Transient process spectroscopy for the direct observation of inter-molecular photo-dissociation

Transient process spectroscopy has previously been thought to be applicable only to the analysis of intra-molecular processes. Two metal ion bridges used in the present work have allowed us to visualize real-time variations of the molecular vibration frequencies during photo-disproportionation inside bimolecule aggregates, which directly shows transient inter-molecular reactions.


INTRODUCTION
Rapid processes that cannot be tracked visually can often be observed by acquiring photographic images under rapid strobe lighting. The development of femtosecond strobe lights has enabled the study of the electronic and vibrational dynamics of transition states in photoreactions. As a result, reaction pathways such as A ! B ! C in Fig. 1 can now be observed. 1 The availability of 5-fs laser pulses, 2 the duration of which is much shorter than molecular vibration periods, has enabled real-time observations of atomic motions as well. 3 The burst capture of strobe spectra has also allowed the tracking of transient processes such as bond breaking and bond reformation (indicated by the red curve in Fig. 1) in chemical reactions. 4 The functional groups of organic compounds typically generate specific absorption bands in the range of 1000-2000 cm À1 , corresponding to their molecular vibrational modes. As an example, the stretching modes of C¼C and C-C bonds appear at 1600 and 1100 cm À1 , in association with vibrational periods of 20 and 30 fs. These molecular vibrations can be temporally resolved by measurements employing sub-10 fs laser pulses that allow observations of vibrational motions in real-time. In addition, examination of changes in instantaneous molecular frequencies allows the visualization of transient processes such as chemical bond breaking and reformation. The observation of transition states has also been reported in the case of various intra-molecular reactions, based on the use of sub-10 fs laser pulses. [4][5][6] The majority of organic photo-reactions proceed as inter-molecular reactions via intermolecular collisions or inter-system crossing occurring in the picosecond to nanosecond time scale. However, the coherent molecular vibrations produced by impulsive photoexcitation dephase as fast as a few picoseconds, 5,7 and moreover, the inter-molecular collision destroys the coherence of the molecular vibration. Therefore, previously it had been thought to be impossible to observe the inter-molecular reactions via coherent molecular vibration dynamics. The present work investigated a compound consisting of two molecules (anion dimer) bridged by two metal ions. The bridged structure allowed us to observe coherent molecular vibration dynamics suppressing inter-molecular collision.

Ultrashort visible pulses
A Ti:sapphire regenerative amplifier (SpectraPhysics, Spitfire model) was used to generate near infrared (NIR) femtosecond pulses (duration 100 fs, central wavelength 800 nm, repetition rate 1 kHz, and pulse energy 3 mJ) so as to produce ultrashort visible pulses using a home-made non-collinear optical parametric amplifier (NOPA). 8 The setup of the optical system is almost the same as the one previously described in detail. 16 In the previous work, we have compressed the pulse duration using a pulse compressor consisting of a diffraction grating and a deformable mirror; however, high order chirp was still remaining in the compressed pulse. Thus, we have added a chirped mirror pair to compensate the high order chirp component. The amplified broadband visible pulse, extending from 500 to 740 nm, was compressed to a sub-10 fs pulse.

Real-time measurements of vibrational motions in molecules
A typical molecular vibration has a period of 20 fs, and so cannot be temporally resolved by time-resolved spectroscopy systems employing laser pulses with durations of 35 fs or longer. Therefore, ultrashort visible laser pulses with sub-10 fs durations have been developed, since these can temporally resolve real-time molecular vibrations. To allow the observation of both electronic and vibrational dynamics, a time-resolved absorption pump-probe spectroscopy system was designed in the present work, as follows.
In this system, the intense broadband visible laser pulse generated by the NOPA was separated into two copies, at a power ratio of 10:1, and these were employed as the pump and probe pulses in pump-probe spectroscopy. The chirps of the pump and probe pulses were adjusted to have a pulse duration of less than 10 fs at the point of impingement on the solution sample held in a synthetic fused silica glass cell. The chirp adjustment was accomplished as follows.
The glass cell used in the present work (GL Sciences Inc., S15-IR-1) has 1-mm optical path length and its glass walls have a thickness of 1.1 mm. We have broken one of the glass cells into half to get one of the glass walls of the glass cell. The glass wall plate was inserted in front of the beam sampler in the pump-probe setup. Thus, both the pump pulse and the probe pulse transmit through the glass wall plate for once. By using a parabolic mirror with 101.6mm reflected focal length, these pulses were focused in the beta barium borate (BBO) crystal with 10-lm thickness to generate the sum frequency between the two pulses. The sum frequency pulse was clipped by an iris and coupled into optical spectral analyzer. The sum frequency spectrum was measured as a function of the delay between the pump and probe pulse in the second harmonic generation (SHG) frequency resolved optical gating (FROG) measurement. Therefore, the pulse duration estimated in the SHG FROG measurement reflects that of the pulse in the glass cell for the solution sample. We have adjusted the grating compressor to let the estimated pulse duration as short as possible in this situation. Thus, the visible pulse transmitted through one glass wall plate has a pulse duration of sub-10 fs. On the measurement of the solution sample, we have removed the glass wall plate and put the solution sample filled in the glass cell. Therefore, the solution sample was excited and probed by the sub-10-fs ultrashort visible pulse.
The probe pulse transmitted through the sample was coupled into a polychromator (Princeton Instruments, SpectraPro 2150i). The probe spectrum was subsequently dispersed by the polychromator and measured by a fast scan rate CCD line scan camera (Entwicklungsbuero Stresing, Series 2000) with a line scan rate of 1 kHz. The probe spectrum was acquired for every pulse at a repetition rate of 1 kHz. The pump pulse was modulated by a mechanical chopper running at a frequency equal to half the laser repetition rate. Thus, the acquired probe spectrum contained the signal from the sample excited by the pump pulse (T þ DT) and the signal from the sample in the unexcited state (T) for every two probe pulses. Absorption changes were calculated as DA ¼ Àlog10 (1 þ DT/T). The absorption changes were determined by scanning the optical delay between the pump and probe pulses at 500 ms intervals with a step-size of 0.2 fs, from À30 to 1800 fs. In the subsequent data analysis, we averaged every five delay points to improve the signal-to-noise ratio.

