Coherent Nuclear Wave Packets in Q States by Ultrafast Internal

Letter pubs.acs.org/JPCL

Coherent Nuclear Wave Packets in Q States by Ultrafast Internal Conversions in Free Base Tetraphenylporphyrin So Young Kim and Taiha Joo* Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea S Supporting Information *

ABSTRACT: Persistence of vibrational coherence in electronic transition has been noted especially in biochemical systems. Here, we report the dynamics between electronic excited states in free base tetraphenylporphyrin (H2TPP) by time-resolved fluorescence with high time resolution. Following the photoexcitation of the B state, ultrafast internal conversion occurs to the Qx state directly as well as via the Qy state. Unique and distinct coherent nuclear wave packet motions in the Qx and Qy states are observed through the modulation of the fluorescence intensity in time. The instant, serial internal conversions from the B to the Qy and Qx states generate the coherent wave packets. Theory and experiment show that the observed vibrational modes involve the out-of-plane vibrations of the porphyrin ring that are strongly coupled to the internal conversion of H2TPP. packet dynamics during the S2 → S1 internal conversion in βcarotene by pump−probe transient absorption combined with electronic population control.11 Suzuki et al. studied the ultrafast S2 → S1 internal conversion in pyrazine by timeresolved photoelectron imaging spectroscopy, and identified the vibrational wave packet dynamics associated with it.12 Such an electronic transition-driven wave packet motion may provide valuable information on the reaction coordinate and vibronic coupling.13,14 Although the wave packet motion can be observed in time domain by various time-resolved techniques, time-resolved fluorescence (TRF) with a resolution higher than the vibrational period of interest is the most direct and unambiguous way, because TRF probes excited-state dynamics exclusively, whereas transient absorption and resonant thirdorder nonlinear techniques may be complicated by ground-state bleach, excited-state absorption, and product absorption. Here, we report the ultrafast internal conversion dynamics from the B state to the Qy and Qx states in H2TPP. We have measured TRF and TRF spectra (TRFS) with high time resolution following the photoexcitation of the B state to establish the kinetics between the excited states and to record the coherent wave packet dynamics in each Q state. Surprisingly, nuclear coherences survived the internal conversions, and moreover, the wave packets in the Qy and Qx states are distinct. In conjunction with theoretical calculations, we were able to assign the wave packets to the out-of-plane vibrations of the porphyrin ring and proposed that those

P

igments based on porphyrin play a central role in many fundamental natural biological systems and artificial photodevices. Light-harvesting antenna complexes, cytochrome c, and many other proteins participating in energy or electron transfer contain porphyrin-based chromophores. Also, porphyrins are effectively applied to solar energy conversion,1−3 photodynamic therapy,4 molecular switch,5 and other photonic devices.6 For potential applications as well as their fundamental importance, photoinduced relaxation processes in porphyrins have been investigated extensively. However, excited-state dynamics of porphyrin often occurs in a femtosecond time scale with a manifold of excited states involved, and therefore, nuclear coordinates responsible for the relaxation processes are not clear as well as the accurate rates of internal conversion between the excited states. Free base tetraphenylporphyrin (H2TPP) is one of the representative simple porphyrins. Baskin et al. reported femtosecond time-resolved spectroscopies on H2TPP to show the ultrafast internal conversions from the B to Qy and to Qx states.7 The lifetime of the B band8 and the time-resolved fluorescence spectra after the Q excitation9 have also been reported. In a femtosecond time-resolved experiment, an ultrashort pump pulse may generate the vibrational wave packets on the excited potential surface. An ultrafast internal conversion from the high-lying electronic state, as in H2TPP, can also generate such a coherent superposition of vibrational states on the lower electronic state, provided the internal conversion occurs faster than the vibrational period, that is, the internal conversion is impulsive on the nuclear motion. Strong vibronic coupling in β-carotene was reported from the amplitude modulation in early transient spectra, and the observed oscillations were found to originate from the S2 → S1 internal conversion.10 Liebel et al. reported the nuclear wave © XXXX American Chemical Society

