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Exploring Nuclear Photorelaxation of Pyranine in Aqueous Solution: An Integrated Ab-Initio Molecular Dynamics and Time Resolved Vibrational Analysis Approach Maria Gabriella Chiariello, and Nadia Rega J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b12371 • Publication Date (Web): 21 Feb 2018 Downloaded from http://pubs.acs.org on February 27, 2018

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The Journal of Physical Chemistry

Exploring Nuclear Photorelaxation of Pyranine in Aqueous Solution: an Integrated Ab-Initio Molecular Dynamics and Time Resolved Vibrational Analysis Approach Maria Gabriella Chiariello,a Nadia Rega,a,b∗ a

Dipartimento di Scienze Chimiche, Università di Napoli Federico II, Complesso Universitario di M.S.Angelo, via Cintia, I-80126 Napoli, Italy

b

Interdisciplinary Research Centre on Biomaterials (CRIB) Universit` a di Napoli Federico II, Piazzale Tecchio 80, I-80125, Napoli, Italy E-mail: [email protected],phone:+39-081674207

∗

To whom correspondence should be addressed

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ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Advances in time resolved vibrational spectroscopy techniques provided a new stimulus for understanding the transient molecular dynamics triggered by the electronic excitation. The detailed interpretation of such time dependent spectroscopic signals is a challenging task from both experimental and theoretical points of view. We simulated and analyzed the transient photorelaxation of the pyranine photoacid in aqueous solution, with special focus on structural parameters and low frequency skeleton modes that are possibly preparatory for the photoreaction occurring at later time, as suggested by experimental spectroscopic studies. To this aim, we adopted an accurate computational protocol that combines excited state ab-initio molecular dynamics within an hybrid quantum mechanical/molecular mechanics framework and a time resolved vibrational analysis based on the Wavelet transform. According to our results, the main nuclear relaxation on the excited potential energy surface is completed in about 500 fs, in agreement with experimental data. The rearrangement of C-C bonds occurs according to a complex vibrational dynamics, showing oscillatory patterns that are out of phase and modulated by modes below 200 cm−1 . We also analyzed in both the ground and the excited state the evolution of some structural parameters involved in excited state proton transfer reaction, namely those involving the pyranine and the water molecule hydrogen bonded to the phenolic O-H group. Both the hydrogen bond distance and the intermolecular orientation are optimized in the excited state, resulting in a tighter proton donor-acceptor couple. Indeed, we found evidence that collective low frequency skeleton modes, such as the out of plane wagging at 108 cm-1 and the deformation at 280 cm-1 are photoactivated since the ultrafast part of the relaxation and modulate the pyranine-water molecule rearrangement, favoring the step preparatory for the photoreactivity.

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1

Introduction

Excited state proton transfer (ESPT) reactions 1–3 can occur between a photoacid molecule, acting as proton donor once the pKa value is drastically lowered upon the electronic excitation, and a proton acceptor, which is often a solvent molecule. The 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS or pyranine) is a widely studied weak photoacid, 4–10 showing a ESPT kinetics slower than other examples such those involving the N-methyl-6-hydroxyquinolinium 11 or the quinone cyanine 9. 2 Specifically, in the excited state pyranine donates a proton to a nearby solvent water molecule with time constants of 3 and 90 ps. 12 Indeed, previous studies demonstrated that pyranine photoacidity cannot be simply interpreted and explained in terms of the electronic density redistribution responding to the external perturbation. 10 High resolution time resolved vibrational spectroscopy techniques, such as femtosecond stimulated Raman spectroscopy (FSRS), are particularly suitable to watch nuclear motions of molecules in real time upon excitation. 13,14 Phototriggered reactions mechanisms can be revealed at atomistic level, also in complex environments. 15–17 FSRS experiments revealed that in the electronic excited state the pyranine chromophore shows a transient and sequential activation and decay of several low frequency (< 1000 cm-1) skeleton modes. 12,18 This peculiar vibrational activity precedes and apparently promotes the ESPT reactive event. Indeed, these modes seem to play key role in activating the ESPT, although a direct demonstration of this connection has not been given yet. As matter of fact, such experimental spectra are often very complex, and a direct molecular interpretation of the signals is not a simple task. In this context, interpretative and predictive skills of a smart theoretical protocol can be essential to clarify and complete the information experimentally accessible. In particular abinito molecular dynamics (AIMD) methods 19–21 allow for monitoring the molecular response to the photoexcitation in real time. 22–24 In the present work we simulated and analyzed the photoinduced relaxation of the pyra3



