The interplay of nonlinear multi-photon processes and vibrational population effect on vibration-modulated fluorescence

Abstract

Vibrationally promoted electronic resonance offers a powerful strategy for modulating the electronic properties of molecular systems through vibrational–electronic (vibronic) coupling. A detailed understanding of the underlying coupling dynamics is essential for elucidating excited-state relaxation pathways. In this study, we investigate the influence of vibrational excitation on the electronic response of coumarin 6 using mode-selective mid-infrared (IR) pre-excitation fluorescence spectroscopy, complemented by IR/visible (IR/Vis) and IR/IR transient absorption techniques. Significant enhancements in both absorption and fluorescence are observed, particularly on the red edge of the electronic transition. Two distinct mechanisms contribute to these enhancements: (1) a nonlinear multi-photon absorption process, which dominates at low visible photon energies and when IR and visible pulses are temporally overlapped; and (2) a vibrationally excited population effect, which prevails at shorter visible wavelengths and persists over picosecond timescales, strongly influencing electronic excitation efficiency. Notably, the maximum enhancement in visible photon absorption arising from the vibrational population effect is orders of magnitude greater than that produced by nonlinear optical contributions. The interplay of these mechanisms yields several key observations: (1) a delay-dependent peak shift in the visible absorption enhancement; (2) a maximum fluorescence enhancement of approximately 10 times at a visible excitation wavelength of 515 nm; and (3) the appearance of two temporally distinct enhancement peaks in both absorption and fluorescence upon IR excitation at 1620 cm⁻¹. The close correlation between IR-induced changes in visible absorption and fluorescence indicates that fluorescence can serve as a sensitive proxy for transient absorption dynamics. This work provides fundamental insight into vibrationally mediated modulation of electronic transitions and demonstrates the potential for controlling fluorescence through dual-mode excitation. These findings advance our understanding of vibronic coupling dynamics and open new avenues for applications in molecular sensing, photochemical control, and bond-selective fluorescence imaging.

---

1. Introduction

Elucidating the interplay between electronic and vibrational states is fundamental to understanding the behavior of organic molecules in solution. Electronic transitions are typically investigated using ultraviolet-visible (UV-Vis) spectroscopy, while mid-infrared (mid-IR) spectroscopy provides access to vibrational information. Combining these two spectroscopic regimes offers a more comprehensive picture of excited-state relaxation processes. Fluorescence spectroscopy, due to its exceptional sensitivity and molecular specificity, serves as a powerful tool for tracking electronic dynamics. In particular, time-resolved methods such as Kerr-gated fluorescence spectroscopy enable the observation of vibrational relaxation dynamics within electronically excited states on femtosecond (fs) to picosecond (ps) timescales.^1–5 However, in solution-phase systems, vibrational resolution is often hindered by rapid molecular diffusion and complex solute–solvent interactions. Additionally, the short lifetimes of molecular vibrations (typically a few picoseconds) often preclude their direct influence on longer-lived fluorescence signals that persist on nanosecond timescales.

To overcome these limitations, vibrationally promoted electronic resonance (VIPER) provides a strategy for modulating fluorescence via vibrational–electronic coupling. By selectively exciting a specific vibrational mode, it is possible to transiently alter the molecular geometry and thereby modulate both absorption cross-sections and fluorescence quantum yields.^6–9 The VIPER approach uses a narrowband ps mid-IR pulse to excite a targeted vibrational mode, followed by a femtosecond (fs) visible pulse that promotes electronic excitation before vibrational relaxation occurs. This double-resonance technique affords high temporal resolution and sufficient excitation power, enabling a mechanistic interrogation of vibronic interactions in real time. This methodology has been employed across a range of systems for luminescence modulation in various systems,^10–12 extending vibrational observation windows or improving detection sensitivity,^13–17 controlling photochemical reactions,^{12,16,18–20} and many vibrationally resolved fluorescence imaging, including bond-selective fluorescence-detected infrared-excited (BonFIRE).^21–27 These applications have broadened the spectroscopic utility of mid-IR/visible techniques and enabled selective control of photophysical and photochemical pathways.

Despite the growing body of applications, the mechanistic origin of fluorescence modulation by vibrational excitation remains complex. Several intertwined factors contribute to the observed phenomena, including nonlinear multi-photon processes, changes in Franck–Condon factors, vibrational energy redistribution and relaxation, and structural transformations.^16,28–36 These effects can be difficult to disentangle experimentally and complicate the interpretation of fluorescence modulation in vibrationally excited systems.

One particularly intriguing question remains unresolved: when the visible and IR pulses are temporally overlapped (i.e., at time zero), two distinct mechanisms may enhance the absorption of visible photons. The first involves nonlinear multi-photon processes, where a visible photon and IR photons interact via second or higher order nonlinearity to generate a sum-frequency photon, which can then be absorbed by the molecule. The second mechanism arises from vibrational population effects: vibrational excitation modifies the molecular geometry such that the vibrationally excited state lies closer to the Franck–Condon active configuration, thereby increasing the absorption cross-section for visible photons and enhancing fluorescence. While previous studies have intuitively favored the vibrational population effect, the conditions under which each mechanism dominates remain poorly understood.^37–41

In this study, we address this open question by investigating the influence of vibrational excitation on the absorption and fluorescence properties of coumarin 6 (C6), a widely used laser dye with high fluorescence quantum yield^42–48 and favorable photostability.^42,49–51 Using a combination of time-resolved IR-pump/visible-IR-probe spectroscopy,^{18,31,52–55} IR transient spectroscopy, IR/Vis double excitation fluorescence spectroscopy, and quantum chemical calculations, we dissect the relative contributions of nonlinear multi-photon effects and vibrationally induced changes in the Franck–Condon factors. Our findings reveal that the dominant mechanism for fluorescence modulation is strongly dependent on the visible excitation wavelength, providing new insight into vibronic coupling and guiding future applications of vibrational control in molecular photophysics.

2. Methods

2.1. Experimental setup

The ultrafast measurements are conducted with a home-built system introduced briefly as follows.^10,56,57 Details of sample preparations and measurements with routine techniques are provided in SI.

2.1.1. Generation of visible and mid-IR pump and probe pulses. The generation of visible and mid-IR pump and probe pulses are performed according to pervious report.⁵⁶ Briefly, femtosecond laser pulses (1 kHz, ∼40 fs pulse width, 800 nm central wavelength) from an amplified Ti/sapphire laser system (Uptek Solutions Inc.) are split into three parts. The first one is used to pump a femtosecond OPA (TOPAS-Prime) producing ∼60 fs UV/visible pulses with a bandwidth ∼10 nm in a tunable frequency ranging from 250 nm to 800 nm at 1 kHz, serving as pump pulses (VE). The second one is used to pump another femtosecond OPA (Palitra, QUANTRONIX), producing mid-IR probe pulses (IP) with a bandwidth ∼200 cm⁻¹ in a tunable central frequency range from 1000 cm⁻¹ to 3500 cm⁻¹ at 1 kHz. The last one is focused on a 2 mm sapphire plate with a plano-convex len with 100 mm focal length to generate white light continuum of ∼60 fs covering 470–730 nm, serving as visible probe pulses (VP) after going through a short-pass filter to filter out 800 nm light. The VE excites the electronic transition and the excitation power is ∼200 µW with a spot diameter of 245 µm.

The output (1 kHz, ∼1.5 ps pulse width, 800 nm central wavelength) from a ps amplified Ti/sapphire laser system (Uptek Solutions Inc.) is used to pump a ps OPA (TOPAS-ps) producing ∼ 1.5 ps, ∼2 mW IR pulses with a bandwidth of ∼10–20 cm⁻¹ in the range from 900 cm⁻¹ to 3600 cm⁻¹, serving as the mid-IR pump beam (IE). The power of each wavenumber is measured, shown in Fig. S9.

