Ultrafast metal-to-ligand electron transfer driven by bond shortening revealed through dual-edge computational X-ray spectroscopy

Abstract

Understanding electron flow during chemical reactions is fundamental to ultrafast chemistry, particularly in transition-metal complexes where redox processes involve intricate coupling between electronic and nuclear dynamics. While time-resolved X-ray spectroscopy offers insight into these dynamics, interpreting spectral data to identify transient intermediates and electron transfer mechanisms remains challenging. We employ a dual-edge strategy that simultaneously simulates O K-edge and Cu L-edge X-ray absorption spectra for the paradigmatic ${\mathrm{CuO}}_2^{+}$ system. We show that symmetric Cu–O bond shortening drives metal-to-ligand electron transfer, converting Cu(I):O₂ to Cu(II):${\mathrm{O}}_2^{\bullet -}$. Peak-by-peak analysis along the binding coordinate resolves concurrent dioxygen reduction and copper oxidation, leveraging the interpretable ligand K-edge to decode the complex metal L-edge spectrum. A Born-Oppenheimer molecular dynamics simulation further captures thermally-driven transitions between side-on and end-on configurations, showing distinct spectral signatures, and identifies the O K-edge as a sensitive probe for Cu-O bond fluctuations. We establish a dual-edge protocol for decoding metal L-edge spectra and demonstrate the complementary power of static and dynamical simulation: the former offers a practical route to statistically averaged spectral trends, while the latter delivers explicit time-resolved insight into stochastic events. They provide a robust framework for mapping atomic-level electron flow in ultrafast X-ray studies of catalysis and energy science.

While time-resolved X-ray spectroscopy offers insight into electron dynamics in chemical reactions, interpreting spectral data to identify transient intermediates and electron transfer mechanisms remains challenging. Here, the authors report a dual-edge strategy that simultaneously simulates O K-edge and Cu L-edge X-ray absorption spectra for the paradigmatic CuO2+ system, reporting a protocol for decoding metal L-edge spectra and mapping atomic-level electron flow in ultrafast X-ray studies.

Introduction

Tracking the dynamic evolution of oxidation states (OS) during chemical reactions represents a central challenge in ultrafast chemistry. As a fundamental descriptor of electron distribution, the OS framework provides a rigorous basis for understanding redox processes, bridging formal chemical bookkeeping with the underlying quantum mechanical electron density^1–4. This interplay between electronic structure and nuclear geometry manifests in the bidirectional coupling where “structural changes-induced OS changes”^5,6 and “oxidation-induced structural changes”^7,8 are two sides of the same coin.

In transition metal complexes, a particularly subtle yet vital process occurs on the electronic ground state: structurally-driven electron transfer. Unlike the instantaneous vertical valence transitions probed by optical spectroscopy (e.g., metal-to-ligand and ligand-to-metal charge transfer), this ground-state electron flow represents a continuous reorganization of the chemical bond. Examples include metal-to-ligand electron transfer (MLET) triggered by vibrational coherences or thermal fluctuations. Deciphering these correlated electronic-nuclear motions on the ground-state potential energy surface (PES) is essential for understanding the intrinsic mechanisms of catalysis, energy conversion, and metalloenzyme function.

Modern time-resolved X-ray spectroscopy, enabled by X-ray free electron lasers (XFELs)^9–12 and high harmonic generation (HHG) table-top systems^13–18, provides powerful access to these dynamics via techniques like transient X-ray absorption (TXAS)¹⁹ and photoelectron (TXPS) spectroscopy²⁰, and time-resolved resonant inelastic X-ray scattering²¹. However, interpreting these complex spectral measurements requires theoretical frameworks that can accurately and efficiently capture the ultrafast dynamics, which can be modeled via static or dynamical approaches²².

In the static framework, computing theoretical TXAS spectra against a reaction coordinate ξ, S_TXAS(ω, ξ), has proven to be an economical and effective strategy. By synthesizing these static maps with experimental delay-time data, S_TXAS(ω, t), one can resolve the structural drivers of spectral evolution–a method successfully applied to K-edge studies of photochemical^22–24 and thermal^25,26 reactions. However, extending this rigor to transition metal L-edges is substantially more demanding, as accurate treatment requires accounting for spin-orbit (SO) coupling, multiplet effects, and dynamic correlation^27–30. This presents unique challenges for constructing smooth PESs and tracking continuous spectral evolution.

This challenge is further magnified in dynamical approaches, which must balance the dual burden of trajectory simulations and high-fidelity X-ray spectral calculations. This requirement exemplifies the intrinsic trade-off between spectroscopic accuracy and dynamical feasibility in transition metal complexes³¹. Indeed, while non-adiabatic dynamics (e.g., surface hopping) have been coupled with X-ray scattering to elucidate ultrafast spin-crossover³², the analogous task for L-edge spectra remains an open challenge. Accurately simulating continuous, peak-resolved L-edge spectra along trajectories requires treating SO coupling and multiplet effects across a vast ensemble of electronic states–a computational cost far exceeding that for scattering signals, which are primarily determined by nuclear pair distribution functions. Consequently, most time-resolved studies of metal L-edge spectra have been limited to one or a few discrete, representative geometries^21,33. To date, this discrete-geometry approach has also been the predominant strategy for interpreting time-resolved metal K-edge spectra³⁴. Even for K-edge data, despite methodological advances–including spectra computed from static geometries displaced along normal modes³⁵ and multi-configurational time-dependent Hartree (MCTDH) approaches³⁶ coupled with vibronic Hamiltonians^37,38–a continuous, peak-resolved analysis that tracks the evolution of electronic transitions and their underlying orbital character across a sequence of snapshots remains unavailable.

