Introduction

Photoexcited charge and energy transfer are essential steps in many natural and artificial light-harvesting processes1,2,3,4, which often rely on transition metal complexes with characteristically dense manifolds of charge transfer excited states5,6,7,8,9,10,11. The orchestration of electronic, vibrational, and electronic–vibrational (vibronic) couplings that drive charge and energy transfer in light-harvesting complexes involve structural rearrangement, spin–vibronic interactions, and a dynamic solvent environment making these systems fundamentally interesting and challenging to understand. A wealth of experimental and computational studies on Ru-centered complexes have measured their photoexcited dynamics following singlet metal-to-ligand charge transfer (MLCT) excitation, such as ultrafast intersystem crossing (ISC). These past studies have established that the excited triplet MLCT states can provide sufficiently long-lived charge separation to yield a useful chemical potential for energy harvesting applications12,13,14,15,16,17,18. Yet, an essential open question remains: what intramolecular coordinates define the trajectory of a photoexcited complex’s evolution into these desirable long-lived charge separated states?

Addressing this requires a continually advancing spectroscopic toolbox to move beyond measuring kinetics of photoexcited states toward building detailed molecular-level descriptions of important charge and energy transfer mechanisms utilized by transition metal complexes19,20,21,22,23. Exciting progress in experimental techniques is making investigations related to the following questions tractable: how do specific molecular coordinates control photoexcited energy transfer dynamics? What role do vibronic couplings and coherences play during photoexcited energy transfer and relaxation? Third-order nonlinear Fourier transform (FT) techniques such as two-dimensional (2D) electronic (ES) and 2D infrared (IR) spectroscopy have greatly advanced our understanding of coherent molecular phenomena in solution24,25,26,27,28,29,30,31,32,33. While vibronic information may be measured indirectly by 2D IR and ES spectroscopies, the recently developed 2D electronic–vibrational (2D EV) and 2D vibrational–electronic experiments directly access vibronic information through resonant interactions with electronic and IR-active vibrational transitions34,35,36,37.

In this article, we use multidimensional (2D and 3D) EV spectroscopy to directly follow vibronic coherence evolution in a photoexcited Ru-centered complex: the solar cell dye molecule, [Ru-(dcbpy)2(NCS)2] (dcbpy = 4,4′-dicarboxy-2,2′-bipyridine), commonly known as N3. We demonstrate 3D EV spectroscopy (Fig. 1d), where vibronic couplings between three disparate molecular coordinates are resolved: electronic excitations (ω1: 24,100–25,500 cm−1), low-frequency vibrations (0 < ω2 < 0–833 cm−1), and high-frequency vibrations (ω3: 1250–1500 cm−1). A real-time microscopic view of photochemical reactivity may be obtained by following the temporal evolution of the vibronic states measured in the 3D EV spectrum. As depicted in Fig. 1d, vibrational coherences (red/yellow spheres, L1/L1′) can be directly identified by an electronically localized 3D EV feature, and its time-dependent behavior (L1 (red) → L1′ (yellow)) characterized through its ω2-dependent spectral phase. Population and coherence transfer (blue and purple spheres, L2) between vibronic states can follow internal conversion (IC) from the perspective of specific vibrational coordinates that may be directly involved. Vibronic coherences can also be identified through out-of-phase oscillatory dynamics between different 3D EV features. In this way, the 3D FT experiment can unveil additional dark coordinates actively coupling the two motions measured in the 2D experiment, as well as coherences between molecular states facilitating energy transfer. While 3D FT studies have yielded exciting insight related to vibrations driving singlet fission38, quantum coherence in photosynthesis39, and tracking excited-state photoisomerization40, no reported study to date has fully exploited the potential of 3D FT spectroscopy to most completely describe molecular eigenstates in terms of three energetically disparate molecular coordinates. Here, the complete capability of multidimensional EV spectroscopy is demonstrated by directly following vibronic coherence evolution in the photoexcited aqueous N34− molecule (fully deprotonated N3) while it undergoes ultrafast ISC and nonadiabatic IC. An in-depth characterization of an excited-state vibrational wave packet is reported here in photoexcited N34− as it propagates during the initial 600 femtoseconds (fs), answering an outstanding question about the wave packet’s existence within the N3 triplet manifold12. Consequent energy transfer from the initial vibrational wave packet to a second coherence is observed, which propagates further for ~1 picosecond (ps). Interestingly, the electronic character of the evolving secondary coherence oscillates between two different MLCT states with 340 ± 40 fs periodicity. Our measurement identifies this as a vibronic coherence promoting nonadiabatic IC. We simulate the experimental result and extract the 50 cm−1 nonadiabatic coupling driving IC during the excited-state triplet relaxation. This study provides an unambiguous view of a photoexcited vibronic mechanism driving long-lived charge separation in a solar cell dye.

