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Vibrational amplitude profile of molecular vibrational modes for vibrational mode assignment
Chemical Physics Letters 400 (2004) 301–307 www.elsevier.com/locate/cplett
Vibrational amplitude profile of molecular vibrational modes for vibrational mode assignment Takayoshi Kobayashi *, Masakatsu Hirasawa, Yuzo Sakazaki, Hiroki Hane Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan Received 30 April 2004; in final form 1 October 2004 Available online 13 November 2004
Abstract Ultrashort pulse lasers with 6- and 20-fs durations were utilized for phthalocyanine thin film sample to induce several vibrational modes and vibration amplitude spectra were determined by multi-wavelength measurement technique. From the spectra we could identify the electronic states, which couple to two vibrational modes with frequencies of 670 and 750 cm1. It was shown that the vibrational amplitude profile obtained by the method can be used for providing information for the assignment of the vibrational mode. 2004 Elsevier B.V. All rights reserved.
1. Introduction Much attention has recently paid to the ultrafast dynamics of the excited states in macrocyclic compounds, of which typical examples are phthalocyanine (Pc) and their derivatives including metallophthalocyanines (MPcs). There are several reasons for this interest. The first reason is that they are closely related to porphyrin, which is of vital importance in biological phenomena, such as energy transfer in photosynthesis processes [1,2]. It is well known that the excited-state dynamics of MPc strongly depends on the central metal atom [3], peripherals [4] and the molecular aggregation [4,5]. The second reason is that they are considered to form a group of candidate materials in various photonics and optoelectronics devices [6–9]. The third reason is their large optical nonlinear responses due to their two-dimensional conjugated p-electron system. In some cases they show ultrafast dynamics
*
Corresponding author. Fax: +81 3 5841 4165. E-mail addresses: [email protected], kobayashi@ phys.s.u-tokyo.ac.jp (T. Kobayashi). 0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.10.125
to be used in nonlinear optical devices [10], such as optical switches and optical limiters [11–13]. To be really useful in such applications the mechanism of the nonlinearity and its dynamics must be clarified in full detail. For this purpose, internal conversion (IC), photocarrier yields, and lifetimes of fluorescence from the second excited state, S2, and intersystem crossing (ISC) [14–18] have also been studied for these molecules. Dynamical processes including vibronic coupling is also highly relevant with such optical nonlinearity because it substantially changes the electronic spectra in such highly symmetric system as Pcs. Raman spectroscopy is also useful for this purpose since it is a valuable tool for the identification of the relevant states to the nonlinear processes and the relaxation processes. The Raman spectra obtained from Pcs are relatively sharp, molecularly specific, and can be resonance enhanced, allowing clear identification of the species. Pcs are characterized by two broad strong electronic absorption bands in the UV–Vis region [19,20], chemical and thermal stability [21], relatively easy of thin-film fabrication [22], and a high laser damage threshold [21]. In this Letter, we applied a new method of real-time spectroscopy to a sample of Pc thin film
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to clarify the mechanism of vibronic coupling which are relevant to chemical reactions and carrier transport.
3. Results and discussion 3.1. Time-resolved spectra
2. Experimental A thin film sample of phthalocyanine tin (IV) dichloride (SnPc) was prepared by evaporation in a vacuum (base pressure 1.6 · 105 Torr) on a glass substrate. The sample thickness was measured using a surfaceroughness tester (SurfTest SV-400; Mitutoyo Corp.) ranging between 200 and 400 nm between two ends with nearly constant inclination. The evaporated thin film of SnPc is supposed to be in an amorphous phase [22] with so-called Ôshuttlecock-shapedÕ molecules stack normal to the molecular planes in one-dimensional columns [23]. We carried out stationary absorption and pump–probe measurements at the thinner (200 nm) and thicker end (400 nm), respectively, of the sample to enhance absorbance difference at the CT-band. The pulsed light sources and the setup for femtosecond time-resolved absorption spectroscopy was described previously [24–27]. The 6-fs, 1-kHz pulse train was generated from the noncollinear optical parametric amplifier (NOPA) with a pulse compressor [24,25] and its wavelength ranged is from 500 to 750 nm. The pulse energies (intensities) of the pump and probe at the sample position were 20 and 5 nJ (1.6 · 1015 and 4.0 · 1014 photon/cm2), respectively. In order to measure weak pump–probe signals at various wavelengths, we used a multi-channel lock-in amplifier, which was specially designed for the detection of low-intensity signals simultaneously over the whole probing spectral region. In the present experiment, 128-channel signals, spectrally resolved by a polychromator (JASCO M25-TP), were detected by avalanche photodiodes and the lock-in amplified in reference to the modulated pump pulse at 230 Hz by a mechanical chopper. The normalized transmittance changes in 500–720 nm region were measured for 2 to 4 ps range with a 2.5-fs interval. In order to investigate the longer wavelength range of QY-band, another Ti:sapphire laser system (FemtoSource (sPRO); FemtoLasers) with an 8-path bow-tie amplifier (FemtoPower; FemtoLasers) was used. The width, energy, and repetition rate of the pulses were 20 fs, 30 lJ, and 1 kHz, respectively. The laser spectrum extends from 750 to 870 nm with a peak wavelength around 795 nm. The pulse energies (intensities) of the pump and probe were 50 and 5 nJ (2.5 · 1015 and 2.5 · 1014 photon/cm2), respectively. Probe light dispersed by a monochromator was detected by a silicon photodiode and a conventional digital-signal-processing (DSP) lock-in amplifier (Model 7265; Perkin–Elmer) in 750–875 nm region from 0.6 to 4 ps range with a 5-fs interval.
