Vibronic coherence evolution in multidimensional ultrafast photochemical processes

The complex choreography of electronic, vibrational, and vibronic couplings used by photoexcited molecules to transfer energy efficiently is remarkable, but an unambiguous description of the temporally evolving vibronic states governing these processes has proven experimentally elusive. We use multidimensional electronic-vibrational spectroscopy to identify specific time-dependent excited state vibronic couplings involving multiple electronic states, high-frequency vibrations, and low-frequency vibrations which participate in ultrafast intersystem crossing and subsequent relaxation of a photoexcited transition metal complex. We discover an excited state vibronic mechanism driving long-lived charge separation consisting of an initial electronically-localized vibrational wavepacket which triggers delocalization onto two charge transfer states after propagating for ~600 femtoseconds. Electronic delocalization consequently occurs through nonadiabatic internal conversion driven by a 50 cm−1 coupling resulting in vibronic coherence transfer lasting for ~1 picosecond. This study showcases the power of multidimensional electronic-vibrational spectroscopy to elucidate complex, non-equilibrium energy and charge transfer mechanisms involving multiple molecular coordinates.


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flow cell (Harrick) with a 25 μm path length (25 μm Teflon spacer (Lebow) sandwiched between 1 mm and 2 mm CaF2 windows) circulates sample solution driven by a peristaltic pump to refresh the volume of molecules illuminated by every laser shot (>1 kHz). Additionally, the sample cell was raster scanned in the plane orthogonal to the beam propagation to refresh the illuminated region of the sample cell window, which avoided sample build up inside the sample cell during long laser runs. The sample was enclosed in a septum-capped vial with needle connections to the flow cell tubing to minimize solvent evaporation during experiments; the samples with D2O solvent were sealed carefully and stored in a desiccator. The N3 4purity was confirmed by UV-Vis and FTIR spectral measurements during several experiments using JASCO V-630 and JASCO FT/IR 4100 spectrometers with the same sample cell setup described above. UV-Vis and FTIR spectra taken before and after each experimental run confirmed there was no photodegradation during the tIR and 2D EV experiments. This sample configuration yields an electronic absorption optical density (OD) ≤ 1.0 OD across the frequency range spanned by our pump pulse. The vibrational absorption OD (without solvent subtraction) of the carboxylate stretches is ~ 0.45 OD with D2O solvent contributions of ~0.2 OD throughout the fingerprint region.

Linear Absorption Characterization (UV-Vis and FTIR)
The electronic absorption spectrum of the aqueous N3 4in Supplementary Figure 1(a) includes two singlet metal-to-ligand charge transfer (MLCT) excitations at 20000 cm -1 (500 nm) and 26880 cm -1 (372 nm). As shown in our earlier work on this compound, 1 many singlet MLCT states underlie these broad absorption bands forming a dense excited state manifold. The tIR and 2D EV experiments discussed in the main text excite the red edge of the higher energy 1 MLCT absorption band.
The solvent subtracted vibrational absorption spectrum of the aqueous N3 4in Supplementary Figure 1(a) show the ground electronic state vibrational features for both the Ru-(NCS)2 charge donor region and the dicarboxybipyridine (dcbpy) ligand charge acceptor region. The CN symmetric and asymmetric stretches of Ru-(NCS)2 are overlapped in the vibrational peak appearing at 2116 cm -1 . The carboxylate asymmetric stretch (1596 cm -1 ) and symmetric stretch (1375 cm -1 ) feature prominently for the charge accepting dcbpy ligand. A number of bipyridine (bpy) localized ring modes are also present in the 1400-1550 cm -1 region. 1