Fig. 1
figure 1

Multidimensional Electronic–Vibrational (EV) Spectroscopy. In each technique, the pulse sequence (a) induces an electronic excitation (pumps: k1, k2) and measures a high-frequency vibrational response (probe: k3) in a sample. Consider a system where one high-frequency vibration (H) vibronically couples to two electronic excited states (A, B) and to two low-frequency vibrations (L1, L2) in A and/or B. b The pump–probe experiment (1D EV) measures the H vibrational spectrum (ω3) and kinetics during its relaxation times (τ2). At a given τ2 delay, (c) the 2D EV experiment resolves the electronic excitation spectrum (ω1) for H, defining the excited vibronic eigenstates (ψ(t)) by the couplings between H, the ground electronic state and either A or B. Collecting 2D EV spectra over a τ2 range measures population relaxation and coherent superpositions of eigenstates. The latter manifest as peak amplitude modulations; a FT over τ2 yields a (d) 3D EV spectrum where coherences (rainbow-colored spheres) separate in ω2 from population decays (black spheres) according to their beat frequency. The ω2 frequencies can indicate low-frequency vibrations (L1, L2) coupled with vibronic eigenstates. Time-dependent 3D EV features, such as frequency shifts of low-frequency modes as generally indicated by L1 moving to L1’ in the ω2 frequency space, report on the temporal evolution and nonequilibrium relaxation of the vibronic eigenstates during photoexcited processes (depicted by the sphere coloration gradient).

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Results

The MLCT states and the high-frequency vibrational reporter

The aqueous N34− has two 1MLCT electronic absorption bands (Supplementary Fig. 1) centered at 20,000 cm−1 (500 nm) and 26,880 cm−1 (372 nm). The 1MLCT absorption consisting of a dense manifold of MLCT excited states results in electron density with mixed Ru-(NCS)2 character shifting to a dcbpy π* orbital8,41. The 3MLCT excited-state manifold is also dense, which facilitates ultrafast ISC on a timescale comparable with one or two vibrational periods of the ligand high-frequency vibrational modes6,8,13,15. We follow the excited-state intramolecular charge donor–acceptor dynamics vibrationally. Previously, we identified principal high-frequency vibrational signatures of the excited electronic states for both the charge donor and acceptor in the N34− transient IR (tIR), or 1D EV spectra (see Supplementary Note 2, Supplementary Fig. 4, and Supplementary Table 1)34. The symmetric stretching carboxylate vibration (ω3 = 1328 cm−1) in the electronic excited state, referred to as νCOO, is a spectrally isolated reporter of the charge-accepting dcbpy ligand and is the high-frequency mode of interest here.

Using polarization-selective 2D EV spectroscopy of N34− at a single τ2 time delay, we discovered that two excited electronic states with 1MLCT character (1MLCTA and 1MLCTB) are vibronically coupled to charge donor and acceptor vibrations within the excited triplet manifold, likely facilitating ultrafast photoexcited charge transfer34. We now use 3D EV spectroscopy to measure the time-dependent modulation of the vibronic couplings between νCOO and both MLCTA and MLCTB due to low-frequency vibrational modes throughout the initial 1500 fs of the photochemical reaction. Here, we omit the spin label to reflect that MLCTA and MLCTB are strongly spin-mixed states, which is expected from computational work on similar complexes8,10 and supported in our data by a consistent ω1 peak maxima of νCOO (Supplementary Note 8 and Supplementary Fig. 13). The ground-state bleach (GSB, positive signal) and excited-state absorption (ESA, negative signal) of the carboxylate region are shown in the 2D EV spectra (Fig. 2a) with the MLCTA, MLCTB, and νCOO transitions highlighted.

