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Fig. 1 Open and closed structures of 1,2-bis(2,4-dimethyl-5-phenyl-3-thienyl)perfluoro-cyclopentene (CHD).
In particular, time resolved vibrational spectroscopy (TRVS) experiments revealed characteristic oscillations of some time resolved frequencies.21 Oscillation in the vibrational bands can be ascribed to anharmonic coupling between the high and low frequency modes in the excited state. Quantitative measurement of the anharmonic coupling remains a challenging but fascinating task, because it provides unique information about the shape of the potential energy surfaces (PESs) and the energy exchange between vibrational normal modes.
TRVS experiments corroborate the hypothesis that vibrational modes (mainly stretching and bending motions) localized on the central 4-ring moiety are anharmonically coupled to low frequency methyl wagging modes. These modes are defined as ‘reactive’ because that coupling would lead to the open ring product. Vibrational modes delocalized on the peripheral phenyl groups are instead labeled as unreactive, leading the system back to the ground state.
Of course, unveiling at the molecular level the driving forces controlling the CHD photoreactivity is extremely important to plan the rational design of a photochromic system with better performance.
For this reason, in this paper, we aim to study the electronic–nuclear driving forces that lead the photoexcited system toward the conical intersection region. In particular, we focus on the analysis of the vibrational modes responsible for the photoreactive process, and the coupling between them. Theoretical studies of CHD are quite unusual, due to the large size of the system. In principle, non-adiabatic photoreactivity should be described by Multi-Configurational Self Consitent Field (MC-SCF) methods, allowing for a suitable characterization of the PES region where the crossing between the two electronic surfaces takes place.24–28 Unfortunately, they are not feasible for large size systems such as CHD due to their high computational cost.
Indeed, these regions far from the conical intersection branching space can be accurately described within the adiabatic approximation by running single surface excited state dynamics and getting information about the evolution of the vibrational properties by means of a rational analysis of the trajectories.
Following this line of research, the vibrational analysis is here expanded to investigate anharmonic coupling between vibrational signals of the CHD photoswitch. More closely, the time resolved vibrational bands, as a result of the wavelet transform, are further analyzed with the purpose of recognizing the frequency ruling the characteristic oscillations of time resolved vibrational signals. The wavelet maps show characteristic oscillations of the frequencies, mainly CC stretching and CCC bending localized on the central 4-ring moiety. Moreover, we have identified the main frequency (methyl wagging) involved in the modulation of these oscillations. The anharmonic coupling within this group of vibrational modes was, therefore, highlighted, in good agreement with experimental evidence.
This paper is organized as follows: after a brief description of the computational details and the wavelet based vibrational analysis (Section 2), the static characterization of the reaction profiles is discussed in Section 3.1. The dynamical sampling and the vibrational analysis are then presented in Sections 3.2 and 3.3. Final remarks and future perspectives are given as conclusions.
In order to characterize the ground and the excited state PESs of the CHD closed ring isomer (see Fig. 1), DFT and TD-DFT levels of theory were employed. The global hybrid functional B3LYP was adopted in combination with the 6-31g(d,p) basis set.48–50 This method allowed us to reproduce the spectroscopic features of the chromophore, obtaining photophysical signatures in fair agreement with the experimental absorption and fluorescence spectra (see Section 3.1 for more details).
Starting from the CHD minimum energy structure, constrained energy profiles were built by partial relaxed structural optimizations along the central CC distance, hereafter CC1, representing a reasonable simplified reaction coordinate for the ring opening reaction (see Fig. 1). The CC1 distance was scanned from 1.54 Å to 3.98 Å, which correspond to the values that the CC1 bond assumes, respectively, in the closed and open ring isomers in their ground state minimum energy structures. The intermediate points were obtained by keeping the CC1 distance fixed while relaxing in the ground state all the other degrees of freedom. The S1 excited state profile was vertically computed in these points at the TD-B3LYP/6-31g(d,p) level of theory.
In the following, the focus will be on the direct ring opening reaction, namely the photo-isomerization starting from the closed ring reagent that leads to the open ring product. The vertical excitation energy (VEE) is obtained from the ground state minimum geometry of the CHD closed ring form. The computed VEE value is 2.12 eV in the gas phase, which is in nice agreement with the value obtained from the experimental absorption spectrum in cyclohexane of 2.21 eV. In principle, the computational/experimental discrepancy could be reduced by including the effect of the solvent. Nevertheless, the difference of 0.09 eV, corresponding to a small gap of 2 kcal mol−1, can be considered negligible to our aims, as well as the effect of the cyclohexane solvent.
The transition leading to the S1 excited state has a π–π* nature, involving frontier orbitals shown in Fig. 2.