Received: June 5, 2015 Accepted: July 17, 2015

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DOI: 10.1021/acs.jpclett.5b01188 J. Phys. Chem. Lett. 2015, 6, 2993−2998

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The Journal of Physical Chemistry Letters specific nuclear motions are strongly coupled to the B → Q process in H2TPP. Absorption spectrum of H2TPP in toluene shows an intense peak at 419 nm due to the B state (Supporting Information Figure S1). There are four peaks in the visible region at 513, 548, 590, and 646 nm, which are assigned to the Qy(1,0), Qy(0,0), Qx(1,0), and Qx(0,0) transitions, respectively. The front and back numbers in parentheses are the vibrational quantum numbers of the dominant vibrational mode in the upper and lower electronic states, respectively. In contrast to the absorption, only two peaks at 648 and 716 nm appear in the fluorescence spectrum following the excitation of the B band, which are assigned to the Qx(0,0) and Qx(0,1) transitions, respectively. Absence of readily detectable steady-state fluorescence from the Qy as well as the B states implies the ultrafast internal conversion to the Qx state. Fluorescence from the B and Qy states are observed in the TRF and TRFS. Lifetime of the B state can be determined directly by the TRF detected at 445 nm (Supporting Information Figure S2), which can be attributed to the fluorescence of the B band. The decay of the B band fluorescence is well resolved due to the high time resolution of the TRF apparatus. The B state lifetime is determined to be 63 ± 5 fs, which is in agreement with the value (68 fs) reported by Yeon et al.,8 despite their insufficient time resolution. It is also similar to the estimated value of 50 fs proposed by Baskin et al.7 Similar ultrafast B → Q internal conversion rates have been reported for other free base porphyrins.15−18 In all previous reports, a two-step consecutive internal conversion from B to Qx via Qy was assumed. Kinetics of relevant chemical species and molecular states can be obtained most directly by TRFS. Figure 1 shows the TRFS

613 nm,7 and Białkowski et al. reported similar Qy fluorescence bands at 570 and 605 nm following the excitation of the Qy band.9 TRFS at time zero also shows a peak around 660 nm that can be assigned to the Qx(0,0) band. The rise of the 660 nm peak at later times is slower than that of the Qy band and matches well with the decay time of the Qy band. The Qx(0,0) band shows an additional rise time of 10−20 ps. Because the blue (short wavelength) side of the band exhibits a corresponding decay, this component could be assigned to the solvent-induced thermal equilibration process within the Qx state as reported previously.7,16−18 Because the molecules are excited to the B state, they have large excess energy immediately after the ultrafast internal conversion to the Qx state, which should be dissipated through the vibrational relaxation within the Qx state. At 50 ps, TRFS is dominated by the Qx fluorescence and decays by the Qx lifetime of ∼10 ns. Further detailed examination on the kinetics between relevant states was performed by TRF at selected wavelengths. Figure 2 shows the TRFs of H2TPP in toluene measured at

Figure 2. Global fitting results for kinetic model including the direct path from the B to the Qx states. Here, the TRF signals at 445, 570, and 670 nm were used for the B, Qy, and Qx fluorescence, respectively.

Figure 1. Time-resolved fluorescence spectra of H2TPP in toluene. Intensities were calibrated by rhodamine B as described in the Supporting Information, and the spectra were measured directly without the conventional spectral reconstruction. Excitation wavelength was 410 nm and time resolution for the TRF spectra measurement was 80 fs.

different wavelengths following the excitation of the B band. When fitted to a biexponential function, TRF of the Qy band at 570 nm rises by a time constant of 50 fs and decays by 110 fs with a shift of time zero by 20 fs. The TRF of Qx at 670 nm can be fitted well by a rise time constant of 80 fs with a shift of time zero by 20 fs. The TRFs at various wavelengths are certainly consistent with the TRFS. It is tempting to conclude that the excited-state kinetics is a consecutive two-step internal conversion. Close inspection of the TRF data, however, clearly shows that the rise of the Qx fluorescence is faster than the decay of the Qy fluorescence. This indicates that there may be a direct channel from the B to the Qx states. Therefore, we have considered a kinetic scheme of a consecutive two-step reaction with a direct path.

