Non-Phenomenological Description of the Time-Resolved Emission in Solution with Quantum–Classical Vibronic Approaches—Application to Coumarin C153 in Methanol

Round 1

Reviewer 1 Report

Non-Phenomenological Description of the Time-Resolved Emission in Solution with Quantum-Classical Vibronic Approaches. Application to Coumarin C153 in Methanol

In this study, the authors present an excellent experiment-theory study on the steady-state spectroscopy and time resolved emission of the prototypical system, coumarin C153 dye, in methanol.  The study combines a the quantum-classical approach, the Adiabatic Molecular Dynamics generalized Vertical Hessian method, with non-equilibrium molecular dynamics simulations. The goal of this study is to predict transient emission spectral shapes, including both vibronic and solvent effects, without applying any phenomenological broadening.  Overall, this is excellent and thorough research that would be welcomed by the spectroscopy community. The authors also present the research in great detail.

I just have one comment, which I think will strengthen the paper. In the computation of the emission spectrum using TDDFT, is this computed using the S1 minimum geometry followed by a TDDFT calculation using the corresponding reference wavefunction on the S0 surface ?  or is TDDFT performed using the S1 minimum geometry with the S1 reference wavefunction, which may be computed using the maximum overlap approach by swapping the relevant orbitals and reconverging the SCF.

Author Response

Reviewer 1

In this study, the authors present an excellent experiment-theory study on the steady-state spectroscopy and time resolved emission of the prototypical system, coumarin C153 dye, in methanol.  The study combines a quantum-classical approach, the Adiabatic Molecular Dynamics generalized Vertical Hessian method, with non-equilibrium molecular dynamics simulations. The goal of this study is to predict transient emission spectral shapes, including both vibronic and solvent effects, without applying any phenomenological broadening.  Overall, this is excellent and thorough research that would be welcomed by the spectroscopy community. The authors also present the research in great detail.

I just have one comment, which I think will strengthen the paper. In the computation of the emission spectrum using TDDFT, is this computed using the S1 minimum geometry followed by a TDDFT calculation using the corresponding reference wavefunction on the S0 surface?  or is TDDFT performed using the S1 minimum geometry with the S1 reference wavefunction, which may be computed using the maximum overlap approach by swapping the relevant orbitals and reconverging the SCF.

Reply: We thank the Reviewer for her/his nice comments, and for having appreciated the quality of our work. As far has the last suggestion is concerned, it should be first pointed out that, for the computation of the emission spectrum,  we only use the S1 optimized geometry when adopting the “static” approach, whereas in both the CEA-VE and Ad-MD|gVH protocols each spectrum contributing to the average is computed at a thermally equilibrated geometry, extracted from the MD runs and hence not at the equilibrium.

In the former case, where the S1 minimum geometry is employed, the details of the static vibronic approach are given at page 4 (lines 150-158) in the Materials and Methods section : “The optimized, state-specific geometries were employed together with their corresponding Hessian matrices to build up harmonic model PESs and compute the vibronically resolved static spectra with the vertical Hessian (VH) model, which accounts for the effects of normal mode mixings (Duschinsky rotation)[85] on the spectra and it is based on a Taylor expansion of both the initial and final-state PES at the initial-state geometry up to the quadratic terms. Moreover, the Franck-Condon (FC) approach was also applied, an approximation fully adequate due to the brightness of the electronic transition.”

Reviewer 2 Report

The authors studied excited state dynamics of coumarin 153 (C153) and the subsequent solvation process using time-resolved absorption/emission spectroscopy and theoretical calculations. In the theoretical part, they precisely treated solvent effect on the intramolecular charge transfer of C153 beyond the polarizable continuum model. Transient absorption and emission spectroscopies tracked the excited state dynamics in the femtosecond to nanosecond time region. Finally, the analysis based on the radial distribution function revealed non-equilibrium dynamics of solution structure triggered by emergence of the excited state. Although the present study focuses on the model compound, coumarin 153, I think that the results and discussions shown in the manuscript are reliable and valuable in the viewpoint of fundamental physical chemistry, this manuscript may be publishable in Molecules after minor revision shown below.