2.1.2. Transient absorption experiments. The pump/probe studies are performed with a fs/ps synchronized laser system.⁵⁷ Either VE or IE is chosen as the pump beam, and either VP or IP is chosen as the probe beam. The time delay between pump/probe pulses are controlled by a mechanic delay line.

The IP is collected by a 2 × 64 pixels mercury cadmium telluride (MCT) detector (Infrared Associates) cooling with liquid nitrogen with a spectral resolution of ∼3 cm⁻¹. Two polarizers are inserted into the IP path. One is located behind the sample to selectively measure the parallel or vertical polarized signal relative to the pump beam; and another is before the sample, which is used to rotate the polarization of the IP about 45° relative to that of the pump beam. Measuring the transmission of the IP through the sample by chopping the pump beam at 500 Hz, the pump–probe signal P(t) is collected and the vibrational lifetimes are obtained from the rotation-free signal

and the anisotropy A(t) is derived fromwhere P_‖(t) and P_⊥(t) are parallel and vertical signals, respectively.

The VP signal is collected in the shot-to-shot manner by a fast spectrometer equipped with a CMOS detector (Tiger-Vis-4K spectrometer from Tiger Instruments) calibrated by mercury and argon lamps. The spectral resolution is ∼0.5 nm. A polarizer is inserted into the VP path right before the sample to rotate the polarization of VP. The angle between VP and pump beam is the magic angle, from which the rotation-free signal can be directly obtained.

2.1.3. Visible/IR double resonance fluorescence experiment. Briefly, the VE and IE are focused and spatially overlap on the sample. The time delay between visible and ps-IR pulses is controlled by another delay line. The polarization of two pump pulses is set to be parallel. The wavelength-resolved fluorescence is collected with an objective lens and an optical fiber, and sent to a spectrograph (Shamrock SR303i) equipped with an EMCCD (Newton EM, Andor DU970), which promises a spectral resolution of ∼0.1 nm. With a visible excitation power of 10 µW, the integral time is 5 seconds for each scan.

2.2. Results & discussion

2.2.1. Steady state experiments and prediction of IR pre-excited absorption spectra. Fig. 1A displays the UV-Vis absorption (black) and fluorescence spectra of C6. The absorption center is at 450 nm, whereas that of fluorescence redshifts by about 50 nm at 500 nm. The difference in calculated charge distribution between its electronic ground state (S₀) and the first excited state (S₁) shows that the most intense electronic transition occurs primarily on the carbon skeleton of the coumarin core, the principal chromophore of C6, with a minor contribution from the thiazole ring, as shown in Fig. 1B. In principle, the electronic density distribution is dependent on the atomic coordinates, which creates a possibility that the electronic transition probability can be modulated by atomic motions driven by vibrational excitations. According to Fig. 1B, vibrations associated with the carbon skeleton of the coumarin core are expected to have the most salient electron-modulating effect. In the FTIR spectrum displayed in Fig. 1C, three vibrational modes are observed respectively at 1587 cm⁻¹, 1618 cm⁻¹, and 1518 cm⁻¹. The vibrational modes at 1587 cm⁻¹ (102nd mode, Fig. 1D) and 1618 cm⁻¹ (104th mode, Fig. 1E) involve strong stretching vibrations coupled to the coumarin core. Differently, the mode at 1518 cm⁻¹, characterized by prominent N=C double bond stretching coupled with the thiazole ring (98th mode, Fig. S2B).

Fig. 1 (A) Normalized UV-vis absorption spectra (black) and fluorescence spectra (excited by 485 nm) of C6 tetrahydrofuran (THF) solution. The molecular structure of C6 is displayed as the inset in (A). (B) Charge density difference distribution of coumarin 6 molecule. The green regions indicate negative charge differences, and the blue regions represent positive charge differences. The isosurface value is set to 0.001. (C) Experimental and calculated IR spectra of C6 in THF solution from 1500 cm⁻¹ to 1700 cm⁻¹. Detailed calculation methods are provided in Fig. S1. (D) and (E) Calculated skeleton stretching vibrational mode at (D) 1587 cm⁻¹, mode 102nd and (E) 1618 cm⁻¹, mode 104th. The grey, white, red, blue and yellow atoms represent C, H, O, N, S respectively; the blue arrows represent the displacement vector of each atom, and the gold arrow is the vector of transition dipole moment. All vibrational modes are numbered from low to high frequency from the calculation results. (F) Calculated visible absorption differential spectra with different vibrational modes pre-excited.

To quantitatively predict the effect of IR pre-excitation on visible absorption, the steady-state one-photon absorption spectra of C6 with one or two vibrational modes pre-excited are calculated using FCClass3 software,^6–8 as shown in Fig. 1F. Detailed parameters are provided in the SI. The spectra demonstrate that single mode pre-excitation (solid lines) 98th, 102nd are expected to have pronounced red-edge enhancement, whereas mode 104th is less effective. However, when mode 104th is simultaneously excited with other modes through vibrational coupling (dash lines), the red-edge enhancement is greatly augmented.

At a vibrationally excited state, the absorption of a visible photon resembles the process of two-step excitation and results in a red-shifted absorption spectrum. Such a relatively simple scenario, however, becomes much more complexed in time-resolved experiments because of the vibrational relaxations and the intrinsic electric field effect of multi-photon excitation.

2.2.2. Visible absorption change modulated by IR excitation. The vibrationally-excited visible absorption change is experimentally reflected in the IR pump/visible probe signal. Using a ps narrow-band mid-IR pulse, the time-zero point is determined when the coherent signal from the IR pump and visible probe pulses reaches its maximum (details of chirp correction and time-zero-point calibration are presented in Fig. S8). Due to the ∼1.5 ps IR pulse width, the signal remains non-zero before time-zero. Consistent with theoretical predictions, vibrational pre-excitation resonant with the coumarin core results in a significant absorption increase on the red-edge side (Fig. 2A and B). Under 1590 cm⁻¹ pre-excitation of mode 102nd, absorbance is notably enhanced, increasing by ∼0.4 at 475 nm and extending to the far red-edge with a ∼0.01 increase at 540 nm after 0.5 ps (Fig. 2A). The spectral shape evolves over time, the red-edge broadening gradually diminishes, as will be further discussed. The signal remains strong and persists over time, with a magnitude of ∼0.02 at 475 nm even at 20 ps. A similar behavior is observed under 1620 cm⁻¹ excitation of mode 104th (Fig. 2B), but the signal intensity is weaker (∼0.11 at 475 nm and ∼0.001 at 540 nm at 0.5 ps), which is in good accordance to the prediction in Fig. 1F.

Fig. 2 (A) and (B) IR pump/visible probe spectra of C6. The signal is rotation-free. The frequencies of mid-IR pump pulses are respectively (A) 1590 cm⁻¹ and (B) 1620 cm⁻¹; the delay times range from −1 ps to 20 ps, with −10 ps as the background. The red-edge are magnified for clearer display. (C) and (D) Decay of IR pump/visible probe signals at different probe wavelength the frequencies of IR pump are (C) 1590 cm⁻¹; (D) 1620 cm⁻¹. The local maxima are enlarged for clarity, located from 0.2 ps (545 nm) to 0.7 ps (472 nm) for 1590 cm⁻¹ in (C), and −0.1 & 1.1 ps for 1620 cm⁻¹ in (D). (E) and (F) Normalized spectral shape evolution of IR pump/visible probe spectra at different time delay. The optical density difference is normalized by divided from that at 480 nm. The frequencies of IR pump are (C) 1590 cm⁻¹; (D) 1620 cm⁻¹ respectively.