of H2TPP in toluene over the visible region following the excitation of the B band. Two peaks at 550 and 610 nm are observed immediately after the excitation, which are absent in the steady-state fluorescence spectrum. The two peaks can be assigned to the Qy(0,0) and Qy(0,1) bands from the fact that the energies (wavelengths) correspond to the Qy transitions. Their rise and decay time profiles are also the same confirming that they are the vibrational progression of an electronic state. Baskin et al. reported an ultrafast decay of fluorescence around

The TRFs of the B, Qy, and Qx states were fitted globally according to this scheme (see the Supporting Information), and the results are also shown in Figure 2. Although the fit for the Qy state is not as good as the others mostly due to the small slow component present in the TRF of Qy, this scheme including the direct path gives an excellent fit to all TRF data. 2994

DOI: 10.1021/acs.jpclett.5b01188 J. Phys. Chem. Lett. 2015, 6, 2993−2998

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dominated by a low-frequency mode at 33 cm−1 and possibly a shoulder at ∼80 cm−1, whereas the spectrum from Qx is dominated by a peak at 193 cm−1. For the TRFs at intermediate wavelengths between the Qy and Qx bands, both the 33 and 193 cm−1 modes appear (Supporting Information Figure S5), and the 193 cm−1 mode becomes dominant as the detection wavelength increases. Because the internal conversions to the Qy and Qx states occur fast enough, they can act as impulsive excitation to launch the coherent nuclear wave packets in each Q state. The highest vibrational frequency that can be impulsively excited is limited by the internal conversion time considering the fact that the excitation process should be completed within one-half of a vibrational period. For the kinetic scheme described above, the upper limit of the vibrational frequency that can be excited impulsively is around at 220 cm−1 as determined by the decay time of the B state (67 fs). The finite time resolution of the TRF measurement also limits the highest detectable frequency; for the current time resolution of 55 fs, oscillation amplitude of a 268 cm−1 mode is attenuated by a factor of 2. To explicate this unusual, separate wave packet dynamics, we performed quantum mechanical calculations to simulate the vibrational spectrum observed from the TRF measurement. In an analogy to the Franck−Condon transition, we can define a reactive Huang−Rhys factor (RHRF) in reference to the internal conversion process by assuming that it is impulsive, that is, it occurs much faster than the nuclear motion. Amplitude of the wave packet oscillation for a vibrational mode is determined by the RHRF, which is proportional to the square of the displacement between the reactant (B) and the product (Qy or Qx) along the internal conversion coordinate. Thus, a vibrational mode experiencing large displacement along the internal conversion is excited preferentially to generate the wave packet in the product state.13,21 The amplitude, however, is attenuated by the finite internal conversion time depending on the frequency and the finite time resolution. Here, the wave packet is actually created by the two-step process of photoexcitation from the ground to the B states followed by the internal conversion to the Q states. We bypass the complexity by simply calculating the RHRF from the ground to the Q states. This is reasonable because the B band has no distinctive vibronic structure and generally shows a very small Stokes shift, which suggests that the B state potential is much less displaced from the ground state than the Q state. In addition, resonance Raman spectrum upon B band excitation consists of in-plane modes of Ag symmetry, whereas the spectrum upon Q-band excitation shows an enhancement of nontotally symmetric modes of B1g symmetry with appreciable Huang−Rhys factor. 22,23 With this in mind, geometry optimizations and vibrational frequency calculations were carried out by the density functional theory (DFT) and timedependent DFT (TDDFT) methods by using the Gaussian 09 package. B3LYP/6-311G functional was used for the ground and the first (Qx) excited states, and B3LYP/6-31G for the second (Qy) excited state. The optimized structures of the ground and the first two excited states are given in Supporting Information Figure S6. The calculated transition energies for the Qx and Qy bands are 2.12 and 2.30 eV, which are in good agreement with the experimental values in gas phase.24 The difference vector between the geometrical structures of the two relevant states is projected onto the normal modes of the product state to give the displacement and the RHRF.21

