Light-induced singlet-triplet (ST) electronic spin conversion remains fundamental in molecular and materials chemistry, being leveraged in solar energy harvesting, 10 molecular photonics, 11 photocatalysis, 12 and photosensitizing applications. 13 The conventional picture of ST intersystem crossing (ISC) promoted explicitly by direct spin-orbit coupling (SOC) between electronically excited states of different spin-multiplicities breaks down when vibronic coupling introduces strong quantum mechanical mixing of electronic spin-states. 14 Consequently, spin, electronic, and vibrational degrees of freedom cannot be treated independently using the Born-Oppenheimer approximation framework, and a more complicated spin-vibronic picture of combined relativistic and non-relativistic quantum mechanical effects emerges. The spin-vibronic effect specifically induces rapid radiationless transitions at particular nuclear configurations. 14 The spin-vibronic mechanism (SVM) has been predicted to play critical roles in spin crossover, 4 photodynamic therapy, 15 deactivation of DNA bases, 16 and thermally activated delayed fluorescence (TADF). 5 In [Fe(bpy)3] 2+ (bpy-bipyridyl), the SVM promoted by Fe-N stretching vibrations was hypothesized to enable spin crossover in <50-fs. 4 In [Cu(dmp)2] + (dmp -2,9dimethylphenanthroline) an SVM mediated by a pseudo-Jahn-Teller distortion in the angle between the two ligand planes hindered ultrafast ISC. 17 In [Pt2(POP)4] 4-(POP -pyrophosphite) vibrational coherence transfer from the singlet to triplet state suggested nonadiabatic coupling as the primary mechanism for ISC. 18 In donor-acceptor complexes, the SVM adequately described the rate and efficiency of TADF. 5 Despite the apparent ubiquity of spin-vibronic effects, detecting its manifestation in real-time remains elusive. Precise experimental tracking of its mechanism, trajectories, and dynamics can inspire quantum-regulated synthetic design principles for controlling ST conversion through informed structural and compositional modifications beyond simply modifying direct SOC.

Here, we unravel the SVM that drives efficient ST conversion in a series of structurally-related dinuclear Pt(II) complexes by tracking their vibrational wavepacket dynamics using chirpcontrolled broadband pump-probe spectroscopy (BBPP) and two-dimensional electronic spectroscopy (2DES). The wavepacket along the Pt-Pt stretching mode exhibits unique molecular structure-dependent decoherence dynamics that correlate strongly with the timescale of ISC.

Interestingly, we uncovered spontaneous generation of vibronic coherence along the same Pt-Pt stretching mode following ISC in the impulsive rate limit, revealing an elusive intermediate triplet state that couples nonadiabatically to the photoexcited singlet state. We deduced how the Pt-Pt stretching coordinate, with sequential expansion and contraction of the Pt-Pt bond distance, vectorially tunes the multi-level spin and electronic dynamics, efficiently populating the lowestlying triplet state.

The molecules investigated (Fig. 1a, coded as Pt1-Pt4 19 ) are Pt(II) dimeric complexes joined by two 6-substituted-2-hydroxypyridyl bridging ligands having pseudo-two-fold symmetry. At sufficiently short inter-Pt(II) distances, the σ-interactions between the 5dz 2 orbitals enable metalmetal-to-ligand charge-transfer (MMLCT) transitions. 19,20 Structural differences in the bridges (6-methyl in Pt1 and Pt2; 6-phenyl in Pt3 and Pt4) and the cyclometalating ligands (2-phenylpyridine in Pt1 and Pt3; benzoquinoline in Pt2 and Pt4) modifies electronic state energies, affecting the rate of ISC. 20 Excited state energetics and SOC depend on the distance and relative orientation of interacting cofacial 5dz 2 orbitals dynamically modulated by the Pt-Pt stretching vibration. 21 Broadband laser pulses compressed to ~7-fs were used to generate superpositions of vibrational states, resulting in vibrational wavepackets or coherences along the Franck-Condon active modes of the four molecules. These coherences are subsequently probed by another laser pulse(s) delayed with respect to the pump pulse, using BBPP and 2DES apparatus. 22 The probe pulse detects the phase-evolution of vibrational coherences as superimposed oscillatory features on the electronic population dynamics, from which the frequency spectrum of the vibrational modes is extracted by taking the Fourier transform (FT) of the oscillations. 8 The laser spectrum spans 500-670 nm (~20000-14900 cm -1 ) and resonantly excites the 1 MMLCT transition (Fig. 1b). All molecules undergo ISC from the photoexcited 1 MMLCT to the 3 MMLCT state on sub-picosecond timescales. 19,20 The BBPP spectra of Pt1-Pt4, dominated by triplet state absorptions, feature oscillations in the time-domain signal, indicative of vibrational coherences modulating the transient signals of the electronic states (Fig. 1c).