Transient-IR and 2D EV Instrumental Setup
The general instrumental configuration has been described elsewhere in great detail. 1,2 All pulses used in the experiment are derived from the fundamental output of a Ti:Sapphire regenerative amplifier (Spectra Physics Spitfire XP Pro; 800 nm, 4.0 W, ~40 femtoseconds (fs), 1 kHz). 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). We use a similar multi-plate spectral broadening method reported by He et al. 3 and Lu et al. 4 The spectral broadening of the fundamental beam is achieved by placing three thin BK7 windows (140 μm thick) just after the beam waist of a focusing 250 μJ/pulse portion of the 800 nm fundamental beam in a transmissive Keplerian telescope geometry [focusing lens (BK7, AR 800 nm): f = 1 m, recollimating lens: (BK7 AR 600-1000 nm) f = 0.4 m]. The windows are oriented at approximately Brewster's angle to maximize beam transmission. At each transmission, self-phase modulation induces spectral broadening; by adjusting the inter-window spacing, the spectral broadening and pulse energy is optimized. The plates are mounted to allow for vertical translation to periodically refresh the incident spot being used for broadening which avoids accumulated photodamage to the windows and maintains a consistent BBUV spectral profile and pulse energy for the duration of experiments. After the spectrally broadened fundamental is frequency-doubled in the BBO crystal, a dichroic high reflective mirror isolates the BBUV pulse and routes it through a λ/2 waveplate and polarizer before entering a UV prism compressor (Newport 10SB10 prism pair). After the prism compressor, an additional Keplerian telescope (UV fused silica plano-convex lenses, UV AR coated, f=100mm) is used to optimize beam collimation for further propagation.
The BBUV pump pulse is then amplitude and phase shaped using an acousto-optic programmable dispersive filter (UV-Dazzler, Fastlite) in both the tIR and 2D EV experiments. In these experiments, ~10 μJ / pulse of BBUV enters the Dazzler. To perform the 2D EV experiments, a collinear pump pulse pair is generated using the Dazzler and sequentially delayed over a time delay ( 1 τ ) between the two pump pulses. The shaped UV pump pulse(s) exit the Dazzler with vertical (S) polarization and are routed to the sample area and focused with a UV-fused silica plano-convex lens (UV AR coated, f = 300 mm) through a machined hole in the first of two off-axis parabolic (OAP) mirrors. At the sample area, 240 nJ/pulse (S polarization, 220 μm 1/e 2 diameter) is used to excite the sample. The BBUV is chopped at 500 Hz to collect differential absorption (pumped -unpumped) spectra. The mid-IR is generated from difference frequency generation of the near-IR signal and idler outputs of an in-house built collinear two-stage optical parametric amplifier and routed through a delay stage (Newport ILS150PP) to control the τ2 delay time.
The mid-IR polarization incident to the sample is set at the magic angle (54.7 o ) with respect to the BBUV pump polarization using a ZnSe holographic wire grid polarizer (ThorLabs WP25H-Z) to remove orientational contributions to the measured signal and collect purely the isotropic signal. The mid-IR probe pulse (480 nJ/pulse, 195 μm 1/e 2 diameter) is focused at the sample to be spatially overlapped with the pump beam. Another wire grid polarizer is set immediately after the sample cell, before the second of two off-axis parabolic mirrors, to be parallel to the incident mid-IR polarization which ensures measurement of only the isotropic signal components. The mid-IR signal is routed to a spectrometer (Jobin-Yvon Horiba Triax 190, 75 g/mm grating) and dispersed onto one stripe of a 2x64 mercury cadmium telluride pixel array (Infrared Systems). Signal within the instrument response due to pulse overlap at early Supplementary Figure 2 The instrument response function is assessed using the non-resonant tIR signal of a 250 μm Si wafer (black). The N3 4molecular response is observed outside of pulse overlap for τ2 > 200 fs from the transient-IR trace for the νCOO excited state absorption (ω3=1328 cm -1 , red ). The signals are normalized by the absolute value of the greatest magnitude signal and overlaid for comparison. The non-resonant solventonly tIR signal (blue; circles are data and line is three-point moving average) is scaled and offset such that zero signal is ΔT/T = -1 for comparison; the solvent response diminishes for τ2 > 200 fs, consistent with the decay of the Si signal and the onset of the N3 4molecular signal. times has diminished by τ2 ≅ 180-200 fs as estimated by the rise time of the non-resonant integrated pump-probe signal in a 250 μm Si wafer.