The impact of vibrational excitation on visible absorption is probe-wavelength-dependent. At shorter probe wavelengths, besides the increasing signal magnitude, distinct dynamics are evident (Fig. 2C and D). Under 1590 cm⁻¹ excitation, several key phenomena emerge. First, the local maxima exhibit a delayed trend, from 0.2 ps at 545 nm to 0.7 ps at 472 nm. Second, the decay rate becomes slower. The dynamics are modeled with bi-exponential and the time constants are provided in Table 1. At the red edge, e.g. 545 nm and 535 nm, single-exponential dynamics are observed with a time constant of ∼0.9 ps. However, at shorter wavelengths, the decay becomes slower and exhibit a bi-exponential behavior. For example, the time constants are 0.6 ps/3.1 ps at 525 nm, and 1.2 ps/7.5 ps at 472 nm.

Table 1 Biexponential fitting results of different detection with 1590 cm⁻¹ excitation

Detection (nm)	τ 1 (ps)	τ 2 (ps)	A 2
a A 2 represents the amplitude of component with lifetime τ2 after normalization, which means the same in the tables below.
545	0.85 ± 0.03	—	Not detected
535	0.93 ± 0.03	—	Not detected
525	0.65 ± 0.03	3.1 ± 0.6	∼0.22
515	0.70 ± 0.03	3.1 ± 0.2	∼0.30
505	0.69 ± 0.03	3.7 ± 0.2	∼0.35
495	0.83 ± 0.03	5.5 ± 0.3	∼0.37
485	1.09 ± 0.03	7.8 ± 0.3	∼0.46
475	1.15 ± 0.04	7.4 ± 0.2	∼0.52
472	1.19 ± 0.04	7.5 ± 0.2	∼0.60

---

The signal decay at far red-edge side (e.g., 0.9 ps at 540 nm) is comparable to the pulse duration of the IR excitation beam, but significantly faster than the vibrational lifetime of about 7.5 ps (Fig. 4) at 1590 cm⁻¹. At longer wavelengths in the range of 600–700 nm that are far away from the absorption center, the decay time remains ∼0.9 ps (Fig. S8 in SI).

The results indicate that the nonlinear multi-photon absorption induced by electric field of the IR pulse rather than the vibrationally excited population is dominantly responsible for the absorption increase at 540 nm and longer wavelengths. In contrast, at wavelengths closer to the absorption center, e.g., 472 nm, the decay dynamics of absorption change are much longer, and resemble that of the vibrational relaxation (Fig. 4), implying that the main reason for the absorption change at 472 nm is the vibrationally excited population. The probe wavelength dependent delayed maximum observed in the insert of Fig. 2C is the natural consequence of the two effects. The appearance of maximum results from the convolution of the decay dynamics and width of IR pulse. At longer wavelengths, the nonlinear effect is dominant and the decay is fast, so the maximum appears at earlier times. At shorter wavelengths, the vibrational excitation is more important and its relaxation is slower, resulting in a delayed maximum appearance.

With 1620 cm⁻¹ excitation, the interplay between the two effects results in the appearance of two peaks (Fig. 2D). Compared to 1590 cm⁻¹ excitation, a bi-peak shape is observed, with peaks at −0.1 ps and 1.1 ps, shifting from the former to the latter as visible photon energy increases. Additionally, the proportion of long-lived components, primarily from vibrational excitation, becomes dominant at shorter wavelengths, reaching ∼97% at 472 nm (Table 2). It is noted that the variation in the two-component dynamics is intricately linked to the vibrational relaxation, which will be further analyzed with Fig. 4. Therefore, the delay of the signal maximum and the increase in long-lived components with higher visible photon energy are primarily governed by the vibrational excitation, rather than the nonlinear multi-photon effect.

Table 2 Biexponential fitting results of different detection with 1620 cm⁻¹ excitation

Detection (nm)	τ 1 (ps)	τ 2 (ps)	A 2
525	1.29 ± 0.10	6.6 ± 1.1	∼0.31
515	1.16 ± 0.06	7.0 ± 0.5	∼0.40
505	1.25 ± 0.06	7.6 ± 0.4	∼0.52
495	1.40 ± 0.09	9.1 ± 0.3	∼0.70
485	1.17 ± 0.12	9.6 ± 0.2	∼0.92
475	0.80 ± 0.17	9.3 ± 0.3	∼0.97
472	0.88 ± 0.29	9.1 ± 0.4	∼0.97

---

To confirm the existence of two distinct mechanisms, nonlinear multi-photon absorption and vibrational excitation, power-dependent IR pump/visible probe experiments are performed. Under 1590 cm⁻¹ excitation, the dynamics at two representative wavelengths, 480 nm and 540 nm, corresponding to vibrationally excited population and multi-photon absorption effects, respectively, are investigated (Fig. 3A and B). As the IR pulse energy is varied from 0.5 µJ to 2.5 µJ, the signal intensity at 480 nm showed an approximately linear dependence on the IR pulse energy (Fig. 3A), whereas a clearly nonlinear response is observed at 540 nm (Fig. 3B). These results indicate that the vibrational population effect, which is proportional to the number of vibrationally excited molecules, scales linearly with the number of IR photons, whereas multi-photon absorption exhibits a strong nonlinearity.

Fig. 3 (A) and (B) Excitation-power-dependent 1590 cm⁻¹ IR pump/visible probe signal intensities at (A) 480 nm and (B) 540 nm. The IR pulse energy varies from ∼0.5 µJ to ∼2.5 µJ. (C) and (D) Linear fitting results of log I versus log P. The selected wavelengths and delay times are (C) 490–474 nm, 1 ps and (D) 545–525 nm, −0.5 ps, representing vibrationally excited population and nonlinear multi-photon absorption region respectively. (E) Schemes illustrating nonlinear multi-photon absorption and vibrational relaxation. Upon temporal overlap of IR and visible pulses, simultaneous absorption of one or more IR photons (red) and a low-energy visible photon (green) directly promotes the system to an electronically excited state, exhibiting nonlinear dependence on IR pulse energy. In contrast, absorption of an IR photon populates vibrationally excited states, followed by ps vibrational relaxation (dark red), which generates intermediate states that enhance the absorption of higher-energy visible photons (blue). This vibrational process demonstrates linear scaling with the number of IR photons.

Fig. 4 (A) and (B) IR pump/IR probe spectra at different time delay, with (A) 1590 cm⁻¹ and (B) 1620 cm⁻¹ excitation respectively. The blue circle in (A) emphasizes the spectral shape evolution at the first ∼1 ps. (C) and (D) Normalized dynamics of IR pump/IR probe signal with (C) 1590 cm⁻¹ and (D) 1620 cm⁻¹ excitation. The near-zero region is enlarged to clarify the time scale of IVR. (E) Anisotropy decay dynamics in 10 ps of pump/IR probe diagonal signals for 1590 cm⁻¹ and 1620 cm⁻¹ excitation. The region near zero-point is enlarged to present the fast decay at initial ∼1 ps.

Assuming that the signal intensity I(λ, t) is proportional to the ath power of IR pump power P,

I(λ, t) = S(λ, t)·P^a, (3)

We can obtain

log I = log S + a log P. (4)

Linear fitting log I versus log P yields the exponent a. In the vibrational region (490–474 nm at 1 ps, Fig. 3C), a is close to 1, whereas in the multi-photon absorption region (545–525 nm at −0.5 ps, Fig. 3D), a is basically bigger than 2. Moreover, within the multi-photon absorption region, a increases substantially at longer visible wavelengths, demonstrating that the higher-order multi-photon absorption involving more IR photons becomes more significant as the energy gap widens. The fitting results are summarized in Table 3. Power-dependent data for 1620 cm⁻¹ excitation are provided in the SI part 12. Schematic diagrams of the two absorption enhancement mechanisms, nonlinear multi-photon absorption, and vibrational relaxation, are summarized in Fig. 3E.