The integrated FT spectra from BBPP of Pt1-Pt4 reveal two vibrational coherences that peaked near 110 and 150 cm -1 (Fig. 1d), with noticeable variations in their relative intensities, shapes, and widths. Pt1 displays a 107 cm -1 band much narrower than the 147 cm -1 band; Pt2 shows no distinct band in the 150 cm -1 region but a broad attenuated feature on the higher frequency side of the 112 cm -1 band; Pt3 and Pt4 feature a narrow, intense band at 145 and 148 cm -1 respectively, and a broad, significantly attenuated feature in the ~110 cm -1 region. Variations in the intensities, shapes, and widths in their FT peaks, despite structural similarity and dynamics, likely originate from nontrivial electronic-nuclear dynamics and report on the intertwined spin, electronic, and vibrational dynamics. Unraveling the intricacies between vibrational coherences and ISC requires knowledge of the state origins of these coherences, i.e., from the ground, singlet, or triplet electronic states, as well as their dephasing dynamics.

The origin of these vibrational coherences was revealed using the state-selectivity of positivelyand negatively-chirped (PC and NC) pump pulses in BBPP spectroscopy. Conceptually, a PC pump pulse disfavors ground-state wavepacket generation whereas an NC pump pulse favors its formation. 23 Thus, one can identify the state origin of the vibrational coherence by monitoring the FT bands' relative intensity under chirped laser pulse excitation. Pt1 has two FT bands at 107 and 147 cm -1 , the former gaining intensity when excited by an NC pulse and losing intensity upon PC pulse excitation, Fig. 2a, upper panel. Conversely, the 147 cm -1 band loses intensity under NC pulse excitation and gains intensity when the PC pulse was used (Fig. 2a, lower panel); Pt2 exhibits similar trends, Extended Data Fig. 1. These observations confirm that the ~110 and ~150 cm -1 bands in Pt1 and Pt2 respectively originate on the ground and 1 MMLCT states. The excitationdetection beat-maps of these bands in Pt1 constructed from 2DES (Extended Data Fig. 2) support these assignments as the spectrally resolved intensities of these bands peak at the ground state bleach (GSB) and stimulated emission signals, respectively. The higher frequency vibration observed in the excited state results from shortening the Pt-Pt bond by ~0.25Å during the 1 MMLCT transition. 20 The dephasing dynamics of the coherences in Pt1 and Pt2 were modeled by nonlinear least squares fitting of the raw time-domain oscillations using exponentially decaying cosine functions (Fig. 2b). For Pt1, fitting the oscillatory traces at ωprobe = 18200 cm -1 and ωprobe = 16200 cm -1 revealed dephasing time-constants (τdephasing) of 615±60 fs and 460±40 fs, corresponding to the ground and excited state vibrational coherences at 107 and 147 cm -1 , respectively. For Pt2, the respective dephasing time constants of the ground and excited state coherences were 505±55 fs (ωprobe = 18000 cm -1 ) and 290±40 fs (ωprobe = 15500 cm -1 ). Probe frequencies were selected because they constitute a predominantly singular oscillatory component. The dephasing time-constants estimated from nonlinear least squares fitting are within ±60 fs of the time-constants obtained from the Lorentzian lineshape widths (Fig. 2c) of the FT bands (τPt1,107 = 617 fs, τPt1,147 = 420 fs, τPt2,110 = 440 fs, τPt2,140 = 280 fs). Further, a multipeak fitting procedure using Lorentzian lineshapes was also extended to chirped excitation conditions (Extended Data Fig. 3, Table 1). These results illustrate the Pt-Pt vibrational coherence on the singlet state in Pt1 (τdephasing,singlet=460 fs) and Pt2 (τdephasing,singlet=290 fs) dephase faster than their ground states. The vibrational coherence does not transfer to the triplet states even though the electronic population transfers rapidly from the singlet to the triplet manifold. Instead, the vibrational coherence becomes wholly attenuated in the 1 MMLCT state of Pt1 and Pt2 at the same rate as the ISC.

The ISC-rate-limited decoherence of the Pt-Pt wavepacket in the 1 MMLCT state illustrates how this vibration enables the SVM. The induced decoherence is ascribed to the energy-tuning capability of this vibration bridging the singlet and triplet manifolds that promote ISC and prevent coherence survival through the conical intersection, suggesting the SVM at play. The rapidly changing character of the electronic states due to motion along the energy-tuning Pt-Pt vibration and large anharmonicities near the conical intersection appear responsible. [24][25][26] Similar behavior has been observed for tuning modes in rhodopsin isomerization, 27,28 and promoter modes in nearballistic electron transfer reactions. 9,29 Besides a few weak high-frequency ligand-centered modes (1200 -1600 cm -1 ) revealed by 2DES, no other Franck-Condon mode activity was observed experimentally (Extended Data Fig. 4).

