Ultrafast Curve Crossing Dynamics through Conical Intersections in

A , 2010, 114 (13), pp 4501–4506. DOI: 10.1021/jp910786s. Publication Date (Web): March 12, 2010. Copyright © 2010 American Chemical Society .... F...
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J. Phys. Chem. A 2010, 114, 4501–4506

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Ultrafast Curve Crossing Dynamics through Conical Intersections in Methylated Cyclopentadienes Fedor Rudakov† and Peter M. Weber*,‡ Computer Science and Mathematics DiVision, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, and Department of Chemistry, Brown UniVersity, ProVidence, Rhode Island 02912 ReceiVed: NoVember 12, 2009; ReVised Manuscript ReceiVed: February 17, 2010

We explored the curve crossing dynamics of 1,2,3,4-tetramethyl-cyclopentadiene (TMCPD) and 1,2,3,4,5pentamethyl-cyclopentadiene (PMCPD) upon π f π* excitation to the 1B2 state using time-resolved, resonanceenhanced multiphoton ionization mass and photoelectron spectroscopy. Upon excitation with a femtosecond laser pulse at 267 nm, the energy relaxation pathway is observed by a time-delayed probe pulse at 400 nm, which ionizes the molecule through Rydberg states that reveal the momentary state of the molecule in the photoelectron spectra. We observe that the initially populated 1B2 state decays to the 2A1 surface in 135 fs in TMCPD and 183 fs in PMCPD, followed by a crossing to the ground state 1A1 surface on 57 and 60 fs time scales for TMCPD and PMCPD, respectively. The spectroscopic signatures of the 2A1 states are clearly revealed in the two-photon ionization photoelectron spectra. In both systems we observe that the ground states are recovered completely, indicating that no new molecular structures are created on the time scale of the experiment. Introduction Ultrafast electronic relaxation processes through conical intersections in cyclic polyenes play an important role in photobiological processes such as vision1 and vitamin D synthesis.2-4 Photoexcitation at UV wavelengths promotes the molecules to a 1B2 state from where relaxation to the 1A1 ground state proceeds through a spectroscopically dark 2A1 state (the labels strictly apply to molecules with C2V symmetry). The relaxation path proceeds through conical intersections and, depending on the particular molecule, may be accompanied by atom migration or electrocyclic ring opening followed by cis-trans isomerization.5-9 The direct observation of the molecules just as they go through the curve crossings is quite challenging for several reasons: First, due to the involvement of conical intersections in the relaxation pathway the time constants for transitions from 1B2 to 2A1 and from 2A1 to 1A1 states are very short, on the order of 100 fs or less.5,10-12 Second, the relaxation proceeds through the 2A1 state that cannot be accessed directly from the ground state as it is spectroscopically dark.5,13,14 Moreover, it is very difficult to observe the molecules after they return to the ground state. The relaxation process deposits very large amounts of energy into vibrational motion of the molecule, rendering most spectroscopic and diffraction techniques inapplicable to probing the relaxation dynamics and the resulting structure of the molecule. Studies of ultrafast relaxation dynamics in small cyclic polyenes have been performed in solution using techniques such as resonance Raman and transient absorption spectroscopy.7-9,14,15 In the gas phase, studies have been performed using electron diffraction16,17 and high intensity ultrafast photoionization coupled with mass spectrometry to identify the decay kinetics of the molecule.5,18 Yet, since mass * Corresponding author: e-mail, [email protected]; fax, +1-401863-2594. † Oak Ridge National Laboratory. ‡ Brown University.