Table 3 Power-dependent fitting results of different detection in vibrational (490–474 nm, 1 ps) and nonlinear region (545–525 nm, −0.5 ps) with 1590 cm⁻¹ excitation

Detection (nm)	a	Detection (nm)	a
490	1.01 ± 0.07	545	2.97 ± 0.11
486	1.00 ± 0.06	540	2.79 ± 0.09
482	0.97 ± 0.05	535	2.51 ± 0.13
478	0.96 ± 0.05	530	2.23 ± 0.13
474	0.94 ± 0.04	525	1.99 ± 0.12

---

To further illustrate the influence of IR excitation, normalized probe spectra (divided by spectral magnitude at 480 nm) at different delay times are shown in Fig. 2E and F. Under 1590 cm⁻¹ excitation, three distinct states are evident (Fig. 2E). At early times (∼−0.9 ps, blue line), the multi-photon absorption dominates, producing a strong 500 nm response with a weaker 520 nm response. During the intermediate state (0–1 ps), the signal at 500 nm is reduced while the 520 nm response is enhanced. Finally, beyond 10 ps (red line), signals at both wavelengths diminish sharply. Similar trends are observed under 1620 cm⁻¹ excitation (Fig. 2F), though with a weaker multi-photon absorption. The results imply that at least two distinct processes occur during the vibrational relaxation, which will be investigated as follows.

In the above discussion, it is deduced that the relaxations of vibrational excitations at 1590 and 1620 cm⁻¹ involve at least two processes. A well-established model describes vibrational relaxation following pulse excitation, consisting of intramolecular vibrational energy redistribution (IVR) within a few ps, during which energy is transferred from one mode to all vibrational modes, effectively heating the molecule. This is followed by Vibrational Relaxation (VR) about tens of ps, where the excess energy dissipates into the solvent environment.^58–63

To further investigate the vibrational states of C6 and their impacts on absorbance enhancement, IR pump/IR probe spectra with 1590 cm⁻¹ and 1620 cm⁻¹ excitation are measured (Fig. 4A and B). The time-zero point was determined by the absorption signal at 1606 cm⁻¹ reaching its maximum. Clear absorption-bleaching peaks are observed for the three vibrational modes. The delayed dynamics of these absorption peaks are shown in Fig. 4C and D. For 1590 cm⁻¹ excitation (Fig. 4C), the lifetimes of each process are summarized in Table 4. The signal at 1606 cm⁻¹ peaks at 0 ps, then rapidly decays within ∼0.5 ps (blue trace). Simultaneously, the 1572 cm⁻¹ signal rises to its maximum at 0.4 ps (red trace). In Fig. 4A, the bleaching peak position (blue circle) blueshifts from 1583 cm⁻¹ to 1595 cm⁻¹ within ∼0.5 ps, suggesting that the initially excited vibrational state is not the 102nd mode (1588 cm⁻¹) but a coupled state involving the 104th mode (1617 cm⁻¹) with an absorption peak at 1606 cm⁻¹. After a rapid IVR of ∼0.5 ps, a bleaching peak at 1595 cm⁻¹ and an absorption peak at 1572 cm⁻¹ indicate excitation of the 102nd mode, followed by a decay with a lifetime of ∼0.9 ps. Subsequently, the 1503 cm⁻¹ signal increases, peaking at ∼1 ps, representing further IVR from the 102nd mode to other modes, possibly including the 98th mode (1516 cm⁻¹). These processes characterize the IVR dynamics within ∼1 ps under 1590 cm⁻¹ excitation, explaining the fast component observed in Fig. 2C, particularly at the blue-edge detection (475 or 472 nm). However, distinguishing these processes in visible probe spectra remains challenging due to the temporal resolution of IR pulse. Finally, all three absorption peaks exhibit a long-lived component (∼7.5 ps), corresponding to VR. This value is consistent with the 7.5 ps lifetime observed at 472 nm visible detection in Table 1, confirming that the long-lived absorbance increase is attributable to VR. For 1620 cm⁻¹ excitation (Fig. 4D), similar analyses are applied, with results detailed in Table 5. Based on the computational results in Fig. 1F, rapid vibrational coupling between mode 102nd and 104th within 1 ps significantly enhances red-edge absorption compared to excitation of mode 104th mode alone. Therefore, the visible signal dynamics as well as the bi-peak structure observed in Fig. 2B under 1620 cm⁻¹ pre-excitation is primarily attributed to this vibrational coupling. Notably, since only the initially excited vibration undergoes the IVR process, the fast component has a larger proportion for diagonal peaks, reflected in the greater A₁ : A₂ ratio.

Table 4 Biexponential fitting results with 1590 cm⁻¹ excitation

Detection (cm^−1)	τ 1 (ps)	τ 2 (ps)	Ratio A1 : A2
1606	0.36 ± 0.04	9.2 ± 0.4	∼1.23
1572	0.87 ± 0.42	7.7 ± 0.2	∼1.08
1503	—	7.5 ± 0.1	Mono-exponential

---

Table 5 Biexponential fitting results with 1620 cm⁻¹ excitation

Detection (cm^−1)	τ 1 (ps)	τ 2 (ps)	Ratio A1 : A2
1606	0.58 ± 0.04	9.7 ± 0.6	∼1.60
1572	1.10 ± 0.45	8.9 ± 0.5	∼0.53
1503	—	7.4 ± 0.2	Mono-exponential

---

Combining these findings, a comprehensive vibrational-electronic coupling picture under visible/mid-IR double excitation is summarized in Table 6. During the initial overlap of visible and IR pulses (typically < 0 ps), the multi-photon absorption primarily drives the absorbance increase. Vibrational effect contains two parts. As vibrational modes are excited (0–1 ps), these states influence absorbance to various degrees before full IVR. After ∼10 ps, when IVR is complete, low-frequency vibrational modes are fully populated, stabilizing the spectral shape observed in Fig. 2E and F, and the energy slowly dissipates through VR. As mentioned above, at higher visible excitation photonic energies, vibrational excitation increasingly dominates the absorbance enhancement relative to multi-photon absorption.

Table 6 Summarized intermediate vibrational states and electronic coupling effect

Typical timescale	500 nm	520 nm	Causes
<0 ps	Strong	Weak	Multi-photon
0∼1 ps	Medium	Medium	IVR
∼10 ps	Weak	Very weak	VR

---

Additionally, anisotropy measurements of the diagonal peaks, reflecting molecular rotational dynamics, are shown in Fig. 4E. The data also reveal a biexponential decay, with the fast components (blue circle) within 1 ps corresponding to energy redistribution from the rapid IVR process. The slow components persist beyond 10 ps, indicating that after VR, localized solvent heating remains highly orientational. This suggests that the molecular rotation of C6 is significantly slower than 10 ps. The results are important for understanding the visible/IR double excitation fluorescence enhancement discussed in the next section.

2.2.3. Feasibility of mode-selective fluorescence modulation via visible/IR double excitation and verification with absorbance change dynamics. C6 exhibits exceptionally strong fluorescence when excited by blue light. Even under 515 nm excitation, approximately 50 nm away from its maximum absorption wavelength (Fig. 1A), a clear fluorescence response is detected using an EMCCD detector. By mapping the frequency range from 1500 cm⁻¹ to 1700 cm⁻¹ (Fig. 5A), a significant fluorescence enhancement—up to ∼10 times (Fig. 5B)—is observed upon mode-selective IR pre-excitation. The fluorescence enhancement peak positions align with the FTIR spectra, though the amplitude is not proportional. The most pronounced fluorescence enhancement occurs at 1588 cm⁻¹ when a delay time is 0.5 ps. Here, the positive delay time is defined as the interval in which the mid-IR pulse precedes the visible pulse. The time when maximum fluorescence enhancement occurs is set to 0.3 ps, the same as the visible probe peak, for comparison, as further discussed in Fig. 6. Excitations at 1518 cm⁻¹ and 1618 cm⁻¹ also show notable enhancement effects, although significantly lower compared to their corresponding IR absorbance (Fig. 4C). In Fig. 1F, pre-excitation of mode 102nd leads to a more substantial enhancement in absorbance at the far red-edge region (>505 nm) compared to mode 98th. As a result, excitation at 1588 cm⁻¹ proves more effective for fluorescence modulation than 1518 cm⁻¹ at 515 nm.