Data Acquisition
A well-averaged tIR data set used for 2D EV normalization is obtained by averaging 500 laser shots per difference spectrum while scanning over the range -1 ≤ τ2 ≤ 200 picoseconds consecutively in the forward direction; 20 completed τ2 scans are then averaged together for the final tIR data set. The entire tIR data set was collected in ~1.5 hours during the same laser run as the 2D EV data with the same experimental configuration to maintain consistency in as many systematic experimental parameters as possible. The tIR data set is divided by a well-averaged (5000 laser shots) sample spectrum collected with the BBUV pump blocked to obtain ΔT/T.
A single 2D EV spectrum at a given τ2 delay time is collected by scanning τ1 over the range [0:150] fs in 1.15 fs steps to expedite data acquisition using a partially rotated frame. The integrated field autocorrelation of the pump pulses scanned over τ1 is collected and Fourier transformed to ensure that the shape of the excitation spectrum is not compromised due to under sampling. At each fixed τ1 delay time and τ2 delay time, 500 laser shots are averaged to obtain the differential absorption spectrum. The total range of pump-probe delay times collected in these 2D EV experiments are 10 ≤ τ2 ≤ 2010 fs at 20 fs intervals. Six 2D EV scans were averaged for each τ2 delay yielding a single averaged 2D EV data set. To minimize artifacts due to laser drift throughout the experiment, the entire τ2 range studied was collected in two parts: first by scanning 250 ≤ τ2 ≤ 2010 fs and then scanning 10 ≤ τ2 ≤ 250 fs. Acquisition of the first range (250 ≤ τ2 ≤ 2010 fs) was further divided into two separate experimental scans with 40 fs intervals: one for 250 ≤ τ2 ≤ 2010 fs and the other for 270 ≤ τ2 ≤ 1990 fs. Each of these subranges scanned with 40 fs intervals were scanned three times in the forward direction and three times in the reverse direction to further reduce artifacts from laser drift during the ~4.5 hour collection time of the 2D EV scan over the τ2 range. Acquisition of the second range (10 ≤ τ2 ≤ 250 fs) was collected in 20 fs intervals using the same approach, each scan taking ~1.5 hours of experimental collection time. Solvent-only 2D EV spectra were collected over 10 ≤ τ2 ≤ 450 fs in 20 fs intervals to ensure no significant solvent features were present in the sample data (see Supplementary Figure 2(a) below). The pump power dependence of the 2D EV signal was measured to be linear with respect to pump power, ensuring that no multiphoton absorption signals were present in the tIR or 2D EV data (see Supplementary Figure 2(b)).

2D EV Data Processing -Fourier Transform over τ1
Traditional FT data processing techniques are employed here. 2,5 A constant offset of the vibrational differential absorption signal due to the τ1-independent pump-probe signal is initially subtracted. The τ1dependent differential absorption data is zero-padded to 2048 points, and a tanh apodization function is applied to smoothly transition the data to zero at long τ1 times prior to the Fourier transform (FT). 6 The FT over the spectrally-detected, τ1-dependent vibrational differential absorption data yields the electronic excitation spectrum, ω1. The resulting 2D EV spectra are divided by a well-averaged (5000 laser shots) sample spectrum collected with the BBUV pump blocked to maintain the correct ω3 spectral profile (proportional to ΔT/T, as in tIR). The well-averaged sample spectra used for division were collected throughout the experiment and indicate negligible change in spectral shape. Additional steps were also taken to correct for remaining instrumental noise to better isolate τ2-dependent oscillatory signals, as detailed in the Supplementary Note 3.