spectrometry does not provide a direct means to probe the molecular structure and electronic states populated at any point in time, the interpretation of those experiments often focused on the time-dependent changes of the fragmentation patterns, rather than the identification of molecular structures and states. In our recent work we demonstrated that molecular Rydberg states may be particularly useful to identify time-dependent molecular structures and electronic relaxation dynamics.19-23 Transitions between Rydberg states, or between a Rydberg state and the corresponding molecular ion state, are not broadened by vibrational or rotational transitions. Thus, the photoionization out of a Rydberg state reveals a highly resolved and purely electronic spectrum that is largely insensitive to vibrational excitation.21,24 Our studies also have demonstrated that the low primary quantum number Rydberg states are remarkably sensitive to the molecular structure.19,22,23,25 This sensitivity toward molecular structure and insensitivity toward vibrational excitation make photoionization out of a Rydberg state an ideal tool to study electronic curve crossing phenomena. In our recent studies we have applied this method to initial model systems. We studied the early stages of the ring-opening reaction of cyclohexadiene and determined the rise and the decay times of the 2A1 state that previously had not been observed spectroscopically.26 In another study we observed structural changes in cyclohexadiene immediately upon relaxation to the ground state by following the molecular evolution through the Rydberg state binding energies.25 In the current publication we apply photoelectron spectroscopy and mass spectrometry to study the curve crossing dynamics in 1,2,3,4-tetramethylcyclopentadiene and 1,2,3,4,5-pentamethyl-cyclopentadiene upon excitation to the 1B2 state. As shown below, we observe the spectroscopic signatures of the 1B2 and 2A1 states and determine the time constants for relaxation from 1B2 to 2A1 and the decay of the 2A1 state to the ground 1A1 state. Part of the motivation of the present work is the indication of structural changes in cyclopentadiene upon crossing through the conical intersections observed by Fuss et al.5 Our optical system was not able to

10.1021/jp910786s  2010 American Chemical Society Published on Web 03/12/2010

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Rudakov and Weber Experiment Our experimental setup, consisting of a photoelectron spectrometer and ultrafast pulsed laser systems, has been described in detail elsewhere.27,28 Briefly, we use a regenerative amplifier (Spitfire, Spectra-Physics) seeded by a Ti:sapphire laser (Tsunami, Spectra-Physics) and pumped by a 5 kHz Nd:YLF laser (Evolution 30, Coherent). The Ti:sapphire laser is pumped by the 532 nm output of an intracavity doubled Nd:YVO4 6 W laser (Millennia Xs, Spectra-Physics). The output pulse energy of this laser system was 280 µJ at 800 nm. The fundamental beam is frequency doubled and tripled by 0.1 mm thick BBO crystals, yielding pulses at wavelengths of 400 and 267 nm. The laser beams were mildly focused onto the molecular beam that was formed by coexpanding the sample (purchased from Sigma-Aldrich) with helium as a carrier gas through a nozzle and a skimmer. To minimize off-resonance processes, above-threshold ionization, and saturation effects, the light intensity at the molecular beam was kept low (on the order of 1010 W/cm2).

Figure 1. Time-resolved excitation and ionization scheme of TMCPD and PMCPD. 4.65 eV photons are used to excite the 1B2 state. The ionization is achieved by one, two, or three 3.1 eV photons as follows: the 1B2 state can be ionized by one probe photon, the 2A1 state requires two probe photons, and, upon relaxation to the 1A1 ground state, the molecule can be ionized in a three photon process. The decay time of 1B2 and the rise time of 2A1 are denoted by τ1; the decay time of 2A1 is denoted by τ2. The spectroscopic notation for the excited states assumes C2V symmetry of the five-membered ring.

reach the absorption wavelength necessary to excite the cyclopentadiene parent compound, necessitating the use of methylated compounds. The experiment is schematically illustrated in Figure 1. Ionization is accomplished in a multiphoton pump-probe scheme that is coupled with the detection of the molecular ions and the ejected photoelectrons. The excitation to the 1B2 state with an ultrashort laser pulse at 267 nm initiates the process. The time-dependent state and structure of the molecules are sampled by a delayed probe pulse at 400 nm. As long as the system is at the originally excited 1B2 surface, one photon is sufficient to ionize. Upon conversion to 2A1, two photons are required to reach the ionization state. This two-photon transition proceeds via intermediate Rydberg states, which manifest themselves through their characteristically sharp Rydberg peaks. Ionization from the ground state is also possible but requires three photons. Since this photoionization from the ground state again proceeds through Rydberg states, we can record the characteristic spectra and identify the product molecules formed as a result of the curve crossing events.25 From the combination of the time-dependent mass and photoelectron spectra, we can assemble a rather complete picture of the curve crossing pathway and kinetic constants. This picture and its construction are described below.