nine molecule in water solution. AIMD trajectories were collected in both the ground and the excited state for the molecular system modeled according to a hybrid quantum mechanical/molecular mechanics (QM/MM) scheme. In order to investigate the transient vibrational features of the photoexcited molecule, a time resolved multiresolution wavelet analysis was performed on signals extracted from the excited state AIMD simulation. 25–30 WT was already successfully adopted in combination with AIMD simulations in studies aimed to disentangle the time evolution of a simulated Stokes shift, 31 of the dipole moment in exciton dynamics, 32 and to analyse the evolution of structural parameters in the frequency domain. 33 Here, the wavelet analysis was applied on both key structural parameters of pyranine nuclear skeleton and vibrational modes extracted from the AIMD trajectory. We focused on structural parameters involved in excited state proton transfer reaction, namely those involving the pyranine and a water molecule hydrogen bonded to the phenolic O-H group. Moreover, we considered low frequency skeleton modes that are possibly preparatory for the photoreaction occurring at later time, as suggested by experimental spectroscopic studies. According to our findings, the main nuclear relaxation occurs in about 500 fs through a complex vibrational dynamics modulated by modes below 200 cm−1 . Importantly, during this time the pyranine-water hydrogen bond distance and the intermolecular orientation rearrange to form a tighter proton donor-acceptor couple. Two photoactivated low frequency skeleton modes, namely an out of plane at 108 cm-1 and a ring deformation at 280 cm-1 , modulate this pyranine-water molecule rearrangement. The remaining of the paper is organized as follows: in the next Section we describe details about the computational protocol adopted. In Sections 3.1-3.3 we illustrate and discuss results regarding the pyranine in aqueous solution in the ground state, the photoinduced relaxation of the pyranine and the rearrangement of the pyranine-water couple. Final remarks are given in Section 4.

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2

Methods

2.1

Simulation details

In order to take into account solvent effects on the photorelaxation of the pyranine chromophore, we adopted an hybrid explicit/implicit solvent scheme within non-periodic boundary conditions (NPBC). 34–36 The explicit description of the water solvent molecules is indeed necessary to account for solute-solvent specific interactions, especially those involving the polar (phenolic) and charged (sulfonic) groups of pyranine. Moreover, it has been hypothesized that some low frequencies skeleton modes of photoexcited pyranine play a key role in promoting the excited state proton transfer reaction toward the water molecule that is hydrogen bonded to the phenolic acid group of pyranine. Therefore, the explicit description allows for the analysis of pyranine vibrational modes that are naturally coupled to the water molecule motions (vide infra). The pyranine molecule, featuring a structure close to the energy minimum, was accommodated at the center of a sphere with radius of 19 ˚ A, and embedded by 1024 water molecules, corresponding to about three solvent shells with a a density of 1 g/cm3 . Pyranine chromophore was treated at density functional theory (DFT) level, adopting the global hybrid functional B3LYP 37–39 in combination with the 6-31g(d,p) basis set. The excited state potential energy surface was explored by the time-dependent DFT (TDDFT). 40–42 This level of theory was already validated in a previous study involving pyraninewater molecules clusters, 10 and it has proven to be reliable to describe the electronic features of the pyranine photoreactivity. The water molecules in the sphere have been represented by the TIP3P model. 43 The energy potential including QM and MM regions was combined according to the hybrid ONIOM extrapolation scheme. 44,45 In addition, NPBC have been enforced during the simulations, in order to account for the bulk solvent surrounding the sphere. NPBC avoid the dissolution of the water molecules sphere and account for the interactions between the explicit molecular