Fig. 1 shows the stationary absorption spectrum of the SnPc film sample and spectra of the 6- and 20-fs pulsed lasers, and the time-resolved difference absorption spectra extending from 11 500 to 19 000 cm1 obtained by the 6- and 20-fs lasers at several delay times. There are very broad and intense bleaching in the range of 15 700–19 500 cm1 and an absorption peak in the range of 14 000–14 900 cm1. Though the stationary absorption spectrum shown in Fig. 1 is inhomogeneously broadened because of amorphous character, the peaks at 13 300 and 14 600 cm1 are well established to be assigned as QY and QX bands [19,20]. The difference between the sign-reversed ground-state absorption spectrum and the transient spectrum is caused by the existence of the excited-state absorption spectrum which is known to have peaks around 14 800 cm1 and at lower than 18 000 cm1 [28]. In the 11 600–13 200 cm1 range pump–probed by the 20-fs pulse laser, bleaching is observed. 3.2. Real-time spectrum Left-side panels of Fig. 2 represent a dozen examples of the real-time traces of the normalized difference transmittance (DT/T) induced by 6- or 20-fs laser pulse excitation. The former and the latter cover the spectral
Fig. 1. (a) Stationary absorption spectrum of SnPc thin film and the laser intensity (dotted curve: 20-fs laser, dashed curve: 6-fs laser). (b)–(c) Time-resolved difference absorption spectra at several probe delay times.
T. Kobayashi et al. / Chemical Physics Letters 400 (2004) 301–307
303
(a)
(a')
(b)
(b')
(c)
(c')
(d)
(d')
(e)
(e')
(f)
(f')
(g)
(g')
(h)
(h')
(i)
(i')
(j)
(j')
(k)
(k')
(l)
(l')
Fig. 2. (a)–(l) Delay time traces of normalized difference transmittance of SnPc thin film after being excited with 6-fs ((g)–(l)) or 20-fs ((a)–(f)) pulses. The spectral resolutions are 3 nm for both excitation cases. (a 0 )–(l 0 ) Fourier transformation of (a)–(l).
ranges of 530–700 nm (14 300–18 900 cm1) and 750– 875 nm (11 400–13 300 cm1), respectively. The signal sizes of DT/T were integrated over the spectral width of 16 nm. In the spectral ranges of 850–875 and 530– 550 nm (not shown) the signals do not decay substantially up to 4 ps. The lifetime is previously reported to be longer than one nanosecond and at shorter delay time it decays slightly because of exciton–exciton interaction induced by the Auger process as discussed in our previous paper [30]. 3.3. Comparison between the vibrational amplitude spectra and Raman excitation profiles Right-side panels of Fig. 2 exhibit the Fourier amplitude spectra obtained by the Fourier transform of the real-time spectra shown in the right-side panels of the figure. There are several commonly observed frequency
components with different intensity distribution profiles depending on the probe photon energy. In order to obtain a global view of the probe wavelength-dependent vibrational amplitude, a contour map of two-dimensional (vibrational frequency vs. probe photon frequency) amplitude is shown in Fig. 3 for the molecular vibration of the time-resolve difference absorption spectra obtained with the use of the 20- and 6-fs lasers. The map extends from 11 500 to 13 300 cm1 in probe-photon frequency and from 100 to 2000 cm1 in molecular vibrational frequency. Similar contour map for 6-fs pulse experiment in the electronic spectral and vibrational frequency regions of 550–660 nm (15 150–18 200 cm1) and 100–2000 cm1, respectively, was shown in our previous Letter [28]. It can be seen that there are Fourier components due to molecular vibrations with mode frequencies of 590, 670, 750 and 1340 cm1. They were assigned as A1g
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ulated to become DA 0 (x) by the molecular vibration with the mode frequency of X in the following way:
Wavelength (nm) 850
800
750
650
600
550
1500
(a) 1
-1
Wavenumber (cm )
2
ð1aÞ
dxðtÞ ¼ dx cosðXt þ /1 Þ;
ð1bÞ
duðtÞ ¼ du cosðXt þ /2 Þ:
ð1cÞ
4
1000 8 16
500
11.5
12
12.5
13
15.5
16
16.5
17 17.5 18
Wavenumber ( × 10 cm ) 2.5
-1
-1
-1
(c) 670 cm Qx+Qy Qx+Qy+CT
(b)
2.0
750 cm Qx+Qy Qy
4 3
1.5 2 1.0 1
0.5 0.0
Absorbance
3
Amplitude (arb. units)
DA0 ðxÞ ¼ DAðx þ dxðtÞÞð1 þ duðtÞÞ;
12
13
14
15
16
17
1812
13
14
15
16
17
0 18
Wavenumber ( × 10 cm ) 3
-1
Fig. 3. (a) Contour map of two-dimensional (vibrational frequency vs. probe photon frequency) amplitude calculated from the normalized transmittance difference (DT/T). The vibrational amplitude is indicated on the logarithmic scale with a step of two. (b) The Fourier amplitude of the 670-cm1 mode (circles and squares) and absorbance of the Qand CT-bands. (c) The Fourier amplitude of the 750-cm1 mode (circles and squares) and absorbance of QY- and Q-bands. The circles and squares were data obtained by using 6- and 20-fs lasers, respectively.