We have tried, unsuccessfully, a simple B → Qy → Qx scheme to fit the data (Supporting Information Figure S3). The rate constants k1, k2, and k3 are (170 fs)−1, (110 fs)−1, and (110 fs)−1, respectively. The k1 turns out to be quite slow considering the actual decay of the B state because of the direct channel, whereas the rate of the direct path (k3) is faster than the path via Qy. The lifetime of the B state from the fit, (k1 + k3)−1 = 67 fs, is consistent with the observed value of 63 fs. For the kinetic scheme, population rise times of both Q states are determined by the decay of the B state and, therefore, should be the same. The rises shown in Figure 2 are seemingly different because of the subsequent Qy → Qx internal conversion. This detailed analysis was possible due to the high time resolution of the TRF measurement. In addition to the ultrafast relaxation dynamics, TRF signals of both Qx and Qy bands shown in Figure 3 display oscillations

Figure 3. Femtosecond time-resolved fluorescence of H2TPP in toluene detected at (a) 570 nm for Qy fluorescence and (b) 650 nm for Qx fluorescence. Red solid lines represent the exponential fits and instrument responses are also shown. Insets show the frequency spectra obtained by Fourier transform (solid line) compared to the calculated frequency spectra (dotted line).

arising from the nuclear wave packet motions in each electronic state. Residuals of the exponential fits were Fourier transformed to give the frequency spectra shown in the insets of Figure 3. Spectral analysis by the linear prediction singular value decomposition (LPSVD) method19,20 also gives similar spectra (Supporting Information Figure S4). They represent the first observation of the impulsive wave packet oscillations in H2TPP and must arise from the Qy and Qx states, not from the ground state, as the signals come from the spontaneous fluorescence. Surprisingly, the frequency spectra originated from the Qy and Qx states are in stark contrast. The spectrum from Qy is 2995

DOI: 10.1021/acs.jpclett.5b01188 J. Phys. Chem. Lett. 2015, 6, 2993−2998

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character. Although most Qy population transfers to the Qx state, a small part of the population remains in the Qy state for several picoseconds, which allows the observation of the lowfrequency oscillation in the Qy fluorescence. The long-lived Qy fluorescence may originate from the leftover population that fails to pass a small barrier for the internal conversion. Internal conversion from Qy to Qx occurs in finite 110 fs, and a finite potential barrier along the Qy → Qx is expected. Because of the large amount of initial excess energy, most of the population in Qy is transferred to the Qx in 110 fs. Nevertheless a small fraction of population may remain in the Qy state for a much longer time. If the coherent excitation of the vibrations originated from the Franck−Condon excitation of the B state, both Q states should show the same wave packet motion with the frequency limited only by the time resolution of the TRF measurement. What is most interesting is that only one vibrational mode plays a significant role in the B → Qx (Qy) internal conversion, indicating that the internal conversion dynamics is localized in one dominant mode. Moreover, each internal conversion is promoted by a unique vibrational mode. Kuhlman et al. also reported that specific vibrational motions promote the S2 → S1 internal conversion in cyclobutanone and 2-methylcyclobutanone27,28 and claimed that internal conversions between electronic excited states are nonergodic which are innately different from ergodic thermalized reactions. Persistence of the vibrational coherence in the transition between excited electronic states is important and may have implications on the recent discussion on the role of vibronic coherence for the energy transfer in a photosynthetic system.29,30 It has been postulated that a low-frequency, outof-plane vibrational mode near 40 cm−1, called heme doming mode, contributes to diatomic ligand binding in a fivecoordinate heme species.31−33 Notably, the 40 cm−1 oscillation was observed in all of the iron-based heme proteins by femtosecond coherence spectroscopy (pump−probe), and it is associated with the core of the porphyrin and does not depend strongly on the peripheral substituents. Additional modes near 80, 120, and 160 cm−1 are observed in the photochemically active samples.33 A heme ruffling or saddling distortion near 70 cm−1 has been also suggested as an important reaction coordinate to control electron transfer to the heme.34 Although there is no direct connection between H2TPP and those porphyrin-based proteins, the observed out-of-plane oscillations at 33 and 193 cm−1 may be related to the low-frequency vibrations in heme. Or it can be the common feature in porphyrin-based systems but further experiments for other porphyrins will be necessary to prove it.

