## 3 Results and Discussion
### Ground-State FSRS of Laser Dye LD390  
To demonstrate the feasibility of the aforementioned UV-FSRS setup, we select LD390 as the molecular sample system because this laser dye in methanol strongly absorbs 355 nm light, while the solvent only has two major Raman peaks at \(\sim\)1033 and 1460 cm\({}^{-1}\). To our best knowledge, the standard or spontaneous Raman spectrum of LD390 has not been reported, so the measurement here represents a new spectroscopic characterization of this commercial laser dye molecule and its vibrational motions in solution. After equal amount of solution and solvent data collection, average and subtraction which remove most of the systematic noise and laser fluctuation effect, the pure ground-state Raman spectrum of LD390 is shown in Figure 3a that has a number of prominent peaks between _ca_. 300-1700 cm\({}^{-1}\). These are Stokes Raman spectra because the probe pulse is S\({}_{-1}\) on the WL side (Figure 1) and to the red of the pump pulse (Figure 2b). Based on the UV/Vis spectrum in Figure 3a insert, the 402 nm Raman pump represents the closest frequency position to the electronic absorption peak (_i.e._, 355 nm) among the three Raman pump wavelengths being used, and the pre-resonance enhancement factor reaches \(>\)21 at the 1317/1348 cm\({}^{-1}\) peak doublet while all the other experimental conditions are unchanged. The observed peak intensity decreases if the Raman pump wavelength is tuned away from the electronic absorption peak position. Notably, minimal interference below 400 cm\({}^{-1}\) makes it feasible to study lower frequency regime of the Raman spectrum. This likely arises from good solubility of the dye molecule in methanol and less Raman pump scattering into the Raman probe beampath (_i.e._, FSRS signal direction) [11,13]. \begin{table}
\begin{tabular}{c c c} \hline \(S_{\text{\text{\text{\text{\text{\textasci  
Since the standard Raman spectrum of LD390 is not readily available from literature and it is useful to correlate observed peaks to characteristic nuclear motions, we perform electronic ground-state DFT calculations in _Gaussian_ program [26] to facilitate vibrational normal mode assignment. The overall match between the experimental and calculated spectrum is very good with a frequency scaling factor of 0.99 [37]. The major vibrational modes are listed in Table 1. Notably, the correspondence between the calculated Raman spectrum and the measured one is not exact (Figure 3). This is understandable because the Gaussian DFT calculation concerns an \"unrestricted\" single molecule in a polarizable continuum to model solvation effects (_i.e._, we used IEFPCM-methanol, see above). In the real spectroscopic measurement, the ensemble average of solvated dye molecules LD390 in methanol solution is measured and the Raman mode polarizability is intimately determined by the extensive hydrogen (H)-bonding network around the chromophore. For example, the calculated strong modes between _ca._ 1450-1600 cm\({}^{-1}\) (see Figure 3b) become much weaker in the ground-state FSRS spectrum (Figure 3a), suggesting that the corresponding mode polarizability decreases significantly and/or mode frequency shifts as a result of H-bonding matrix. It is also notable that the two strongest peaks observed at \(\sim\)1317, 1348 cm\({}^{-1}\) both consist of C-N stretching and ring-H rocking motions plus ring  
Figure 3: Ground-state Stokes FSRS of LD390 in methanol. (**a**) Experimental stimulated Raman spectra in S\({}_{0}\) with the Raman pump at 550 nm (green), 487 nm (blue), and 402 nm (violet) and Raman probe to its red side, respectively. The former two spectral traces are enlarged by 5 times for direct comparison with the spectrum collected with 402 nm pump. Prominent vibrational peaks are marked with frequencies labeled in black. The UV/Vis electronic absorption spectrum is shown in the insert. (**b**) Density functional theory (DFT)-based _Gaussian_ calculated spectrum of LD390 in methanol with a uniform peak width of 8 cm\({}^{-1}\) (_i.e._, default fwhm in the program).