Fig. 5 (A) Normalized fluorescence enhancement difference spectra, excited by 515 nm visible pulse. The x-axis represents the central frequency of mid-IR pulse, and the y-axis is the fluorescence emission wavelength. The concentration of C6 THF solution is 0.002 M, and the thickness is 100 µm. The delay time between mid-IR pulse and visible pulse is 0.5 ps. The actual intensity enhancement at each IR wavenumber, including (C) and (D), has been corrected by the infrared excitation pulse energy (Fig. S9). (B) Comparison of fluorescence spectra with and without 1588 cm⁻¹ mid-IR pre-excitation at 515 nm excitation (most of the scattering is eliminated). (C) IR wavenumber-dependent emission enhancement spectrum (red) at 500 nm, extracted from (A). The FT-IR spectrum (black) is provided for comparison. (D) The ratio of absorbance increases with 1590 cm⁻¹ (black) and 1620 cm⁻¹ (red) pre-excitation at 0.5 ps from Fig. 2. The truncation after 515 nm is due to the original absorbance reaching zero. (E) 485 nm visible pump/IR probe spectra of C6 at different time delay. (F) Anisotropy decay dynamics of 485 nm visible pump/IR probe signal of C6 at 1587 cm⁻¹ (black) and 1616 cm⁻¹ (red), from which the cross angle of two transition dipole moments can be calculated.

Fig. 6 (A) and (B) Normalized decay of fluorescence enhancement at 500 nm (black) and 550 nm pumped (red) by (A) 1590 cm⁻¹ and (B) 1620 cm⁻¹ with 515 nm excitation, as well as the visible probe signal decay at 500 nm (blue). The data of the first 3 ps at different emission wavelengths are enlarged for the convenience of comparison. (C) and (D) Fluorescence enhancement difference spectra with 515 nm visible and different IR double excitation at (C) 3 ps and (D) 10 ps after IR pump energy correlation. (E) Comparison of IR frequency-dependent fluorescence enhancement spectra at different delay times at 500 nm emission, extracted from Fig. 5A and 6C, D.

The absorbance change is the primary contributor to fluorescence enhancement. By calculating the absorbance increase ratio at each wavelength, it is evident that although the IR/visible transient signal in Fig. 2 is weaker, the gain multiplier increases as the probe visible photonic energy decreases, with the largest gain occurring at 515 nm (Fig. 5D). At longer visible wavelengths, the absorption becomes too weak and is buried in noise (Fig. 5D). Consequently, the vibrational excitation induced fluorescence enhancement effect has a maximum at a certain visible excitation wavelength, reaching a maximum increase of ∼10-fold at 515 nm (Fig. 5B). A similar trend is observed with 1620 cm⁻¹ excitation, though with a less pronounced enhancement (Fig. 5D).

In addition to absorbance increase, the polarizations of excitation pulses must be considered. The transition dipole moments of vibrational and electronic transitions have well defined relative orientations, leading to preferential absorption of visible photons with a certain polarization relative to that of the IR photons. Theoretical calculations indicate that the cross angles between the vibrational transition dipole moments at 1587 cm⁻¹ and 1616 cm⁻¹ and the electronic transition dipole moment of S₀ → S₁ are 17° and 0.4°, respectively, nearly parallel (in Table S1 for details). Their theoretical anisotropy values are 0.348 and 0.399 according to the equation:

where θ(0) represents the inherent cross angle between the two transition dipole moments. Experimentally, these angles are determined using visible pump/IR probe spectroscopy (Fig. 5E). Around time-zero, the anisotropy values at 1587 cm⁻¹ and 1616 cm⁻¹ are approximately 0.33 and 0.35 (Fig. 5F), consistent with theoretical predictions. Since the polarizations of the visible and IR pulses in the double excitation experiments are set to be parallel, IR-excited molecules can efficiently absorb visible photons with parallel polarization within a few ps. While molecular rotation can reduce macroscopic anisotropy and influence polarization-selective absorption, it occurs on a much longer timescale than the vibrational lifetime and can thus be neglected (Fig. 4E). Therefore, the fluorescence enhancement observed in the double excitation experiments is primarily mode-selective rather than polarization-selective.

By varying the delay time between the IR/Visible excitation pulses, the fluorescence enhancement decay dynamics under double excitation with 515 nm visible and mid-IR pulses are presented (dots) and compared to the visible probe signal (lines) with 1590 cm⁻¹ and 1620 cm⁻¹ IR excitation (Fig. 6A and B). First, the fluorescence enhancement at different emission wavelengths, such as 500 nm and 550 nm, exhibits similar dynamics, indicating a single emitting species. Second, the fluorescence decay closely follows the visible probe signal dynamics at 500 nm after time-zero correction. Under 1590 cm⁻¹ excitation, the fluorescence intensity peaks at 0.3 ps, followed by a biexponential decay with a fast component of 0.8 ps (∼85%) and a slower component of 4.9 ps (∼15%) (Fig. 6A). As for 1620 cm⁻¹ excitation, two peaks respectively at −0.1 ps and 1.1 ps are observed, with a nearly identical amplitude ratio to the visible probe signal, followed by a biexponential decay with lifetimes of 1.4 ps (∼67%) and 8.2 ps (∼33%) (Fig. 6B). These time components correspond well to the fast IVR and subsequent VR processes. Notably, due to the spectral width of the visible excitation pulse, stronger absorption occurs at the blue edge. Consequently, the fluorescence decay dynamics resemble the blue-edge pattern (∼500 nm in this work) more closely than the visible probe signal at the corresponding wavelength of 515 nm.

Since different excited vibrations exhibit distinct relaxation behaviors, the fluorescence enhancement effect at each wavenumber is expected to vary over time. Full enhancement spectra at 3 ps and 10 ps are shown in Fig. 6C and D. Compared to the 1 ps spectrum (Fig. 6A), the modulation effect at 1618 cm⁻¹ gradually increases relative to 1588 cm⁻¹. This occurs because, under 1620 cm⁻¹ excitation, vibrational excitation dominates the absorbance increase rather than multi-photon absorption, leading to slower fluorescence decay compared to 1590 cm⁻¹ excitation (Fig. 6A and B). A direct comparison of fluorescence enhancement extracted at 500 nm is presented in Fig. 6E. Over longer delay times, fluorescence enhancement under 1620 cm⁻¹ excitation reaches up to 70% of that under 1590 cm⁻¹ excitation, while the modulation effect at 1516 cm⁻¹ also increases significantly. Additionally, a redshift of the optimal modulation wavenumber around 1588 cm⁻¹ is observed at longer delays, reflecting the coupling and relaxation of adjacent vibrational modes, consistent with previous reports.¹⁰ The results indicate that the IR excitation induced fluorescence modulation dynamics resemble those of the visible absorption change, governed by the interplay of the vibrational excitation and nonlinear optical response.