Fig. 2 HOMO and LUMO contour plots computed for CHD in the ground-state minimum energy structure obtained at the B3LYP/6-31g(d,p) level of theory.
Upon excitation, the main part of the charge redistribution concerns the π conjugation localized on the central rings, namely the thiophene rings, the central cyclohexadiene and the fluorinated cyclopentane, the latter acting as an electron acceptor. On the other hand, the peripheral phenyl rings are only slightly involved in the charge rearrangement associated with the excitation. A side perspective of the orbitals (see lower panel of Fig. 2) makes it possible to observe the new electronic arrangement on the central CC1 bond, i.e. the bond subject to break in the excited state. The electronic charge is strongly reduced along the CC1 bond when going from the ground to the first excited state.
In order to get a first picture of the potential energy surfaces involved in the ring opening reaction, constrained potential energy profiles along a suitable reaction coordinate (namely the CC1 central bond) were calculated in the ground state and in the first excited state (see Section 2.1 for details). In principle, DFT and its time dependent version, as a single reference electronic structure theories, are not able to characterize the crossing points between two electronic surfaces. Nevertheless, this procedure aims at understanding where the two surfaces start to become degenerate along the reaction coordinate, so that it will be possible to identify some regions of the PESs that can be treated in an adiabatic way. The ground and the excited state energy profiles are shown in Fig. 3. The profiles represent relative energies with respect to the energy of the closed ring CHD, which was instead set to zero. Moreover, the ground-to-excited state non-adiabatic couplings are also shown in Fig. 3 (green dashed line). The NAC computation is here employed to report the coupling between the ground and the first excited states along the constrained PES, with the CC1 bond as the reaction coordinate.
Fig. 3 Ground (blue) and excited (red) constrained energy profiles calculated for the ring opening reaction at the B3LYP/6-31g(d,p) level of theory. Blue circles indicate energy values of the fully relaxed open and closed ring structures. The non-adiabatic couplings (green dashed line) computed along the profile are also shown. The grey surface represents the non-adiabatic region. The violet area defines the adiabatic region considered in this work.
As already mentioned above, DFT does not allow characterization of the intersection points, although we can get information about the region of the PESs in which the ground and excited state surfaces are well separated and the adiabatic approximation still holds. More closely, within the range of values of the CC1 bond from 1.54 to 1.75 Å, the two electronic surfaces are clearly non degenerate (see the violet area in Fig. 3). Within the given level of theory, the two surfaces become too close in energy at a CC1 distance of about 1.80 Å, where the NAC profile reaches its maximum value. After that, it decreases with increasing CC1 distance. On the other hand, within the 1.54–1.75 Å range, NACs undergo little variations and are always low. Interestingly, in the 1.50–1.75 Å range, we can also observe a significant decrease of the profile slope when passing from S0 to S1, suggesting that the CC1 stretching motion becomes less stiff upon the electronic excitation.
The adiabatic dynamical sampling of that region will be the subject of the next section.
A first insight into the response of the CHD nuclei to the photoexcitation and to the new electronic arrangement can be obtained by analyzing the average values of some key CC distances of the central moiety, in both ground and excited states. The average values and labels of all the bonds of the central 4-ring system are shown in Fig. 4. It is worth comparing the ground and excited state behaviors by considering the contours of the frontiers orbitals (HOMO–LUMO in Fig. 2) involved in the electronic transition. When going from the ground to the excited state, some CC distances of the cyclohexadiene ring (CC5 and CC6) and of the thiophene ring (CC9 and CC10) become more stretched, going from a typical double bond value in the ground state (1.37 Å) to the average values of 1.42 (CC5, CC6) and 1.40 Å (CC9, CC10) in the excited state. This change occurs according to a depletion of electron density on these bonds, as is possible to observe from the frontier orbital contours. On the other hand, an increase of density on CC2, CC3, CC4 (cyclohexadiene), CC7, and CC8 (thiophenes) bonds is observed, making the distance shorter in the excited state.
Fig. 4 Average distances (Å) obtained from the AIMD simulation of CHD in the ground state (central structure) and the S1 excited state (structure on the right). Structure on the left shows numbering of the bonds.
It is interesting to note that the excited state nuclear rearrangement leads the CC bond in the CC7–CC5–CC2–CC6–CC8 chain to assume the same length of 1.42 Å on average, in the middle of a single and double bond value.