Fig. 2
figure 2

Low-frequency amplitude modulations in two-dimensional electronic–vibrational (2D EV) spectra. a τ2-dependent 2D EV spectra show oscillatory amplitude; notably, the νCOO (ω3 = 1328 cm−1) excited-state vibration characterized by MLCTB (ω1 ≅ 25,200 cm−1) excitation. Contour lines: solid (dashed) = positive (negative) signal, 5% intervals beginning at ± 10%. Residual intensity of the integrated (ω1, ω3) 2D peak area for the νCOO coupled to the (b) MLCTA (ω1 ≅ 24,700 cm−1) and (e) MLCTB electronic excited states (gray, circles). Temporal filtering (dashed) isolates early relaxation times (0 < τ2 < 600 fs, red) or later relaxation times (400 < τ2 < 1500 fs, blue) to identify transient, low-frequency amplitude modulations in either time range. Fourier Transform (FT) spectra of the temporally filtered [(c) early = red; (d) later = blue] 2D residuals of MLCTA excitation show principal low-frequency components (i.e., νRu-N and/or νRu-bpy) responsible for the 2D EV peak amplitude modulation. Corresponding FT spectra for MLCTB excitation are shown in (f) and (g). In all FT spectra, the gray spectra are the background (no EV signal); the shaded regions represent ±1 standard deviation from the average data (shown by circles). See Supplementary Note 3 for discussion of data processing. The number of (ω1, ω3) points: MLCTA = 45; MLCTB = 24; Background (signal ≤ 5% max) = 3295.

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τ2-Dependent amplitude oscillations in 2D EV spectra

Nontrivial 2D EV amplitude modulations are observed over the initial 1500 fs of the τ2 delay. The oscillatory amplitude of the 2D EV peak for νCOO vibronically coupled with MLCTB is highlighted in Fig. 2a. To observe the amplitude modulations more clearly, the exponential population kinetics are subtracted to obtain the residual amplitude of the integrated 2D area (ω1, ω3) for the greatest ~10–15% signal of the 2D EV peaks measuring the νCOO vibronic coupling with MLCTA and MLCTB (gray in Fig. 2b, e, respectively; see Supplementary Fig. 7 and Supplementary Table 2). In accord with previously reported wave packet formation in N312, two different τ2 ranges of the residuals are temporally selected (red and blue; Fig. 2b, e), and Fourier transformed to identify the principal low-frequency components modulating the 2D EV signal within those τ2 ranges (Fig. 2b–g; Supplementary Fig. 7). The details of the FT analysis are given in Supplementary Note 3. Careful consideration of instrument noise is required, as the oscillations are weak compared with the population decay (Supplementary Fig. 5). Hence, we only consider the ω2 features most prominently above experimental noise (i.e., νRu-N and νRu-bpy) in Fig. 2c, d, f, g. The noise floor is set by performing the identical FT analysis on the 2D EV spectral region, where the signal level is ≤5% of the maximum 2D EV signal (Supplementary Note 3 and Supplementary Fig. 6). We exclude features at ω2 ≥ 790 cm−1 given our 833 cm−1 Nyquist sampling limit and the features approaching 0 cm−1 (DC limit) due to imperfect population kinetics subtraction. During early relaxation times (0 < τ2 < 600 fs, Fig. 2c, f), a peak at ω2 = 340 cm−1 is measured only for the νCOO vibration of MLCTB character. The electronically-localized nature of this excited vibrational wave packet reported here reveals a stricter electronic characterization of this previously reported wave packet12. At later relaxation times (400 < τ2 < 1500 fs), a low-frequency vibrational mode at ω2 ≅ 742 cm−1 is clearly coupled to the νCOO vibration of both MLCTA and MLCTB character. These spectra show a markedly different vibrational and electronic character of the measured coherences between the early and later relaxation periods.

