Excited-State Energy Surfaces in Molecules Revealed by Impulsive Stimulated Raman Excitation Profiles

Photophysical and photochemical processes are ruled by the interplay between transient vibrational and electronic degrees of freedom, which are ultimately determined by the multidimensional potential energy surfaces (PESs). Differences between ground and excited PESs are encoded in the relative intensities of resonant Raman bands, but they are experimentally challenging to access, requiring measurements at multiple wavelengths under identical conditions. Herein, we perform a two-color impulsive vibrational scattering experiment to launch nuclear wavepacket motions by an impulsive pump and record their coupling with a targeted excited-state potential by resonant Raman processes with a delayed probe, generating in a single measurement background-free vibrational spectra across the entire sample absorption. Building on the interference between the multiple pathways resonant with the excited-state manifold that generate the Raman signal, we show how to experimentally tune their relative phase by varying the probe chirp, decoding nuclear displacements along different normal modes and revealing the multidimensional PESs. Our results are validated against time-dependent density functional theory.


Impulsive Stimulated Raman Spectroscopy maps
In Figure S1 we report cresyl violet ISRS spectra obtained with a negatively chirped (C 2 = -80 fs 2 ) broadband resonant PP as a function of the time delay between Raman and probe pulses and the corresponding map in the frequency domain. Figure S1: Cresyl Violet broadband two-color ISRS signal in time domain as a function of the probe wavelength λ P and RP-PP relative delay ∆T (left panel) measured for a negatively chirped PP (C 2 = -80 fs 2 ). The blue box indicates the region covered by the coherent artifact. The corresponding spectrum in the frequency domain has been obtained upon FFT and is reported in the right panel. The region around 592 cm −1 has been scaled by a factor 0.1 to enhance the visibility of the weaker Raman modes.

Chirp Measurement
The measurement of the PP chirp can be performed using the Coherent Artifact (CA) signal generated within the temporal overlap of two pulses, the Raman and the probe in our case, S2 inside the sample, identifying a wavelength dependent time delay between the two beams as where [−τ λs , +τ λs ] are the wavelength-dependent time window containing the CA. An alternative approach to t the wavelength dependent delay∆T 0 (λ P ) is to exploit the time-domain ISRS signal generated by the solvent. This latter can be isolated applying a lter centered around the 1040 cm −1 Raman mode of the solvent to the frequency domain data and anti-Fourier transforming. The slope of the coherent oscillation in the resulting trace (reported in Fig. S2) can be exploited to extract∆T 0 (λ P ). Finally the probe chirp can be evaluated Sample Absorption In Fig. S3, the absorption spectrum of methanol and aqueous CV solutions are compared.
Interestingly, the aqueous solution shows a blue shifted more pronounced shoulder, indicating higher displacements between the ground and the excited potential energy surfaces.
where µ ij indicate the dipole moment between the i and j states and where we have considered only exponential dephasing of the |i j| coherences:

S4
More generally, considering an additional inhomogeneous dephasing function G(τ ) for the electronic coherence |e k g|, we have In the present work we have considered Gaussian dephasing functions G(τ ) with a standard deviation equal to 330 cm −1 , while the Lorentzian broadening is equal to 70 cm −1 .
The Raman and the probe pulses in the time domain can be expressed by anti-Fourier as a function of their representation in the frequency domain: where E (0) R (ω) and E (0) P (ω) are the square of the RP-PP spectra, respectively. By Fourier transforming Eq. S4 over t, we can obtain the third order nonlinear polarization in the frequency domain, which reads as Expressing also the inhomogeneous dephasing function in terms of their representation in S5 the frequency domain G( By integrating over t, τ 1 , τ 2 and τ 3 , we have where the δ(ω − ω 1 + ω 2 − ω 3 ) represents the energy conservation and can be exploited to solve the integral over ω 3 : that can be expressed also as introducing the new variable ∆ = ω 1 − ω 2 .
By dening the RP preparation function By similar steps, the nonlinear polarization of diagram B k can be expressed as S8 been extracted xing the eigenfrequencies equal to the ground state, while for the dashed lines they have been set as a tting parameter. In Fig. S5, the TD-DFT calculated electron density dierence (EDD) map is reported in order to evaluate the relation between the electronic structure and excited state displacements. The EDD indicates a modication of the electron density in the excited state around the oxazine oxygen and nitrogen atoms, which have strong displacement along the 592 cm −1 normal mode (Fig. S4). Figure S5: Electron density dierence map between the ground and the excited state calculated using CAM-B3LYP functional and 6-311++G(2d,2p) basis set Table 1: Peak positions and displacements between ground and excited state PESs are reported with the corresponding 90% condence intervals. In the third column we report the CAM-B3LYP eigenfrequencies obtained using the CAM-B3LYP functional and the 6-311++G(2d,2p) basis set, 7 while in the fourth one the corresponding displacements along the dierent normal coordinates.