (fully optimized S₂/S₁ CoIn), IV′ (fully optimized S₁/S₀ CoIn), and V′ (V optimized with R _OH = 3.00 Å). Frozen-coordinate PECs from Figure a are overlaid (faint lines). (b–d) Simulated O 1s TXAS at and around the S₁/S₀ CoIn: (b) IV (all additional coordinates frozen at equilibrium), (c) IV* (same R _O–H as IV′ but with additional coordinates frozen as in IV), and (d) IV′ (fully relaxed). Insets show structures with key parameters. (e–g) NTOs for valence (S₀ → S₁) and core (S_0,1 → e₁) excitations of the lowest-energy spectral peak in (b)–(d), with state character and occupation numbers indicated.

Crucially, the valence PECs obtained from the relaxed coordinate path retain the same qualitative topology as those from the constrained R _OH scan (Figure a). The fully optimized conical intersections are stabilized by only 0.3–0.4 eV relative to their unrelaxed counterparts, confirming that the one-dimensional unrelaxed coordinate captures the dominant energetics of the dissociation.

Although a full core-excitation mapping along the relaxed path was not repeated, we computed TXAS spectra at the optimized conical intersections III′ and IV′. While spectral differences are discernible between each pair (III vs III′; IV vs IV′), the overall spectral profiles remain qualitatively similar (Figure b,d). For instance, the dominant S₀ and S₁ excitations appear at 528.4 eV for IV (R _OH= 1.96 Å) and 529.2 eV for IV′ (1.73 Å), differing by 0.8 eV with an intensity change of approximately −9%. A spectrum calculated at a frozen geometry with a nearly identical O–H distance of 1.72 Å (labeled as IV*) interpolates between those of IV and IV′ in both energy and line shape (Figure c), demonstrating that R _OH is the principal coordinate governing spectral evolution. NTO analysis confirms that corresponding transitions at the three structures show very similar valence and core excitations (Figure e–g). An analogous analysis at around CI ₁ is provided in Figure S4. The comparisons show a consistent trend, validating the robustness of our computational protocols. The analysis also provides a separate estimate of the influence of R _OH and other coordinates, demonstrating that R _OH is the principal coordinate governing spectral evolution.

In summary, the relaxation of additional nuclear coordinates does not qualitatively alter the overall PEC topography or spectral evolution. The primary goal of this work is to establish pathway-specific XAS signatures for hydrogen atom detachment in UV-excited phenol. The level of accuracy achieved here is sufficient to distinguish among the proposed pathways. We therefore conclude that the constrained R _OH approach provides an efficient and practical means to capture the essential features of the photodissociation process and does not affect the main conclusions of this study.

Balance of Accuracy and Efficiency

Accurate theoretical prediction of core excitation/ionization energies and X-ray spectra poses a significant challenge in quantum chemistry even at ground-state geometries. , This difficulty is compounded when mapping entire PESs for photochemical reactions, which demands a method that accurately captures electron correlation across a range of nuclear configurations while remaining computationally feasible. For K-edge spectra of light elements (C, N, O), the widely used ΔKohn–Sham (ΔKS) DFT method offers a practical compromise, typically achieving errors of 0.5–1.0 eV for excitation energies (at ground-state geometries). ,, While it can be extended to the Franck–Condon region and slightly even stretched geometries, , successfully reproducing PECs and vibrationally resolved XAS spectra, its single-reference nature becomes inadequate for describing the strongly correlated electronic states and intricate nonadiabatic couplings encountered in full photochemical dynamics.

Multiconfigurational methods are the natural choice for this regime. The RASSCF method provides a robust framework for capturing static correlation–the dominant effect governing PES topography and state crossings in photochemical processes. While it typically yields absolute core-excitation energies with an accuracy of several eVs, it reliably reproduces experimental spectral profiles and has been successfully applied to map PECs and interpret photochemical dynamics. , The RASPT2 method additionally includes dynamic correlation through perturbation theory. For transition metal L-edge XAS calculations, where systems exhibit dense electronic states, dynamical correlation is usually necessary for reproducing weak spectral features. In organic K-edge spectroscopy, however, spectral shapes and nonadiabatic pathways are primarily dictated by static correlation. It has been demonstrated for carbon–nitrogen systems that RASPT2 and RASSCF generate similar valence and C 1s core-state PECs and comparable high-resolution XAS spectra.

Equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) provides improved treatment of dynamical correlation and is often considered a reference for core-level spectral modeling, with applications extending to representative excited-state structures. Meanwhile, MRCI has demonstrated high accuracy (mean absolute errors ∼0.25 eV for core excitations), , yet current applications are largely restricted to ground-state geometries. Further methodological developments are needed to fully realize their potential for PEC constructions in photochemistry, particularly in managing computational demands and ensuring size consistency.