The depletion of electron density on the CC1 bond makes it weaker and longer in the excited state, showing an average value of 1.55 Å in S0 and 1.60 Å in S1. Hence, the CC1 bond shows on average longer distances in S1, as a result of the new electronic arrangement. Fig. 5 shows the time evolution of the CC1 distance in both S0 and S1. Larger oscillations are observed in the excited state, with a maximum value of 1.75 Å. As already shown in the previous section, a CC1 distance of 1.75 Å represents a threshold value for which the non-adiabatic coupling remains low. Therefore, starting from the Franck–Condon region, our trajectories describe the pathway toward the CI zone, although remaining in the adiabatic region. Indeed, oscillations of the CC1 bond strongly affect the S0–S1 energy gap.
Fig. 5 (a) Ground (blue) and excited (red) state time evolution of the CC1 distance. (b) Comparison between the normalized fluctuactions of the CC1 distance in the excited state (red line) and the S0 − S1 energy gap ΔE (blue line).
where (t) is the average value over time. In Fig. 5, we show normalized fluctuations of the CC1 distance in S1 (red line) and of the S1 − S0 energy difference (ΔES1−S0) (blue line).
The graph clearly shows that the two curves oscillate out of phase, i.e. maxima of the energy difference correspond to minima of the CC1 distance over time. This means that the larger the CC1 distance, the smaller the energy gap between S1 and S0. Moreover, analyzing the behaviour of ΔES1−S0 over time, we computed an average value of 1.50 eV (corresponding to 35 kcal mol−1) with a standard deviation of 0.17 eV, with maximum and minimum values of 2.14 and 0.97 eV, respectively.
Upon excitation, CHD undergoes a strong vibrational activity, mirroring the nuclear evolution on the excited state PES. The photoinduced vibrational dynamics was recently analyzed by two-dimensional femtosecond stimulated Raman techniques,21 which were specifically employed to reveal the anharmonic coupling between vibrational modes. In particular, in a recent work,71 authors inferred a quantitative relationship between high frequency oscillating bands and low frequency modes, modulating them by means of an anharmonic coupling constant. In the case of the CHD molecule, the dynamics of a group of vibrational bands was identified as strongly coupled. These bands were labeled as ‘reactive’, because the coupling was responsible for the barrier crossing and the subsequent ring opening reaction through the conical intersection. In particular, the coupling was proven by observing the oscillation patterns in both the intensity and the frequency time evolution of high and low frequency modes.
In the following discussion, the focus is on the modes belonging to the ‘reactive’ group and the coupling between them. First, we identified reactive modes from the frequency calculation of the CHD S1 minimum energy structure, by using the B3LYP/6-31g(d,p) level of theory. Then, we chose the key structural parameters mainly involved in these normal modes and constructed the corresponding averaged relaxation functions from the collected excited state trajectories. Finally, the adopted strategy included a time resolved vibrational analysis based on the wavelet transform of these relaxation functions.
In Table 1, we show the harmonic frequencies calculated for the reactive modes in the CHD S1 minimum energy structure. These values are compared with the corresponding frequencies averaged on the three excited state trajectories. The experimental data are also shown.21 Both simulated and experimental data refer to averages over a period of 3 ps, namely approximately the relaxation time spent on the S1 PES, prior to entering the conical intersection region. Moreover, we recall that the simulated frequencies are intrinsically anharmonic. As a matter of fact, we observe a nice agreement between simulated and experimental values.
The AIMD simulation allows for an exploration of the ground and excited state potential energy surfaces that are intrinsically anharmonic, hence a quantitative analysis of the time resolved oscillating frequencies allows one to get information about the anharmonic coupling.
The CC1 distance oscillations, discussed in the previous section, affect other nuclear motions, in particular, the vibrational modes involving the methyl groups of the CC1 bond. In the closed ring form, the methyl groups are basically perpendicular to the thiophene ring plane. The open ring product is instead characterized by the methyl groups in the plane of the thiophene rings. The methyl wagging normal mode at 191 cm−1 21 (see the ESI†) describes the motion from the perpendicular toward the in plane arrangement, and vice versa. The structural parameter chosen as representative of the methyl wagging mode is the (H3)C–CC1–C(H3) dihedral angle, and the 2D wavelet map of the methyl wagging extracted from the excited state trajectories is shown in Fig. 6. The time resolved vibrational band of the wagging mode is centered at 200 cm−1, in fair agreement with the experimental one.
Fig. 6 Left panel: CHD structure with the atoms participating in the methyl wag (AIMD frequency 208 cm−1) highlighted in red. Right panel: 2D wavelet map of the methyl wagging motion in the excited state. The color scale represents the intensity in arbitrary units.