Identifying the triplet electronic state intersecting with the singlet state remains contentious towards invoking the SVM. 5,14,[30][31][32][33] A distinct feature of the vibrational coherence dynamics in Pt3 and Pt4 is the narrow and intense band at 145 and 148 cm -1 , respectively (Fig. 1d). Instead of exhibiting monotonic intensity decay kinetics, the amplitude of their oscillations features an initial growth followed by a longer decay (Fig. 3). 2DES beat-maps of these two bands peak at the 3 MMLCT absorption signal (Extended Data Fig. 5). Chi-squared analysis of the FT lineshape fitting indicates these bands conform to Gaussian lineshape contrary to the Lorentzian lineshapes in Pt1 and Pt2 (Extended Data Fig. 6), suggesting distinct generation and dissipation mechanisms in the coherences in Pt3 and Pt4 concerning those observed in Pt1 and Pt2 (see Methods). 34 BBPP beat-maps illustrate the spectrally-resolved amplitude of these bands in Pt3 and Pt4 do not shift to lower probe energy with respect to the GSB, as observed in Pt1 and Pt2 (Extended Data Fig. 7).

Additionally, oscillatory maps of the 145 cm -1 frequency band in Pt3 (148 cm -1 in Pt4) display a phase flip in their oscillations, evidenced by a node of zero amplitude at ωprobe = ~16300 cm -1 for Pt3 (ωprobe = ~15000 cm -1 in Pt4), shifting towards lower probe frequency with time (Extended Data Fig. 8). The position of the node occurs in the same spectral region as the triplet absorption peaks.

Therefore, the persistent 145 and 148 cm -1 vibrational coherences in Pt3 and Pt4 do not originate from the 1 MMLCT state; instead, they originate from the 3 MMLCT state, where ISC spontaneously generates them in the impulsive rate limit. Due to the impulsive generation of these coherences on the triplet state through ISC -not by direct laser excitation -the chirp-dependent BBPP measurements of Pt3 and Pt4 do not exhibit similar correlations in the FT band intensities concerning Pt1 and Pt2 (Extended Data Fig. 9). Previous examples supporting the spontaneous generation of coherences due to an impulsive reaction rate include electron transfer at a dyesemiconductor interface, 35 electron transfer in a system of acceptor dissolved in a donor solvent, 9 and a theoretical prediction where vibrational coherence was generated along a mode that directly drives the curve crossing. 36 The extended dephasing times indicate that the lifetime of the corresponding electronic state is long, and the higher frequency suggests a more significant force constant due to the contracted Pt-Pt equilibrium distance in the 3 MMLCT state.