Given the trade-offs among accuracy, computational cost, and applicability to excited-state trajectories, the RASSCF approach adopted here offers a balanced compromise for modeling photochemical processes. This approach has been shown to reproduce MRCI PECs for structurally similar systems such as uracil, , and the RASSCF-simulated S₁ dark state signature (526–527 eV) of uracil in O1s TXAS matches well with that observed in the XFEL experiment of thymine. Specifically for phenol, RASSCF produces spectra at the ground-state geometry in good agreement with experiment (Figure S5). Our RASSCF valence PECs are essentially similar to the reported MRCISD PECs. Therefore, we consider the RASSCF method both efficient and sufficiently accurate for the present goal of identifying pathway-specific spectral signatures along photodissociation coordinates.

Conclusion

We have systematically simulated O 1s transient X-ray absorption spectra (TXAS) along the O–H dissociation pathways of phenol following UV excitation to the S₁ (ππ*) state. Our results provide three key advances that address the mechanistic questions outlined in the Introduction. First, the TXAS evolution during early stage S₁ dynamics (min S ₀ → CI ₁ → CI ₂ ) reveals abrupt spectral changes at CI ₁ , serving as a clear signature of the ππ* → πσ* transition and enabling tracking of the passage of the first conical intersection. Second, each of the three post-CI ₂ pathways–direct dissociation to H + PhO^•(Ã) (Path 1), fast dissociation via S₀ to H + PhO^•(X̃) (Path 2), and S₀ recrossing (Path 3)–exhibits a distinct spectral fingerprint. These signatures allow for unambiguous mechanistic discrimination in future TXAS experiments. Third, we identify unique TXAS features for the vibrationally hot S₀ state formed via direct internal conversion on the bound side of the potential curves (Path 4). Together with the signatures from the dissociative side (Path 3), these features provide complementary experimental handles to probe the elusive ground-state statistical decay channel.

These theoretical predictions arrive at a pivotal moment, as emerging XFEL − and HHG − light sources now enable experimental TXAS studies of such ultrafast processes. By providing the essential spectral reference S _TXAS(ω, ξ) for phenol, this work lays the foundation for translating future experimental S _TXAS(ω, τ) data into atomically resolved mechanistic insightsdirectly addressing the long-standing controversy over competing dissociation pathways.

Outlook

The “snapshots along the PESs” approach offers a practical solution for representing statistical averages, complementing the advantage of capturing stochastic events with explicit time dependence offered by non-adiabatic molecular dynamics in photochemistry and Born-Oppenheimer molecular dynamics (BOMD) for ground-state thermal reactions. This strategy proves particularly efficient for systems with a dominant one-dimensional reaction coordinate, as thoroughly demonstrated herein for the textbook case of phenol O–H fission. A similar 1D philosophy applies to proton-transfer , and other scenarios where a dominant collective coordinate can be defined, , demonstrating the broad applicability of the approach. This conceptual framework lays a foundation for addressing more complex photochemical problems.

From One-Dimensional to Multidimensional Photochemistry

A natural question is whether this static approach can be generalized to systems with two or more coupled reaction coordinates, such as the photoisomerization of azobenzene, where the dynamics are primarily controlled by the NN torsion dihedral ϕ and the CNN bending angle θ. In principle, one could compute a static spectral map S _TXAS(ω, ϕ, θ) over a predefined grid in the (ϕ, θ) space. A seemingly intuitive simplification would be to define a single, predetermined photochemical reaction path–effectively taking a 1D “slice” through the landscape–and compute spectra along it. Slices at fixed ϕ or θ can also provide useful preliminary insights into spectral trends.

However, the S _TXAS(ω, ϕ, θ) data cannot determine a unique dynamical sequence. At conical intersections, for instance, dynamics proceed through a continuum of pathways rather than a single trajectory, rendering any predetermined path inadequate to represent the ensemble. Consequently, there is no direct way to translate the static map S _TXAS(ω, ϕ, θ) into a time-resolved spectrum S _TXAS(ω, τ) without additional dynamical input.