Results and Discussion A. Dynamics Probed by Photoelectron Spectroscopy. Figure 2 shows photoelectron spectra of TMCPD and PMCPD. Photoionization of TMCPD and PMCPD with only the second harmonic (400 nm) pulses causes three-photon ionization via several Rydberg states (Figure 2a). In this ionization process, the first photon is too low in energy to be resonant, but there are two-photon transitions to Rydberg states. Ionization from those states yields sharp peaks that reflect the binding energies of the respective Rydberg levels. While the spectrum of Figure 2a is not sufficient to derive a complete assignment, the peaks with binding energies in the region of 1.5 eV are likely due to 3d and 4s levels, while the ones around 2.2 eV are likely from 3p. The individual peaks of TMCPD are at 1.39, 1.47, 1.63, and 2.10 eV, while for PMCPD (inset in Figure 2a) they are at 1.425, 1.594, 1.963, 2062, and 2.60 eV. Excitation to those Rydberg levels is possible even without tuning of the laser wavelength because the Franck-Condon envelopes are likely broad, so that resonance excitation to several states is possible even with the fixed 400 nm wavelength. Photoionization with third harmonic pulses (267 nm) proceeds with two photons via the 1B2 state. The photoelectron spectrum of TMCPD shows a broad, featureless band starting at about 2.65 eV (Figure 2b). In this ionization process, one photon excites the short-lived 1B2 state and the second photon ionizes from there. Since 1B2 is a valence state, ionization is accompanied by a structure change and therefore associated with a broad Franck-Condon envelope. No vibrational structure is observed, likely because the four methyl groups of TMCPD give the molecule too many low-frequency vibrations for us to spectrally resolve. Similar spectra were obtained for PMCPD. Photoionization of TMCPD with temporally coincident pulses at 267 and 400 nm leads to the photoelectron spectrum of Figure 2c. The ionization process only uses the 1B2 resonance, so that no sharp peaks from Rydberg states would be expected. The onset of ionization, at a binding energy of 2.63 eV, allows us to estimate the adiabatic ionization potential of TMCPD: with a pump pulse energy of 4.65 eV, and a binding energy at time zero of 2.63 eV, we infer an ionization threshold at 7.28 eV. This value is in excellent agreement with a value of 7.3 eV for the adiabatic ionization energy given in the literature.29 A similar analysis for PMCPD gives an ionization energy of 7.29 eV for PMCPD.29

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Figure 3. Time-resolved photoelectron kinetic energy spectra of TMCPD (panel a) and PMCPD (panel b). Photoelectrons with kinetic energy below 0.47 eV (a) and 0.46 eV (b) mostly originate from the 1B2 state and arise from single photon ionization with the probe pulse. The signals at higher electron kinetic energies are the spectroscopic signatures of the 2A1 state, which results from photoionization through the Rydberg states using two photons. Upon crossing to the ground state, the contour spectra, which have the one-color signals subtracted, do not show any further signals, indicating complete recovery of the original ground state structure. The color bars indicate the intensity on a logarithmic (base e) scale.

Figure 2. Photoelectron spectra obtained by (a) one-color ionization with 400 nm (3.1 eV) pulses, (b) one-color ionization with 267 nm (4.65 eV) pulses, and (c) two color ionization with zero time delay using 267 and 400 nm pulses (the underlying one-color spectra are subtracted). The main graphs are for TMCPD, while the insets are for PMCPD.

Figure 3 shows the time-dependent photoelectron spectra of TMCPD and PMCPD. In these plots, the time-independent onecolor signals are subtracted, and since ionization at different