1.      The authors parameterized QMD-FFs respectively for the S0 and S1 states of C153. I guess that the point charges are constant during the simulation. But the actual charge transfer dynamics proceeds in parallel with the solvation process in a mutual manner. Namely, the charge transfer induces with orientation polarization due to the solvation, and the solvation further increase the degree of charge transfer. In this context, please comment on the validity of the approach in the present work.

2.      Fig. 7 caption is a little bit fuzzy to me. These spectra are inversion of the transient absorption spectra and contain contribution of excited state absorption and ground state bleaching (around 2.75 eV). Thus, “transient emission spectra” in the caption is not accurate. Although the derivation of the spectra is shown in the main text, I recommend that it is also shown in the caption.

3.      Something is wrong with Fig. 7 caption. Dashed lines are missing.

4.      In page 12, the authors compared calculated emission spectra with the stimulated emission and steady-state emission spectra. In the experimental viewpoint, I would like to comment that the spectral shape is affected by (1) spectral overlap of excited state absorption and (2) different transition probability of spontaneous emission and stimulated emission (Einstein A and B coefficients). First, the stimulated emission band in Figure 7 is overlapped with the excited state absorption and ground state bleaching, and it makes the spectra narrower especially in the longer wavelength region. Second, due to the relation between Einstein A and B coefficients, the stimulated emission spectra extend up to longer wavelength than the corresponding spontaneous emission. Please comment on this issue for the spectral comparison.

Author Response

Reviewer 2

The authors studied excited state dynamics of coumarin 153 (C153) and the subsequent solvation process using time-resolved absorption/emission spectroscopy and theoretical calculations. In the theoretical part, they precisely treated solvent effect on the intramolecular charge transfer of C153 beyond the polarizable continuum model. Transient absorption and emission spectroscopies tracked the excited state dynamics in the femtosecond to nanosecond time region. Finally, the analysis based on the radial distribution function revealed non-equilibrium dynamics of solution structure triggered by emergence of the excited state. Although the present study focuses on the model compound, coumarin 153, I think that the results and discussions shown in the manuscript are reliable and valuable in the viewpoint of fundamental physical chemistry, this manuscript may be publishable in Molecules after minor revision shown below.

Reply: We thank the Reviewer for the global positive judgement of our work. A point-by-point reply to his/her questions follows.

1. The authors parameterized QMD-FFs respectively for the S0 and S1 states of C153. I guess that the point charges are constant during the simulation. But the actual charge transfer dynamics proceeds in parallel with the solvation process in a mutual manner. Namely, the charge transfer induces with orientation polarization due to the solvation, and the solvation further increase the degree of charge transfer. In this context, please comment on the validity of the approach in the present work.

Reply: The Reviewer is right: the excited state charges during the MD simulations are fixed and are the charges that we calculated at the optimized S1 geometry with linear response PCM in equilibrium regime. (The usage of LR and equilibrium regime is now specified at page 7 of the revised manuscript). During the non-equilibrium run, therefore, the solute charges correspond to the “equilibrium” excited state charges, where the charge transfer has been stabilized by the presence of an equilibrated polarizable medium. Clearly, as argued by the Reviewer, by using “equilibrated” charges we lose the mutual polarization between solvent and solute along the non-equilibrium dynamic. The use QM/MM approaches combined with polarizable force fields would be able to capture these effects by providing a finer description of the solvent-solute equilibration dynamic following the S0 S1 excitation. Although this is beyond the scope of our work., we want to stress that the QM treatment of the first solvation shell when calculating the spectra, however, partially reintroduce the solute-solvent electronic polarization. The following comment has been added at pages 10-11 in the manuscript.

“It is worthwhile to stress that the effects of the mutual polarization of the solute and the solvent are not included in the MD, since charges are frozen, and a QM/MM dynamics would be required, ideally with a polarizable FF. Notwithstanding this, application of Ad- MD| gVH allows to introduce these effects on the vibronic Hamiltonians that describe the motion of the stiff degrees of freedom. In fact, according to all the three models listed above, these Hamiltonians are built with QM calculations of energies, forces and Hessians that take into account the solute polarization due to the instantaneous position of the solvent. In addition, when models II or III are employed, such vibronic Hamiltonians do account also for the solute/solvent mutual polarization, either considering only the first solvation sphere (model II) or also the average impact of the outer spheres (with PCM, model III).”