Herein, we address these challenges through a theoretical investigation of the side-on ${\mathrm{CuO}}_2^{+}$ cation (Fig. 1a)–a paradigmatic system exhibiting variable valences (Cu^I/II/III) without spin-state complications common in iron systems. As the fundamental Cu-O₂ motif in key copper oxygenases (e.g., PHM, DβM)^39,40 and synthetic catalysts^41,42, this cation provides an ideal platform to isolate intrinsic metal-dioxygen interactions from ligand-specific effects. While enzymatic environments stabilize the side-on geometry via steric constraints⁴³, the dynamic interconversion between coordination modes and its manifestation in transient spectra remain poorly understood. Crucially, the captured dynamics depend on the pump wavelength. While ultraviolet-visible pumps initiate dynamics on excited electronic states^19,44, infrared (IR) pumps resonantly excite vibrational coherences on the electronic ground state^45–47. Given that thermally driven ET in ${\mathrm{CuO}}_2^{+}$ occurs on the ground state, we propose an IR pump–X-ray probe setup (Fig. 1f), where an IR pulse initiates vibrational coherences on the PES. While the X-ray probe inherently involves transitions to core-excited manifolds, the observed spectral evolution acts as a sensitive mapping of the underlying ground-state orbital reorganization and covalent mixing (Fig. 1b–e).

Fig. 1. Molecular structures, electronic structure, and proposed TXAS experimental scheme.

a Structures of Cu-O₂ complexes under study: 1 (LCuO₂), 2a and 2b (${\mathrm{CuO}}_2^{+}$). Coordinates of 1 were taken from the crystal structure⁶⁴ with distant groups truncated by hydrogens. 2a, ${\mathrm{CuO}}_2^{+}$ unit extracted from 1 with ligand L⁻ removed. 2b, gas-phase optimized transition state geometry of 2a by B3LYP (triplet state). Bond lengths (in Å) and the O-Cu-O angle (in ^∘) are labeled. b Schematic energy level diagram for the three key orbitals^53,54 of ${\mathrm{CuO}}_2^{+}$ at its triplet ground electronic state with Cu(II):${\mathrm{O}}_2^{-}$ (left) or Cu(I):O₂ (right) configurations. c Evolution of the three key canonical MOs (Cu 3$d_{xz}+{\mathrm{O}}_2{\pi }_{\mathrm{ip}}^{*}$, ${\pi }_{\mathrm{oop}}^{*}$, and Cu 3d_xz--${\mathrm{O}}_2{\pi }_{\mathrm{ip}}^{*}$) at varying r_Cu-O distances (in Å). Integer occupation numbers are included in parentheses (detailed real numbers at each geometry provided in Table S3). Compositions of Cu 3d and ${\mathrm{O}}_2{\pi }_{\mathrm{ip}}^{*}$ in (d) Cu 3$d_{xz}+{\mathrm{O}}_2{\pi }_{\mathrm{ip}}^{*}$ and (e) Cu 3d_xz--${\mathrm{O}}_2{\pi }_{\mathrm{ip}}^{*}$ in RASSCF calculations with varying r_Cu-O. f IR pump--X-ray probe setup proposed to detect the binding: a resonant IR pulse initiates vibrational coherences (t = 0) on the ground-state PES, while subsequent X-ray pulses track the transient electronic and structural reorganization.

The goal of this study is to investigate the OS transition and spectral responses to different Cu-O₂ interactions by computing soft TXAS spectra of ${\mathrm{CuO}}_2^{+}$ at both the Cu L_2,3- and O K-edges. This dual-edge framework leverages the metal L-edge’s sensitivity to 3d features and the ligand K-edge’s direct probe of ligand environments. The synergistic power of such dual-edge (or multi-edge) X-ray spectroscopy has been well established for elucidating complex electronic and structural dynamics^23,34,48,49. The central advance of this work is the strategic use of the more interpretable O K-edge as a key to decode the intricate features of the Cu L_2,3-edge. We combine two complementary approaches: (1) snapshots along static PESs to provide an efficient, well-defined mapping of statistically averaged spectral evolution; and (2) room-temperature Born-Oppenheimer molecular dynamics (BOMD) simulations to capture explicit time-dependence and stochastic structural fluctuations inherent to real systems. This integrated framework allows us to decode how geometric changes drive electronic state evolution–specifically, whether and how symmetric Cu-O bond shortening triggers MLET. Furthermore, it enables us to resolve the unique signatures of the side-on motif and its dynamic transition to end-on configurations, providing essential benchmarks for future ultrafast X-ray experiments in bioinorganic chemistry and energy science.