Previous calculations34 of the lowest energy triplet state vibrational spectrum of N34− (Supplementary Note 9 and Supplementary Fig. 14) and resonance Raman experiments42,43 aid us in assigning the 340 cm−1 mode and the 742 cm−1 mode as involving the stretching coordinate between the Ru and the dcbpy nitrogens (respectively called νRu-N and νRu-bpy here), with the νRu-bpy primarily localized to the dcbpy ring. A recent surface-hopping trajectory calculation on [Ru(bpy)3]2+, a molecule similar to N38, included on-the-fly, spin–orbit coupling and found low-frequency vibrations analogous to νRu-N and νRu-bpy promoting ultrafast ISC due to excited-state mixing. To understand the ligand’s role in realizing long-lived charge separation, the relevant electronic and vibrational coordinates and their couplings must be mapped out. From Fig. 2, the vibronic eigenstate basis explored here for N34− is established and consists of: the excited electronic states (MLCTA/MLCTB), the charge-accepting high-frequency vibration (νCOO), and the low-frequency vibrations (νRu-N, νRu-bpy). An effective Hamiltonian for a complicated, multi-coordinate system is distilled down to these measured vibronic eigenstates. We introduce the eigenstates and a density matrix element notation for use in the remaining discussion: \(\rho _{ab}(\tau _2) = \left| {a(\tau _2)} \right\rangle \left\langle {b(\tau _2)} \right|\) specifies a density matrix element, and a, b ∈ {1–8} are the numbered vibronic eigenstates given in Fig. 3 (e.g., the νRu-N coherence is represented: \(\left| {B;0,0,0} \right\rangle \left\langle {B;1,0,0} \right| = \rho _{35}\)).

Fig. 3
figure 3

Vibronic eigenstate basis and energy-level diagram. The measured eigenstate basis of N34− is cast in terms of \(\left| {{\mathrm{elec}};\upnu _{{\mathrm{Ru}} -{\mathrm{N}}},\upnu _{{\mathrm{Ru}} - {\mathrm{bpy}}},\upnu _{{\mathrm{COO}}}} \right\rangle\), where elec = A (MLCTA, purple) or B (MLCTB, blue) and the three following quantum numbers relate the quanta in each of the vibrational modes listed in increasing transition energy. The relative energies are derived from the multidimensional EV measurements: ΔEelec ≅ 500 cm−1 from ω1; νRu-N = 340 cm−1 and νRu-bpy = 742 cm−1 from ω2; and νCOO = 1328 cm−1 from ω3. The eigenstates are numbered in increasing energy for reference throughout the discussion. The N34− structure (top) schematically depicts the electronic excitation (light blue) and the vibrational motions involved with photoexcited charge transfer. The vibrational mode arrow colors correspond to the respective transitions given in the energy-level diagram below.

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The early-time excited-state vibrational wave packet

The 3D EV experiment provides a more complete description of the vibronic states involved in the coherent superposition composing the MLCTB excited-state vibrational wave packet measured at ω2 = 340 cm−1. The red ω2 spectrum in Fig. 2f demonstrates that the 2D EV peak intensity oscillations at early times arise from the ρ35 density matrix element. We characterize the time-dependence of the frequencies in the vibrational wave packet by the spectral phase, \(\phi (\omega _2) = \tan ^{ - 1}\left( {\frac{{{{\mathrm{Im}}} [{\mathrm{FT}}(S(\tau _2))]}}{{{{\mathrm{Re}}} [{\mathrm{FT}}(S(\tau _2))]}}} \right)\), where S(τ2) is the 2D EV residual signal during 0 < τ2 < 600 fs for MLCTB shown in Fig. 2e (red). The group delay is obtained from the spectral phase, and is defined as \(\tau _d(\omega _2) = - {\mathrm{d}}\phi (\omega _2)/{\mathrm{d}}\omega _2\). The spectral phase contains time versus frequency information of a wave packet; for example, a quadratic variation in ϕ(ω) corresponds to a linear group delay because the frequencies of the wave packet are changing linearly in time (see Supplementary Note 4 and Supplementary Fig. 8a, b). We note that the extracted group delay (Fig. 4, green), resulting from the best fit of the spectral phase, is positive and predominantly quadratic within the ω2 region defined by the spectral FWHM (gray arrows). Interestingly, this form of the group delay describes the wave packet shifting to higher frequencies (300 cm−1 → 370 cm−1 over 140 fs → 520 fs in τd) in time. The blue-shift of the vibrational frequencies as a function of τ2 is also revealed through a sliding window short-time Fourier transform (STFT) (Supplementary Fig. 9). We attribute the change in vibrational frequencies to the nonequilibrium relaxation of the excited wave packet with respect to the νRu-N coordinate measured experimentally during 0 < τ2 < 600 fs. This dynamic blue-shift is suggestive of a rapid vibrational relaxation of the highly excited νRu-N coordinate on MLCTB down the multidimensional anharmonic potential of the νRu-N. Similar observations of blue-shifting of vibrational modes on photoexcited multidimensional surfaces have been made in organic complexes44 and in reports of bridging cyanide ligand vibrational relaxation in mixed-valence complexes during photoexcited charge transfer45. Consistent with earlier studies12, the initial wave packet has largely disappeared by 600 fs as shown by the absence of an ω2 = 340 cm−1 peak in Fig. 2d, g and it reflects the diminishing of the ρ35 density matrix element, triggering subsequent electronic delocalization.