Sample
A saturated methanol solution of 2,2 0 -(2,5-Cyclohexadiene-1,4-diylidene) dimalononitrile (TCNQ) 9 was stored in a glass bottle and placed under natural light for five weeks to produce a radical anion dimer bridged by two sodium cation (Na þ 2 [TCNQ À• ] 2 ). A transition from the original yellow color of the initial TCNQ solution to green provided evidence for the charge transfer (CT) band of the [TCNQ À• ] 2 at 643 nm. [10][11][12][13] A portion of the resulting Na þ 2 [TCNQ À• ] 2 solution, with a concentration of 3.6 Â 10 À4 M, was transferred into a fused silica cell in preparation for the pump-probe measurements. The glass cell was put on a mechanical motorized stage to be continuously moved in a circle shape in a plane orthogonal to the light path. Thus, the system has been adjusted to implement that the sample probed by the last pulse will not be probed by the next pulse coming 1 ms later. The sample existing at the irradiated point goes away by convection in the glass cell after running the glass cell through the whole arc of the circle. Therefore, the degradation effect of the sample can be excluded during the measurement. It was also confirmed that the stationary absorption spectrum of the sample does not show any recognizable difference between before and after the measurement. All trials were performed at a room temperature of 22 6 1 C.

Theoretical calculations
The Gaussian 09 program 14 was used for calculations, without assuming symmetry. Theoretical calculation for Na þ 2 [TCNQ À• ] 2 was performed replacing sodium with potassium. Geometric optimization was performed at the B3LYP/6-31G* level, and 5d functions were employed for the d orbitals. Raman active molecular vibration frequencies were calculated for each of the obtained structures at the same level.