C–N–C bending, B1g macrocycle deformation, B2g C– N–C bending, and the first over-tone (the second harmonic) of the Blg macrocycle deformation (670 cm1), respectively [31]. In order to study detailed probe frequency dependence of several modes, the Fourier amplitude is plotted for 670 and 750 cm1 modes against probe photon energy in Figs. 3b,c, respectively. The former figure shows that the vibrational amplitude of the mode of 670 cm1 fits well with the absorption spectrum composed of both QX and QY transitions. Since the absorption cross section of CT transition is small, it is difficult to tell whether the CT absorption ranging in the 16 000–18 000 cm1 region is or is not contributing to the 670 cm1 mode. The latter figure shows that the mode of 750 cm1 has only the contribution from QY transition. The mode can be described by the following equation. The difference absorption spectrum DA(x) is mod-
Here du(t) and dx(t) correspond to the normalized amplitude modulation and spectral shift with initial phases of /1 and /2, respectively. The mechanism of the former process is Ôdynamic intensity borrowingÕ which is described as the deviation from the Condon approximation as discussed in our previous papers [32,33]. There are two mechanisms in the latter process. One is due to the change in the coefficients ci(t) and cj(t) of the vibrational wavefunctions vie and vjg associated with the excited and the ground electronic states, respectively. The time-dependent ÔFranck–CondonÕ P overlap i;j ci ðtÞcj ðtÞhvie j vjg i gives the transient absorption spectrum following the wavepacket motion. A coherent-phonon (molecular vibration) generated by a short pulse oscillates on the potential curve and the peak wavelength of the absorption (induced emission) spectrum is swept from the higher energy side to the lower side of the stationary absorption spectrum resulting in the spectral shift. This was argued previously in relation with the phonon squeezing [29]. In case of coherent-phonon excitation condition, where pulse width is much shorter than the vibrational oscillation period as satisfied in our present study, the spectral shape during the sweeping process does not change but only its peak is shifted with time. The other mechanism is the modulation of transition energy during the process of molecular vibration. Both of the above mechanisms give the frequency dependence proportional to the first derivative of the absorption spectrum with respect to the probe frequency x in case the shift is small as shown below DA0 ðxÞ ’ DAðxÞ þ duDAðxÞ cosðXt þ /1 Þ þ dx
dDAðxÞ cosðXt þ /2 Þ: dx
ð2Þ
Since the intensities of electronic absorption of Q-bands are borrowed from the allowed transitions to B bands [32,33] the contribution of the second term in Eq. (2) due to the deviation from Condon approximation is larger than the third term due to the energy shift. It is also the case for the CT band, since the probability of intrinsically weak CT transition is also borrowed from the transitions to the locally excited states. The vibrational amplitude profile (VAP) and the ground-state absorption (GSA) spectrum agree fairly well with each other as shown in Fig. 3b for 670 cm1. From the results it can be concluded that the modes of 670 and 750 cm1 are to be attributed to those which
T. Kobayashi et al. / Chemical Physics Letters 400 (2004) 301–307
changes the electronic distributions of both QX and QY (and CT) bands and dominantly QY band, respectively. Thus the previous assignment of the 670 cm1 Raman line to the macrocyclic deformation mode which is expected to modify QX, QY, and CT bands is then well supported [31]. There are some deviations in the 12 000–13 500 cm1 range between VAP of the 670 cm1 mode and GSA. In this spectral range the derivative of absorption spectrum has a peak and hence it may give a negative contribution resulting in the shifting of the amplitude spectra to blue. In order to discuss further we analyzed the data of Raman excitation profiles (REPs) of the two modes in PbPc, which are available in [19]. Figs. 4a–d show the REPs measured by Smith et al. [19] for 670 and 750 cm1, respectively. The REPs are composed with the decomposed spectra of QY, QX and CT. Both REPs of 670 and 750 cm1 are in fair agreement with the QYband absorption as seen in Figs. 4c and d, respectively. The REPs were calculated with the following equation using the stationary absorption spectrum of the SnPc sample. The excitation frequency dependence of the Raman cross section is given for the fundamental transition of a mode ÔaÕ with a mode frequency of xa as follows [35]: 3 2
xðx xa Þ n 2 Da j AðxÞ Aðx xa Þj2 8c2 p3 3 xðx xa Þ n2 2 2 2 ¼ Da j AðxÞj þ j Aðx xa Þj 8c2 p3 AðxÞ Aðx xa Þ AðxÞAðx xa Þ :
rR ðxÞ /
ð3Þ
305