Results and discussion

Ground-state chemical and electronic structures

The ${\mathrm{CuO}}_2^{+}$ cation (2) structures are derived from the crystal structure of the enzyme model complex [Cu(O₂)(β-diketiminate)]⁵⁰ (LCuO₂, 1) by removing its nitrogen-containing ligand L⁻ (Fig. 1a). 1 was identified as having Cu(III):peroxide (Cu(III):${\mathrm{O}}_2^{2-}$) character combining Cu K- and L-edge XAS, valence bond configuration interaction simulations, and broken-symmetry density functional theory (DFT) calculations⁵¹. Our recent restricted active-space second-order perturbation theory (RASPT2) study³⁰ successfully reproduced the experimental Cu L-edge XAS, and demonstrated that minor Cu-O₂ distance fluctuations ( ~ 0.03 Å) sensitively influence the spectral features³⁰. However, extending such high-level analysis across a broader configuration space to comprehensively characterize the binding dynamics faces technical challenges: maintaining a consistent and sufficiently large active space across all geometries to ensure smooth PESs and spectral evolution. To isolate the intrinsic nature of Cu-O₂ bonding, we utilize the simplified model 2. This reduction in computational complexity enables a more extensive exploration of the configuration space, providing fundamental insights that will inform future studies of biologically relevant systems featuring diverse ligand environments.

The configuration space of ${\mathrm{CuO}}_2^{+}$ spans from the crystal-phase geometry (2a, r_Cu-O=1.82 Å, r_O-O=1.39 Å) and its gas-phase optimized structure (2b, r_Cu-O=2.24 Å, r_O-O=1.23 Å) (Fig. 1a). The significant 0.42 Å Cu-O elongation and 0.16 Å O-O contraction upon relaxation reflect significant electronic reorganization. Internal reaction coordinate (IRC) calculations confirm 2b as a transition state (TS) connecting two equivalent end-on minima on the intrinsic gas-phase PES (Supplementary Fig. S1). However, as the side-on motif is frequently stabilized in enzymatic active sites by steric constraints^27,43, our study focuses on this enzyme-constrained pathway, modeling the symmetric Cu-O shortening from 2b to 2a via an interpolated path. Based on experimental O-O bond lengths (${\mathrm{O}}_2^{2-}$:1.49 Å, ${\mathrm{O}}_2^{-}$:1.34 Å, O₂:1.21 Å, ${\mathrm{O}}_2^{+}$:1.12 Å)⁵², we preliminarily assign 2a as Cu(II):${\mathrm{O}}_2^{-}$ and 2b as Cu(I):O₂, assignments to be rigorously tested via XAS.

A triplet ground state was identified at both geometries (Supplementary Note 1, Tables S1-S2). The singlet-triplet splitting (ΔE_ST ≡ E_S − E_T) increases from 0.66 eV (2a) to 0.92 eV (2b) at the RASPT2 level, with B3LYP-DFT showing a similar trend (Supplementary Table S2). The enhanced splitting at longer Cu-O distances reflect the system’s approach toward isolated O₂ character. Three key molecular orbitals (MOs) govern the electronic structure^53,54: the bonding ($d_{xz}+{\pi }_{\mathrm{ip}}^{*}$) and antibonding ($d_{xz}-{\pi }_{\mathrm{ip}}^{*}$) combinations of Cu 3d_xz and ${\mathrm{O}}_2{\pi }_{\mathrm{ip}}^{*}$ (in-plane) orbitals, and the primarily O₂-based ${\pi }_{\mathrm{oop}}^{*}$ (out-of-plane) orbital, with minor Cu 3d_yz contribution (Fig. 1b). Restricted active space self-consistent field (RASSCF) calculations confirm the expected single occupation (1.04-1.05) of both $d_{xz}-{\pi }_{\mathrm{ip}}^{*}$ and ${\pi }_{\mathrm{oop}}^{*}$ orbitals (Supplementary Note 2B, Table S3), consistent with DFT frontier orbitals (Supplementary Fig. S2a).

Using r_Cu-O as an effective reaction coordinate (ξ), we track orbital evolution along this binding pathway (2b  → 2a). While orbital occupations remain stable (Supplementary Table S3), significant covalent mixing develops in the $d_{xz}\pm {\pi }_{\mathrm{ip}}^{*}$ pair (Fig. 1c-e): the Cu contribution to $d_{xz}+{\pi }_{\mathrm{ip}}^{*}$ decreases from  ~ 100% to 80%; while its contribution to $d_{xz}-{\pi }_{\mathrm{ip}}^{*}$ increases from  ~ 0% to 20%. This reveals competing electron transfer processes: (1) MLET via $d_{xz}+{\pi }_{\mathrm{ip}}^{*}$ stabilization; (2) Ligand-to-metal ET (LMET) through $d_{xz}-{\pi }_{\mathrm{ip}}^{*}$ destabilization. Net atomic charge analysis confirms dominant MLET character, with Cu charge increasing from +1.0e (2b) to +1.2e (2a) (Supplementary Note 2C, Fig. S3). These systematic electronic structure changes consistently support an OS transition from Cu(I) in 2b to Cu(II) in 2a, setting a clear target for validation by time-resolved X-ray spectroscopy. (See Supplementary Note 2D for vibrational analysis relevant to the proposed IR-pump scheme.)