A map of oscillations obtained by inverse Fourier filtering of the sharp peak centered at 148 cm -1 in Pt4, along with the broad feature, displays more robust oscillations up to ~700 fs, followed by persistent but relatively less intense oscillations (Fig. 3a). The filtered inverse FT trace is overlayed with the raw oscillatory trace for a representative ωprobe = 17000 cm -1 to illustrate that filtering- induced artifacts are insignificant. Nonlinear least squares fitting of the raw oscillations at ωprobe = 18000 cm -1 reveal a predominantly single frequency component of ω = 120 cm -1 with τdephasing= 320±55 fs (Fig. 3b). This ~120 cm -1 frequency component (τdephasing= 290±70 fs) was also observed in the fitting of the oscillations at ωprobe = 17000 cm -1 in addition to the 148 cm -1 frequency component. Fitting the 148 cm -1 oscillatory component required simultaneous exponentially growing and decaying cosine functions (Fig. 3b). At ωprobe = 17000 cm -1 , for the148 cm -1 oscillations, τdephasing,growth = 800±240 fs (negative amplitude) and τdephasing,decay = 1060±280 fs (positive amplitude) were observed. The growth and decay components' time constants (and amplitudes) for the 148 cm -1 mode feature a strong probe frequency dependence ranging from 500-1000 fs for the τdephasing,growth component and 1-2 ps for the τdephasing,decay component. The growth of the 148 cm -1 in Pt4 oscillations can be observed when the frequency filtering window selected only the sharp band at 148 cm -1 (Fig. 3c). The more robust oscillations in the initial ~700-fs time window appear attenuated. Sliding the window to the broad and weaker lower frequency band revealed short-lived but intense oscillations in the same ~700-fs window (Fig. 3d). This was further supported by the FT of the oscillatory trace windowed from t2=500-fs to 3-ps at a representative ωprobe = 17000 cm -1 showing only the 148 cm -1 component (Extended Data Fig. 10). Nonlinear least squares fitting of Pt3 revealed similar vibrational coherence dynamics with respective timeconstants of τdephasing,growth = 800±120 fs and τdephasing,decay = 1000±140 fs for the 145 cm -1 oscillations (Fig. 3e and Extended Data Fig. 11). Such dynamics suggest that the growth of the 145/148 cm -1 oscillations is synchronous with the decay of the short-lived oscillations, confirming that they likely originate from two distinct electronic states. Furthermore, the short-and long-lived oscillations have frequencies of ~120 and 148 cm -1 , respectively. ISC impulsively generates the short-lived oscillations at ~120 cm -1 in Pt3 and Pt4 on a transitory intermediate state of triplet character. The long-lived ~145 cm -1 (Pt3) and 148 cm -1 (Pt4) oscillations growing with time-constants of ~500-1000 fs are a consequence of electronic population transfer and the associated vibrational coherences (within the Born-Oppenheimer approximation) from the intermediate state to the lowest 3 MMLCT state (<500-fs). The growth in vibrational coherence amplitude parallels the growth in triplet population dynamics. Another contributor could be wavepacket relaxation from upper vibrational levels to the bottom of the potential well. 36 The existence of a close-lying intermediate of ligand-centered ππ* triplet character having similar equilibrium Pt-Pt distance as the ground state has been predicted by calculations. 20,21 Thus, the Pt-Pt stretching vibration must have a similar frequency in the intermediate and ground states, consistent with our experimental observations. This supports investigations predicting the crucial role of intermediate electronic states in spin conversion based on energetics, symmetry selection rules, and geometry. 4,5,37 The complete decoherence of the Pt-Pt vibrational wavepacket (~150 cm -1 ) on the 1 MMLCT state -without transferring to the triplet manifold -is a hallmark of spin-vibronic crossing of the electronic states energetically tuned by the Pt-Pt vibration. The ISC process initiates from photoexcitation, preparing the 1 MMLCT state with a contracted Pt-Pt distance, interceded by an intermediate state with an expanded Pt-Pt distance. This variation in Pt-Pt geometry bridges the singlet and intermediate energy gap at the conical intersection, and the presence of a SOC leads to spin-vibronic coupling of the states (Fig. 4). Spin-vibronic coupling near the conical intersection lowers the symmetry and induces ultrafast ISC. Due to the impulsive rate of ISC in Pt3 and Pt4, the instantaneous change in the displacement of the Pt-Pt coordinate results in the impulsive generation of vibrational coherence (recoherence) on the intermediate state, which oscillates at ~120 cm -1 (Fig. 4). Subsequently, the intermediate state coherence in Pt3 and Pt4 transfers to the lowest triplet state due to population transfer in <~500-fs, resulting in a changeover in frequency from ~120 to ~150 cm -1 due to the contraction of the equilibrium Pt-Pt distance (Fig. 4).

Contrarily, no new coherence was generated in the intermediate states of Pt1 and Pt2 because of the slower rate of ISC-not in the impulsive limit -that eventually leads to the absence of any coherence on their lowest 3 MMLCT states. These vectorial motions along the Pt-Pt stretching coordinate generate an irreversible population funneling effect driven by an SVM through structural reorganization and relaxation steps that eventually enable efficient ST conversion.

The rates of ISC, and hence the impulsive or non-impulsive ISC, are determined by the position along the Pt-Pt stretching trajectory where the singlet and intermediate states cross in Pt1-Pt4.

Calculations predict that the crossing point is closer to the Franck-Condon geometry in Pt3 and Pt4 than in Pt1 and Pt2. 20 Therefore, less energy-tuning is required by the Pt-Pt stretching coordinate to bridge the 1 MMLCT-intermediate gap in Pt3 and Pt4 than for Pt1 and Pt2 (Fig. 4).

For this SVM, in addition to tuning the Pt-Pt motion, a coupling mode that is typically a highfrequency vibration is also required. 37 2DES of each molecule revealed two high-frequency modes of relatively minor Franck-Condon activity with frequencies of ~1243 and ~1305 cm -1 (Extended Data Fig. 4), possibly resulting from in-plane breathing vibrations of the coordinated ligands that could potentially act as coupling modes.