Here A(x) and A(x xa) are the absorption spectral shape and that shifted by the vibrational frequency xa, respectively, and Da, n, and c, are the dimensionless displacement, the refractive index of the sample, and the light velocity in vacuum, respectively. The REP results show that both 670 and 750 cm1 modes found for PbPc are coupled dominantly to QY band as seen from Figs. 4c,d, respectively. The Raman signal of 750 cm1 in literature [31] was assigned mainly to B2g C–N–C bending with 30% contribution for lead Pc (PbPc). While VAP measured for SnPc indicate that 670 cm1 mode is coupled to QX, QY and probably to CT bands as shown in Figs. 3b,c, respectively. In order to evaluate the quality of argument between the absorption spectra and VAP, we calculate the standard deviation of the VAP signal and the absorption bands. The results are shown in Table 1. In case of 670 cm1 mode provides best fit while in the case of 750 cm1 mode QY offers the best value. The above results can be explained in terms of several reasonings. The first one is because of difference in the macrocycle planarity of Pcs. Since the REPs are measured for Cu phthalocyanine (CuPc) with a planar macrocycle having a central metal with a smaller ion size, the Table 1 Standard deviation between the absorption bands and the VAP signals for 670 and 750 cm1 modes Absorption band
670 cm1
750 cm1
QY QX + QY QX + QY + CT
3.23 1.07 0.74
1.10 1.15 1.15
(a)
(b)
(c)
(d)
Fig. 4. (a), (c) Raman cross section of 670 cm1 mode, which are assigned as a B1g macrocycle deformation, calculated from the deconvoluted absorbance for Q- and CT-bands. The Raman excitation profile measured by Smith et al. [19] of the mode is also plotted with solid squares, (b), (d) Calculated Raman cross section of 750 cm1 mode due to the B2g C–N–C bending [31].
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vibronically coupled electronic state in SnPc in the present study can be different from that of CuPc [34]. The second possible reasoning is related to the expression of REP given by Eq. (3). In case of a mode which couples with both the QX and QY electronic transitions, REP represented by Eq. (3) cannot be used because in the equation A(x) and A(x xa) are both simply the sums of the two electronic transitions of QX and QY bands and those shifted ones. Not only the cross terms between AQx(x) and AQx(x xa) or corresponding QY terms, but also those between AQx(x) and AQy(x) and other combination are expected to contribute resulting in much more complicated situation as seen from the following equation: AðxÞ ¼ AQx ðxÞ þ AQy ðxÞ;
By combining the two methods we can obtain even more detailed insight into the vibronic coupling, molecular vibration, and electronic-state characterization. Since molecular vibrational modes which modify the polarizability are active in both Raman and real-time spectra, the vibrational modes appear in common and can be compared. In conclusion, we have for the first time compared vibrational amplitude profile (VAP) with the Raman excitation profile (REP), and focused the difference between them. The VAP obtained by ultrashort pulse was shown to be one of a useful tool for the mode assignment of those molecular vibrations which commonly appear in the Raman and real-time spectra.
ð4Þ
while in the case of VAP there is no such cross terms and it is simply proportional to the intensity of the absorption spectrum and insensitive to the phase of the electronic transitions. In this sense VAP is more appropriate for the vibrational mode assignment for systems with isotropically distributed transition moments. Hereafter more general discussion or the difference between REP and VAP is to be made. Both of them are related to the Raman processes, the former is related to the spontaneous Raman and the latter is induced by the stimulated Raman process. Therefore there is a possibility of difference induced by the mode density at the frequencies of the fields. However the difference in the density between the two frequencies related to the Raman process is expected to be very small because of the small frequency difference in the process. REP has been used extensively to clarify the mechanism of vibronic coupling, assignment of molecular vibration and characterization of electronic state. However, it has the following three drawbacks. The first is that the method requires widely tunable CW laser(s) with the same spectral width and similar power. If there are differences in mode pattern, intensity, and spectral width among the laser lines and/or lasers, they must be corrected properly but usually it is difficult to correct precisely these differences. The second is that it is a time-consuming pointby-point method. Data obtained may contain a lot of systematic errors associated with long time measurement and with the intensity corrections and takes very long experimental time to verify the reproducibility of the data. The third problem is that the data taken by REP method suffer from the cross-term effect as discussed above and makes it difficult to analyze the data. In spite of the efforts made: to improve the situation, the problems have not yet been solved satisfactorily yet. In case of the present novel VAP method using a multi-channel measuring technique, it is free from these three problems. VAP can be more direct method for the assignment of the vibrational modes, though the system of short pulse may require high laser technology.
Acknowledgements The authors are grateful to Messrs. N. Ishii and S. Adachi for their help in experiment. This research was conducted as part of a program for the ÔBroadband Light SynthesizeÕ and received Special Coordination Funds for Promoting Science and Technology from the Ministry of Education, Culture, Sports, Science and Technology. This work was also partly supported by a Grant-in-Aid for Specially Promoted Research (Grant No. 14002003).