Supplementary Note 2. Transient-IR Spectroscopy of N3 4-
We have previously identified the principal high-frequency vibrational signatures of the excited electronic states for both the charge donor and acceptor using parallel-polarized tIR spectroscopy of aqueous N3 4-. 1 Briefly, the charge donor CN stretches shift to lower frequency by 50-70 cm -1 as electron density transfers away from the Ru-(NCS)2 and a stronger anharmonic coupling results in the observed ~20 cm -1 excited state splitting of the symmetric and asymmetric stretches. As electron density arrives at the acceptor, the bipyridine (bpy) ring vibrations shift to higher frequencies by ~45 cm -1 while the carboxylate (COO) stretches lower in vibrational frequency by ~50 cm -1 due to increased aromaticity of the dcbpy ligands. The excited state symmetric stretching carboxylate vibration (ω3 = 1328 cm -1 ), which we refer to as νCOO, is a strong excited state vibration and rather isolated spectrally; it is the main high frequency vibration discussed for reasons below and in the main manuscript. Another spectrally isolated, electronically excited state vibration appears at 1271 cm -1 that is bpy-localized and referred to as νBPY. As noted in previous work, 1 the 1328 cm -1 carboxylate vibration is one of four excited triplet state symmetric stretching carboxylate normal modes in the 1300-1400 cm -1 frequency region; the other three are of higher The magnitude of the νCOO ESA (ω3=1328 cm -1 ) plotted at different pump pulse energies shows the data measured are linearly dependent on pump energy. Blue squares are average of five difference spectra with the error bars reflecting +/-1 standard deviation from the mean; the black line is a linear fit with the fit parameters shown on the right. centered at ω3=1375 cm -1 .
The timescales of the excited state vibrational features measured by parallel polarized tIR (see Supplementary Figure 4 and Supplementary Table 1) show that the triplet state CN stretches are formed within the instrument response and consequently static for the duration of the experiment (200 picoseconds). The constant intensity and center frequency of the CN excited state vibrational features indicate negligible intramolecular structural reorganization of the charge donor for at least 200 picoseconds (ps) following photoexcitation and ultrafast intersystem crossing (ISC). This is consistent with other tIR studies on N3 which typically focused only on the CN stretching region, and with the fact that its 3 MLCT manifold has a lifetime on the order of nanoseconds. The νCOO ESA also forms significant amplitude shown by the τ2-dependent full-width-at-half-max for all three peaks; the carboxylate symmetric stretch ESA is most sensitive to excited state charge transfer dynamics in the first few picoseconds of relaxation. within the instrument response but then continues to grow on a 2.7 ± 0.8 ps timescale. Additionally, the carboxylate symmetric stretching GSB at 1375 cm -1 rises to its maximum intensity during the instrument response before decaying in amplitude on a 2.5 ± 0.8 ps timescale -effectively the same timescale as the νCOO ESA growth. This is readily explained by the ESA dynamics of the overlapping carboxylate symmetric stretches noted above. Although much weaker, other bpy ESA features also grow in over the first several picoseconds of delay time.
While many charge acceptor vibrations display ESA signal growth during the triplet manifold relaxation, they are not all equally sensitive to the intramolecular structural dynamics involved with this relaxation process. The time-dependent tIR vibrational peak widths of the νCOO and the νBPY features demonstrate that the νCOO vibration is the most sensitive coordinate to triplet relaxation processes probed in our experiments as its full-width-at-half-maximum (FWHM) broadens to 28 cm -1 and narrows to 25 cm -1 within the first three ps of relaxation; whereas, the νBPY rises to 9 cm -1 within the instrument response and is unchanged thereafter. Together, the measured tIR timescales, line shapes, and negligible frequency shifts for both charge donor and acceptor ligand vibrations establish the photophysical picture of ultrafast triplet formation of N3 4and charge donation by the Ru-(NCS)2 while the dcbpy ligand vibrations relax in a dense triplet manifold over the first several picoseconds post-excitation.
These tIR measurements provide an initial characterization of the charge donor-acceptor timescales and they identify excited state high-frequency vibrational coordinates involved with the ultrafast intramolecular charge transfer in N3 4-. However, these measurements necessarily convolve the intramolecular dynamics involving different electronic states which are resolved in the 2D EV experiment. We have already demonstrated using polarization-selective 2D EV spectroscopy that three different excited 1 MLCT electronic states are coupled with the CN charge donor vibrations, and that only two of these initially excited 1 MLCT states are coupled with the charge acceptor vibrational modes which likely provide avenues for ultrafast ISC and triplet relaxation in N3 4-. 1 The time traces for the tIR data discussed in the manuscript and shown in Supplementary Figure 4 were fit to a Gaussian function convoluted with the sum of two exponentials to check that our data is consistent with reported N3 relaxation time scales, which has the form:  (2) 4 ln (2) 1 erf 2 ln(2) where A1 and A2 are amplitude factors for the two convolutions, B is the temporal FWHM of the Gaussian instrument response function, t0 is time zero, short τ is the ~picosecond time constant of one exponential decay and long τ is the nanosecond time constant of the second exponential decay, erf is the error function.
An additional constant offset (C) was also considered in fitting but did not significantly change the fitting results. Supplementary Table 1 gives the parameters obtained for the optimized fits of the time traces. The 95% confidence interval is given for each fitting parameter, all time values are in units of picoseconds.