times proceeds with different numbers of photons, the photoelectron kinetic energy spectrum is plotted. The photoelectron kinetic energies are the directly observed quantity; binding energy spectra, such as those plotted in Figure 2, are derived by subtracting the electron kinetic energy from the photon energy of the ionizing radiation. At early times, right around the time of excitation, there are very strong signals from electrons with kinetic energies below 0.47 and 0.46 eV, respectively. As discussed above, most of this signal originates from ionization out of the 1B2 state. As the wavepackets move out of the Franck-Condon region of 1B2 and cross into the 2A1 state, the signal intensity for electrons with kinetic energy below 0.47 (0.46) eV declines since the probe photon energy (3.1 eV) is insufficient to ionize out of 2A1. At this point in time, photoionization out of the 2A1 state requires two photons and proceeds through the Rydberg states. Thus, the 2A1 states are reflected in the contour plots as a series of sharp peaks. In TMCPD, these peaks are at 1.02, 1.47, 1.63, and 1.72 eV of kinetic energy, while in PMCPD they are at 0.93, 1.02, 1.34, 1.45, and 1.49 eV. They reach their maximum intensity around 100 fs after the initial excitation. Photoelectrons with higher kinetic energy (above 1.7 eV) also originate from the 2A1 state by two-photon ionization through the Rydberg states. Yet since photoionization is performed through Rydberg states with high

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principal quantum number, the density of states is high so that the Rydberg spectra at high electron kinetic energy are poorly resolved. The molecules do not remain in for 2A1 for long: within several hundred femtoseconds, the photoelectron signals decay as the molecules cross to the 1A1 ground state. Importantly, the signals completely vanish for time delays greater than 500 fs. Since we know that the ground state can be ionized and spectrally observed in our spectrum (see Figure 2a as well as the mass spectra discussed below), the complete disappearance of any signal in the background-subtracted contour plots implies that the molecules return back to the ground state. We note that in molecules that do change their structure, the experiment does reveal a decrease of the signal resulting from the ionization of the parent molecule.25 In the methylated cyclopentadienes studied here, there apparently is no structural isomerization, and the molecules are recovered in their initial states. Of course, after undergoing the optical excitation and electronic curve crossing dynamics, the molecules are much more energetic. However, this extra energy does not affect the ionization from the Rydberg state21 and is therefore not observed in the background-subtracted spectra. B. Dynamics Probed by Mass Spectrometry. With the pathways of the electronic curve crossings firmly established by the time-resolved photoelectron spectra, we now turn to photoionization mass spectrometry experiments. In our instrument, the detection of photoions is more efficient than that of photoelectrons, so that the mass spectra provide us with better quality data. Even so, all the dynamics measurements using mass spectrometry are completely consistent with the time-resolved photoelectron spectra. Figure 4 shows a contour plot of the time-dependent mass spectrum of TMCPD (Figure 4a), as well as its projection onto the mass and time delay coordinates (Figure 4, panels b and c, respectively). Upon excitation, TMCPD (parent mass 122.2) displays little fragmentation, the main fragment beng trimethylcyclopentadiene (mass 107.2), which is generated by cleavage of a methyl group from TMCPD. Other fragments have masses of 93.2, 92.2, 91.2, and 79.2 u. Similar mass spectra were measured for PMCPD. All the fragments exhibit identical temporal profiles, an indication that fragmentation takes place on the ion surface while the molecular ions are on their way to the ion detector, rather than fragmentation on the excited state surface. We also point to the shading of the mass peaks, a further indication of fragmentation during the flight time. For the analysis of the time dependence, it is therefore sufficient to analyze the sum of all the fragment signals. The two-color photoionization signal of the parent mass starts immediately with the overlap of the pump and probe laser pulses and decays quickly to a baseline level that is below zero, i.e., below the level before the initial excitation by the pump pulse. The fragment ion signal starts later than the parent ion signal and reaches a maximum intensity approximately 100 fs after the parent signal. The fragment signal decays quickly to the baseline that is elevated compared to the signal at negative delay times. The ionization energy of the TMCPD, as determined from the photoelectron spectra, is 0.47 eV below the sum of second and third harmonic photons (3.1 eV + 4.65 eV). Thus, by onephoton ionization out of 1B2 no more than 0.47 eV of vibrational energy can be deposited into vibrational motions of the ion. This energy is not sufficient to fragment the molecular ion. Since one-photon ionization out 1B2 is far more efficient than multiphoton ionization from other states, we conclude that the