Cu 2p XAS spectral fingerprints of Cu(I), Cu(II), and Cu(III)

Interpreting future transient signals necessitates a firm understanding of the static endpoints, 2a and 2b. As a first step, we compute steady-state Cu L_2,3-edge spectra for LCuO₂ (1) and ${\mathrm{CuO}}_2^{+}$ (2a, 2b) and benchmark them against experimental references with well-known OSs (Fig. 2a-d). These references include Cu(III) (1⁵¹, Cu(II) (CuO⁵⁵, D_4h-${\mathrm{CuCl}}_4^{2-}$⁵⁶, and Cu(II) plastocyanin⁵⁶), and Cu(I) (Cu₂O⁵⁵ and Cu(I) plastocyanin⁵⁶). Spectra of complexes with the same OS show similar energy and profile. Especially, the pronounced Cu(I) signature allows immediate identification in 2b, whereas Cu(II)/Cu(III) spectra have similar shapes but differ mainly in energy positions.

Fig. 2. Simulated and experimental Cu L_2,3-edge XAS of Cu-O₂ complexes.

a Cu L_2,3-edge XAS spectra of LCuO₂ (1) and two ${\mathrm{CuO}}_2^{+}$ structures (2a and 2b) simulated by RASPT2. b Experimental spectrum⁵¹ of 1 is recaptured on the top for comparison. c, d Recapture of experimental spectra of other Cu complexes with known OSs^55,56. Stick spectra of (e) 2a and (f) 2b are shown with dominant transitions marked by indexes of final SO states (all initially from SO state 1). Stick spectra of the same type are marked with the same color. The inset gives the SO-NTO analysis for labeled peaks. All particle NTOs are shown. The hole orbitals are all Cu 2p orbitals with different orientations; only one representative is displayed for clarity.

While multiconfigurational methods exhibit systematic deviations of several eV in absolute soft X-ray transition energies^23,30,57, we established a robust calibration protocol. By aligning the first peak of 2b to the experimental Cu(I) reference (931.5 eV; averaged from 931.4 eV of Cu(I) plastocyanin⁵⁶ and 931.6 eV of Cu₂O⁵⁵), we determined a -5.9 eV energy correction. We assume the same shift for all ${\mathrm{CuO}}_2^{+}$ structures. As a result, the first peak of 2a appears at 931.7 eV, intermediate between 931.9 eV (CuO) and 931.0 eV (D_4h-${\mathrm{CuCl}}_4^{2-}$ and Cu(II) plastocyanin), indicating a Cu(II) assignment. The 0.2 eV relative shift between 2a and 2b matches the 0.3 eV difference between CuO and Cu₂O references⁵⁵, further validating our OS assignments.

Decoding the XAS spectrum of ${\mathrm{CuO}}_2^{+}$: gas- vs. crystal-phase assignments

To elucidate the electronic origins of the Cu L_2,3-edge features, we performed spin-orbit natural transition orbital (SO-NTO)⁵⁸ calculations for 2a and 2b (Fig. 1e). Atomic orbital decomposition of the final states (Supplementary Note 2E, Table S4) reveals four distinct transition classes in 2a. The dominant features arise from (i) d_xz-${\pi }_{\mathrm{ip}}^{*}$ antibonding orbitals, producing main transitions at 931.7 eV (L₃, states 21-22) and 951.1 eV (L₂, states 146-147). These are accompanied by three types of minor transitions: (ii) Cu 4s-hybridized states (with minor contributions from Cu 3d and O 2p) most evident at 936.6 eV (state 72) and 943.1 eV (state 114); (iii) O-O ${\pi }_{\mathrm{oop}}^{*}$ contributions at 933.0 eV (state 31) and 952.4 eV (state 151) embedded within main peaks; and (iv) a 3d-π_ip antibonding transition at 937.1 eV (state 83) that overlaps with primary features.

The spectral signature simplifies dramatically in 2b (Fig. 2f), where we observe only two transition types: (i) the characteristic $d_{xz}-{\pi }_{\mathrm{ip}}^{*}$ orbitals generating peaks at 934.8 and 954.0 eV, and (ii) Cu 4s contributions at 931.5, 941.1, and 951.0 eV. This simplification correlates with the Cu(I) character identified in our spectra, where the disappearance of ${\pi }_{\mathrm{oop}}^{*}$ features reflects weakened Cu 3d_yz–O₂ interactions at longer bond lengths. These findings establish that the side-on binding process not only shifts transition energies but fundamentally alters the density of states available for X-ray excitation.