3. Concluding remarks

In this study, we employ ultrafast IR/visible and IR/IR transient absorption spectroscopy, along with IR/visible double-excitation fluorescence spectroscopy, to investigate the dynamics of vibrational-electronic (vibronic) coupling in Coumarin 6 (C6) and its impact on visible absorbance and fluorescence following mid-IR pre-excitation. Substantial enhancements in both absorption and fluorescence are observed, particularly on the red-edge of the electronic transition. Two distinct mechanisms are identified as contributors to these enhancements: a nonlinear multi-photon absorption process and a vibrationally excited population effect, which are verified through power-dependent experiments. The multi-photon effect dominates at low visible photon energies, especially when the IR and visible pulses are temporally overlapped (i.e., near time zero). In contrast, the vibrational population effect is more pronounced at shorter visible wavelengths and persists over longer timescales—from a few to tens of picoseconds—indicating its stronger influence on the electronic transition pathways.

Importantly, the maximum enhancement in visible photon absorption due to the vibrational excitation population effect is found to be orders of magnitude greater than that resulting from the nonlinear optical response. The interplay of these two mechanisms leads to several notable observations:

(1) The maximum visible absorption enhancement exhibits a delay-dependent shift;

(2) A maximum fluorescence enhancement factor of approximately 10 times is achieved at a visible excitation wavelength of 515 nm;

(3) At an IR excitation frequency of 1620 cm⁻¹, the enhancement dynamics of both visible absorption and fluorescence exhibit two temporally distinct peaks.

In coumarin 6, the dynamics of IR-induced changes in visible absorption closely mirror those observed in fluorescence modulation, suggesting that fluorescence can serve as a sensitive proxy for tracking transient absorption dynamics. These findings offer new mechanistic insight into IR-modulated electronic excitation and provide a foundation for the selective control of photophysical processes through vibrational pre-excitation.

Author contributions

Q. Y., and J. Z. designed experiments. J. Z. supervised the project. Q. Y., Y. S. prepared materials and performed spectroscopy experiments. Q. Y., Y. S., J. G., X. L. and Z. Y. performed ultrafast experiments. Q. Y., Y. S., J. G., X. L., and J. Z. analyzed data. Q. Y. conducted theoretical calculations. Q. Y. and J. Z. prepared and revised the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: materials and methods, supplemental FT-IR spectra, theoretically vibrational calculation results of coumarin 6, Theoretically electronic calculation of coumarin 6, wavelength and concentration dependence of fluorescence emission spectra, temperature-dependent absorption spectra, fluorescence lifetime and delayed fluorescence, Chirp correction and coherent signal in IR pump/visible probe experiments, power correlation of IR pump pulses, IR pump/visible probe spectra with heat effect, fluorescence enhancement spectra with 485 nm excitation. See DOI: https://doi.org/10.1039/d5cp02055g.

If needed, the data that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgements

This material is based upon work supported by the National Science Foundation of China (NSFC-92261206, 22203006, 21927901, 21627805, 12174012, 21673004, 21821004, 21674001 and 21790363), MOST (a special talent program) China, and the Beijing City.