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Vibrational amplitude profile of molecular vibrational modes for vibrational mode assignment Takayoshi Kobayashi *, Masakatsu Hirasawa, Yuzo Sakazaki, Hiroki Hane Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan Received 30 April 2004; in final form 1 October 2004 Available online 13 November 2004
Abstract Ultrashort pulse lasers with 6- and 20-fs durations were utilized for phthalocyanine thin film sample to induce several vibrational modes and vibration amplitude spectra were determined by multi-wavelength measurement technique. From the spectra we could identify the electronic states, which couple to two vibrational modes with frequencies of 670 and 750 cm1. It was shown that the vibrational amplitude profile obtained by the method can be used for providing information for the assignment of the vibrational mode. 2004 Elsevier B.V. All rights reserved.
1. Introduction Much attention has recently paid to the ultrafast dynamics of the excited states in macrocyclic compounds, of which typical examples are phthalocyanine (Pc) and their derivatives including metallophthalocyanines (MPcs). There are several reasons for this interest. The first reason is that they are closely related to porphyrin, which is of vital importance in biological phenomena, such as energy transfer in photosynthesis processes [1,2]. It is well known that the excited-state dynamics of MPc strongly depends on the central metal atom [3], peripherals [4] and the molecular aggregation [4,5]. The second reason is that they are considered to form a group of candidate materials in various photonics and optoelectronics devices [6–9]. The third reason is their large optical nonlinear responses due to their two-dimensional conjugated p-electron system. In some cases they show ultrafast dynamics
*
Corresponding author. Fax: +81 3 5841 4165. E-mail addresses: [email protected], kobayashi@ phys.s.u-tokyo.ac.jp (T. Kobayashi). 0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.10.125
to be used in nonlinear optical devices [10], such as optical switches and optical limiters [11–13]. To be really useful in such applications the mechanism of the nonlinearity and its dynamics must be clarified in full detail. For this purpose, internal conversion (IC), photocarrier yields, and lifetimes of fluorescence from the second excited state, S2, and intersystem crossing (ISC) [14–18] have also been studied for these molecules. Dynamical processes including vibronic coupling is also highly relevant with such optical nonlinearity because it substantially changes the electronic spectra in such highly symmetric system as Pcs. Raman spectroscopy is also useful for this purpose since it is a valuable tool for the identification of the relevant states to the nonlinear processes and the relaxation processes. The Raman spectra obtained from Pcs are relatively sharp, molecularly specific, and can be resonance enhanced, allowing clear identification of the species. Pcs are characterized by two broad strong electronic absorption bands in the UV–Vis region [19,20], chemical and thermal stability [21], relatively easy of thin-film fabrication [22], and a high laser damage threshold [21]. In this Letter, we applied a new method of real-time spectroscopy to a sample of Pc thin film
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to clarify the mechanism of vibronic coupling which are relevant to chemical reactions and carrier transport.
3. Results and discussion 3.1. Time-resolved spectra
2. Experimental A thin film sample of phthalocyanine tin (IV) dichloride (SnPc) was prepared by evaporation in a vacuum (base pressure 1.6 · 105 Torr) on a glass substrate. The sample thickness was measured using a surfaceroughness tester (SurfTest SV-400; Mitutoyo Corp.) ranging between 200 and 400 nm between two ends with nearly constant inclination. The evaporated thin film of SnPc is supposed to be in an amorphous phase [22] with so-called Ôshuttlecock-shapedÕ molecules stack normal to the molecular planes in one-dimensional columns [23]. We carried out stationary absorption and pump–probe measurements at the thinner (200 nm) and thicker end (400 nm), respectively, of the sample to enhance absorbance difference at the CT-band. The pulsed light sources and the setup for femtosecond time-resolved absorption spectroscopy was described previously [24–27]. The 6-fs, 1-kHz pulse train was generated from the noncollinear optical parametric amplifier (NOPA) with a pulse compressor [24,25] and its wavelength ranged is from 500 to 750 nm. The pulse energies (intensities) of the pump and probe at the sample position were 20 and 5 nJ (1.6 · 1015 and 4.0 · 1014 photon/cm2), respectively. In order to measure weak pump–probe signals at various wavelengths, we used a multi-channel lock-in amplifier, which was specially designed for the detection of low-intensity signals simultaneously over the whole probing spectral region. In the present experiment, 128-channel signals, spectrally resolved by a polychromator (JASCO M25-TP), were detected by avalanche photodiodes and the lock-in amplified in reference to the modulated pump pulse at 230 Hz by a mechanical chopper. The normalized transmittance changes in 500–720 nm region were measured for 2 to 4 ps range with a 2.5-fs interval. In order to investigate the longer wavelength range of QY-band, another Ti:sapphire laser system (FemtoSource (sPRO); FemtoLasers) with an 8-path bow-tie amplifier (FemtoPower; FemtoLasers) was used. The width, energy, and repetition rate of the pulses were 20 fs, 30 lJ, and 1 kHz, respectively. The laser spectrum extends from 750 to 870 nm with a peak wavelength around 795 nm. The pulse energies (intensities) of the pump and probe were 50 and 5 nJ (2.5 · 1015 and 2.5 · 1014 photon/cm2), respectively. Probe light dispersed by a monochromator was detected by a silicon photodiode and a conventional digital-signal-processing (DSP) lock-in amplifier (Model 7265; Perkin–Elmer) in 750–875 nm region from 0.6 to 4 ps range with a 5-fs interval.