Rudakov and Weber

Figure 4. Time-dependent mass spectrum of TMPCP (a) and its projections onto the mass coordinate (b) and the time coordinate (c). Ionization proceeds via time-delayed two-color ionization using 4.65 and 3.1 eV photons. Positive delay times indicate that the 4.65 eV pulse precedes the 3.1 eV pulse. The mass spectrum of panel b represents a sum over all delay times. Panel c shows the time dependence of the parent mass (black circles) and the sum over all fragment masses (red circles).

parent signal observed in the time-dependent mass spectra reflects the time-dependent population of the 1B2 state. As the wavepacket moves out of the 1B2 and into the 2A1 state, electronic energy is converted into vibrational energy. Two-photon ionization out of the 2A1 state results in deposition of additional energy into vibrational motion. The energy

Ultrafast Curve Crossing deposited into vibrational motion is apparently sufficient to fragment the ions. The molecular ions have plenty of time to fragment on their way to the mass spectrometer detector, so that mostly the fragments are observed. Consequently, the observed decay of the parent signal and the accompanied rise of the fragment signal reveal the transition of the molecule from the 1B2 to the 2A1 state. When the wavepacket moves out of 2A1 and onto the 1A1 ground state, even more energy is deposited into vibrations. This energy deposited into the molecule during the transition through the conical intersections remains with the molecule upon photoexcitation and again results in fragmentation subsequent to ionization. This explains the depletion of the parent signal and the increase in fragment signals at long time delays, after the molecules have finished the curve crossing processes (Figures 4 and 5). On the basis of this interpretation, we analyze the timedependent mass spectra by fitting the parent signal to an exponential decay with a baseline that decays in a step function, both convoluted by the instrument function. The exponential decay represents the transition from 1B2 to 2A1. The fragment signals are represented as growing with the decay of the parent ions, and decaying themselves with a time constant that reflects the curve crossing from 2A1 to 1A1. The fragment signal also has a step function, but one that rises during the curve crossing as a result of the increased deposited energy. Details of this analysis are given in the Appendix. The result is that in TMCPD the transition from 1B2 to 2A1 proceeds on a time scale of 135(7) fs, and the decay from 2A1 to 1A1 through the conical intersection happens on a time scale of 57(12) fs. The errors (in parentheses) are three standard deviations. The corresponding time constants in PMCPD are 183(32) and 60(26) fs. Apparently, the additional placement of a methyl group in the 5-position slows down the dynamics of the first curve crossing slightly. This may be because the additional mass at that position slows down the motion of the wavepacket in 1B2 or because the wave packet has a more convoluted path to take to clear the cusp in the region of the conical intersection. To further analyze this phenomenon, more detailed computational studies of the methylated cyclopentadienes would be required. The crossings into the ground states have essentially identical time constants, suggesting that at this point the vibrational energies are more evenly spread over those coordinates that matter for the curve crossing, so that the crossing becomes a purely electronic phenomenon. Summary and Conclusion Time-resolved pump-probe photoionization coupled with mass spectrometric detection has frequently been used to study the dynamics of molecules in excited electronic states. Mass spectrometry by itself is, however, inherently insufficient because ions can fragment on their way to the mass spectrometer detector, masking the true dynamics. In contrast, photoelectron spectroscopy measures the electrons ejected during the ionization process and thus provides an instantaneous measure of the state of the ion. In the present project we have used both photoelectron spectroscopy and mass spectrometry to explore the ultrafast curve crossing through the conical intersections of TMCPD and PMCPD. Using the photoelectron spectra, we are able to follow the relaxation dynamics during all time steps and to identify the time-dependent electronic states and structures of the molecules. The decay times of the 1B2 and the synchronous rise time of the 2A1 states are 135 and 183 fs for TMCPD and

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Figure 5. Time-dependent mass spectra of TMCPD for (a) the parent ions and (b) the fragment ions. The dots are the experimental data, while the solid black lines show the fitted curves. The blue and red dashed lines show the components of the fit signals. In panel a, the rise and fall of the parent signal (blue dashed line) correspond to the population of the 1B2 state, while the decreasing step function represents the loss of cold molecules. As the wavepacket moves toward the 2A1 state, the electronic energy is transferred into vibrational motions, giving rise to a fragment signal (panel b) with a rise representing the population out of the initially excited 1B2 state and a decay to the ground state. The increase in the baseline signal of the fragments, red dashed line, represents the overall increase in hot molecules from the optical excitation.