RESULTS AND DISCUSSION
The spectrum of the ultrashort visible laser pulses overlapped most part of the CT absorption band of the methanol solution of Na þ 2 [TCNQ À• ] 2 (Fig. 2). Therefore, these pulses were able to trigger the photo-disproportion reaction: [TCNQ À• ] 2 ! TCNQ þ TCNQ 2À . 12,15 It results in that the electronic decay dynamics observed in the vicinity of 700 nm (see Appendix A) reflects the stimulated emissions of [TCNQ À• ] 2 and TCNQ 2À . 16 The former exhibited decay within the observed delay region, while the latter showed a rise and subsequent decay. We have studied this reaction process analysing molecular vibration dynamics of the transient absorption trace probed at 700 nm as follows. The observed dynamics was confirmed performing the same analysis also at other probe wavelengths (see Appendix B).
The transient absorption trace includes slow relaxation reflecting electronic dynamics and fast oscillation reflecting vibrational dynamics. We have an applied high pass filter to the transient absorption trace and got the fast oscillating components, which is plotted in Fig. 3. The fast oscillation of the trace was caused by the wave packet motion on the potential energy surface oscillating with the period of the molecular vibration. The molecular vibration dynamics can be examined via a spectrogram analysis. 17 Scalogram analysis (see Appendix C) was also performed to confirm the vibrational dynamics observed by the spectrogram analysis. The spectrogram is obtained by short-time Fourier transform (STFT). 18,19 Calculation of the spectrogram is performed to obtain Fourier transform of the product of the transient absorption trace DA(t) and the gate function g(t À s) shifting s (the center position of the gate function). When s ¼ s 0 , the product DA(t)g(t À s) contains oscillating components around t ¼ s 0 because g(t À s 0 ) is non-zero only in ÀT/2 < t À s 0 < T=2. Therefore, its Fourier spectrum, i.e., spectrogram for s ¼ s 0 , S(x, s 0 ), represents the vibrational spectrum at around t ¼ s 0 . Calculating the Fourier transform shifting s, spectrogram is obtained reflecting the dynamics of the molecular vibrational spectrum. The spectrogram was calculated using the Blackman window function with a full width at half-maximum of 200 fs, as shown in the below equation The resulting spectrogram is provided in Fig. 4, where the horizontal axis, vertical axis, and color bar represent the delay time, the instantaneous molecular vibration frequency, and the signal intensity, respectively. The spectrogram was shown from 200 fs because the spectrogram is noisy at earlier than 200 fs reflecting the coherent artefact existing around the zero delay region. Density-functional theory (DFT) calculations at the B3LYP/6-31G* level were performed to assign the vibrational modes appearing in the spectrogram (Table I).
The vibrational modes immediately after photo-excitation reflect those of Na þ 2 [TCNQ À• ] 2 . The frequency region below 820 cm À1 shows inter-fragment vibrational modes 20 (d TCNQ-TCNQ ), while the peaks at 1060, 1200, 1425, and 1560 cm À1 are assigned to the symmetric stretching mode of the benzene ring ( Bn ), the C-H bending mode (d CH ), the C-C 1.5 bond stretching mode of the side chain group ( CCs1.5 ), and the C-C double bond stretching mode of the benzene ring ( CCr ), respectively. The d TCNQ-TCNQ modes between the TCNQ anion radical dimer below 820 cm À1 were found to disappear approximately 300 fs after photo-excitation. This result implies that the dimer dissociates within this time span.
The CCs1.5 peak at 1425 cm À1 just after photo-excitation was separated into blue-shifted and red-shifted bands and transitioned to a new peak at approximately 400 fs. The mode separation between the blue-shifted mode and the red-shifted mode is comparable with the bandwidth of the modes appearing in the spectrogram. The result shown in Appendix D shows that the observed mode branching is not artifact but really exists in the transient reaction. The observed mode branching can be explained by noting that the CCs1.5 mode has a bond order of 1.5. One of the disproportionation products, TCNQ, has a C-C double bond, which generates the blue-shifted band. The other product, TCNQ 2À , has a C-C single bond that corresponds to  the red-shifted band. The TCNQ is generated in the electronic ground state and generates a peak at 1470 cm À1 , corresponding to the C-C double-bond stretching mode ( CCs2 ). In contrast, the TCNQ 2À was in the electronic singlet excited state and produced a band due to the C-C single bond stretching mode ( CCs1 ) at 1340 cm À1 . This frequency of CCs1 higher than C-C single bond stretching mode agrees with the theoretical calculation. The blue shift of the frequency is thought to be because the methylene carbon in malononitrile unit has a negative charge of À0.5.
The changes in bond order can be understood as follows. The HOMO (LUMO) of TCNQ, / 52 (/ 53 ), is the bonding (antibonding) orbital of the C-C bond of the side chain group (Fig. 5). Therefore, the bond order of this C-C bond increases in the order of TCNQ > TCNQ À• > TCNQ 2À when a single electron is promoted to the / 53 orbital of TCNQ À• and TCNQ 2À . The TCNQ 2À produced in the singlet excited state makes the transitions to a triplet excited state via inter-system crossing. This results in the gradual blue-shift of the peak from 1340 to 1360 cm À1 with a new peak appearing approximately 900 fs after photo-excitation.
The 1560 cm À1 peak seen just after photo-excitation broadens 400 fs after photoexcitation. The DFT calculations (Table I) indicated that this peak is associated with frequency shifts of þ15 and À5 cm À1 for the disproportionation products TCNQ and singlet excited state TCNQ 2À , respectively. These frequency shifts were observed to occur in $400 fs. The CCr mode of triplet excited state TCNQ 2À was predicted to undergo a red-shift to 1550 cm À1 and to be Raman inactive. Therefore, this peak should disappear approximately 800 fs after photo-excitation.
The d C-H mode appearing at 1200 cm À1 immediately after photo-excitation exhibited a gradual red-shift to 1140 cm À1 and is attributed to singlet excited state TCNQ 2present 400 fs after photo-excitation. This same peak separated into blue-and red-shifted bands at 1180 and 985 cm À1 , respectively, around 900 fs after photo-excitation, as the result of the formation of triplet excited state TCNQ 2À . These data agree with the results of DFT calculations ( Table I).
The Bn mode observed at 1060 cm À1 just after photo-excitation was also split into two peaks, with a gradual frequency shift to 950 cm À1 in the case of TCNQ and 1140 cm À1 for singlet excited state TCNQ 2À . This mode was no longer present about 600 fs after photoexcitation because it also becomes Raman inactive due to the formation of triplet excited state TCNQ 2À , as predicted by DFT calculations (Table I).
The results of the spectrogram analysis demonstrate that the Na þ 2 [TCNQ À• ] 2 dissociated within approximately 400 fs and that the inter-system crossing of TCNQ 2occurred at about 900 fs. These observations are in good agreement with the results of electronic dynamics analysis. 16 The agreement between the spectrogram and the electronic dynamics was confirmed again using the present sample data as follows.
When the fluorescence spectrum of TCNQ 2À was subtracted from the fluorescence spectrum of [TCNQ À• ] 2 , its spectral shape agrees with DA 314 [see Fig. 6(d)]. It indicates that the decay of [TCNQ À• ] 2 occurs simultaneously with production of TCNQ 2À in $300 fs. When TCNQ is produced, the C-C bond of the side chain group changes bond order from 1.5 to 2. Meanwhile, the bond order changes from 1.5 to 1 when TCNQ 2À is produced. The obtained time constant of $300 fs reflects that TCNQ and TCNQ 2À took $300 fs to be stabilized into FIG. 5. HOMO(/ 52 ) and LUMO(/ 53 ) orbitals of TCNQ calculated using B3LYP/6-31G*. their most stable structure. Then, the vibrational modes corresponding to the ground state of TCNQ and singlet excited state of TCNQ 2have appeared at $400 fs on the spectrogram (see Fig. 4). The spectral shape of DA 915 agrees with the fluorescence spectrum of TCNQ 2À [see Fig. 6(e)], which implies that the fluorescence lifetime of TCNQ 2is $900 fs. It agrees with that the intersystem crossing from the singlet excited state to triplet excited state was observed in $900 fs in the spectrogram (see Fig. 4).
This analysis shows that the disproportionation of Na þ 2 [TCNQ À• ] 2 is complete within 350 fs and that the emission lifetime of singlet excited state TCNQ 2À is on the order of 900 fs. The lifetime of singlet excited state agrees with that reported for TCNQ derivatives. 21,22