Fig. 1 shows the stationary absorption spectrum of the SnPc film sample and spectra of the 6- and 20-fs pulsed lasers, and the time-resolved difference absorption spectra extending from 11 500 to 19 000 cm1 obtained by the 6- and 20-fs lasers at several delay times. There are very broad and intense bleaching in the range of 15 700–19 500 cm1 and an absorption peak in the range of 14 000–14 900 cm1. Though the stationary absorption spectrum shown in Fig. 1 is inhomogeneously broadened because of amorphous character, the peaks at 13 300 and 14 600 cm1 are well established to be assigned as QY and QX bands [19,20]. The difference between the sign-reversed ground-state absorption spectrum and the transient spectrum is caused by the existence of the excited-state absorption spectrum which is known to have peaks around 14 800 cm1 and at lower than 18 000 cm1 [28]. In the 11 600–13 200 cm1 range pump–probed by the 20-fs pulse laser, bleaching is observed. 3.2. Real-time spectrum Left-side panels of Fig. 2 represent a dozen examples of the real-time traces of the normalized difference transmittance (DT/T) induced by 6- or 20-fs laser pulse excitation. The former and the latter cover the spectral
Fig. 1. (a) Stationary absorption spectrum of SnPc thin film and the laser intensity (dotted curve: 20-fs laser, dashed curve: 6-fs laser). (b)–(c) Time-resolved difference absorption spectra at several probe delay times.
T. Kobayashi et al. / Chemical Physics Letters 400 (2004) 301–307
303
(a)
(a')
(b)
(b')
(c)
(c')
(d)
(d')
(e)
(e')
(f)
(f')
(g)
(g')
(h)
(h')
(i)
(i')
(j)
(j')
(k)
(k')
(l)
(l')
Fig. 2. (a)–(l) Delay time traces of normalized difference transmittance of SnPc thin film after being excited with 6-fs ((g)–(l)) or 20-fs ((a)–(f)) pulses. The spectral resolutions are 3 nm for both excitation cases. (a 0 )–(l 0 ) Fourier transformation of (a)–(l).
ranges of 530–700 nm (14 300–18 900 cm1) and 750– 875 nm (11 400–13 300 cm1), respectively. The signal sizes of DT/T were integrated over the spectral width of 16 nm. In the spectral ranges of 850–875 and 530– 550 nm (not shown) the signals do not decay substantially up to 4 ps. The lifetime is previously reported to be longer than one nanosecond and at shorter delay time it decays slightly because of exciton–exciton interaction induced by the Auger process as discussed in our previous paper [30]. 3.3. Comparison between the vibrational amplitude spectra and Raman excitation profiles Right-side panels of Fig. 2 exhibit the Fourier amplitude spectra obtained by the Fourier transform of the real-time spectra shown in the right-side panels of the figure. There are several commonly observed frequency
components with different intensity distribution profiles depending on the probe photon energy. In order to obtain a global view of the probe wavelength-dependent vibrational amplitude, a contour map of two-dimensional (vibrational frequency vs. probe photon frequency) amplitude is shown in Fig. 3 for the molecular vibration of the time-resolve difference absorption spectra obtained with the use of the 20- and 6-fs lasers. The map extends from 11 500 to 13 300 cm1 in probe-photon frequency and from 100 to 2000 cm1 in molecular vibrational frequency. Similar contour map for 6-fs pulse experiment in the electronic spectral and vibrational frequency regions of 550–660 nm (15 150–18 200 cm1) and 100–2000 cm1, respectively, was shown in our previous Letter [28]. It can be seen that there are Fourier components due to molecular vibrations with mode frequencies of 590, 670, 750 and 1340 cm1. They were assigned as A1g
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T. Kobayashi et al. / Chemical Physics Letters 400 (2004) 301–307
ulated to become DA 0 (x) by the molecular vibration with the mode frequency of X in the following way:
Wavelength (nm) 850
800
750
650
600
550
1500
(a) 1
-1
Wavenumber (cm )
2
ð1aÞ
dxðtÞ ¼ dx cosðXt þ /1 Þ;
ð1bÞ
duðtÞ ¼ du cosðXt þ /2 Þ:
ð1cÞ
4
1000 8 16
500
11.5
12
12.5
13
15.5
16
16.5
17 17.5 18
Wavenumber ( × 10 cm ) 2.5
-1
-1
-1
(c) 670 cm Qx+Qy Qx+Qy+CT
(b)
2.0
750 cm Qx+Qy Qy
4 3
1.5 2 1.0 1
0.5 0.0
Absorbance
3
Amplitude (arb. units)
DA0 ðxÞ ¼ DAðx þ dxðtÞÞð1 þ duðtÞÞ;
12
13
14
15
16
17
1812
13
14
15
16
17
0 18
Wavenumber ( × 10 cm ) 3
-1
Fig. 3. (a) Contour map of two-dimensional (vibrational frequency vs. probe photon frequency) amplitude calculated from the normalized transmittance difference (DT/T). The vibrational amplitude is indicated on the logarithmic scale with a step of two. (b) The Fourier amplitude of the 670-cm1 mode (circles and squares) and absorbance of the Qand CT-bands. (c) The Fourier amplitude of the 750-cm1 mode (circles and squares) and absorbance of QY- and Q-bands. The circles and squares were data obtained by using 6- and 20-fs lasers, respectively.