PMCPD, while the decay times of the 2A1 states are 57 and 60 fs, respectively. Importantly, the depression of the parent mass signal at long delay times and the elevation of the fragment mass signals reflect the energy deposited into the molecules during the curve crossing processes and reveal that photoionization subsequent to the curve crossing is quite viable. Even so, the time-dependent photoelectron spectra show no such signal elevation or depression, indicating that the molecules quantitatively recover their original structures without isomerization processes such as those that have been postulated in the unmethylated cyclopentadiene.5 As stated previously,25 the resonant ionization through the Rydberg states yields a binding energy spectrum that is independent of the deposited energy, allowing us to make such important inferences.

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The discrepancy between the dynamics of the methylated cyclopentadiene and the unsubstituted cyclopentadiene could conceivably be due to the presence of large heat baths provided by the low-frequency methyl groups. These heat baths would distribute the available energy over many degrees of freedom, thereby reducing the energy available for a reaction to isomers. However, it is difficult to see how this heat bath could be activated within less than 200 fs, as would be needed to affect the reaction on the time scale of our experiment. This explanation also is not consistent with our finding that the crossing from 2A1 to 1A1, where the isomerization would take place, is not sensitive to the addition of a fifth methyl group in PMCPD. The discrepancy of experimental results in cyclopentadiene and its methylated derivatives merits further investigation. Acknowledgment. This project is supported by the Division of Chemical Sciences, Geosciences, and Biosciences, the Office of Basic Energy Sciences, the U.S. Department of Energy by Grant Number DE-FG02-03ER15452. Fedor Rudakov’s research is performed as a Eugene P. Wigner Fellow and staff member at the Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract DEAC05-00OR22725. Numerical Analysis of the Decay Kinetics. To model the dynamics in the TMCPD, we assumed first-order kinetics for transitions between electronic states. As discussed in the text, the following processes contribute to the time-dependent parent signal function: 1. Ionization out of the 1B2 state, which decays to the 2A1 state, giving the single exponential decay of the molecular parent function

(

P1 ) exp -

t - τ0 τ1

)

for t - τ0 g 0, and zero otherwise. (All formulas use the following notations: P, scaling constants; t, time delay between pulses; τ0, time zero; τ1, the decay time of the 1B2 state and the rise time of 2A1 state; τ2, decay time of the 2A1 state (see Figure 1.) 2. Decrease of the signal due to a reduced number of cold parent molecules upon optical excitation. The molecular function for this process is

(

-P2 ) 1 -

( (

)

-(t - τ0) 1 τ2 exp τ2 - τ1 τ2

(

τ1 exp

-(t - τ0) τ1

)))

for t - τ0 g 0, and zero otherwise. For the fragments, contributions to the time-resolved signal arise from the following processes: 1. Ionization out of 2A1 with time-dependent signal given by

P3 )

(

)( (

)

(

τ2 -(t - τ0) -(t - τ0) exp - exp τ2 - τ1 τ2 τ1

for t - τ0 g 0, and zero otherwise.

))

2. Ionization out of the ground state after relaxation with molecular function given by

(

P4 ) 1 -

( (

)

-(t - τ0) 1 τ2 exp τ2 - τ1 τ2

(

τ1 exp

-(t - τ0) τ1

)))