The complex interplay of vibrational coherence dynamics (decoherence and recoherence) along the Pt-Pt stretching vibration and ISC trajectory provides unequivocal evidence for the SVM while informing design principles on how molecular structures exploit nonrelativistic quantum mechanics to favor fast and efficient ST population funneling. Applying Pt(II) dimers featuring MMLCT excited states introduced a unique low-frequency vibronic coordinate along the dynamic vibrational motion of the Pt-Pt internuclear axis. Moreover, the steric constraints introduced by the bulkier bridging ligands in Pt3 and Pt4 promoted ISC in the impulsive rate limit, ensuring that the conical intersection along the Pt-Pt coordinate lies close to the Franck-Condon geometry, favoring efficient ST spin conversion. These results demonstrate that the interplay of spin, electronic, and nuclear dynamics can defy conventional rules of spin conversion by introducing quantum mechanical funnels. Spin-vibronic effects can have far-reaching implications for a broad range of applications in solar energy conversion, photocatalysis, light-emitting diodes, highdensity magnetic data storage, and molecular devices in terms of how quantum mechanics can be used as a tuning element to manipulate or design spin-conversion in functional inorganic, organic, and materials systems even in the absence of heavy atoms.

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgments, peer review information; details of author contributions and competing interests; and statement of data and code availability are available at Upper and lower panels show FT spectra normalized to the 147 and 107 cm -1 peaks respectively. b, The exponentially decaying cosine functions were used to fit the raw oscillatory time-domain signal at two probe frequencies for Pt1 (ω probe =18200 and 16200 cm -1 ) and Pt2 (ω probe =18000 and 15500 cm -1 ). These probe frequencies were chosen because they predominantly had only one oscillatory component. The rapidly oscillating component is due to the THF solvent Raman mode of frequency ~913 cm -1 . c, Lorentzian fitting of the FT bands corresponding to the raw oscillatory traces at the above probe frequencies in Pt1 and Pt2. The values provided in cm -1 units are full-width-half-maximum (FWHM) of the fits. The dephasing time-constants obtained from nonlinear least square fitting in (b) are within ±60fs of the dephasing time-constants obtained from the widths of the Lorentzian fits. A representative inverse-FT is overlayed on the raw oscillatory trace to showcase complete agreement between the two, and that Fourier filtering induced artefacts are negligible. b, Nonlinear least square fitting of the raw oscillatory trace of Pt4 using exponentially decaying cosine functions at ω probe =18000 and 17000 cm -1 probe frequencies. The high-frequency oscillating component is due to the 313 cm -1 THF solvent Raman mode. c, Map of oscillatory signal extracted for the 148 cm -1 mode in Pt4. The white dashed line is an eye guide tracking the peak amplitude of the oscillations along time as a function of probe frequency. d, Map of oscillatory signal corresponding to the broad feature to the low-frequency side of the 148 cm -1 peak in Pt4. e, Nonlinear least square fitting of a representative oscillatory trace at ω probe =17000 cm -1 in Pt3 showing similar dynamics as that of Pt4.

Pt1/Pt2 (upper panel) and Pt3/P4 (lower panel) is illustrated here. Photoexcitation prepares the Pt-Pt wavepacket on the singlet 1 MMLCT state with a contracted Pt-Pt equilibrium position. The singlet wavepacket (~150 cm -1 ) decoheres completely as the excited state evolves from the Franck-Condon region to the conical intersection. In Pt3/Pt4, a new vibrational coherence (~120 cm -1 ) is generated on the intermediate state due to the impulsive rate of the ISC reaction. This transition involves expansion of the Pt-Pt equilibrium bond distance. The intermediate state internally converts to the lowest triplet state leading to initial growth of the wavepacket, which oscillates with ~150 cm -1 frequency due to re-contraction of the Pt-Pt equilibrium bond distance.

All Pt(II) dimers studied in this work were synthesized and structurally characterized as described in a previous study. 19

The steady-state absorption spectra of all the complexes dissolved in tetrahydrofuran (THF) solvent were obtained in Shimadzu UV-3600 UV-vis NIR spectrophotometer. The measurements were performed in a 1 mm pathlength quartz cuvettes at room temperature.

The 35-fs pulses from a 10 kHz Ti:Sapphire regeneratively amplified laser system (Solstice Ace, Spectra-Physics) seeds a secondharmonic pumped noncollinear optical parametric amplifier (NOPA) producing broadband pulses spanning 520-670 nm. The NOPA output is compressed to the Fourier transform limit by a 4-f pulse shaper (MIIPSBox640, BioPhotonic Solutions) using the MIIPS algorithm, yielding ~7-fs pulses. 22 The compressed pulses then traverse a partially-common path 4-arm interferometer to generate a square BOXCARS beam geometry of three 40 nJ excitation pulses and one reference pulse with computer-controlled pulse delays. The sample was held at the common focus (~40 µm) of the four beams. The 2DES signal field, generated in the direction of the reference pulse, is spatially filtered from the excitation pulses and then coupled into a spectrograph (Shamrock SR-303i, Andor) equipped with a cooled EMCCD camera (Newton, Andor) for detection of signal-reference spectral interferograms.