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system and the implicit bulk solvent, including both long-range electrostatic and short-range dispersion interactions. Moreover, NPBC have been specifically designed to properly represent the local density of water within the sphere during the simulations. The energy potential obtained according to the QM/MM/continuum scheme described above ruled AIMD simulations in both the ground (S0 ) and the first singlet (S1 ) excited state. The ground state sampling, representing the equilibrium conditions prior the electronic excitation, was performed by means of the atom-centered density matrix propagation (ADMP) approach. 46–49 After an equilibration time of 5 ps, the trajectory was collected for 10 ps, using a time step of 0.2 fs, keeping a constant temperature of 298 K. From the ground state equilibrium four configurations were extracted as starting points for the propagation of excited state trajectories. In particular, starting coordinates and momenta were chosen in order to represent, on average, both the chromophore structure and the microsolvation features in the ground state. Born-Oppenheimer molecular dynamics 50,51 of the QM/MM molecular system were performed on the electronic excited state of interest. Each excited state trajectories was collected on-the-fly for 1 ps, with a time step of 0.5 fs. Energy and energy derivatives were computed at each time step by means of TD-DFT. All the calculations were carried out with the Gaussian16 program suite. 52

2.2

Time resolved frequency multiresolution analysis

Key structural parameters of the pyranine and an hydrogen bonded water molecule were extracted from the ground and the excited state trajectories and investigated in both the time and the frequency domain. In the latter case we adopted a multiresolution vibrational analysis based on the wavelet transform. 25,29 The continuous WT expression was considered: 26

W (a, b) =

Z

C(t)ψa,b (t)dt 6


(1)

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The time dependent signal C(t) is the relaxation function of the parameter under study, which is analyzed and decomposed in terms of the wavelet basis ψa,b . The wavelet basis is obtained from a prototype (mother) wavelet from dilatation, contraction and translation. As mother wavelet we used the Morlet wavelet. 27,30 The scale parameter a, proportional to the inverse of frequency, regulates the dilatation and contraction of the mother wavelet and extracts the different frequencies hidden in the time-dependent signal. The translation of the wavelet basis, ruled by the b parameter, ensures the localization of the frequencies in time domain. The unique features of the wavelet transform allow for the decomposition of the time dependent signals into basis functions able to keep the temporal information, so that the signals are eventually localized in both time and frequency domain. In order to facilitate the assignment of time resolved bands, static harmonic frequency analysis on S0 and S1 energy minimum structures of the pyranine and the pyranine-H2 O complex were performed at B3LYP/6-31g(d,p) level of theory, including solvent effects implicitly by means of a Polarizable Continuum Model in its Conductor-like version (CPCM). 53 In order to establish a comparison between the simulated photoinduced nuclear rearrangement of pyranine and experimental vibrational signals, the multiresolution analysis was also carried out on two generalized vibrational modes extracted from dynamics. The extraction of the vibrational modes was carried out from the trajectory in the ground state, according to the procedure previously reported. 54–56 Nevertheless, the main goal is the investigation of the transient vibrational signals appearing upon electronic excitation. Upon inspection of modes obtained by the static analysis on S0 and S1 energy minimum structures, we verified that the two generalized vibrational modes obtained from dynamics in the ground state are an acceptable approximation of the corresponding ones in the excited state.

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3

Results and discussion

3.1

Pyranine in aqueous solution at equilibrium in the ground state

We start our analysis with the characterization of the solvent microsolvation around the acid group of the pyranine solute, at equilibrium in the ground state. In Figure 1 radial distribution functions (RDFs) of the pyranine acid oxygen-water oxygen (Opyr -Ow ) and the pyranine acid hydrogen-water oxygen (Hpyr -Ow ) distances are reported, respectively. In both the cases a well defined peak, corresponding to the first solvation shell around the phenolic acid group, is recognizable. Peaks are centered at around 1.7 and 2.5 ˚ A for Hpyr -Ow and Opyr -Ow RDFs, respectively, according to the typical hydrogen bond distances. The first peak is limited by a pronounced minimum in both the RDFs, reaching a zero value for the (Hpyr -Ow ) RDF. This is a clear indication that there is no exchange of water molecules from and toward the first solvation shell during the sampling period (10 ps). It is noteworthy that the integration number of this peak (black dashed line in Figure 1) indicates that one water molecule is hydrogen bonded to the pyranine acid group during the simulation time. In Figure 1 we report the time evolution of the main hydrogen bond structural parameters between the phenolic O-H group of pyranine and the H-bonded water molecule, namely the intermolecular distances Hpyr -Ow , Hpyr -Ow and the intermolecular angle Hpyr -Opyr -Ow . Intermolecular Hpyr -Ow and Opyr -Ow distances oscillate around 1.7 and 2.4 ˚ A values, while the Hpyr -Opyr -Ow , which reports about the orientation of the hydrogen bond, also assumes small values, below 30◦ . A strong hydrogen bond between pyranine and water is therefore retained during the whole simulation time. The resulting solvation layout represents the equilibrium conditions in ground state. A representative configuration of this equilibrium was chosen as starting point for the simulation in the excited state.