Instrumental Noise Correction
The purpose of the FT analysis over the τ2 delay time is to identify the frequencies of coherent oscillations that modulate the amplitude of the 2D EV peaks. These signatures reveal further information about the degrees of freedom coupling the vibronic states involved with the excited state charge transfer dynamics in N3 4-. Since these oscillations are very weak in our experiments, careful corrections for signal intensity fluctuations due to instrumental noise are required to isolate the coherent oscillations in 2D EV signal amplitude. As can be seen by comparing the blue and red time traces in Supplementary Figure 5 (bottom), instrumental noise can significantly overwhelm weaker oscillatory signals. We correct for this noise to isolate the τ2 oscillations of interest by normalizing the raw 2D EV data for each τ2 delay to a separate, well-averaged tIR data set which was collected within the same laser run using an identical experimental configuration. The six 2D EV scans at a given τ2 delay are first averaged in the time domain (τ1). Then the differential absorption spectrum from the 2D EV data set for τ1 = 0 is normalized to the well-averaged tIR spectrum for the same τ2 delay. Since these two data sets reflect an exactly identical experiment, the only difference between them is the experimental noise due to fewer scans averaged in the 2D EV experiment than in the tIR experiment. To ensure accurate comparison of spectra, the tIR spectrum is cubic spline interpolated to have finer time steps for the normalization procedure. The 2D EV (τ1 = 0) spectrum is fitted to the tIR spectrum with the following Supplementary Equation: ( ) where a constant spectral intensity scalar (α ) and a constant offset ( β ) are applied to the averaged 2D EV spectrum (  . Initial values are set to α =1 and β =0 in the fitting routine; we find α = 0.97 (±0.06) and β =0.00015 (±0.00048) (where the bar denotes the average over the optimized parameters for all τ2 spectra). While the optimized parameters indicate that minimal adjustment to the original 2D EV spectrum is needed (i.e., on average, the intensities of the difference signals are scaled by less than 5% and offset by less than 2% of the signal magnitude for the νCOO mode), this procedure effectively corrects for instrumental noise present in the 2D EV data as shown in Supplementary Figure 5. The optimized scalar and offset for each τ2 spectrum are then applied to the raw 2D EV spectra over the complete range of τ1 composing the 2D EV data set using Supplementary Equation (2). Then the tIR-normalized 2D EV data undergoes the usual FT processing over τ1 described in Supplementary Note 1 to obtain the tIR-normalized 2D EV spectrum for further analysis.

