Probing the Lifetimes of Internally Excited Amyl Nitrite Cations - The

Jun 11, 2010 - ... ionization of amyl nitrite, C5H11ONO, using ultrafast laser pulses deposits up to 3.7 eV of energy into internal degrees of freedom...
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J. Phys. Chem. A 2010, 114, 7021–7025

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Probing the Lifetimes of Internally Excited Amyl Nitrite Cations Martin Rosenberg,† Michael P. Minitti,‡ Nerijus Rusteika,† Christer Z. Bisgaard,† Sanghamitra Deb,‡ Peter M. Weber,‡ and Theis I. Sølling*,† Department of Chemistry, UniVersity of Copenhagen, UniVersitetsparken 5, DK-2100 Copenhagen, and Department of Chemistry, Brown UniVersity, ProVidence, Rhode Island 02912 ReceiVed: March 16, 2010; ReVised Manuscript ReceiVed: May 26, 2010

The photoelectron spectrum shows that multiphoton ionization of amyl nitrite, C5H11ONO, using ultrafast laser pulses deposits up to 3.7 eV of energy into internal degrees of freedom. As a result, the molecules fragment to produce various daughter ions of masses 87, 71, 60, 57, 41, 30, 29, and 27. Absorption of an additional photon with 3 eV of energy by the ions yields transients with picosecond decay times, revealing the time scale of the decomposition dynamics of the initially prepared parent ion. Each mass peak has a distinct time constant, in the range of 1.2 to 7.9 ps, emphasizing the dependence of the fragmentation mechanism on the ion internal energy. 1. Introduction Femtosecond time-resolved mass spectrometry is a convenient technique for probing ultrafast reaction dynamics such as bond dissociation on repulsive excited state surfaces.1 Measuring reaction dynamics using an ionizing probe pulse is attractive, because the ionization step is always an allowed process, while the charged particles can be detected with high efficiency.2 Previous time-resolved mass spectrometry experiments have shown that pumping to a repulsive valence state with low oscillator strength may result in multiphoton absorption leading to the generation of excited-state ions.3 Excited-state ions will be in play also when the focus is on the dynamics of the neutral molecules, and it is important to separate the part of the time dependent signal that arises from neutral species from the part that arises from ions. Excited-state ions have been studied by Johnson’s group using photoinduced Rydberg ionization (PIRI) spectroscopy.4-6 More recently, Ho et al. used femtosecond time-resolved mass spectrometry to investigate the dynamics of the azo-benzene cation on the ionic ground state surface.7 The scope and limitations of solely using mass spectrometry to probe ion state dynamics deserves further attention. The possible influence of ionic excited states in such femtosecond time-resolved mass spectrometry investigations has to our knowledge not been discussed elsewhere. It is therefore desirable to gain knowledge of how widely excited ionic state dynamics may influence the results from such experiments. The bond dissociation of alkyl nitrites through the first singlet excited (S1) state has been subject to several investigations.8-14 Because of the (n,π*) character of the S1 state the oscillator strength for excitation from S0 is low, and it is therefore likely that multiphoton ionization will occursespecially if a nonresonant excitation wavelength is used. The second excited singlet state, (S2), has a much higher absorption cross section stretching over a wide range of wavelengths as it stems from a (π,π*) transition.14,15 Ionization via short-lived states inserts sizable quantities of energy into the molecular ion, making the alkyl nitrites suitable compounds in an investigation of excited ionic * To whom correspondence should be addressed. E-mail: [email protected]. † Department of Chemistry, University of Copenhagen. ‡ Department of Chemistry, Brown University.