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Figure 1: a) Hpyr -Ow (black) and Opyr -Ow (red) radial distribution functions b) the pyranine chromophore surrounded by water molecules c) Ground state time evolution of Hpyr -Ow (blue) and Opyr -Ow (red) intermolecular distances. d) Ground state time evolution of Hpyr Opyr -Ow angle (grey, the dark line indicates average values over the time).

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3.2

Photoinduced relaxation of pyranine

The S1 excited state of pyranine is obtained from S0 by a single HOMO-LUMO excitation, with π-π∗ character. Contours of the involved frontier orbitals are shown if Figure 2, as obtained by a TD-DFT calculation on the ground state energy minimum of the HPTS molecule, including solvent effects in implicit way according the polarizable continuum model in its conductor-like version. From a simple inspection of HOMO and LUMO contours, we note that the charge transfer character of the transition is low, also in proximity of the acid group. That means, the depletion of electronic density on the acid group associated to the electronic transition is not able alone to induce an immediate dissociation of the proton, as it can be expected from the weak photoacidity of pyranine. Instead, upon the excitation an electronic redistribution occurs over the whole nuclear skeleton, involving an exchange of alternating bond order among C-C bonds. In particular, the overall reorganization mainly corresponds to the π electronic density depletion on C-C bonds aligned with the red arrows shown in Figure 2, while the π electronic density on C-C bonds that are almost perpendicular to the red arrows increases when going from the ground to excited state. Therefore, we can expect a C-C elongation (lowering of the bond order) and a C-C shortening (increasing of the bond order) in the first and second case, respectively, when going from the ground to excited state. Overall, the excitation leads to the lengthening of the whole molecule along the axis approximately aligned with OH bond. From the static frequency analysis on minimum energy structures in S0 and S1 , we observe that C-C stretching modes of the pyranine system are collective in nature. In the ground state, C-C contributions can be found in several modes with harmonic frequency going from 1300 to 1670 cm−1 . Upon the electronic excitation, composition of these modes undergoes an important shuffle, while harmonic frequency values shift toward the red or blue, within an overall range of 1270-1633 cm−1 . We started our investigation of the pyranine rings photoinduced relaxation by comparing 10


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equilibrium C-C values assumed in S0 with those evolved in S1 after 1 ps. In the excited state, values were averaged over the four AIMD collected trajectories (TrJI-IV). A detailed comparison of the evolution in S0 and S1 from points with the same initial configuration (coordinates and momenta) is reported as Supporting Information (SI). In Table 1 we report average values of C-C distances calculated from AIMD trajectories in the ground and the excited state. As expected, upon the excitation we observe elongation of up to 0.04 ˚ A for C-C bonds 1, 3, 5, 6, 8 and 10, and a shortening of about 0.02 ˚ A for the remaining ones.

Figure 2: Left: HOMO and LUMO contours of pyranine computed at B3LYP/631g(d,p)/CPCM level of theory; right: labels used to tag C-C bonds analyzed in the present work.

As an example, in Figures 3a and 3c we show the time evolution in both the ground and the excited state of 1 and 2 C-C distances, which in the excited state become longer and shorter respectively. We can recognize how the C-C 1 distance in the excited state oscillates around greater values when compared to the corresponding evolution in the ground state. An opposite behavior is instead observed for the C-C 2 distance.

11



Figure 3: a) Ground (blue) and excited (red) state time evolution of the C-C 1 distance. b) 2D wavelet spectra of the C-C 1 distance in excited state. c) Ground (blue) and excited (red) state time evolution of the C-C 2 distance. d) 2D wavelet spectra of the C-C 2 distance in the excited state.