Fig. 4
figure 4

Early MLCT relaxation dynamics: electronically localized excited-state vibrational wave packet. The ω2 spectral amplitude (black; FWHM = gray arrows) of the MLCTB excited-state vibrational wave packet arises due to coherence between the νCOO and one quantum of a Ru-N stretching mode (νRu-N = 340 cm−1) within the excited-state manifold. The τd-dependence of the ω2 frequencies composing the wave packet (green) indicate blue-shifting as the wave packet propagates. Although the analytical form of τd(ω2) depends heavily on the polynomial function used to fit ϕ(ω2), the blue-shifting behavior of the wave packet is consistent across many functions. See Supplementary Note 4, Supplementary Fig. 8, and Supplementary Table 3 for spectral phase fits.

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Vibronic coherence aids nonadiabatic internal conversion

The later time (400 < τ2 < 1500 fs) dynamics utilize different low-frequency vibrational mode couplings with the vibronic states. The ω2 ≅ 742 cm−1 features in Fig. 2d, g demonstrate that νRu-bpy has a time-dependent coupling with νCOO and participates in the ρ14 and ρ36 coherences. The νRu-bpy mode also changes the Ru-N (of dcbpy) distance, emphasizing the importance of this coordinate for ultrafast relaxation in N34−. Since the ω2 spectra (Fig. 2) lack dynamical information occurring on shorter timescales within the 400 < τ2 < 1500 fs period, a careful time–frequency analysis25 (Fig. 5a,b) is used to resolve oscillatory electronic character of the coherences involving νRu-bpy. Proper selection of the temporal filter used in our analysis is required to extract the transient νRu-bpy dynamics and reasonably interpret the result (Supplementary Note 6). Importantly, the ω2 spectra during the later time period (400 < τ2 < 1500 fs, Fig. 2d, g) show that the data sufficiently resolve only one low-frequency mode coupling: the νRu-bpy mode at 742 cm−1 which has a vibrational period of 45 fs. This is a case where a reliable time–frequency analysis is obtainable with a sliding window STFT method46. We use a temporal window that targets the presence of 45 fs oscillations in the τ2-dependent data to understand the dynamical behavior of the νRu-bpy mode (see Supplementary Note 6 and Supplementary Figs. 11, 12 for extensive discussion of temporal windowing). We emphasize that our STFT analysis provides a stand-alone interpretation of the data, because only one low-frequency mode is relevant in our later time data as identified in Fig. 2d, g, which is independent of the time–frequency analysis used in Fig. 5. It is worthwhile to note here that the STFT method becomes less suitable as multiple frequency components contribute to a time-dependent signal of interest. This is because no single temporal window can be optimal for resolving many different frequency components in a time–frequency analysis, especially if they vary significantly in frequency and transient behavior. For those complicated cases, more advanced time–frequency transforms are required for reliable interpretation46. From our STFT analysis, a vibronic coherence is uncovered persisting throughout this later ~1 ps of relaxation, which facilitates nonadiabatic IC.