state dynamics. This paper focuses on the excited state dynamics of the amyl nitrite cation using femtosecond time-resolved mass spectrometry measurements and proposes a model for how the signal resulting from ionic excited state dynamics contributes and affects the overall transient signal. 2. Experimental Setup Time-resolved photoelectron and photoion experiments were conducted in the laboratories of the investigators at the University of Copenhagen and at Brown University. While the two apparatus and laser systems were functionally similar, some of the experimental conditions such as laser pulse energies, durations, pump-probe polarization, and repetition rates varied. Even so, the results were reproducible and consistent. For simplicity, only the experimental data collected at Brown University will be presented. Amyl nitrite molecules were seeded in 1 bar of helium carrier gas and passed through a 96 µm skimmer before entering a differentially pumped chamber where they underwent photoexcitation and ionization. The spectrometer was outfitted with a tunable (750-850 nm), commercial regenerative amplifier laser system (Positive Light, Spitfire) operating at 5 kHz. The amplified near-IR fundamental output was frequency upconverted to the second and third harmonics for the investigations. The third harmonic (3ω, 266 nm) was used as the pump pulse and subsequently the second harmonic (2ω, 400 nm) as the probe pulse. The pulse energies (power densities) of the 3ω and 2ω were approximately 2 µJ (4.07 × 1011 W/cm2) and 10 µJ (1.02 × 1012 W/cm2), respectively. Both photoelectrons and ions were detected using multichannel plate detectors while the time-of-flight spectra were acquired using ultrafast timing electronics. The details of the Brown University time-of-flight photoelectron/photoion spectrometer have been described elsewhere.16,17 Amyl nitrite was purchased from TCI Europe (purity >96%), and the purity was verified by both 1H- and 13C NMR spectroscopy. To reduce the amount of clustering observed in the molecular beam, the amyl nitrite sample was placed in a temperature controlled bath of 0 °C. The setup in Copenhagen consists of a Ti:sapphire laser system from Spectra Physics (Tsunami oscillator, Spitfire Pro amplifier), which delivers 130 fs, 1 mJ pulses at 1 kHz. The

10.1021/jp102393g  2010 American Chemical Society Published on Web 06/11/2010

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Rosenberg et al.

Figure 1. Gas-phase UV-vis absorption spectrum of amyl nitrite recorded at room temperature. The S0 to S1 transition is located around 355 nm. The intense band corresponds to the S0 to S2 transition and is centered at 225 nm. The solid and dashed arrows represent the 3ω excitation wavelength used in this study.

system is tunable from 760-860 nm but in this study the amplifier was operated with a fixed wavelength of 800 nm. The fundamental output of the laser was frequency doubled and tripled with two successive BBO crystals (0.5 mm, types I and II). The third harmonic (4.64 eV) was passed onto an automated delay stage and merged with the second harmonic before entering the sample chamber. In Copenhagen, the two pulses were overlapped on a molecular beam that was generated by expansion of the amyl nitrite vapor (21 °C) seeded in He at 1 bar. Both photoelectrons and ions were detected using multichannel plate detectors, and the time-of-flight spectra were acquired by a multiscaler card (FastComTec) at different delays between pump and probe. The gas-phase absorption UV-vis spectrum of amyl nitrite (Figure 1) was recorded at room temperature on a Cary 50 (Varian Inc.) spectrometer by placing one drop of amyl nitrite in a 1 cm quartz cuvette. All calculations were performed using the GAUSSIAN 03 suite of programs.18 The structure of amyl nitrite in the ground state (S0) and the ionic ground state (D0) was calculated at the UB3LYP/6-31+G(d,p) level. The frequencies were calculated to verify the true nature of the calculated structures. 3. Results and Discussion Absorption Spectrum of Amyl Nitrite. A suitable wavelength for directly ionizing amyl nitrite was determined from the gas phase absorption spectrum of amyl nitrite shown in Figure 1, recorded at room temperature. An excitation wavelength of 266 nm (4.64 eV) generated ions via the low side of the S2 absorption band. The vertical ionization energy is known to be 10.6 eV.19 The absorption of two 3ω photons (9.28 eV) is therefore insufficient to ionize amyl nitrite. Three 3ω photons (13.92 eV) will ionize amyl nitrite and have the ability to deposit significant amounts of energy into the internal modes. For this reason, ionization with 3ω was deemed to be a good choice. For the time-resolved mass and photoelectron spectrometric experiments, the 3ω was used as the pump pulse while the 2ω pulse was used as the probe. Thus, positive time delays correspond to exclusively pump induced processes. Photoelectron Spectroscopy. To experimentally determine the internal energy content of the ions generated upon 3-photon ionization at 266 nm, photoelectron spectra were recorded. The steady-state spectrum of amyl nitrite using 3 × 3ω ionization

Figure 2. Photoelectron spectrum of amyl nitrite resulting from threephoton ionization with 266 nm light. Vertical ionization from the neutral ground state is expected to result in electrons with a kinetic energy of 3.3 eV. The adiabatic ionization is estimated to be at an electron kinetic energy of 4.14 eV.