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˚) obtained from AIMD simulations of pyranine in aqueous Table 1: Average C-C distances (A solution in the ground and the first singlet excited state. Standard deviations are 0.02 ˚ A and A for S0 and S1 trajectories, respectively. See Figure 2 for the numbering of C-C bonds. 0.03 ˚ C-C bond

S0 average distance S1 average distance

1

1.415

1.438

2

1.432

1.415

3

1.365

1.393

4

1.439

1.416

5

1.417

1.444

6

1.417

1.441

7

1.438

1.422

8

1.364

1.389

9

1.436

1.419

10

1.417

1.442

We then analyzed the time relaxation of C-C bonds in the excited state in the frequency domain by means of the wavelet analysis. Time resolved vibrational analysis in the excited state of C-C bonds 1 and 2 have been perfomed by computing corresponding wavelet spectra, which are reported as time-frequency 2-dimentional maps in Figures 3b and 3d, respectively. Values used to construct relaxation functions were averaged over the four TrjI-IV trajectories. It is important to recall here that by wavelet transforming the time evolution of C-C 1 and C-C 2 distances, we capture the relaxing vibrational dynamics of all those modes with C-C 1 and C-C 2 stretching contributions that are activated by the electronic excitation. From the static frequency calculations, we learn that the C-C 1 stretching is a component of modes at 1313, 1622, and 1670 cm−1 in S0 , and at 1275, 1537, 1633 cm−1 in S1 . The C-C 2 stretching motion, on the other hand, mainly contributes to a collective stretching mode at 1492 cm−1 in S0 , which blue-shifts at 1569 cm−1 in S1 . Composition of some of these C-C 1 and C-C 2 modes are reported as SI. 13



From inspection of Figure 3 several interesting features of the pyranine photoinduced vibrational dynamics can be inferred. In the ultrafast part of the relaxation, namely for times below 100 fs after the excitation, signals associated to the C-C distances 1 and 2 are close around 1500 and 1300 cm−1 respectively, i.e. around values close to those adopted in the ground state. Then, clear blue and red shifts are observed in the two cases, testifying an exchange of force constants associated to the two bonds. Available FSRS data do not report about frequency values above 1300 cm−1 . 12,18 Hence, a direct comparison between our C-C vibrational dynamics with experimental data is not possible. However, several low frequency skeleton modes show a decay or a rise time of 550-600 fs, suggesting this period as a key time necessary to complete an important part of the nuclear rearrangement on the excited state potential energy surface. 12,18 Our results show frequency shifts of the C-C bonds vibrational dynamics occurring within the first hundreds of fs, namely a time compatible with the experimental relaxation time. Another important observation regards the evolution of the intensity of both signals. Indeed, the vibrational dynamics shows a clear oscillatory behaviour. In particular, periods between intensity maxima strongly suggest that the pyranine skeleton relaxation is modulated by low frequency modes (below 200 cm−1 ), possibly collective ring modes, which accompany the electronic redistribution of the molecule, and the consequent rearrangement of forces among nuclei. These low and high frequency modes appear therefore anharmonically coupled. Moreover, the C-C 1 and 2 vibrational bands are almost out-of-phase in the ultrafast part, indicating that rearrangement of forces in bonds with alternating order are anticorrelated in the time. A similar oscillatory and out-of-phase trend has been already experimentally observed in the photorelaxation of C-O and C-N stretching modes of the Green Fluorescent Protein chromophore, indicating the modulation of a 120 cm−1 mode that is also important in promoting the ESPT. 15 This behaviour has been recently reproduced and interpreted by means of our wavelet analysis. 33 A similar low/high frequency anharmonic coupling imposing

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and oscillatory behaviour to the relaxation of stretching modes has been also observed in 2D FSRS studes regarding the tetramethylbenzene-tetracyanoquinodimethane π stacked charge transfer complex 57 and a photochemical ring opening reaction. 58 Therefore, our results also suggest that the anticorrelated relaxation modulated by collective low frequency modes could be a common motif in photoinduced vibrational dynamics of aromatic or conjugate systems.