Tracking the dioxygen reduction: O 1s TXAS along the Cu–O₂ binding pathway

Figure 3 a-b displays the simulated O 1s TXAS spectra of ${\mathrm{CuO}}_2^{+}$ along the binding pathway, obtained by RASPT2⁵⁹ and time-dependent DFT with the Tamm-Dancoff approximation⁶⁰ (TDDFT/TDA). Both methods yield consistent spectral evolution. At structures 2b and 2a, the ${\mathrm{CuO}}_2^{+}$ spectra match experimental spectra of O₂ and KO₂ crystals⁶¹ (with clearly identified oxygen OS of 0 and  − 1), confirming their oxygen OS of 0 and  − 1, respectively. The O₂ spectrum exhibits a strong π^* peak A at 530.9 eV, a medium σ^* peak B at 540.3 eV, and a broad σ^* peak at 543.9 eV; while KO₂ shows analogous peaks redshifted to 529.2, 535.0, and 539.9 eV. The experimental π^*-σ^* separation between peaks A and B (Δ) decreases by 3.6 eV (9.4  → 5.8 eV) upon OS change (0  →  − 1). RASPT2 produced a smaller reduction of 3.1 eV (9.5  → 6.4 eV), while TDDFT/TDA produced a larger change of 4.1 eV (9.9  → 5.8 eV). The complementary under- and overestimation by the two methods provides a comprehensive perspective that bounds the experimental Δ evolution. The comparison with O₂/KO₂ experiments indicates an OS change of oxygen from 0 to -1 in ${\mathrm{CuO}}_2^{+}$ along the Cu-O₂ binding pathway, with a corresponding change in the OS of copper from +1 to +2. The redshifts of peaks A (1.7 eV) and B (5.3 eV) in the experiment are reproduced by RASPT2 (1.6 and 4.7 eV) and TDDFT/TDA (0.8 and 4.9 eV). These shifts reflect MLET⁶² and the increasing Cu OS.

Fig. 3. O K-edge TXAS and NTO evolution along the Cu-O bond stretching pathway.

Simulated O 1s TXAS spectra of ${\mathrm{CuO}}_2^{+}$ along the Cu-O bond stretching pathway by using the (a) RASPT2 and (b) TDDFT/TDA methods. Comparisons were made to experiments⁶¹ of KO₂ and O₂ crystals. Inset, (a) hole SO-NTO and (b) hole NTO at an ordinary snapshot showing our calculation based on a localized core hole picture (green color indicates the MO is localized on O2). Evolution of the (c) particle SO-NTOs by RASPT2 and (d) particle NTOs by TDDFT/TDA corresponding to peaks A and B. Note that peak A in panels a-b is assigned from two stick transitions, distinguished by colors (green and orange), and the corresponding particle NTOs were enclosed in frames with consistent colors.

Figure 3 c–d analyzes transitions via NTOs. Peak A originates from $d_{xz}-{\pi }_{\mathrm{ip}}^{*}$ (green) and ${\pi }_{\mathrm{oop}}^{*}$ (orange) states with comparable intensities at 2b, indicating the degeneracy in ${\pi }_{\mathrm{ip}}^{*}$ (with minimal d_xz contributions) and ${\pi }_{\mathrm{oop}}^{*}$ orbitals. Progressing along the binding pathway, the intensity of the ${\pi }_{\mathrm{oop}}^{*}$ transition gradually increases over the intensity of the $d_{xz}-{\pi }_{\mathrm{ip}}^{*}$ transition, due to the increasing d_xz components. Both methods exhibit a reversal in the energy ordering of the two states that constitute peak A. The physical origin of this reversal is core-hole relaxation, which we examine via DFT-based core-hole analysis (Supplementary Note 2A, Fig. S4). TDDFT/TDA yields a larger splitting than RASPT2 at 2a. For peak B (O1s → σ^*), RASPT2 reveals clearer (i.e., without the entanglement of numerous weak transitions) evolution but lacks high-energy states due to limited state coverage; including more states in the RASPT2 calculation would require careful balancing of state weights⁶³. TDDFT/TDA, including more states, better reproduces the broad high-energy features.

Tracking the copper oxidation: Cu 2p TXAS along the Cu–O₂ binding pathway

The Cu L_2,3-edge spectral evolution along the binding pathway (Fig. 4a) directly evidences the Cu oxidation state transition, complementing the O K-edge analysis. As r_Cu-O shortens from 2.24 to 1.82 Å, the L₃ and L₂ main peaks (i and n) intensify. In the molecular orbital picture, this enhancement arises from increased Cu 3d character in the particle SO-NTOs (Fig. 4d), which strengthens the 2p → 3d transition dipoles. This description aligns with the atomic orbital view: the system evolves from a Cu(I) 3d¹⁰ configuration at 2b toward a Cu(II) 3d⁹ configuration at 2a. The transition from a fully filled to a partially filled 3d shell enhances excitation intensity because the 3d⁹ configuration allows the excited electron to occupy an orbital vacancy, creating a stable 3d¹⁰ final state with favorable electron correlation. The dominant transitions i (934.9  → 931.6 eV) and n (954.2  → 951.0 eV) exhibit significant redshifts. Figure 4b traces this progression through particle SO-NTOs, revealing the redshift mechanism: increased Cu 3d and diminished O 2p character in the excited states (Fig. 4d-e); quantitative data in Supplementary Table S5. Similar trends of redshift are found for weak peaks j and o.