References

1. L. A. Diverdi and M. R. Topp, Subnanosecond Time-Resolved Fluorescence of Acridine in Solution, J. Phys. Chem., 1984, 88(16), 3447–3451,  DOI:10.1021/j150660a016.
2. Y. Kanematsu, H. Ozawa, I. Tanaka and S. Kinoshita, Femtosecond Optical Kerr-Gate Measurement of Fluorescence Spectra of Dye Solutions, J. Lumin., 2000, 87–89, 917–919,  DOI:10.1016/S0022-2313(99)00472-X.
3. R. Nakamura, R. Fujii, H. Nagae, Y. Koyama and Y. Kanematsu, Vibrational Relaxation in the 1Bu+ State of Carotenoids as Determined by Kerr-Gate Fluorescence Spectroscopy, Chem. Phys. Lett., 2004, 400(1), 7–14,  DOI:10.1016/j.cplett.2004.10.069.
4. R. Nakamura, N. Hamada, H. Ichida, F. Tokunaga and Y. Kanematsu, Transient Vibronic Structure in Ultrafast Fluorescence Spectra of Photoactive Yellow Protein, Photochem. Photobiol., 2008, 84(4), 937–940,  DOI:10.1111/j.1751-1097.2008.00329.x.
5. D.-E. Zacharioudaki, I. Fitilis and M. Kotti, Review of Fluorescence Spectroscopy in Environmental Quality Applications, Molecules, 2022, 27(15), 4801,  DOI:10.3390/molecules27154801.
6. J. Von Cosel, J. Cerezo, D. Kern-Michler, C. Neumann, L. J. G. W. Van Wilderen, J. Bredenbeck, F. Santoro and I. Burghardt, Vibrationally Resolved Electronic Spectra Including Vibrational Pre-Excitation: Theory and Application to VIPER Spectroscopy, J. Chem. Phys., 2017, 147(16), 164116,  DOI:10.1063/1.4999455.
7. M. Horz, H. M. A. Masood, H. Brunst, J. Cerezo, D. Picconi, H. Vormann, M. S. Niraghatam, L. J. G. W. Van Wilderen, J. Bredenbeck, F. Santoro and I. Burghardt, Vibrationally Resolved Two-Photon Electronic Spectra Including Vibrational Pre-Excitation: Theory and Application to VIPER Spectroscopy with Two-Photon Excitation, J. Chem. Phys., 2023, 158(6), 064201,  DOI:10.1063/5.0132608.
8. J. Cerezo and F. Santoro, FCclasses3: Vibrationally-resolved Spectra Simulated at the Edge of the Harmonic Approximation, J. Comput. Chem., 2023, 44(4), 626–643,  DOI:10.1002/jcc.27027.
9. A. Guha, L. Whaley-Mayda, S. Y. Lee and A. Tokmakoff, Molecular Factors Determining Brightness in Fluorescence-Encoded Infrared Vibrational Spectroscopy, J. Chem. Phys., 2024, 160(10), 104202,  DOI:10.1063/5.0190231.
10. Q. Yu, X. Li, C. Shen, Z. Yu, J. Guan and J. Zheng, Blue-Shifted and Broadened Fluorescence Enhancement by Visible and Mode-Selective Infrared Double Excitations, J. Phys. Chem. A, 2024, 128(15), 2912–2922,  DOI:10.1021/acs.jpca.3c07060.
11. Q. Yu, X. Li, C. Shen, Z. Yu, J. Guan and J. Zheng, Direct Observation of Long-Lived Vibrational Hot Ground States by Ultrafast Spectroscopy and Visible/Infrared Double Excitation Fluorescence, Chin. J. Chem. Phys., 2024, 37(3), 411–419,  DOI:10.1063/1674-0068/cjcp2311116.
12. J. Guan, X. Li, C. Shen, Z. Zi, Z. Hou, C. Hao, Q. Yu, H. Jiang, Y. Ma, Z. Yu and J. Zheng, Vibrational-Mode-Selective Modulation of Electronic Excitation, ChemPhysChem, 2024, e202400335,  DOI:10.1002/cphc.202400335.
13. L. J. G. W. van Wilderen, A. T. Messmer and J. Bredenbeck, Mixed IR/Vis Two-Dimensional Spectroscopy: Chemical Exchange beyond the Vibrational Lifetime and Sub-Ensemble Selective Photochemistry, Angew. Chem., Int. Ed., 2014, 53(10), 2667–2672,  DOI:10.1002/anie.201305950.
14. H. Brunst, H. M. A. Masood, A. R. Thun, A. Kondratiev, G. Wille, L. J. G. W. van Wilderen and J. Bredenbeck, A Triplet Label Extends Two-Dimensional Infrared Spectroscopy from Pico- to Microseconds, Angew. Chem., 2022, 134(49), e202211490,  DOI:10.1002/ange.202211490.
15. J. N. Mastron and A. Tokmakoff, Two-Photon-Excited Fluorescence-Encoded Infrared Spectroscopy, J. Phys. Chem. A, 2016, 120(46), 9178–9187,  DOI:10.1021/acs.jpca.6b09158.
16. D. Kern-Michler, C. Neumann, N. Mielke, L. J. G. W. Van Wilderen, M. Reinfelds, J. Von Cosel, F. Santoro, A. Heckel, I. Burghardt and J. Bredenbeck, Controlling Photochemistry via Isotopomers and IR Pre-Excitation, J. Am. Chem. Soc., 2018, 140(3), 926–931,  DOI:10.1021/jacs.7b08723.
17. L. Whaley-Mayda, S. B. Penwell and A. Tokmakoff, Fluorescence-Encoded Infrared Spectroscopy: Ultrafast Vibrational Spectroscopy on Small Ensembles of Molecules in Solution, J. Phys. Chem. Lett., 2019, 10(8), 1967–1972,  DOI:10.1021/acs.jpclett.9b00748.
18. J. D. Gaynor, J. Sandwisch and M. Khalil, Vibronic Coherence Evolution in Multidimensional Ultrafast Photochemical Processes, Nat. Commun., 2019, 10(1), 5621,  DOI:10.1038/s41467-019-13503-9.
19. L. J. G. W. Wilderen, D. van; Kern-Michler, C. Neumann, M. Reinfelds, J. Cosel, M. von; Horz, I. Burghardt, A. Heckel and J. Bredenbeck, Choose Your Leaving Group: Selective Photodeprotection in a Mixture of p HP-Caged Compounds by VIPER Excitation, Chem. Sci., 2023, 14(10), 2624–2630,  10.1039/D2SC06259C.
20. D. V. Makhov and D. V. Shalashilin, Simulation of the Effect of Vibrational Pre-Excitation on the Dynamics of Pyrrole Photo-Dissociation, J. Chem. Phys., 2021, 154(10), 104119,  DOI:10.1063/5.0040178.
21. Y. Bai, J. Yin and J.-X. Cheng, Bond-Selective Imaging by Optically Sensing the Mid-Infrared Photothermal Effect, Sci. Adv., 2021, 7(20), eabg1559,  DOI:10.1126/sciadv.abg1559.
22. Y. Zhang, H. Zong, C. Zong, Y. Tan, M. Zhang, Y. Zhan and J.-X. Cheng, Fluorescence-Detected Mid-Infrared Photothermal Microscopy, J. Am. Chem. Soc., 2021, 143(30), 11490–11499,  DOI:10.1021/jacs.1c03642.
23. H. Wang, D. Lee, Y. Cao, X. Bi, J. Du, K. Miao and L. Wei, Bond-Selective Fluorescence Imaging with Single-Molecule Sensitivity, Nat. Photonics, 2023, 17(10), 846–855,  DOI:10.1038/s41566-023-01243-8.
24. H. Wang, P. A. Kocheril, Z. Yang, D. Lee, N. Naji, J. Du, L.-E. Lin and L. Wei, Room-Temperature Single-Molecule Infrared Imaging and Spectroscopy through Bond-Selective Fluorescence, Angew. Chem., Int. Ed., 2024, 63(52), e202413647,  DOI:10.1002/anie.202413647.
25. W. Xiong; C. Yan; C. Wang and J. Ren, Multi-Dimensional Widefield Infrared-Encoded Spontaneous Emission (MD-WISE) Microscopy, Advanced Chemical Microscopy for Life Science and Translational Medicine 2024, SPIE, 2024, vol. PC12855, p. PC128550U DOI:10.1117/12.3003566.
26. P. Fu, Y. Zhang, S. Wang, X. Ye, Y. Wu, M. Yu, S. Zhu, H. J. Lee and D. Zhang, INSPIRE: Single-Beam Probed Complementary Vibrational Bioimaging, Sci. Adv., 2024, 10(50), eadm7687,  DOI:10.1126/sciadv.adm7687.
27. D. Lee, H. Wang, P. A. Kocheril, X. Bi, N. Naji and L. Wei, Wide-Field Bond-Selective Fluorescence Imaging: From Single-Molecule to Cellular Imaging beyond Video Rate, Optica, 2025, 12(2), 148–157,  DOI:10.1364/OPTICA.545195.
28. P. Hamm, Coherent Effects in Femtosecond Infrared Spectroscopy, Chem. Phys., 1995, 200(3), 415–429,  DOI:10.1016/0301-0104(95)00262-6.
29. Y. Huang, C. T. Rettner, D. J. Auerbach and A. M. Wodtke, Vibrational Promotion of Electron Transfer, Science, 2000, 290(5489), 111–114,  DOI:10.1126/science.290.5489.111.
30. J. Bredenbeck, J. Helbing and P. Hamm, Labeling Vibrations by Light: Ultrafast Transient 2D-IR Spectroscopy Tracks Vibrational Modes during Photoinduced Charge Transfer, J. Am. Chem. Soc., 2004, 126(4), 990–991,  DOI:10.1021/ja0380190.
31. T. L. Courtney, Z. W. Fox, K. M. Slenkamp and M. Khalil, Two-Dimensional Vibrational-Electronic Spectroscopy, J. Chem. Phys., 2015, 143(15), 154201,  DOI:10.1063/1.4932983.