3.3

Photoinduced rearrangement of the pyranine-water couple

The pyranine ESPT reaction involves the motion of the proton from the photoacid molecule to a solvent molecule of the first solvation shell, and from here to the bulk through the diffusion process along hydrogen bond networks. The first and essential step, even before the proton hopping, is the formation of a tight proton donor-acceptor couple, i.e. the photoexcited pyranine and an hydrogen bonded water molecule. Upon excitation, the pyranine molecule undergoes a remarkable vibrational dynamics. FSRS results highlighted a characteristic and transient Raman activity in the excited state, associated to the sequential activation of low frequency vibrational modes. Several efforts have been made in order to individuate, among the complex sequence of activation/decay of vibrational signals, possible driving forces for the pyranine photoacidity. It has been hypothesized that low frequencies skeleton modes of photoexcited pyranine play a key role in promoting the excited state proton transfer reaction toward the water molecule hydrogen bonded to the phenolic acid group. Here, we analyzed the structural rearrangement involving the pyranine and the water molecule hydrogen bonded to the acid O-H group. Moreover, we individuated two generalized normal modes extracted according to the procedure described in Refs. 54–56 that are mainly involved in the pyranine-water relaxation, and analyzed their vibrational dynamics in the excited state. In figure 4 we compare the time evolution in the ground and the excited state of the 15



intermolecular distances between the pyranine phenolic oxygen and the H-bonded water oxygen (Opyr -Owat ), and between the pyranine acid group hydrogen the water oxygen (Hpyr Owat ). Data refer to TrjI and the corresponding period in the ground state, with the same initial coordinates and momenta. Similar trends are delivered by the other excited state trajectories, reported as SI. It can be noted that in the excited state these distances are shorter since about 50 fs, indicating that the phototriggered relaxation induces a tighter arrangement of the proton donor-acceptor couple. It is interesting also to observe in the frequency domain the trend shown by the Hpyr -Owat distance as extracted from the excited state TrjI. Indeed, the wavelet spectrum in Figure 5 of the Hpyr -Owat distance shows a band around 180 cm-1 that is activated in the ultrafast part of the spectrum, with a time decay of about 400 fs.

Figure 4: Ground (red) and excited (blue) states evolution of intermolecular Hpyr -Owat and Opyr -Owat distances (˚ A).

A pyranine low frequency mode photoactivated at about 280 cm−1 has been extensively investigated by FSRS techniques, and an important role played in promoting the pyranine photoacidity has been pointed out. 12,18 From the ground state trajectory we extracted a collective deformation mode involving all the 4-rings of the molecule, with an important 16


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Figure 5: Wavelet spectra of the intermolecular Hpyr -Ow stretching in excited state.

contribution from the phenolic O-H stretching, as a result of the coupling with the water molecule hydrogen bonded to the phenolic group and explicitly considered in the dynamical sampling. This generalized mode corresponds to the collective normal mode obtained from the static frequency analysis of the pyranine-H2 O complex (see SI), showing an intermolecular O-O stretching contribution, with harmonic frequency values calculated at 290 and 295 cm−1 in S0 and S1 , respectively. It is reasonable to expect, therefore, that the activation of this band is mainly responsible of the early tightening of the pyranine-water couple. Composition of the mode and corresponding wavelet spectra in the excited state are reported in Figure 6.

Figure 6: Wavelet power spectra (left panel) showing the excited state evolution of the band corresponding to the generalized mode that is composed by a collective ring deformation and a phenolic O-H stretching (right panel).

The vibrational dynamics shown by this mode is quite involved. We observe a signal at about 280 cm−1 appearing in the ultrafast time of the pyranine relaxation, showing several 17