for t - τ0 g 0, and zero otherwise. The optimization of all adjustable parameters (time zero, decay times, scaling constants, and the standard deviation for the instrument function) was performed using the LevenbergMarquardt algorithm30 for all curves at once. As shown in Figure 5 for TMCPD, the theoretical model with the optimized parameters provides excellent fits to the measured data. References and Notes (1) Birge, R. R. Biochim. Biophys. Acta 1990, 1016, 293. (2) Dauben, William, G.; Disanayaka, Bimsara; Funhoff, Dirk, J. H.; Kohler, Bryan E.; Schilke, David E.; Boli Zhou, Boli J. Am. Chem. Soc. 1991, 113, 8367. (3) Jacobs, H. J. C.; Havinga, E. AdV. Photochem. 1979, 11, 305. (4) Vitamin D; Feldman, D., Glorieux, F. H., Pike, J. W., Eds.; Academic: San Diego, CA, 1997. (5) Fuss, W.; Schmid, W. E.; Trushin, S. A. Chem. Phys. 2005, 316, 225. (6) Horspool, W. M.; Song, P. S. CRC Handbook of Organic Photochemistry and Photobiology; CRC Press: Boca Raton, FL, 2003. (7) Lochbrunner, S.; Fuss, W.; Schmid, W. E.; Kompa, K.-L. J. Phys. Chem. A 1998, 102 (47), 9334. (8) Harris, D. A.; Orozco, M. B.; Sension, R. J. J. Phys. Chem. A 2006, 110 (30), 9325. (9) Pullen, S. H.; Anderson, N. A.; Walker, L. A., II; Sension, R. J. J. Chem. Phys. 1998, 108 (2), 556. (10) Hofmann, A.; de Vivie-Riedle, R. J. Chem. Phys. 2000, 112 (11), 5054. (11) Trulson, M. O.; Dollinger, G. D.; Mathies, R. A. J. Chem. Phys. 1989, 90 (8), 6404–6408. (12) Fuss, W.; Lochbrunner, S.; Muller, A. M.; Schikarski, T.; Schmid, W. E.; Trushin, S. A. Chem. Phys. 1998, 232 (1,2), 161. (13) Garavelli, M.; Page, C. S.; Celani, P.; Olivucci, M.; Schmid, W. E.; Trushin, S. A.; Fuss, W. J. Phys. Chem. A 2001, 105 (18), 4458. (14) Schalk, O.; Unterreiner, A.-N. J. Phys. Chem. A 2007, 111 (17), 3231. (15) Ohta, Kaoru; Naitoh, Yukito; Tominaga, Keisuke; Yoshihara, Keitaro J. Phys.Chem. A 2001, 105 (16), 3973. (16) Dudek, R. C.; Weber, P. M. J. Phys. Chem. A 2001, 105, 4167. (17) Ruan, C.-Y.; Lobastov, V. A.; Srinivasan, R.; Goodson, B. M.; Ihee, H.; Zewail, A. H. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 7117. (18) Kotur, Marija; Weinacht, Thomas; Pearson, Brett J.; Matsika, Spiridoula J. Chem. Phys. 2009, 130, 134311. (19) Minitti, M. P.; Weber, P. M. Phys. ReV. Lett. 2007, 98 (25), 253004/ 1. (20) Gosselin, J. L.; Weber, P. M. J. Phys. Chem. A 2005, 109, 4899. (21) Minitti, M. P.; Cardoza, J. D.; Weber, P. M. J.Phys.Chem. A 2006, 110, 10212. (22) Kuthirummal, N.; Weber, P. M. J. Mol. Struct. 2006, 787 (1-3), 163. (23) Cardoza, Job D.; Rudakov, Fedor M.; Hansen, Nils; Weber, Peter M. J. Electron Spectrosc. Relat. Phenom. 2008, 165 (1-3), 5. (24) Cardoza, Job D.; Weber, Peter M. J. Chem. Phys. 2007, 127 (3), 036101/1. (25) Rudakov, F.; Weber, P. M. Chem. Phys. Lett. 2009, 470 (4-6), 187–190. (26) Kuthirummal, N.; Rudakov, F. M.; Evans, C. L.; Weber, P. M J. Chem. Phys. 2006, 125 (13), 133307/1. (27) Schick, C. P.; Carpenter, S. D.; Weber, P. M. J. Phys. Chem. A 1999, 103, 10470. (28) Kim, B.; Thantu, N.; Weber, P. M. J. Chem. Phys. 1992, 97, 5384. (29) NIST webbook http://webbook.nist.gov. (30) Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. Numerical Recepies in C: The Art of Scientific Computing Cambridge University Press: Cambridge, 1992; pp 681-688, ISBN 0-521-43108-5.

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