C–N–C bending, B1g macrocycle deformation, B2g C– N–C bending, and the first over-tone (the second harmonic) of the Blg macrocycle deformation (670 cm1), respectively [31]. In order to study detailed probe frequency dependence of several modes, the Fourier amplitude is plotted for 670 and 750 cm1 modes against probe photon energy in Figs. 3b,c, respectively. The former figure shows that the vibrational amplitude of the mode of 670 cm1 fits well with the absorption spectrum composed of both QX and QY transitions. Since the absorption cross section of CT transition is small, it is difficult to tell whether the CT absorption ranging in the 16 000–18 000 cm1 region is or is not contributing to the 670 cm1 mode. The latter figure shows that the mode of 750 cm1 has only the contribution from QY transition. The mode can be described by the following equation. The difference absorption spectrum DA(x) is mod-
Here du(t) and dx(t) correspond to the normalized amplitude modulation and spectral shift with initial phases of /1 and /2, respectively. The mechanism of the former process is Ôdynamic intensity borrowingÕ which is described as the deviation from the Condon approximation as discussed in our previous papers [32,33]. There are two mechanisms in the latter process. One is due to the change in the coefficients ci(t) and cj(t) of the vibrational wavefunctions vie and vjg associated with the excited and the ground electronic states, respectively. The time-dependent ÔFranck–CondonÕ P overlap i;j ci ðtÞcj ðtÞhvie j vjg i gives the transient absorption spectrum following the wavepacket motion. A coherent-phonon (molecular vibration) generated by a short pulse oscillates on the potential curve and the peak wavelength of the absorption (induced emission) spectrum is swept from the higher energy side to the lower side of the stationary absorption spectrum resulting in the spectral shift. This was argued previously in relation with the phonon squeezing [29]. In case of coherent-phonon excitation condition, where pulse width is much shorter than the vibrational oscillation period as satisfied in our present study, the spectral shape during the sweeping process does not change but only its peak is shifted with time. The other mechanism is the modulation of transition energy during the process of molecular vibration. Both of the above mechanisms give the frequency dependence proportional to the first derivative of the absorption spectrum with respect to the probe frequency x in case the shift is small as shown below DA0 ðxÞ ’ DAðxÞ þ duDAðxÞ cosðXt þ /1 Þ þ dx
dDAðxÞ cosðXt þ /2 Þ: dx
ð2Þ
Since the intensities of electronic absorption of Q-bands are borrowed from the allowed transitions to B bands [32,33] the contribution of the second term in Eq. (2) due to the deviation from Condon approximation is larger than the third term due to the energy shift. It is also the case for the CT band, since the probability of intrinsically weak CT transition is also borrowed from the transitions to the locally excited states. The vibrational amplitude profile (VAP) and the ground-state absorption (GSA) spectrum agree fairly well with each other as shown in Fig. 3b for 670 cm1. From the results it can be concluded that the modes of 670 and 750 cm1 are to be attributed to those which
T. Kobayashi et al. / Chemical Physics Letters 400 (2004) 301–307
changes the electronic distributions of both QX and QY (and CT) bands and dominantly QY band, respectively. Thus the previous assignment of the 670 cm1 Raman line to the macrocyclic deformation mode which is expected to modify QX, QY, and CT bands is then well supported [31]. There are some deviations in the 12 000–13 500 cm1 range between VAP of the 670 cm1 mode and GSA. In this spectral range the derivative of absorption spectrum has a peak and hence it may give a negative contribution resulting in the shifting of the amplitude spectra to blue. In order to discuss further we analyzed the data of Raman excitation profiles (REPs) of the two modes in PbPc, which are available in [19]. Figs. 4a–d show the REPs measured by Smith et al. [19] for 670 and 750 cm1, respectively. The REPs are composed with the decomposed spectra of QY, QX and CT. Both REPs of 670 and 750 cm1 are in fair agreement with the QYband absorption as seen in Figs. 4c and d, respectively. The REPs were calculated with the following equation using the stationary absorption spectrum of the SnPc sample. The excitation frequency dependence of the Raman cross section is given for the fundamental transition of a mode ÔaÕ with a mode frequency of xa as follows [35]: 3 2
xðx xa Þ n 2 Da j AðxÞ Aðx xa Þj2 8c2 p3 3 xðx xa Þ n2 2 2 2 ¼ Da j AðxÞj þ j Aðx xa Þj 8c2 p3 AðxÞ Aðx xa Þ AðxÞAðx xa Þ :
rR ðxÞ /
ð3Þ
305
