Resonance Raman Spectroscopy

3.5. Resonance Raman Spectroscopy

Figure 3.5.2.:Upper panel: Computed non-resonant Raman spectrum of Uracil in gas phase(green)and water(black)compared to experiment⁴³⁰(red); Lower panel:

Computed resonance Raman spectrum of Uracil in gas phase (green) and water(black)at 340 nm compared to experiment⁴³¹at 266 nm(red).^MB36

As the next step, we discuss the resonance Raman spectrum. In the bottom panel of Figure 3.5.2, we show the AIMD-based spectra of uracil in gas phase and aqueous solution together with an experimental resonance Raman spectrum.⁴³¹While the experiment was conducted with a laser energy of 4.66 eV / 266 nm, we used a value of 3.65 eV / 340 nm in our prediction. This difference can be explained by the fact that GGA functionals often underestimate electronic excitation energies, and is therefore not related to our method. Our approach works also with hybrid functionals, where the agreement between experimental and computed excitation energies is known to be far better.

Similarly to the non-resonant case above, the predicted spectrum of the gas phase system(green curve in bottom panel of Figure 3.5.2)shows some significant deviations from experiment(red curve), while the bulk phase simulation(black curve)is in very good agreement with the experimental spectrum. This was the firstab initio predic-tion of a liquid phase resonance Raman spectrum in the literature. We conclude that for both non-resonant and resonance Raman spectra, it is definitely required to take the solvent influence explicitly into account in the case of uracil. When comparing the ordinate axes in both panels of Figure 3.5.2, it is visible that the absolute signal intensity is increased by around three orders of magnitude due to the resonance Raman effect, as also observed in the experiment.⁴³¹

As described in Section 2.10, our computational approach does no only yield the resonance Raman spectrum for one laser wavelength at a time—it predicts all resonance Raman spectra for all possible laser wavelengths in one pass. Based on this information, an excitation profile can be created. This is a contour plot with the vibrational frequency on the horizontal axis and the laser wavelength on the vertical axis—see Figure 3.5.3.^MB36,MB40

Figure 3.5.3.:Predicted excitation profile of uracil in water, i. e., resonance Raman spectra for all possible laser wavelengths (vertical axis).^MB36,MB40 Rows are normalized to show relative intensity ratio.

Such an excitation profile is not only helpful to understand the coupling between vibrational modes and electronic excitations(vibronic coupling)in the system

inves-3.5. Resonance Raman Spectroscopy

tigated, but can even help to design new interesting experiments by picking laser wavelengths at which interesting resonance effects can be expected. In the lower part of the contour plot, the non-resonant Raman spectrum is reproduced, while the intensity ratio between the spectral bands changes drastically in the resonant upper part of the plot.

We can conclude that—by using our novel approach—it is now possible to di-rectly compute resonance Raman spectra of bulk phase systems. This has not been achieved before to the best of our knowledge, therefore constituting an important contribution to the field of computational vibrational spectroscopy. In contrast to existing methods, our approach includes the full solvent influence and some anhar-monic effects. We have computed the resonance Raman spectrum of an aqueous solution of uracil and find that it is in very good agreement with the experiment.

The computational protocol for the prediction of the spectra was as follows. For the bulk phase simulation, one uracil molecule was placed in a cubic box together with 32 water molecules (cell size ≈ 1050pm), and a force field pre-equilibration in NpT ensemble was carried out to converge the density. A snapshot of the sim-ulation cell is shown in Figure 3.5.4. For the gas phase simsim-ulation, these steps were skipped. Subsequently, BOMD simulations of both systems at a temperature of 300 K were started with CP2k. After another equilibration interval, production runs of 20 ps were performed. More computational details for these steps are de-scribed in Section 3.7 below.

Figure 3.5.4.:Snapshot of the simulation cell for predicting the bulk phase resonance Raman spectrum of uracil in water.^MB36

From these BOMD production trajectories, snapshots were taken every 2.5 fs (i. e., every 5 steps), so that 8 000 snapshots per system resulted. For each of these snap-shots, a real-time propagation run (RTP)³⁷² was started with CP2k.^212–214 The initial wave function for the propagation was optimized under the influence of an external periodic electric field in X, Y, and Z direction. For each field direction, a separate RTP run was performed. The absolute value of the electric field amounted to|E|=_5.0·10⁻⁴a.u.=_2.57·10⁸V m⁻¹. Directly in the beginning of the RTP runs, the electric field was switched off (step response). The propagation time step was set to 0.0125 fs, and 1 280 steps were performed (i. e., 16 fs of total physical time).

In the RTP runs, we chose EPS_DEFAULT to 10⁻¹⁰ and EPS_ITER to 10⁻⁶. Every 0.0625 fs (i. e., every 5 propagation steps), the total electron density was written to disk in Gaussian Cube file format, so that 256 frames per BOMD snapshot resulted.

The spatial resolution of the volumetric grid was 108×108×108 for all three systems. The Cube files were compressed to bqb format^MB34 directly after each RTP run. The computational cost was 1 350 core hours for the BOMD production run, 230 000 core hours for the RTP runs, and 430 core hours for compressing the electron density and performing the Voronoi integration. The resonance Raman spectra were calculated as described in Section 2.10 above.

3.5. Resonance Raman Spectroscopy

ortho-Nitrophenol in Gas Phase

In addition to uracil, we computed resonance Raman spectra foro-nitrophenol in the gas phase. Resonance Raman spectra of this system have been investigated in the literature before,^76,376 in particular also by means of RT-TDDFT within the static–harmonic approximation.³⁷⁶ In Figure 3.5.5, we compare the spectra from our approach (black curves)to these previously reported results (red bars)for two different laser wavelengths. The top and bottom panels correspond to the non-resonant and non-resonant regime, respectively. As expected, there are some differences because the AIMD-based spectra take into account some anharmonic effects which are completely missing in the static spectra. This leads both to shifts in band positions and to line broadening which alters the peak heights. Apart from these effects, we find that the change in relative band intensities and the total increase in intensity due to the resonance Raman effect is captured by our approach very well.

Figure 3.5.5.:Resonance Raman spectra of o-nitrophenol in the gas phase pre-dicted from AIMD^MB36(black curves)compared to results from static–

harmonic calculations³⁷⁶ (red bars) for two different laser energies (see panels). Note the change in intensity due to the resonance effect.

As explained above, our method does not require a set of laser energies as input, but yields the resonance Raman spectra for all possible laser energies in one pass.

In Figure 3.5.6, we present the set of all such spectra foro-nitrophenol, with the laser energy on the ordinate axis, and the vibrational frequency shown on the abscissa. Each spectrum (i. e., each row of the plot) has been normalized to uniform maximum band height, because otherwise the non-resonant spectra would not be visible at all due to the strong increase in intensity caused by the resonance Raman effect. It is clearly visible how bands which are almost invisible in the non-resonant Raman spectrum become very intense at certain laser energies (e. g., the bands at 850, 1050, and 1600 cm⁻¹). Such an increase in intensity only happens if the spectral band involves movement of atoms which take part in the electronic excitation at a given laser energy(vibronic coupling).

Figure 3.5.6.:Predicted excitation profile of o-nitrophenol in the gas phase,i. e., resonance Raman spectra for all possible laser wavelengths(vertical axis).^MB36Rows are normalized to show relative intensity ratio.