To overcome this while retaining the accuracy of static spectral calculations, we propose a key-snapshot protocol that incorporates statistical sampling from nonadiabatic molecular dynamics. This hybrid strategy decouples conformational sampling from spectral computation: (1) efficient NAMD generates a trajectory ensemble; (2) clustering (aided by projecting trajectory density onto collective variables, e.g., a (ϕ, θ) heatmap for azobenzene) identifies dominant regions and selects representative “key snapshots”; (3) benchmark spectra are computed only at these snapshots, building a compact library {S _k (ω)}. The spectrum is then reconstructed as S _TXAS(ω,τ) ≈ ∑ _k w _k (τ)S _k (ω), with weights w _k (τ) from the trajectory ensemble. This hybrid strategy retains the static method’s efficiency–costly spectra are limited to a limited set of points–while incorporating ensemble statistics. It overcomes the main limitation of brute-force pure NAMD approach, where the time-consuming X-ray spectral calculations are over all (successfully terminated) trajectories. Practical validation of this conceptual framework remains a subject for future study.

Machine-Learning-Accelerated Dynamics and Spectroscopy Calculations

Machine-learning (ML) potentials offer a transformative route to obtain statistically converged dynamical parameters such as branching ratios. By training neural-network potentials on quantum-chemical references, ML-accelerated NAMD can generate statistically converged trajectory ensembles at a computational cost orders of magnitude lower than direct on-the-fly quantum-mechanical calculations, , making previously prohibitive simulations feasible. Moreover, the subsequent step of generating the spectral library can likewise be accelerated by ML. Approaches for speeding up spectral simulations are emerging as a complementary strategy. ,

Extension to Complex Environments

The methodology can be extended to heterogeneous environments through embedding schemes such as quantum mechanics/molecular mechanics (QM/MM). As demonstrated in ground-state thermal chemistry, environmental effects–including those from solvents, protein pockets, or material matrices–can be incorporated via the MM region with appropriate electrostatic embedding. Combined with ML-accelerated dynamics, QM/MM embedding offers a practical route to apply X-ray spectroscopy to ultrafast photochemical processes in realistic settings. The spectral maps S _TXAS(ω, ξ) thereby serve as practical theoretical references for converting experimental S _TXAS(ω, t) data into mechanistic insight.

Computational Methods

The valence potential energy curves along the O–H stretching coordinate of phenol were computed using the CASSCF method, with all other internal coordinates frozen at the equilibrium geometry. While six singlet valence states were included in the state averaging (Figure S6), this study focuses on the lowest three states (S₀–S₂), which govern phenol photodissociation. ,, The active space comprises 10 electrons in 10 orbitals: 2 σ*, 1 σ, 3 π*, 3 π, and 1 oxygen lone pair (n) orbital (Figure S1a). Vertical core-excited state energies at the O 1s edge (states e₁–e₃₀) were obtained with the state-averaged RASSCF method using a (12,1/10/0) scheme, where the numbers denote the total electron count and the orbital counts in the RAS1/RAS2/RAS3 subspaces. The O 1s orbital in RAS1 was constrained to an occupation of 1. All multiconfigurational calculations were performed with the aug-cc-pVTZ basis set using the Molpro package. , Transition dipole moments between the valence states (S₀–S₂) and core-excited states (e₁–e₃₀) were computed using our in-house MCNOX code, , which was also used to generate the TXAS spectra along each PEC path (Figures a and a) and to perform NTO analysis for major spectral features. To examine the influence of additional nuclear degrees of freedom, supplementary computations were performed for valence PECs with relaxed internal coordinates and for TXAS spectra at select point geometries. Further computational details are provided in Supporting Information Note S1. Extensive validation was conducted to ensure accuracy. The UV absorption spectrum (Note S2) and the steady-state O 1s XAS spectrum (Note S3) at the equilibrium geometry were computed by systematically varying key multiconfigurational parameters (active space size, number of states). These results were also benchmarked against time-dependent density functional theory (TDDFT) calculations with the Tamm-Dancoff approximation (TDA), employing a range of exchange-correlation functionals. The good agreement among the different methods and with available experimental data (for XAS) (Figures S5 and S7) validates our computational protocol.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.5c01736.

• Computational details, methodological validations for UV absorption and XAS, Cartesian coordinates of representative geometries, tables of XAS/UV peak positions, and figures depicting active space, NTO analysis for state character evolution, S₀–S₅ PECs, XAS/UV spectra computed with different methods, TXAS comparison at III, III*, and III′, and ground-state frontier orbitals (PDF)

CRediT: Guoyan Ge data curation, formal analysis, investigation, methodology, validation, visualization, writing - original draft; Sheng-Yu Wang data curation, formal analysis, investigation, validation, visualization; Weijie Hua conceptualization, formal analysis, funding acquisition, methodology, project administration, resources, software, supervision, visualization, writing - review & editing.

The authors declare no competing financial interest.