Fig. 4. Cu L_2,3-edge TXAS and NTO evolution along the Cu-O bond stretching pathway.

a Simulated Cu L_2,3-edge TXAS spectra of ${\mathrm{CuO}}_2^{+}$ by RASPT2 along the Cu-O bond stretching pathway. Snapshot structures are interpolated between 2a and 2b (see structures in Fig. 1a). Each curve is labeled by the Cu-O distance in Å. Major stick peaks are labeled by i, j, ⋯  , n. b Evolution of individual peaks interpreted by SO-NTOs (only particle orbitals are shown). Colored shading distinguishes three orbital types: $d_{xz}-{\pi }_{\mathrm{ip}}^{*}$ (orange), ${\pi }_{\mathrm{oop}}^{*}$ (pink), and Cu 4s (green). c Potential energy curves for the ground state and low-lying Cu 2p core-excited states corresponding to peaks i and k. Composition of particle SO-NTOs for transitions i and n as a function of Cu--O distance: (d) Cu 3d and (e) O 2p orbital contributions. SO-NTO particle orbital compositions for transitions k, l, m, and p: (f) Cu 4s and (g) O 2p contributions. Numerical orbital composition data are provided in Supplementary Table S5.

Conversely, peaks k, l, m, and p exhibit noticeable blueshifts while maintaining stable intensities. Their features (Fig. 4b) correlate with a progressive decline in Cu 4s proportions (92%  → 85%, Fig. 4f), alongside minor changes in O 2p (4.0–6.1%, Fig. 4g) and Cu 3d contributions (<0.6%, Supplementary Table S5). Shoulder peaks k and p blueshift from the low- to high-energy sides of their main peaks i and n, intersecting at 2.01 Å along the pathway (Fig. 4c). Despite this energy shift, their intensities remain constant across all configurations, resulting in comparable shoulder-to-main peak ratios at 2b that merge into the main peak at 2a. This NTO analysis collectively elucidates the electronic structural origins of spectral evolution.

Tracking the energy and structural evolution along a BOMD trajectory

Complementary to the static analysis, we performed BOMD simulations at the RASSCF level. This single-trajectory approach is designed to capture spectral responses to specific stochastic events, providing a dynamic counterpoint to the symmetric static method. The system was propagated for 1.45 ps at 300 K using a Nos’e-Hoover thermostat. While the MD simulation required only 18 hours (dual Intel Xeon Platinum 8171M CPUs, 52 cores), each subsequent X-ray spectral calculation per snapshot demanded roughly 6 hours (8 cores), highlighting the computational investment required for high-fidelity time-resolved spectroscopy.

Figure 5 a,b depicts the energetic and structural evolution. Notably, the two Cu-O distances exhibit distinct dynamic behavior. A marked decrease in total energy after  ~ 400 fs correlates with an overall elongation of the Cu-O bonds, signaling a structural transition from a predominantly side-on to the thermodynamically preferred gas-phase end-on configuration. The initial phase (0-400 fs) exhibits pronounced oscillations where Cu-O1 and Cu-O2 distances recurrently exchange relative magnitudes, accompanied by significant O1-O2 vibrations (Supplementary Movie 1). Beyond this point, the geometry stabilizes into a highly asymmetric state where one Cu-O distance (Cu-O2) remains consistently larger, reflecting the end-on binding preference in the absence of environmental constraints. Correspondingly, the O1-O2 distance exhibits markedly reduced oscillatory amplitude.

Fig. 5. Energetic and structural evolution for the BOMD trajectory.

a Potential energy (RASPT2) along the 1.45-ps trajectory. b Key interatomic distances: Cu-O1, Cu-O2, and O1-O2. The simulation separates into two dynamical regimes around 400 fs, characterized by dominant side-on and end-on geometries. The shaded regions (97-242 fs and 581-774 fs) denote the time windows selected for spectral analysis in Fig. 6a and 6b. c, d Representative snapshots from each regime with key geometric parameters labeled.

This observed evolution carries an important implication: the symmetric side-on geometry, while central to enzymatic function in constrained environments such as the active sites of copper oxygenases, is metastable for the isolated cation. Its spontaneous interconversion to the end-on configuration yields distinct spectroscopic signatures that we now examine in detail.

Tracking the spectral evolution along the BOMD trajectory

We analyzed two distinct time windows for both edges: window 1 (97–242 fs, side-on) and window 2 (581–774 fs, end-on). At the Cu L-edge (Fig. 6a-c), window 1 exhibits a double-peak structure (i and k) in the L₃ region, spanning 931.5–933.6 eV. As the Cu–O distances in this window fluctuate between 1.8 and 2.2 Å, a range that fortuitously overlaps with the equilibrium distances of the static models 2a and 2b, the spectra within this window can be viewed as a dynamic modulation of the spectral signatures of 2a and 2b. SO-NTO analysis reveals these features originate from excitations to d_xz–${\pi }_{\mathrm{ip}}^{*}$, ${\pi }_{\mathrm{oop}}^{*}$, and Cu 4s orbitals. Conversely, window 2 (end-on) simplifies to a single feature (k) in the L₃ region spanning a narrower energy range of 931.0–932.1 eV. SO-NTO analysis indicates that the spectral intensity is dominated solely by Cu 2p → Cu 4s transitions, a signature of the asymmetric end-on geometry with single-oxygen coordination. The two windows exhibit markedly distinct spectral features, underscoring the high sensitivity of the Cu L-edge to the side-on versus end-on structural dichotomy.