Rephasing 2D spectra were measured by rapidly scanning coherence time delay ( ) from 0 fs to 120 fs in 5 fs steps. Suboptical steps are unnecessary in the partially-common path interferometer approach since the signal-reference interferogram is acquired in a "quasi-rotating frame" along . 22 2D spectra are acquired sequentially at a range of waiting time (T) delays to track relaxation dynamics. For each sample, 2D spectra were acquired from 50 fs to 3 ps in 5-fs steps. The signal field is isolated from signal-reference interferograms using the Fourier transform spectral interferometry algorithm. After interpolating and transforming the wavelength axis of the signal field to frequency, the signal field is Fourier transformed along the dimension to generate the 2D spectrum as a function of excitation frequency ( ) and detection frequency ( ). The phase of the 2D spectrum is corrected by comparison to the spectrally-resolved pump-probe spectrum using the projection-slice theorem method. This separates physically meaningful real (absorptive) and imaginary (refractive) components of the 2D spectrum. 2DES beat-map spectra are generated by first subtracting off the population relaxation dynamics and then Fourier transforming the residual oscillations along the T dimension, yielding beat-maps for individual frequency bands as a function of excitation and detection frequencies.

The broadband pump-probe (BBPP) measurements reported in this study were measured in the same 2DES setup by blocking one pump beam and the reference beam. A chopper set at 100 Hz was placed in the pump beam that allows us to measure the change in intensity of the probe beam in presence and absence of the pump beam.

All the sample solutions of the dinuclear platinum complexes dissolved in THF solvent were continuously flowed through the beam path using 1 mm quartz flow cells (from Starna Cells) to avoid any photodegradation. The samples were flowed using a peristaltic pump (from Masterflex) maintaining a flow rate of ~2 ml per minute. PTFE tubing (from MasterFlex) was used as it has high chemical resistance and inertness to THF solvent.

The main requirement for performing coherence spectroscopic experiments is the generation and temporal-compression of the broadband laser pulses. In our experiments, we use NOPA to generate the laser pulse spectrum extending ~520-670 nm. These generated laser pulses are spectrally broad, but they are also stretched in time and require phase adjustment between different Fourier components of the pulse to compress it. Typically, the phase mismatch occurs due to the different speed of the Fourier components within the pulse as the pulse travels through air, nonlinear crystals, and other transmissive optics, etc. For a given spectral bandwidth, the theoretically short pulse is known as the Transform Limited (TL) pulse, given by the time-bandwidth product of the pulse. These TL pulses are obtained by optimizing various pulse compressors like prisms, gratings, a combination of prism and a grating, pulse shapers, chirp mirrors, etc. In our case, we used MIIPS pulse shaper. The TL pulses have all the Fourier components locked in the same relative phase. In the simpler terms, all the colors in the pulse arrive at and interact with the sample at the exact same time.

Broadband laser pulses that are not transform limited are identified as the chirped pulses. In the chirped pulses, the different Fourier components of the pulse have shifted relative phase. This chirp is introduced when the pulse travels through dispersive media, as mentioned above. Besides introducing a constant phase shift to the whole spectrum (which does not affect the structure of the pulse), dispersive media also delays some Fourier components of the pulse in time with respect to the other Fourier components. This later effect collectively introduces second-, third-, fourth-and higher-order dispersions. In the visible spectral region, the dispersive optical materials mostly introduce second-order dispersion (significantly larger than the other higher terms) which is also called Group Velocity Dispersion (GVD). This dispersion sweeps the instantaneous frequency of the Fourier components, with respect to the central frequency, and stretches the input pulse in time, thus increasing the pulse duration. If the GVD term is the highest and other higher-order terms are neglected, the laser pulses are identified as linearly chirped pulses, where the instantaneous frequency shifts linearly with time, and the phase changes quadratically.