raise and decay episodes with constant times of about 200 fs. Moreover, another strong band very close in frequency appears at about 500 fs. In Figure 7 we show the time evolution in the excited state TrjI and the same period in the ground state of dihedral angles involving the O-H phenolic group of pyranine and the H-bonded water molecules, namely the CCOH and the CCOO angles. These structural parameters describe the relative orientation between the photoacid and the H-bonded water molecule. We observe that in the excited state (red lines in Figure 7) both angles oscillate around values lower than in the ground state. In both cases, average values become close to 180◦ . A similar behaviour is observed in the other excited state trajectories (see SI). Therefore, the excitation induces a more planar arrangement of the pyranine-water molecule, which is more suited for the proton transfer. Also the hydrogen bond angle, Hpyr Opyr -Ow , becomes tighter, with a value slightly reducing the standard deviation when passing from the ground (σ of 5◦ ) to the excited (σ of 4◦ ) state. Importantly, at variance of the ground state evolution, oscillations of the dihedral angles in the excited state are modulated by a low frequency mode, which we can individuate at about 108 cm−1 from time periods between maximum values. From the ground state AIMD of pyranine in water we extracted a a collective four ring out of plane mode of the pyranine, involving in particular the out of plane motion of the O-H group. In Figure 8 we report the composition of the mode and the wavelet spectra showing the corresponding band evolution in the excited state TrjI. Also in this case the spectrum is quite complex. The lowest frequency component is indeed at 108 cm-1 , and it is active along the time window of 1 ps. Notably, a similar mode is experimentally found at 108 cm-1 , with a decay time constant of about one ps. Along the time, however, coupling to bands at about 190, 300 and 600 cm−1 can be observed. The signal appearing at about 600 cm−1 is reasonably from a deformation mode defined as combination of ring breathing and wagging mode. This is experimentally found at 630 cm−1 , with a rise-time of 300 fs. 18

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Figure 7: Comparison between the ground (blue lines) and excited (red lines) state behaviour of the COOH and CCOO dihedral angles.

Figure 8: Wavelet power spectra (left panel) showing the excited state evolution of the band corresponding to the generalized mode composed by a collective ring out of plane wagging (right panel).

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In summary, we observe a structural reorganization of the couple formed by the pyranine and the H-bonded water molecule in the first picosecond of the photoinduced relaxation. Both intermolecular distances and relative orientation are more favorable for the future proton transfer. From our analysis, this rearrangement is mainly modulated by two low frequency skeleton modes at 108 cm-1 and 280 cm-1 , affecting the water orientation and proximity, respectively. The importance of the mode at 280 cm−1 has been already experimentally revealed, while the role played by the vibrational mode at 108 cm−1 is proposed here for the first time. Indeed, this mode appears to be essential in the proton donor acceptor couple rearrangement that is preparatory for the photoreactivity.

4

Conclusions

In this work, we simulated and analyzed the photoinduced nuclear and vibrational dynamics of the pyranine molecule in aqueous solution. We combined ground and excited state abinitio molecular dynamics with a time resolved vibrational analysis, based on the wavelet transform. Our approach showed important advantages, including the possibility of investigating time resolved vibrational dynamics of the chromophore in aqueous solution, naturally taking into account anharmonicity and coupling of modes. Transient vibrational features can be easily correlated to the structural relaxation and the molecular dynamics in real time. Within the class of photoacid molecules, pyranine is classified as weak. Indeed, the origin of pyranine photoreactivity cannot be simply interpreted and explained in terms of the electronic density redistribution responding to the external perturbation. On the other hand, nuclear dynamics turns out to be preparatory and essential in promoting the ESPT reaction. Our findings support the hypothesis that the nuclear photorelaxation of pyranine is finely controlled by the activation of transient vibrational modes at low frequency. The most

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important stage of the skeleton relaxation is completed in about 500 fs, in agreement with FSRS data. In particular, the exchange of the order among C-C bonds occurs according to a complex vibrational dynamics, showing oscillatory patterns that are out of phase and modulated by modes below 200 cm−1 . We also individuated modes playing a role in optimizing the structural rearrangement of the pyranine and water molecule hydrogen bonded to the O-H group. In particular, a ring out of plane wagging (108 cm-1 ) and a ring deformation mode (280 cm-1 ) support the rearrangement of the intermolecular orientation and distances. As a consequence of the ultrafast relaxation, the pyranine-water couple is tighter and better oriented for the ESPT, occurring at later times.

Acknowledgments The authors gratefully acknowledge funds from Gaussian Inc. (Wallingford, CT). M. G. Chiariello thank the PhD Program in Chemical Sciences of Federico II, Napoli, Italy.

Supporting Information Available Composition of several pyranine modes and corresponding frequency values from harmonic static analysis performed on minimum energy structures in the ground and the S1 excited state; C-C distance values averaged over excited states TrjI-IV and corresponding values obtained in the ground state over 1 ps from the same starting phace space point; time evolution of structural parameters (distances and dihedral angles) in TrjII-IV and corresponding periods in the ground state. This material is available free of charge via the Internet at http://pubs.acs.org/.

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