Fig. 6. TXAS spectra computed from two windows in the BOMD trajectory.

a–c Cu L_2,3-edge and (d–f) O K-edge TXAS spectral evolution from BOMD trajectory analysis. Cu L_2,3-edge spectra for (a) window 1 (side-on, 97--242 fs) and (b) window 2 (end-on, 581--774 fs). c Corresponding one-dimensional (1D) spectral cuts, with individual stick transitions labeled (labels are consistent throughout). Particle spin-orbit NTOs for labeled peaks are summarized to the right. e O K-edge spectra for the same two windows. f Corresponding 1D cuts, with major stick transitions within peaks A/B are color-coded by final-state orbital character. Particle NTOs are displayed to the right. In (c) and (f), orbital categories are distinguished by shaded colors.

The O K-edge (Fig. 6d-f) demonstrates even greater diagnostic power for discriminating between side-on and end-on geometries. The spectral intensity is also notably stronger than at the Cu L-edge. In window 1, the spectra are characterized by two distinct peaks, A and B, analogous to those observed for the static models 2a and 2b (see Fig. 3). The intense peak A centered within a narrow range of 527.8–530.1 eV corresponds to hybridized d_xz–${\pi }_{\mathrm{ip}}^{*}$ and ${\pi }_{\mathrm{oop}}^{*}$ transitions. While the medium peak B oscillates substantially within a wide range of 530.2–536.1 eV. This oscillation directly correlates with the dynamic exchange of the Cu–O1 and Cu–O2 bond lengths, as peak B originates from O 1s → O–O σ^* transitions within the dioxygen moiety, making it a sensitive real-time probe of the Cu–O distance. In window 2, the spectra also display two features, peaks A and B, but with altered electronic origins. Peak A derives from O 1$s\to {\pi }_{\mathrm{ip}}^{*}$ and ${\pi }_{\mathrm{oop}}^{*}$ transitions, with diminished Cu 3d contribution. Peak B exhibits milder oscillations in intensity and energy, consistent with the geometric stabilization of the end-on configuration where only the O1 atom maintains a persistent bond to the copper center.

Collectively, this BOMD analysis validates that the distinct spectral fingerprints identified from static geometries remain robust under dynamic conditions. It crucially highlights the O K-edge, specifically the O–O σ^* feature, as a superior real-time structural probe for tracking metal-ligand bond fluctuations–complementing and clarifying the information from the more complex Cu L-edge.

Conclusions and outlook

We have demonstrated a dual-edge computational spectroscopy framework that tracks coupled electron-nuclear dynamics in the paradigmatic ${\mathrm{CuO}}_2^{+}$ system. This framework strategically integrates static “snapshots along the PESs” with efficiency and practicability to obtain the statistical average and room-temperature BOMD simulations to see the stochastic events, bridging the gap between ideal reaction coordinates and stochastic structural fluctuations inherent to real systems, and providing a comprehensive picture to understand the reaction dynamics. By simultaneously simulating Cu L_2,3-edge and O K-edge spectra, we decoded the electronic evolution from Cu(I):O₂ to Cu(II):${\mathrm{O}}_2^{\bullet -}$ during the side-on binding process. Our analysis reveals that this oxidation state transition is driven by competing electron transfer mechanisms–specifically, a dominant MLET and a secondary LMET process.

The BOMD simulations provide a dynamic validation of our static models, highlighting a clear structural-spectral dichotomy: the side-on geometry is characterized by a diagnostic double-peak structure at the Cu L₃-edge, while the thermodynamically preferred gas-phase end-on configuration yields a simplified spectrum dominated by Cu 2p → 4s transitions. Crucially, the O K-edge emerges as the superior structural reporter; the wide-range oscillation of the O–O σ^* feature directly tracks Cu–O bond fluctuations in real-time, providing a clearer diagnostic than the more complex metal-centered multiplets.

The synergistic use of ligand K-edge data to decode intricate metal L-edge features establishes a general protocol for interpreting ultrafast X-ray experiments. This atomistic tracking of electron flow is immediately applicable to a broad range of localized electronic systems, from single-atom catalysts (SACs) to metalloenzyme active sites in oxygen reduction and evolution reactions (ORR/OER). Looking forward, the integration of advanced methods like density matrix renormalization group (DMRG) with periodic embedding schemes will extend this dual-edge capability to complex functional materials, offering a clear pathway for simulating the next generation of time-resolved X-ray experiments.