Fig. 5
figure 5

Later MLCT relaxation dynamics: nonadiabatic internal conversion through vibronic coherence. a Residual intensity (gray) of the integrated (ω1, ω3) 2D peak areas for the νCOO vibration with MLCTA (top) and MLCTB (bottom) character; data are offset for plotting. Examples of the temporal filters (purple/blue, dashed) used in short-time FT analysis (FWHM = 120 fs, centered at τcenter (top axis)) of the τ2-dependent residual intensity. The purple window (τcenter = 710 fs) highlights the νRu-bpy (742 cm−1) coherent beating with νCOO having exclusively MLCTA character while at a later delay (τcenter = 850 fs) the blue window shows the νRu-bpy coherence having exclusively MLCTB character. b Short-time FT results reveal the oscillatory electronic character of the νRu-bpy coherence signature between MLCTA and MLCTB with 340 ± 40 fs periodicity. c Simulation of the coherence block in the Redfield relaxation tensor for ρ14(purple) and ρ36(blue) during τ2 with an 800 fs coherence decay time where ω14 = ω36 = 742 cm−1 and a 50 cm−1 nonadiabatic coupling reproduces electronic oscillatory behavior for the vibronic coherence involving νRu-bpy with MLCTA and MLCTB (data offset). See Supplementary Note 5 for discussion of Redfield relaxation dynamics and Supplementary Note 7 for simulation details.

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The ρ36 coherence appears (Fig. 5b, blue) as the initially excited wave packet diminishes. Thereafter, the ρ36 coherence transfers to ρ14—changing in electronic character from MLCTB to MLCTA by τ2 ≅ 650–700 fs. This oscillatory dynamic continues for ~1 ps, as the amplitude of the ρ36 and ρ14 coherences oscillate out-of-phase with periodicity of 340 ± 40 fs. We simulate the time-dependent behavior of ρ36 and ρ14 as an isolated two-level system, where a 50 cm−1 nonadiabatic coupling reproduces the 340 ± 40 fs Rabi-like oscillation seen in the experimental data (Fig. 5c; Supplementary Note 7). Here, the observed Rabi-like oscillations result from the vibronic coherence transfer between ρ36 and ρ1447.

Discussion

There is a great need for experimental methods that provide unambiguous measurement of vibronic coherences and couplings in order to uncover their role in ultrafast charge and energy transfer5,24,33. The results presented above clearly demonstrate the capability of multidimensional EV spectroscopy to directly monitor the temporal evolution of vibronic coherences and couplings during multi-coordinate photochemical processes. The progression of the photoexcited charge transfer process in N34− measured in this study is summarized in Fig. 6.

Fig. 6
figure 6

Coherence evolution during the relaxation of photoexcited N34−. A schematic representation of the first two picoseconds of photoexcited relaxation progresses from left to right (a–c). Initial MLCT electronic excitation (a) with MLCT states coupling the donor–acceptor vibrations shown (MLCTA = light gray well; MLCTB = dark gray well) and the initial wave packet passing through ultrafast ISC. The ~600 fs propagation of the initial excited-state vibrational coherence ρ35 (b) involving νRu-N of MLCTB (red wells); a coherence transfer to νRu-bpy of MLCTB (blue wells) is merely suggested with sufficient wavefunction overlap involving the νRu-bpy lowest energy vibration. The ~1 ps propagation of the excited-state vibronic coherences ρ36 and ρ14 involving νRu-bpy (c) depicts the nonadiabatic internal conversion between MLCTA (purple) and MLCTB (blue) through the 50 cm−1 nonadiabatic coupling strength.

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The early-time ρ35 coherence reveals an impressive degree of intramolecular couplings that propagate for the initial ~600 fs. This wave packet is confined to MLCTB electronic character, indicating that the Ru-N distance of the νRu-N stretching coordinate specifically modulates the vibronic coupling between νCOO and the MLCTB during the initial relaxation of photoexcited N34−(Fig. 6b, red well). The early-time vibrational wave packet measurement clearly differentiates the nature of the vibronic coupling between either MLCTA or MLCTB and the νCOO, which is a distinction that could not be made from a single 2D EV, tIR, or transient absorption (TA) experiment. The nature of the initial excited-state wave packet, first reported by Kallioinen12 using TA, can now be confidently assigned as an excited-state vibrational coherence between νCOO and νRu-N due to the electronically localized 3D EV signal. Confirmation of the triplet character of this excited-state vibrational wave packet is clear because the signal is detected through the coherence with the triplet state νCOO, which answers this outstanding question in the field of N3 photophysics. We note that the known ISC time (≤100 fs) leaves the existence of the singlet vibrational wave packet ambiguous because the νRu-N vibrational period is on the same order as ISC, if not longer.