The methyl wagging is the low frequency mode recognized as coupled and modulating the higher frequency modes localized on the central rings. These high frequency modes are the CC stretching on the cyclohexadiene ring (experimental frequency of 1181 cm−1),21 the CC stretching localized on the thiophene rings (exp. 1333 cm−1) and the CCC bending of cyclohexadiene and thiophene rings (exp. 467 cm−1). The corresponding wavelet 2D maps are reported in Fig. 7, 8 and 9, respectively. Two kinds of CC stretching are analyzed: the CC stretching on the central ring and on the thiophene rings, with AIMD frequencies of 1186 cm−1 and 1380 cm−1, respectively.
Fig. 7 Left panel: CHD structure with the atoms participating in the CC stretching (AIMD frequency 1186 cm−1) highlighted in red. Central panel: 2D wavelet map of the CC stretching localized on the cyclohexadiene moiety. The color scale represents the intensity in arbitrary units. Right panel: Discrete Fourier transform of the intensity oscillations.
Fig. 8 Left panel: CHD structure with the atoms participating in the CC stretching (AIMD frequency 1380 cm−1) highlighted in red. Central panel: 2D wavelet map of the CC stretching localized on the thiophene rings. The color scale represents the intensity in arbitrary units. Right panel: Discrete Fourier transform of the intensity oscillations.
Fig. 9 Left panel: CHD structure with the atoms participating in the CCC bending (AIMD Frequency 469 cm−1) highlighted in red. Central panel: 2D wavelet map of the CCC bending localized on the cyclohexadiene and thiophene rings. Right panel: Discrete Fourier transform of the intensity oscillations.
The wavelet maps of the two stretching modes (see Fig. 7 and 8) show clear intensity and frequency oscillations over time. In order to unveil the coupling with the methyl wagging mode, a quantitative analysis of the time dependent frequencies was performed. In particular, frequencies corresponding to the maximum intensity were extracted from the time resolved wavelet output, and a discrete Fourier transform (FT) was performed on the maximum intensity value in order to reveal the oscillation frequency. The discrete Fourier transform of the time resolved maximum intensity associated with the CC stretching modes is shown in Fig. 7 and 8. In both cases, the FT shows that the main frequency modulating the intensity oscillations of the CC stretching mode is at 190 cm−1, matching the methyl wagging frequency.
The 2D wavelet map of the CCC bending of the cyclohexadiene and thiophene rings is quite complex (Fig. 9). The signal of interest is centered at a frequency of 469 cm−1 (AIMD frequency), although other contributions can be observed. As a matter of fact, the CCC bending involving cyclohexadiene and thiophene rings is part of another deformation mode at 690 cm−1.
The wavelet map of the CCC bending also shows a contribution at about 200 cm−1. Because the CCC bending does not participate in any modes around 200 cm−1, the signal appears as a result of the anharmonic coupling with the methyl wags. Moreover, the intensity oscillation corresponding to the frequency centered at 469 cm−1 was extracted and analyzed. The FT of the maximum intensity over time (Fig. 9) shows a signal at 191 cm−1, confirming the coupling with the methyl wagging mode.
Our findings are in agreement with the experimental evidence of a coupling between the methyl wagging (acting as modulating mode) and the CC stretching and CCC bending modes. A similar behavior of low/high frequency anharmonic coupling has been recognized for the photorelaxation processes of the pyranine photoacid37,72 and the photodynamics of the green fluorescent protein, with the subsequent excited state proton transfer reaction.36,73 However, a quantitative analysis of the time resolved bands from AIMD has been applied here for the first time and it has provided satisfactory results.
In this work, we studied the photoinduced vibrational dynamics of a diarylethene photoswitch, combining ab initio molecular dynamics simulations and a time resolved vibrational analysis. As a response to electronic excitation, the central CC bond experiences wider oscillations in the sampled time. These fluctuations are out of phase with respect to the energy gap S1 − S0, suggesting that the CC bond is one of the main coordinates ruling the conical intersection. A great deal of information on the process was obtained by analyzing the relevant structural parameters in both the time and frequency domains, by means of the wavelet transform. The wavelet maps revealed characteristic oscillations of the CC stretching and CCC bending modes localized on the central 4-ring diarylethene core. A quantitative analysis of the oscillating behavior allowed us to recognize the frequency that modulates the CC stretching and CCC bending oscillations. Our results indicate that the methyl wagging mode is mainly involved in the modulation of the CC stretching and CCC bending frequencies, revealing a strong coupling between these vibrational modes, as already experimentally suggested.
In conclusion, ab initio molecular dynamics combined with time resolved vibrational analysis appears to be a suitable tool to disentangle nuclear photoinduced dynamics, even in the case of challenging and complex systems like the CHD molecule. The experimental evidence is well reproduced, suggesting the accuracy and the general reliability of the method.
The authors gratefully acknowledge funding from Gaussian, Inc. (Wallingford, CT).
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