Isolating Coherent Oscillatory Features in τ2-dependent Data
The remaining analysis focuses on the excited state carboxylate symmetric stretching mode (νCOO) at ω3 ≅ 1328 cm -1 which is vibronically coupled to two distinct excited MLCT states (MLCTA and MLCTB) as observed in the 2D EV spectra in manuscript Figure 2(a) and detailed by us previously. 1 Thus, the 2D spectral regions of interest are the (ω1, ω3) areas of the greatest 10-15% signal for these two features which are used throughout the remaining analysis (highlighted by red boxes in Supplementary Figure 6, the (ω1, ω3) ranges are given in Supplementary Table 2). We note that using slightly different bounds for the 2D EV regions of interest in the 10-15% signal range do not alter the conclusions from the analysis. We assume that measured population kinetics within the first 10 ps of the excited state triplet relaxation do not vary considerably between MLCTA and MLCTB because the fits to the tIR time traces described in Once population kinetics are removed, consequent FT analysis over the τ2 delay of the 2D EV regions of interest provides a low-frequency spectrum, ω2, of the τ2-dependent 2D EV signal oscillations. As discussed in the manuscript, dynamics in the early time (0 ≤ τ2 ≤ 600 fs) and the later time (400 ≤ τ2 ≤ surfaces; gray shows background signal and red boxes highlight 2D EV regions of interest for vibronic couplings between νCOO and both MLCTA and MLCTB. Spectra from FT analysis on 0 ≤ τ2 ≤ 600 fs data (b, red) and on 400 ≤ τ2 ≤ 1500 fs data (c, blue) for MLCTA excitation. Spectra from FT analysis on 0 ≤ τ2 ≤ 600 fs data (d, red) and on 400 ≤ τ2 ≤ 1500 fs data (e, blue) for MLCTB excitation. Gray spectra in (b-e) are from FT analysis of the background signal shown in (a). The circles represent the average ω2 spectrum and the shaded areas represent ± 1 standard deviation from the mean. Number of (ω1, ω3) points: MLCTA = 45; MLCTB = 24; Background (signal ≤ 5% max) = 3295.
SI 13 to select the signals in either the earlier or later τ2 periods. In Supplementary Equation (3), τc is the center of the tanh rise, δHW is the half-width of the double-sided tanh filter, and B is the rise time of the tanh function. The early time data is selected with τc = 270 fs, δHW = 350 fs, and B = 40 fs; the later time data is selected with τc = 910 fs, δHW = 550 fs, and B = 40 fs. The filtered data in each τ2 period are zero-padded to 256 points prior to FT. The FT then resolves the ω2 low-frequency spectrum and the absolute value spectra are analyzed ( Supplementary Figure 6 b-e and manuscript Figure 2(c-d, f-g)).
The signal-to-noise of the ω2 spectra is assessed by doing the same FT analysis on the respective τ2 periods for 2D EV spectral regions that are effectively the background -i.e., where there is no 2D EV signal. Since there are regions of the 2D EV spectra with dynamic intensities during τ2, we first averaged all of the 2D EV spectra at every τ2 delay (resulting averaged 2D EV spectrum is shown in Supplementary Figure 6) and then we selected all (ω1, ω3) coordinates which have signal less than or equal to 5% of the 2D EV maximum signal in this averaged spectrum (0.0043). The solid gray contour shown in Supplementary Figure 6(a) highlights this background 2D EV region. The early time (0 ≤ τ2 ≤ 600 fs) ω2 spectra are shown in Supplementary Figure 6(b, d) and the later time (400 ≤ τ2 ≤ 1500 fs) ω2 spectra are shown in Supplementary Figure 6(c,e). The gray spectra show the average ω2 spectrum and standard deviation of the background. The average ω2 spectrum and standard deviation of the early time 2D EV signal for νCOO coupled to both MLCTA and MLCTB are shown in red and the later time 2D EV signals are shown in blue. As discussed in the manuscript, these spectra provide clear evidence for the νRu-N (ω2 = 340 cm -1 ) and the νRu-bpy (ω2 = 742 cm -1 ) low frequency modes coupling with the vibronic eigenstates at different time periods within the first two picoseconds of the excited state triplet charge transfer and relaxation process. Other ω2 regions in the spectra above the background noise approach the DC frequency (ω2=0 cm -1 ), which could be due to imperfect population kinetics subtraction, and as the Nyquist sampling limit is approached (ω2=833 cm -1 ). As a result, we do not consider the signals above ω2 ≅ 790 cm -1 .

Supplementary Note 4. Characterizing the Initially Excited Vibrational Wavepacket
The initially excited state vibrational wavepacket composed of a coherence with the νRu-N mode is characterized by extracting the spectral phase of the ω2 spectrum, 2 ( ) φ ω , fitting the phase to an n th order polynomial, and then obtaining the group delay, The group delay describes the time-dependence of the frequency components in a wavepacket, which in this case reflects the propagation of the wavepacket during τ2 in the excited MLCT manifold during the early time period, 0≤τ2≤600 fs. We fit 2 ( ) φ ω over the spectral range of the ω2 feature obtained in the FT analysis (ω2 = 250-400 cm -1 ) to polynomial functions of increasing order n, the coefficients (P(n)) for each fit are given in Supplementary Table 3. A meaningful description of the wavepacket propagation is obtained by observing the consistencies in evidence for a blue shifting of the initially excited vibrational wavepacket during the first 600 fs of excited state relaxation. We place less emphasis on any interpretation based on the values of the coefficients for a particular fit given their dependence on the polynomial order, and instead consider the general trends observed across all fits. The same blue-shifting behavior is also observed through a short time Fourier transform (STFT) analysis of the earlier time data, as shown in Supplementary Figure 9 below. We give preference to the group delay analysis shown in the manuscript over the STFT because the blue-shifting is occurring during the course of only a few cycles of the νRu-N vibration, which is also comparable to the ~ 600 fs lifetime of the wavepacket. Thus, an appropriate choice of windowing function becomes more difficult. Nevertheless, the consistency between the group delay analysis and the STFT confirms the blueshifting of the νRu-N wavepacket during early times.