The linearly chirped pulses, according to the sign of the GVD, can be positively chirped (PC) pulses or negatively chirped (NC) pulses. In the positively chirped pulses, red components temporally precede blue components of the pulse while as in the negatively chirped pulses, red components temporally succeed blue components of the pulse. In our work, the chirp was introduced by either the insertion (which introduces positive chirp) or removal (which introduces negative chirp) of the 1 mm and 2 mm of the UV grade fused silica broadband window (Thorlabs, WG41010R) in the pump beam. The theoretically calculated GVD for the PC pulses with the 1 mm and 2 mm of fused silica window for our laser pulse spectrum were 60 and 120 fs 2 /rad respectively. The pulse duration thereby increased from ~7.0 fs to 27±2 fs for the 1 mm and to 37±3 fs for the 2 mm thickness glass. For the NC pulses, the GVD listed above was introduced with opposite signs. Such experiments have been performed previously to identify the ground and excited state character of the vibrational coherences. 23,[38][39][40][41] In our case, the experiment was set up by placing two windows of fused silica of thickness 1 mm each in both the pump and probe beams. The MIIPS pulse shaper was then used to optimize the compression that provided transform limited pulses of ~7-fs pulse duration. To run the experiment with the positively chirped pulses of GVD = ~60 fs 2 /rad, an additional 1 mm window was introduced in the pump beam only. For GVD = ~120 fs 2 /rad, one more 1 mm window was introduced in the pump beam. For negatively chirped measurement of GVD = ~-60 fs 2 /rad, one window out of the initial two windows was removed, leaving behind a total of 1 mm fused silica in the pump beam. For another negative chirp measurement of GVD=~-120 fs 2 /rad, the other 1 mm window was also removed from the pump beam, leaving no fused silica windows in the pump beam. Using this procedure of the insertion and removal of silica windows, we were able to measure a total of 5 datasets for each sample. These includes transform limited (TL), positive chirp of GVD=~60 fs 2 /rad (PC1), positive chirp of GVD=~120 fs 2 /rad (PC2), negative chirp of GVD=~-20 fs 2 /rad (NC1), and negative chirp of GVD=~-120 fs 2 /rad (NC2). In all these experiments, the probe beam was consistently Transform limited.

The concept behind using the chirped pulse excitation to achieve the selectivity in terms of the ground or excited state vibrational coherences was previously laid down using numerical simulations. 42 In terms of field-matter interactions in pump probe spectroscopy, we know that the pump field introduces two field-matter interactions at the exact same time to create a population state and/or coherent vibrational superposition state, called a wavepacket. This wavepacket can be generated in the ground or excited state. In this wavepacket picture, 43 the first pump field-matter interaction generates a wavepacket on the excited state surface which then starts to evolve down the potential energy surface. A second pump field-matter interaction can generate more amplitude of the wavepacket on the excited state surface or it can project the amplitude of the wavepacket from the first field-matter interaction back to the ground state. In the latter scenario, the two field-matter interactions give rise to an impulsive resonant Raman process that generates a strong ground state wavepacket. This process is amplified when the Fourier components of the pump pulse are ordered in a manner such that the low energy components (red) follow the high energy components (blue) of the pulse. Thus, a negatively chirped pulse (red follows blue) favors the generation of nonstationary ground state wavepacket while a positively chirped pulse (blue follows red) discriminates against it. Thus, introducing a chirp (positive or negative) in the pump pulse provides a unique and highly selective approach to experimentally bias the wavepacket generation on either the ground or excited states.

The following exponentially decaying cosine function was used to fit the raw oscillations in the time domain to estimate the frequencies and dephasing time-constants of the oscillating components in the experimental kinetic traces. In addition to the above expression, we also used its modified version to accommodate for the growth and decay of the oscillations corresponding to a particular component. For example, in order to fit an oscillating kinetic trace with two frequency components, one of which has only a decaying dynamics while the other has a growing and decaying dynamics.

The pre-exponential factor of the exponentially growing component has a negative value while that of the exponentially decaying component has a positive value.

In addition, the following equation was used to determine the dephasing time-constant from the Lorentzian linewidth of the Fourier transform bands.

(ps) = 0.315 (cm ) * 33.3

The exact lineshape of a vibrational peak (Raman or Infrared) is typically related to the energy dissipation mechanism of the vibrational mode. 34 When all the oscillators are in the same environment and a single dissipation mechanism is at play, Debye relaxation occurs which is characterized by a single lifetime and thus leads to a Lorentzian lineshape of the vibrational peak. On the other hand, if there is some additional broadening associated with the band, which could originate from, for example, different local environments around the oscillators (heterogeneity) or two or more slightly different frequencies overlapping in the same spectral region, that leads to the Gaussian lineshape of the vibrational band. 44 In all the dinuclear platinum complexes studied here, most of the Fourier transform peaks conform to the Lorentzian lineshape as is typically expected from vibrational lineshapes. However, the two bands; 145 cm -1 in Pt3 and 148 cm -1 in Pt4 do not conform to the Lorentzian lineshape instead the Gaussian lineshape was used to fit the two bands. Given that all the four complexes are dissolved in the same solvent and their absorption spectra have a similar shape, we expect an insignificant role of heterogeneity in contributing to the Gaussian shape of the main FT bands in the Pt3 and Pt4. The only other factor that could add broadening to the FT band may be due to the slightly different frequency of the vibrational mode in the ensemble. While we cannot categorically ascribe a reason to this broadening, it is likely that the wavepacket generated on the intermediate state due to the ISC process has multiple frequency components owing to the inherent adiabaticity in the conical intersection region. This is evident to some degree in the structure that is associated with the Fourier transform band of ~120 cm -1 on the intermediate state. The 120 cm -1 wavepacket transfers on a timescale of <500-fs to the final triplet state with a changeover in frequency to 145 cm -1 in Pt3 and 148 cm -1 in Pt4 and survives for > 3-ps. The multiple Fourier components wrapped in the wavepacket with slightly different frequencies could cumulatively result in the Gaussian lineshape instead of the Lorentzian lineshape.