32. B. Xiang, R. F. Ribeiro, M. Du, L. Chen, Z. Yang, J. Wang, J. Yuen-Zhou and W. Xiong, Intermolecular Vibrational Energy Transfer Enabled by Microcavity Strong Light–Matter Coupling, Science, 2020, 368(6491), 665–667,  DOI:10.1126/science.aba3544.
33. C. Grieco, E. R. Kennehan, H. Kim, R. D. Pensack, A. N. Brigeman, A. Rimshaw, M. M. Payne, J. E. Anthony, N. C. Giebink, G. D. Scholes and J. B. Asbury, Direct Observation of Correlated Triplet Pair Dynamics during Singlet Fission Using Ultrafast Mid-IR Spectroscopy, J. Phys. Chem. C, 2018, 122(4), 2012–2022,  DOI:10.1021/acs.jpcc.7b11228.
34. E. Biasin, Z. W. Fox, A. Andersen, K. Ledbetter, K. S. Kjær, R. Alonso-Mori, J. M. Carlstad, M. Chollet, J. D. Gaynor, J. M. Glownia, K. Hong, T. Kroll, J. H. Lee, C. Liekhus-Schmaltz, M. Reinhard, D. Sokaras, Y. Zhang, G. Doumy, A. M. March, S. H. Southworth, S. Mukamel, K. J. Gaffney, R. W. Schoenlein, N. Govind, A. A. Cordones and M. Khalil, Direct Observation of Coherent Femtosecond Solvent Reorganization Coupled to Intramolecular Electron Transfer, Nat. Chem., 2021, 13(4), 343–349,  DOI:10.1038/s41557-020-00629-3.
35. P. P. Roy, C. Leonardo, K. Orcutt, C. Oberg, G. D. Scholes and G. R. Fleming, Infrared Signatures of Phycobilins within the Phycocyanin 645 Complex, J. Phys. Chem. B, 2023, 127(20), 4460–4469,  DOI:10.1021/acs.jpcb.3c01352.
36. C. Grieco, G. S. Doucette, K. T. Munson, J. R. Swartzfager, J. M. Munro, J. E. Anthony, I. Dabo and J. B. Asbury, Vibrational Probe of the Origin of Singlet Exciton Fission in TIPS-Pentacene Solutions, J. Chem. Phys., 2019, 151(15), 154701,  DOI:10.1063/1.5116586.
37. A. G. Lambert, P. B. Davies and D. J. Neivandt, Implementing the Theory of Sum Frequency Generation Vibrational Spectroscopy: A Tutorial Review, Appl. Spectrosc. Rev., 2005, 40(2), 103–145,  DOI:10.1081/ASR-200038326.
38. H. Arnolds and M. Bonn, Ultrafast Surface Vibrational Dynamics, Surf. Sci. Rep., 2010, 65(2), 45–66,  DOI:10.1016/j.surfrep.2009.12.001.
39. L. Velarde and H.-F. Wang, Unified Treatment and Measurement of the Spectral Resolution and Temporal Effects in Frequency-Resolved Sum-Frequency Generation Vibrational Spectroscopy (SFG-VS, Phys. Chem. Chem. Phys., 2013, 15(46), 19970–19984,  10.1039/C3CP52577E.
40. T. L. Courtney; Z. W. Fox; K. M. Slenkamp; M. S. Lynch and M. Khalil, in Two-Dimensional Fourier Transform Infrared-Visible and Infrared-Raman Spectroscopies, Ultrafast Phenomena XIX, ed. Yamanouchi, K., Cundiff, S., de Vivie-Riedle, R., Kuwata-Gonokami, M., DiMauro, L., Springer International Publishing, Cham, 2015, pp. 503–505 DOI:10.1007/978-3-319-13242-6_123.
41. S. Nihonyanagi, S. Yamaguchi and T. Tahara, Ultrafast Dynamics at Water Interfaces Studied by Vibrational Sum Frequency Generation Spectroscopy, Chem. Rev., 2017, 117(16), 10665–10693,  DOI:10.1021/acs.chemrev.6b00728.
42. A. Stefanachi, F. Leonetti, L. Pisani, M. Catto and A. Carotti, Coumarin: A Natural, Privileged and Versatile Scaffold for Bioactive Compounds, Molecules, 2018, 23(2), 250,  DOI:10.3390/molecules23020250.
43. D. Egan, R. O’kennedy, E. Moran, D. Cox, E. Prosser and R. D. Thornes, The Pharmacology, Metabolism, Analysis, and Applications of Coumarin and Coumarin-Related Compounds, Drug Metab. Rev., 1990, 22(5), 503–529,  DOI:10.3109/03602539008991449.
44. B. G. Lake, Coumarin Metabolism, Toxicity and Carcinogenicity: Relevance for Human Risk Assessment, Food Chem. Toxicol., 1999, 37(4), 423–453,  DOI:10.1016/S0278-6915(99)00010-1.
45. A. Lacy and R. O’Kennedy, Studies on Coumarins and Coumarin-Related Compounds to Determine Their Therapeutic Role in the Treatment of Cancer, Curr. Pharm. Des., 2004, 10(30), 3797–3811,  DOI:10.2174/1381612043382693.
46. C. Kontogiorgis, A. Detsi and D. Hadjipavlou-Litina, Coumarin-Based Drugs: A Patent Review (2008 – Present), Expert Opin. Ther. Pat., 2012, 22(4), 437–454.
47. S. V. Gagliotti Vigil de Mello and T. S. Frode, In Vitro and In Vivo Experimental Model-Based Approaches for Investigating Anti-Inflammatory Properties of Coumarins, Curr. Med. Chem., 2018, 25(12), 1446–1476,  DOI:10.2174/0929867324666170502122740.
48. Y. Lu, J. Qi, X. Dong, W. Zhao and W. Wu, The in Vivo Fate of Nanocrystals, Drug Discovery Today, 2017, 22(4), 744–750,  DOI:10.1016/j.drudis.2017.01.003.
49. A. Estévez-Braun and A. G. González, Coumarins, Nat. Prod. Rep., 1997, 14(5), 465–475,  10.1039/NP9971400465.
50. X.-M. Peng, G. L. V. Damu and C.-H. Zhou, Current Developments of Coumarin Compounds in Medicinal Chemistry, Curr. Pharm. Des., 2013, 19(21), 3884–3930,  DOI:10.2174/1381612811319210013.
51. A. Mukhtar, A. Mansha, S. Asim, A. Shahzad and S. Bibi, Excited State Complexes of Coumarin Derivatives, J. Fluoresc., 2022, 32(1), 1–17,  DOI:10.1007/s10895-021-02807-z.
52. T. L. Courtney, Z. W. Fox, L. Estergreen and M. Khalil, Measuring Coherently Coupled Intramolecular Vibrational and Charge-Transfer Dynamics with Two-Dimensional Vibrational–Electronic Spectroscopy, J. Phys. Chem. Lett., 2015, 6(7), 1286–1292,  DOI:10.1021/acs.jpclett.5b00356.
53. J. D. Gaynor and M. Khalil, Signatures of Vibronic Coupling in Two-Dimensional Electronic-Vibrational and Vibrational-Electronic Spectroscopies, J. Chem. Phys., 2017, 147(9), 094202,  DOI:10.1063/1.4991745.
54. C. M. Loe, S. Chatterjee, R. B. Weakly and M. Khalil, Observing Vibronic Coupling in a Strongly Hydrogen Bonded System with Coherent Multidimensional Vibrational–Electronic Spectroscopy, J. Chem. Phys., 2024, 161(17), 174203,  DOI:10.1063/5.0226236.
55. K. Ishii, S. Takeuchi and T. Tahara, Infrared-Induced Coherent Vibration of a Hydrogen-Bonded System: Effects of Mechanical and Electrical Anharmonic Couplings, J. Chem. Phys., 2009, 131(4), 044512,  DOI:10.1063/1.3181777.
56. J. Guan, R. Wei, A. Prlj, J. Peng, K. Lin, J. Liu, H. Han, C. Corminboeuf, D. Zhao, Z. Yu and J. Zheng, Direct Observation of Aggregation-Induced Emission Mechanism, Angew. Chem., Int. Ed., 2020, 59(35), 14903–14909,  DOI:10.1002/anie.202004318.
57. H. Chen, H. Bian, J. Li, X. Wen and J. Zheng, Ultrafast Multiple-Mode Multiple-Dimensional Vibrational Spectroscopy, Int. Rev. Phys. Chem., 2012, 31(4), 469–565,  DOI:10.1080/0144235X.2012.733116.
58. M. D. Morse, A. C. Puiu and R. E. Smalley, Intramolecular Vibrational Relaxation: Effects on Electronic Nonradiative Relaxation Rates, J. Chem. Phys., 1983, 78(6), 3435–3444,  DOI:10.1063/1.445218.
59. P. M. Felker and A. H. Zewail, Picosecond Time-Resolved Dynamics of Vibrational-Energy Redistribution and Coherence in Beam-Isolated Molecules, 1988, vol. 70, pp. 265–364.
60. H.-J. Hübner, M. Wörner, W. Kaiser and A. Seilmeier, Subpicosecond Vibrational Relaxation of Skeletal Modes in Polyatomic Molecules, Chem. Phys. Lett., 1991, 182(3), 315–320,  DOI:10.1016/0009-2614(91)80221-I.
61. J. C. Owrutsky, D. Raftery and R. M. Hochstrasser, Vibrational Relaxation Dynamics in Solutions, Annu. Rev. Phys. Chem., 1994, 45, 519–555,  DOI:10.1146/annurev.pc.45.100194.002511.
62. V. M. Kasyanenko, S. L. Tesar, G. I. Rubtsov, A. L. Burin and I. V. Rubtsov, Structure Dependent Energy Transport: Relaxation-Assisted 2DIR Measurements and Theoretical Studies, J. Phys. Chem. B, 2011, 115(38), 11063–11073,  DOI:10.1021/jp2066315.
63. M. Cho, Molecular Photothermal Effects on Time-Resolved IR Spectroscopy, J. Chem. Phys., 2022, 157(12), 124201,  DOI:10.1063/5.0108826.

---