CONCLUSIONS
The ultrafast molecular vibrational dynamics of an inter-molecular reaction (the photodisproportionation of Na þ 2 [TCNQ À• ] 2 ) were studied. In this compound, two TCNQ -• molecules are bridged by two metal ions, and this structure serves to suppress inter-molecular collisions, which in turn tends to maintain the coherence of molecular vibrations. As such, changes in the molecular vibration frequency during the disproportionation of bimolecule aggregates could be visualized in real time. The data obtained in this manner were found to be in good agreement with the results of DFT calculations. Transient process spectroscopy was previously thought to be solely useful for the observation of intra-molecular reactions. However, the present work has proven that this technique is applicable to many chemical reactions, even those classified as inter-molecular. The measured two-dimensional map of transient absorption has shown a negative signal just after photo-excitation [ Fig. 6(a)]. The measured transient absorption trace was averaged for neighboring ten probe wavelengths corresponding to 10 nm bandwidth. The averaged trace was fitted by triple exponential function of Eq. (A1) assuming the sequential decay process shown in Fig. 7. The time constants obtained in the fitting are plotted in Fig. 6(b). The time constants were averaged for all of the probe wavelength region which give the three lifetimes of s 1 ¼ 12 fs, s 2 ¼ 314 fs, and s 3 ¼ 915 fs. These three decay lifetimes are used to calculate their decay associated spectrum (DAS) shown in Fig. 6(c). Around the probe wavelength of 700 nm, a positive signal corresponding to stimulated emission was found in the DAS of s 2 and s 3 , which can be assigned to the stimulated emission spectrum of [TCNQ À• ] 2 (reactant) and TCNQ 2À (product). Figure 6(d) shows that the spectral shape of DA 314 agrees with the difference of the fluorescence spectrum between TCNQ 2À and [TCNQ À• ] 2 . Figure 6(e) shows that the spectral shape of DA 915 agrees with the fluorescence spectrum of TCNQ 2À . It agrees with our previous work. 16 Therefore, the measured signal probed at $700 nm reflects the reaction dynamics of [TCNQ À• ] 2 and TCNQ 2À , and spectrogram analysis of the transient absorption trace at $700 nm elucidates the molecular vibration dynamics during the reaction from the reactant to the product.  ð Þ þ DA 0 :