Broadband pump probe data measured with temporally compressed broadband laser pulses consists of electronic state population dynamics modulated by the wavepackets in the ground and excited states. These modulations appear in the form of ripples or oscillatory signals along the time domain. [45][46][47] To study these oscillations explicitly we subtract the slow varying population dynamics from the overall dynamics leaving behind residual oscillations. These oscillations are then Fourier transformed to recover the exact mean frequencies of the vibrational modes along which vibrational superpositions or wavepackets were generated. It is highly likely that more than one wavepackets can be modulating the electronic signal and thus Fourier transform spectra can have more than one bands corresponding to different vibrational modes. At times, we want to look at how the amplitude of a selective vibrational wavepacket varies as a function of time, which becomes a challenge when more than one wavepackets are involved. In these circumstances, we apply a procedure called Fourier filtering.

Fourier filtering involves designing a filter in the frequency or time-domain that selects a particular Fourier transform band.

In this case, we mostly deal with filtering in the frequency domain and for this, a super-Gaussian window of varying width was designed to selectively filter out a particular Fourier transform band. Applying this filter reduces the intensity of the FT spectrum to zero everywhere outside the super-Gaussian window. The filtered FT band is then inverse Fourier transformed to convert the filtered frequency domain data back to the time-domain. This process can then be applied to oscillatory traces at all the probe frequencies for generation of a filtered oscillations map. Note that, one must be cautious while applying narrow filters, as that can induces artefacts in the signal.

Apart from filtering out selected FT bands or vibrational frequencies, we can also estimate the dephasing time of a vibrational coherence by fitting the oscillating signal to an exponentially decaying cosine function. The period of the cosine function gives the frequency of the vibrations, and the time-constant of the exponential gives the dephasing time of the oscillations.

It is noteworthy that the 120 cm -1 vibrational wavepacket in Pt4 does not have its origin in ground state because the former not only has been observed to dephase much faster than in Pt1 and Pt2 (Fig. 2), but also does not exhibit similar correlation in the FT intensities for chirp dependent excitation and has a multipeak structure. Additionally, we were able to isolate the ground state coherence in Pt3 plateauing from the broad attenuated feature centered at ~110 cm -1 , indicating that the ISC rate in Pt3 is slower than in Pt4, but still within the impulsive rate limit (Extended Data Fig. 11). The lack of a prominent ground state vibrational coherence at the ~110 cm -1 frequency in Pt4 could result from a high-proportion of population transferred within the total time duration of the pump pulse (20-fs) from the 1 MMLCT to the intermediate state. This argument is supported by the variational nonrelativistic calculations on a related complex which predicted a 15 fs -134 fs time constant for ISC. 48 Therefore, a weak impulsive Raman wavepacket would be projected back onto the ground state close to the equilibrium Pt-Pt coordinate which may be hidden underneath the envelope of the FT spectra.

The nodes can be seen at ωprobe = ~16300 cm -1 probe frequency for Pt3 and ωprobe = ~15000 cm -1 for Pt4, and as the waiting time increases the position of node shifts towards lower probe frequency, typical of time-dependent energy lowering of the corresponding electronic state. The position of the node is in the same spectral region where triplet absorption peaks, clearly indicating that this wavepacket modulates the electronic signal of the triplet 3 MMLCT state. We notice that with a broad filter, two components can be observed in the map based on the distribution of the amplitude. When the filter is tightened to select the 145 cm -1 mode only (b) the oscillation amplitude first grows in time up to ~ 1ps and then decay over >3-ps window. Moving the filter to select the broad and less intense FT band only (c) shows that the oscillations dephase within a time-window of ~500-fs. The dephasing time of these oscillations corroborates with the growth time of the 145 cm -1 mode oscillations. We also selectively filtered out the FT band at 110 cm -1 frequency (d) that peaks out of the broad and less intense band. These oscillations survive for ~>1-ps time-window.