2. 7 caption is a little bit fuzzy to me. These spectra are inversion of the transient absorption spectra and contain contribution of excited state absorption and ground state bleaching (around 2.75 eV). Thus, “transient emission spectra” in the caption is not accurate. Although the derivation of the spectra is shown in the main text, I recommend that it is also shown in the caption.

Reply: We thank the Reviewer for her/his careful reading and spotting out the misleading caption of Figure 7. Following her/his suggestion, the caption of Figure 7 has been changed as follows:

“Figure 7. Comparison between lineshapes of the experimental transient absorption spectra (exp, top panel) and the computed time resolved emission spectra (comp, bottom panel). All signals refer to the C153 dye at 1 atm and 300 K, in methanol solution, which in the computed spectra is accounted through model II. Note that to ease the comparison, all experimental signals were turned to positive and, in line with steady-state emission, all computed spectra were shifted by -0.23 eV.”

3. Something is wrong with Fig. 7 caption. Dashed lines are missing.

Reply: We apologize for this inaccuracy: the caption referred to a previous version of the figure. The whole caption has now been corrected as discussed in the previous point.

4. In page 12, the authors compared calculated emission spectra with the stimulated emission and steady-state emission spectra. In the experimental viewpoint, I would like to comment that the spectral shape is affected by (1) spectral overlap of excited state absorption and (2) different transition probability of spontaneous emission and stimulated emission (Einstein A and B coefficients). First, the stimulated emission band in Figure 7 is overlapped with the excited state absorption and ground state bleaching, and it makes the spectra narrower especially in the longer wavelength region. Second, due to the relation between Einstein A and B coefficients, the stimulated emission spectra extend up to longer wavelength than the corresponding spontaneous emission. Please comment on this issue for the spectral comparison.

Reply: The Reviewer is right in her/his comments on the comparison between calculated emission spectra and experimental spectra (both stimulated and steady-state emission spectra). Since TA spectra are given by the sum of SE, GSB and excited state absorption, all these components have to be considered when “turning them to positive” and compare their shapes with calculated emission spectra. While GSB can affect the high energy region of the spectra, transient absorption can affect the lower energy region of the spectra, leading to an apparent lower intensity of the red wing of the experimental spectra with respect to the calculated ones (Figure 7). The same effect can be observed in the comparison between the experimental SE emission, derived from TA spectra, and the experimental spontaneous steady-state emission (Figure S10). An opposite trend could be expected in this region, since SE can be observable at longer wavelengths than spontaneous emission (C. Ruckebusch et al. J. Photochem. Photobiol. C 2012, 13, 1 – 27), so that the contribution of excited state absorption is likely responsible for the observation of an apparent opposite trend.

 To render these points clearer, we added the following sentences in the discussion at page 13:

“It can be noted that, in TA spectra, SE features are superimposed with GSB and excited state absorption. The latter contribution can explain the reduced intensity of the SE red wing in the experimental spectra with respect to the simulated SE ones (Figure 7).”

“The latter discrepancy can be attributed to the contribution of excited state absorption in the low energy region of the TA spectrum, that apparently lowers the red tail of SE emission.”

Concerning the different transition probability of spontaneous and stimulated emission, connected to the different A and B Einstein coefficients, we would like to point out that we reported all spectra both computed and experimental (the latter one after transformation from the wavelength to the frequency domain) as lineshapes L(w) (where for absorption and stimulated emission L(w)=S(w)/w, whereas for spontaneous emission L(w)=S(w)/w³) so that lineshapes do not carry anymore a different dependence of the transition probability on the frequency and are actually directly proportional to the dipole strength of the transitions. This is now indicated more explicitly in a new sentence at page 11:

“This is done by transforming the quantum distribution of emitted photons Φ(λ) in the frequency domain (Φ(ω)).[104 , 105 ] Moreover both absorption and emission spectra are reported as lineshapes (Labs(ω) = ω−1ε(ω) and for spontaneous emission Lemi (ω) = ω−3Φ(ω)), so that both quantities are directly proportional to the dipole strengths of the underlying vibronic transitions.[61 , 104] When comparing absorption and emission, the usage of lineshapes is particularly attractive because, they are mirror symmetric in the limiting case of simply displaced normal modes.[61,106]”