A transition occurs between the early and later relaxation periods as the wave packet arising from the ρ35 coherence diminishes and the later time wave packet formed by the ρ36 coherence emerges (Fig. 6b, red to blue well). The fact that this transfer occurs between states of the same electronic character suggests that excited-state vibrational coherence transfer bridges the early-time and later time dynamics; however, many other coordinates could also affect the ρ35 coherence. Indeed, we excite only a small window of the 1MLCT absorption; the observed dynamics will depend on the electronic structure of the initially excited states and the solvation environment48,49. Since our pump center frequency and bandwidth cannot directly excite ρ36, this coherence must be accessed through intramolecular energy transfer. Conversely, the ρ14 is directly excitable, yet its signature is negligible until after the ρ36 coherence has formed (Fig. 5b). Importantly, our probe center frequency and bandwidth is insufficient to collapse the coherences observed during τ2 and excite the v = 0 → 1 νCOO vibrational transition required for detecting the ESA at ω3 = 1328 cm−1 (Supplementary Note 5 and Supplementary Table 4). Accounting for the quantum pathways capable of producing the measured oscillatory residuals implies that coherence-to-population transfer50 plays an important role in the ultrafast photophysics of N34− (see Supplementary Fig. 10). Together, these dynamics suggest that the vibronic couplings of MLCTB function as a gateway for the initially excited vibrational coherence to transition into nonadiabatic IC and continue equilibrating within the excited triplet manifold.

Discovering the out-of-phase oscillations between the ρ36 and ρ14 coherences is key to characterizing the wave packet evolving during the later relaxation period as an excited-state vibronic coherence (Fig. 6c). By comparison, a purely vibrational coherence, such as ρ35, would be confined within a single electronic state. A purely electronic coherence would be expected to appear at the earliest delay times, to dephase within 10s–100s of fs, and to yield ω2 features at the difference frequency between the two electronic states independently of any vibrational coordinate. As we report here for 400 < τ2 < 1500 fs, the amplitude of the vibrational coherence oscillates with the electronic character, it appears after 600 fs of relaxation, and it proceeds for ~1 ps. This prolonged coherence is characteristically vibronic, as the expected decoherence time slows when a more complete specification of the system eigenstates occurs;29 we directly observe this quantum coherence with multidimensional EV spectroscopy. The 50 cm−1 nonadiabatic coupling extracted from our simulations is consistent with the 340 ± 40 fs vibronic coherence transfer rate between ρ36 and ρ14, and the near-complete transfer observed in Fig. 5b suggests the system is within the strong coupling regime. The combination of the 2D EV experiment to map out vibronic couplings between νCOO and either MLCTA or MLCTB34, and the 3D EV experiment to resolve additional excited-state coherences involving νRu-N and νRu-bpy allow the evolution of photoexcited vibronic coherence to be unambiguously measured.

Progress toward tackling the long-standing challenge of characterizing nonequilibrated charge transfer mechanisms in photoexcited donor–acceptor complexes is achieved in this study. Our 3D EV measurements provide an account of how intramolecular charge transfer occurs in an archetypal photosensitizer, detailing the complex interplay between valence electron density and molecular structural dynamics on the fs timescale. We have shown that the cascading relaxation through the nonequilibrated MLCT manifold of N34− is heavily influenced by Ru-N (of dcbpy) vibrations, which effectively bridge the charge-donating Ru-(NCS)2 and charge-accepting dcbpy moieties through excited-state vibronic couplings. We conclude that at least one excited-state trajectory in aqueous N34− that facilitates intramolecular charge transfer is initiated through an excited-state vibrational coherence lasting for ~600 fs before transferring to a secondary coherence that is vibronic in nature and promotes nonadiabatic IC proceeding for another ~1 ps of relaxation. These results illuminate a mechanism for how solvated N34− utilizes excited state, time-dependent vibronic couplings to achieve long-lived charge separation. In addition to a high density of states and strong spin–orbit coupling, we contribute evidence that structural relaxation involving metal-ligand bonding nitrogen atoms strongly influences excited-state mixing and efficient formation of long-lived 3MLCT states6,8. This mechanistic insight may be particularly useful for designing more efficient and earth-abundant light-harvesting complexes51, and for harnessing the typically untapped potential of unthermalized photoexcited states to control photochemical efficacy52. Following photochemical reactivity from the perspective of specific vibrational coordinates is a unique advantage of multidimensional EV spectroscopy, which can be exploited to identify critical intramolecular coordinates governing nonequilibrium photoexcited processes. Multidimensional EV spectroscopy will be an incisive tool for understanding photoexcited energy and charge transfer mechanisms during complex, multi-coordinate photochemical processes in molecular and material systems.