Supplementary Note 5 Redfield Theory and Nonsecular Contributions to Relaxation Dynamics
Redfield theory is often useful for describing the time evolution of molecular systems. 8   . Thus, a coherence-to-population transfer must occur during τ2 to justify the observed signals. This is a nonsecular relaxation pathway, 35,33 R , where ω35 -ω33 = νRu-N (340 cm -1 ) that drives the early time excited state vibrational wavepacket dynamics (0≤τ2≤600 fs); a representative double-sided Feynman Diagram for this pathway is given in Supplementary Figure 10 ω ω = . of interest, νRu-bpy, as identified by the ω2 spectra shown in manuscript Fig. 2d and 2g obtained by considering all of the τ2-dependent data in the later time period. As described below, we can reliably use a temporal filter to isolate the νRu-bpy dynamics because this is the only sufficiently resolved mode in the ω2 spectra for both MLCTA and MLCTB during later times. For time-domain signals containing multiple frequency components of interest that have significantly different periods of oscillation, the choice of a single temporal filter may favor a particular frequency component in the analysis over the others. Fortunately, that is not the case in our data.

Supplementary
In this analysis, only the νRu-bpy is of primary interest as it is the strongest signal observed in ω2 when all of the later time relaxation data is Fourier transformed (see manuscript Figure 2). Without a time-frequency analysis, the electronic oscillatory behavior of the νRu-bpy coherence discussed in the main text would be missed. The ~45 fs period of the νRu-bpy appears in 2-3 cycle bursts beginning in MLCTB and then oscillating between MLCTA and MLCTB. Fortunately, this dynamic provides a straightforward choice of filtering window to be used in the analysis: a temporal filter with ~120 fs width sufficiently isolates each 2-3 cycle oscillation of the νRu-bpy to clearly extract the oscillations in electronic population shown in the main text. The single coherence of interest with a well-defined duration in MLCTA and MLCTB render the STFT analysis a suitable method in our case. In Supplementary Figure 11 Supplementary Figures 11 (b,d,f)) among analyses using different windowing functions of consistent temporal width. Conversely, the temporal width of the filter can have a large impact on the obtained results using a STFT in the time-frequency analysis. Supplementary Figure 12 demonstrates the importance of an initial consideration about the nature of the time-domain signals that are of interest in a data set prior to conducting a time-frequency analysis. For a time-domain signal such as ours which contains transient and periodic coherences, a temporal filter that is too wide may result in a large offset in FT signal in addition to a phase relationship between oscillations that is shifted from the true phase relationship (e.g., see Supplementary Figure 12 (a,b)). As the filtering window shrinks, the FT signal passes through a range in which only the offset is observed because the oscillatory information is not isolated well enough by the filter (e.g., see Supplementary Figure 12 (c,d)). When the filter width approaches the duration of the transient coherences of interest, then the time-frequency analysis via the STFT produces a reliable result (e.g., see Supplementary Figure 12 (e-h)). The time-frequency analysis in this paper uses the double-sided hyperbolic tangent window with a 120 fs FWHM temporal width, as shown in Fig. 6.2 (g,h).

Supplementary Note 9. Calculated Low-Frequency Vibrational Modes
The calculated IR spectrum of the N3 4lowest energy triplet, T0, is reproduced from Gaynor et al. 1 to display the full spectrum, including the low-frequency region (see zoom-in of the inset in Supplementary  Figure 14a