We have carried out the normal-mode-projected displacement calculations for the two different cases: ground → Qx and ground → Qy. Table 1 shows the normal modes with large Table 1. Calculated Normal-Mode Frequencies ωex, NormalMode-Projected Displacements δ, and Corresponding Reorganization Energies λa G → Qx

G → Qyc

mode

ωex (cm−1)b

δ

λ (cm−1)

6 16 19 22 5 17 19 21 22

43 122 162 200 37 126 162 188 196

1.006 −1.217 0.746 −2.163 0.571 −0.545 0.601 −0.523 1.114

22.4 93 46.7 483.2 6.2 19.5 30.6 26.8 126.7

a

Selected modes with nonzero reorganization energies are shown here and whole table for each calculation can be found in the Supporting Information. bFrequency scaling factors of 0.9672 and 0.9613 were used for the first (6-311G) and the second (6-31G) excited states to eliminate known systematic errors in calculated frequencies.25 cFor the same condition, the ground state was calculated at the B3LYP/6-31G level here.

projection amplitudes (δ) and corresponding vibrational reorganization energies (λ = ℏωδ2/2) along the internal conversion to each Q state. For the first case (ground → Qx), ν22 at 200 cm−1 is dominant and matches well with the remarkable oscillation at 193 cm−1 observed in the TRF of Qx. The ν22 mode involves mostly out-of-plane motion of the porphyrin ring with some rocking/scissoring motion of the phenyl groups (Supporting Information Figure S7). We can assign ν22 to the 193 cm−1 mode observed in the experiment, which has a half period of 86 fs similar to the internal conversion time of 110 fs. The second case turned out to be similar to the first case with the ν22 mode at 196 cm−1 that shows the largest reorganization energy, which is in strong contrast to the experiment where a single low-frequency mode at 33 cm−1 was observed. The calculation reveals that only one vibrational mode at 37 cm−1 (ν5) out of around 10 modes in the low-frequency region shows nonzero displacement. Therefore, the 33 cm−1 mode observed in the TRF of Qy can be assigned to the ν5 mode. This mode involves mainly the motion of phenyl groups with some out-of-plane motion of the porphyrin ring (Supporting Information Figure S7). Other normal modes with nonzero displacements at 120−180 cm−1 such as ν19, which involves large in-plane ring stretching but little out-of-plane motion, are absent in the experiment. Note that the ν5 mode at 37 cm−1 with a small reorganization energy appears strongly. Previous reports show that the calculation of RHRF is qualitative not quantitative.13 The internal conversion from the B to the Qx states occurs in two channels, the direct path and the two-step consecutive process via the Qy state. The former proceeds faster than the latter. An ab initio calculation shows that the Bx and By states of H2TPP are nearly degenerate with the same oscillator strengths to give a single absorption band.26 Nevertheless, the Bx state lies slightly lower in the calculation. Therefore, the initial photoexcitation creates a mixture of Bx and By states, and the internal conversion from the manifold of B states to the manifold of Q states could very well exhibit multichannel

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ASSOCIATED CONTENT

S Supporting Information *

Experimental details of the femtosecond TRF upconversion, the TRF spectra measurement, and materials. Also, supporting figures including the steady-state spectra, the B band TRF and the frequency spectra at several wavelengths, the whole table including 33 lowest frequency modes for each calculation, the optimized molecular structure of each state, and the motion of vibrational normal modes assigned to the observed 33 and 193 cm−1 modes. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.jpclett.5b01188. 2996

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (2007-0056330) and the Global Research Laboratory Program (2009-00439). We thank Professor Reimers for providing the Dushin program.

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