Methods

Experimental description

The 2D EV experiment is performed in a similar way to a tIR experiment with a pair of electronic pump pulses responsible for creating an excited state (i.e., the “bra” and “ket” interactions) followed by an IR probe pulse; see Supplementary Note 1 and Supplementary Figs. 1–3 for complete experimental details. The τ2 delay time (the typical pump–probe relaxation time) is fixed, and the delay time (τ1) between a pump pulse pair generated in an interferometer is scanned. A FT over τ1 yields the electronic excitation frequency dimension, ω1, while the high-frequency vibrational detection dimension, ω3, is measured using a spectrometer. A single 2D EV spectrum is collected at a given τ2 delay time; it describes the electronic–vibrational frequency correlations present between the electronic states excited in τ1 and the high-frequency vibrations probed in τ3. In this way, 2D EV directly measures vibronically coupled degrees of freedom. A series of 2D EV spectra collected over a range of τ2 delays maps the time-dependence of the vibronic couplings resolved in the 2D EV spectrum. As is common to all 2D spectroscopies, τ2-dependent signal amplitudes measure population dynamics and coherent superpositions that are accessible within the excitation spectral bandwidth of the pump pulses. The UV pump center frequency (ω0) and bandwidth used in these experiments are ω0 = 24,900 cm−1 and full-width-at-20%-max = 1400 cm−1; the mid-IR probe center frequency and bandwidth used here are ω0 = 1375 cm−1, full-width-at-20%-max = 245 cm−1. Amplitude modulations occurring at the difference frequency between the vibronic states involved in the excited τ2 coherences are measured and can be more directly resolved as residual 2D peak intensity following subtraction of signals from population dynamics (see Supplementary Note 3 for complete details). Another FT over the residual intensities during τ2 reveals a third frequency dimension, ω2, that identifies the lower frequency vibrations and molecular coherences responsible for the amplitude modulations in the 2D EV spectra. Resolving all three frequency dimensions yields a three-dimensional (3D) EV spectrum, which in this study contains no common frequencies among any of the three spectral dimensions. Importantly, this means that our 3D EV spectrum requires a high degree of different intramolecular couplings to view 3D EV signal. Moreover, low-frequency mode couplings in ω2 may be time-dependent, appearing only at certain times during various photoexcited molecular relaxation pathways. The time-dependence of the measured vibronic couplings can be ambiguously defined, and perhaps irresolvable, without a time–frequency analysis such as the sliding window short-time FT analysis used in this work (see Supplementary Note 6).

Instrumental details

The fundamental output of a Ti:Sapphire regenerative amplifier (Spectra Physics Spitfire XP Pro; 800 nm, 4.0 W, ~40 femtoseconds (fs), 1 kHz) is used for these studies. The broadband UV (BBUV) pump is generated by the second harmonic of a spectrally broadened portion of the 800 nm fundamental beam using a 100 μm BBO (Type I) crystal (Newlight Photonics); the spectral broadening method is detailed in Supplementary Note 1. An acousto-optic pulse shaper (Fastlite Dazzler) generates the collinear pump pulse pair (k1, k2), delivering 240 nJ/pulse focused to a 220 μm 1/e2 diameter at the sample. The pump is mechanically chopped at 500 Hz to collect differential absorption spectra. The difference frequency between the signal and idler fields of a home-built optical parametric amplifier generates the mid-IR probe, which provides 480 nJ/pulse focused to a 195 μm 1/e2 diameter at the sample. The isotropic signal is collected by setting the polarization angle between the pump and probe to the magic angle (54.7°) for data collection. The instrument response has subsided by τ2 = 180–200 fs given by the solvent only tIR signal and the rise time of the nonresonant integrated pump–probe signal in a 250 μm Si wafer (Supplementary Fig. 2).