Methods

Static approach

The bare ${\mathrm{CuO}}_2^{+}$ structure (2a) was derived from the crystal structure of 1⁶⁴ by ligand truncation. Gas-phase geometric relaxations were performed at singlet, triplet, and quintet states using DFT with the B3LYP functional in GAUSSIAN 09⁶⁵, employing the 6-31G* basis set for O and the modified LanL2DZ basis set with optimized 4p functions⁶⁶ and the LanL2DZ pseudo potential for Cu⁶⁷. Both 2a and the optimized structure 2b were confirmed to have triplet ground states (Supplementary Note 1). Vibrational frequencies were computed at both geometries. Intermediate structures along the binding coordinate were generated by linear interpolation of Cartesian coordinates between 2a and 2b, without further geometry optimization. The transition-state nature of 2b was verified by internal reaction coordinate (IRC) calculations (Supplementary Fig. S1).

Cu L_2,3-edge XAS spectra were simulated using the OPENMOLCAS package^68,69 via state-averaged RASSCF^70,71 and multi-state RASPT2⁵⁹ methods, with analysis mainly based on the RASPT2 results. For all ${\mathrm{CuO}}_2^{+}$ structures, we set n_v = 5 for valence and n_c = 40 for core-excited states, with eight active orbitals (Cu 3d and O2) in RAS2 (Supplementary Fig. S5) and three Cu 2p orbitals in RAS1. The choice of this active space and other parameters was carefully validated (Supplementary Note 3B). Scalar relativistic effects were included using a second-order Douglas-Kroll-Hess Hamiltonian and the ANO-RCC-VDZP basis set⁷². The core hole was treated via the highly excited states method⁷³. To accelerate calculations, the Cholesky decomposition⁷⁴ was applied to approximate two-electron integrals. A level shift of 1.0 a.u. was used for RASSCF convergence, and an imaginary shift of 0.3 a.u. was applied to mitigate intruder states during RASPT2 analyses. Transition dipole moments were calculated using the RAS state-interaction (RASSI) approach^75,76. Additionally, RASPT2 calculations for 1 were performed with optimal parameters³⁰ of n_v = 5, n_c = 18, and n_A = 6.

At the O 1s edge, spectra were computed by RASPT2 with identical parameters to the Cu L-edge calculations (n_v = 5, n_c = 40, n_A = 8), modifying only RAS1 to contain the Boys-localized^77,78 O2 1s orbital. Validation was performed using TDDFT/TDA in Q-CHEM⁷⁹ with the ωB97M-V functional⁸⁰ and mixed basis sets (def2-QZVP for O2; def2-TZVP for O1/Cu)^81,82, restricting excitations to the localized O2 1s orbital to maintain consistency with the RASPT2 treatment. Different basis sets were chosen only to meet the specific requirements of each methodological stage, and these choices do not compromise the accuracy or conclusions of our work (Supplementary Note 4).

All spectra were broadened using a Gaussian lineshape with a half-width at half-maximum (HWHM) of 0.8 eV³⁰. Energy shifts of δ₁ = − 3.9 eV for 1 (aligned to experiment⁵¹) and δ₂ = − 5.9 eV for 2b (matched to Cu(I) references^55,56) were applied, with δ₂ subsequently applied consistently for 2a and all interpolated structures. SO-NTOs (Cu edge) and NTOs (O edge) were computed for major transitions.

BOMD approach

BOMD simulation was performed at the RASSCF level in OPENMOLCAS starting from the 2a geometry and its converged wavefunction as the initial guess. Parameters were set identical to static calculations. An NVT ensemble at 300 K was propagated for 1.45 ps (3000 steps, Δt = 20 a.u.) using the velocity Verlet integrator⁸³ and a Nosé–Hoover chain thermostat. The converged valence electronic wavefunction was archived at every step to provide a robust initial guess for subsequent core state calculations, ensuring stability and efficiency.

XAS were subsequently computed for two consecutive windows of snapshot geometries extracted from the trajectory with dominant side-on (window 1, 97–242 fs) and end-on (window 2, 581–774 fs) configurations. Spectra were computed every 5 steps, yielding 61 (81) snapshots for window 1 (2). For each snapshot, the archived valence wavefunction served as the starting point for the RASPT2 calculation of core-excited states at either the Cu 2p or O 1s edges.

To properly account for the dynamically evolving symmetry-breaking, we modified the active space for the O K-edge: while the static symmetric models used a single pre-localized O 1s orbital in RAS1, the dynamical framework included both O1 and O2 1s orbitals. This adaptation allows for the simultaneous description of core holes localized on either oxygen site, which is essential for capturing the spectral signature of an asymmetric ligand environment. NTO analysis confirms the initial core-hole states span configurations localized on O1, O2, and their coherent superpositions (Supplementary Fig. S6). All graphics were generated by combining Multiwfn⁸⁴ and VMD⁸⁵ (isovalue=0.05).

Author contributions

W.H. conceived and designed the research. S.-Y.W. performed the calculations. J.-R.Z. and G.G. assisted with the graphics. S.-Y.W. and W.H. co-wrote the manuscript. All authors discussed the results.

Peer review

Peer review information

Communications Chemistry thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data that support the findings of this study, including Cartesian coordinates (1, 2a, 2b, and BOMD trajectory) and all simulated spectral data, are openly available in Zenodo at [10.5281/zenodo.18334837], with additional data available from the corresponding author upon reasonable request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s42004-026-02024-4.