Here A(x) and A(x xa) are the absorption spectral shape and that shifted by the vibrational frequency xa, respectively, and Da, n, and c, are the dimensionless displacement, the refractive index of the sample, and the light velocity in vacuum, respectively. The REP results show that both 670 and 750 cm1 modes found for PbPc are coupled dominantly to QY band as seen from Figs. 4c,d, respectively. The Raman signal of 750 cm1 in literature [31] was assigned mainly to B2g C–N–C bending with 30% contribution for lead Pc (PbPc). While VAP measured for SnPc indicate that 670 cm1 mode is coupled to QX, QY and probably to CT bands as shown in Figs. 3b,c, respectively. In order to evaluate the quality of argument between the absorption spectra and VAP, we calculate the standard deviation of the VAP signal and the absorption bands. The results are shown in Table 1. In case of 670 cm1 mode provides best fit while in the case of 750 cm1 mode QY offers the best value. The above results can be explained in terms of several reasonings. The first one is because of difference in the macrocycle planarity of Pcs. Since the REPs are measured for Cu phthalocyanine (CuPc) with a planar macrocycle having a central metal with a smaller ion size, the Table 1 Standard deviation between the absorption bands and the VAP signals for 670 and 750 cm1 modes Absorption band
670 cm1
750 cm1
QY QX + QY QX + QY + CT
3.23 1.07 0.74
1.10 1.15 1.15
(a)
(b)
(c)
(d)
Fig. 4. (a), (c) Raman cross section of 670 cm1 mode, which are assigned as a B1g macrocycle deformation, calculated from the deconvoluted absorbance for Q- and CT-bands. The Raman excitation profile measured by Smith et al. [19] of the mode is also plotted with solid squares, (b), (d) Calculated Raman cross section of 750 cm1 mode due to the B2g C–N–C bending [31].
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vibronically coupled electronic state in SnPc in the present study can be different from that of CuPc [34]. The second possible reasoning is related to the expression of REP given by Eq. (3). In case of a mode which couples with both the QX and QY electronic transitions, REP represented by Eq. (3) cannot be used because in the equation A(x) and A(x xa) are both simply the sums of the two electronic transitions of QX and QY bands and those shifted ones. Not only the cross terms between AQx(x) and AQx(x xa) or corresponding QY terms, but also those between AQx(x) and AQy(x) and other combination are expected to contribute resulting in much more complicated situation as seen from the following equation: AðxÞ ¼ AQx ðxÞ þ AQy ðxÞ;
By combining the two methods we can obtain even more detailed insight into the vibronic coupling, molecular vibration, and electronic-state characterization. Since molecular vibrational modes which modify the polarizability are active in both Raman and real-time spectra, the vibrational modes appear in common and can be compared. In conclusion, we have for the first time compared vibrational amplitude profile (VAP) with the Raman excitation profile (REP), and focused the difference between them. The VAP obtained by ultrashort pulse was shown to be one of a useful tool for the mode assignment of those molecular vibrations which commonly appear in the Raman and real-time spectra.
ð4Þ
while in the case of VAP there is no such cross terms and it is simply proportional to the intensity of the absorption spectrum and insensitive to the phase of the electronic transitions. In this sense VAP is more appropriate for the vibrational mode assignment for systems with isotropically distributed transition moments. Hereafter more general discussion or the difference between REP and VAP is to be made. Both of them are related to the Raman processes, the former is related to the spontaneous Raman and the latter is induced by the stimulated Raman process. Therefore there is a possibility of difference induced by the mode density at the frequencies of the fields. However the difference in the density between the two frequencies related to the Raman process is expected to be very small because of the small frequency difference in the process. REP has been used extensively to clarify the mechanism of vibronic coupling, assignment of molecular vibration and characterization of electronic state. However, it has the following three drawbacks. The first is that the method requires widely tunable CW laser(s) with the same spectral width and similar power. If there are differences in mode pattern, intensity, and spectral width among the laser lines and/or lasers, they must be corrected properly but usually it is difficult to correct precisely these differences. The second is that it is a time-consuming pointby-point method. Data obtained may contain a lot of systematic errors associated with long time measurement and with the intensity corrections and takes very long experimental time to verify the reproducibility of the data. The third problem is that the data taken by REP method suffer from the cross-term effect as discussed above and makes it difficult to analyze the data. In spite of the efforts made: to improve the situation, the problems have not yet been solved satisfactorily yet. In case of the present novel VAP method using a multi-channel measuring technique, it is free from these three problems. VAP can be more direct method for the assignment of the vibrational modes, though the system of short pulse may require high laser technology.
Acknowledgements The authors are grateful to Messrs. N. Ishii and S. Adachi for their help in experiment. This research was conducted as part of a program for the ÔBroadband Light SynthesizeÕ and received Special Coordination Funds for Promoting Science and Technology from the Ministry of Education, Culture, Sports, Science and Technology. This work was also partly supported by a Grant-in-Aid for Specially Promoted Research (Grant No. 14002003).
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