pulses is shown in Figure 2. Vertical ionization with 3 × 3ω gives rise to electrons with kinetic energies of 3.32 eV, as marked in Figure 2. An exact value of the adiabatic ionization energy has not been reported, but on the basis of the spectrum in Figure 2, we estimate it to be where the kinetic electron energy is 4.14 eV, implying an adiabatic ionization energy of about 9.78 eV. As is evident from the photoelectron spectrum, ions can be generated with a wide range of energies. Near the adiabatic ionization energy, the internal ion energy approaches zero, but the fraction of molecules generated with such low energy is small. Dominant in the photoelectron spectrum are electrons with kinetic energies lower than 3.3 eV. These photoelectrons stem from ions that are borne with excess internal energy, i.e., excited-state ions. The absence of well-defined peaks along with a nearly featureless appearance of the photoelectron spectrum suggests that no specific electronically excited state of the radical cations is significantly populated. The energy therefore must be deposited in a multitude of vibrational modes that are spectrally unresolved. With photoelectron kinetic energies observed down to 0.4 eV, the ions must have internal energies up to 3.7 eV. The spectrum in Figure 1 shows that absorption of a 3ω pulse will excite amyl nitrite to the S2 state. This agrees with a recent experimental investigation revealing that 266 nm laser pulse excitation of the homologous n-butyl nitrite leads to direct and fast C4H9O-NO photodissociation via the repulsive S2 state.15 In a recent computational study we showed that the S2 state of amyl nitrite is indeed repulsive,14 so even within the duration of the ultrashort laser pulses a large amount of kinetic energy is accumulated along the repulsive coordinate and remains within the molecule upon ionization. Moreover, when comparing the calculated bond lengths around the chromophore in the Franck-Condon and the minimum structure of the amyl nitrite radical cation, Table 1, it is clear that the [C4H9CH2-ONO]+• and [C5H11O-NO]+• bonds are significantly elongated and shortened, respectively, in the minimum structure. These results imply that the ions are generated with a large amount of

Lifetimes of Internally Excited Amyl Nitrite Cations

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TABLE 1: Calculated Bond Lengths for Amyl Nitrite in the Ground State (S0) and Ionic Ground State (D0) and Differences in the Bond Lengths in the Neutral and Ionic Amyl Nitrite bond

bond length (S0)/Åa

bond length (D0)/Åa

bond length difference/Åb

C5H11ONdO C5H11OsNO C5H11sONO C4H9sCH2ONO

1.192 1.393 1.453 1.522

1.173 1.277 1.591 1.494

0.019 0.116 -0.138 0.028

a

UB3LYP/6-31+G(d,p). b Bond length (S0) - Bond length (D0).

Figure 3. 3ω mass spectrum of amyl nitrite recorded with a pulse energy of 2 µJ. The fragments are identified in the inset.

vibrational energy, especially in the latter two vibrational modes, which is consistent with the nearly featureless photoelectron spectrum. To explore if any other resonant ionization processes are of importance, we measured the time-resolved photoelectron spectra. Purely two-color photoelectron spectra were obtained by subtracting the sum of the one-color signals (2ω and 3ω) from the overall signal. The spectrum exhibited no temporal evolution on an extended picosecond time scale. Very fast transients, on the order of the ultrafast laser pulse, were observed but will be described separately as they relate to different phenomena. We conclude that the entire ion signal must arise from amyl nitrite that is directly ionized with the 3ω excitation laser pulse. Time-Resolved Mass Spectrometry. The energy inserted into amyl nitrite during ionization is sufficient to dissociate the molecule. Consequently, the mass spectra show a rich set of fragments that relate to the loss of NO and NO2 radicals as well as the fracturing of various carbon-carbon bonds along the alkyl chain. As an example, Figure 3 shows the mass spectrum obtained upon ionization with the 3ω laser pulse only. The fragment ions are identified in the inset. We note the observation of a very small amount of protonated parent molecules (m/z 118), and the dehydrogenated parent (m/z 116). Those ions presumably come from clusters that experience H-atom transfer upon ionization. Interestingly, there are no ions observed at the exact parent mass (m/z 117). The fragment with next lower mass, m/z 87, arises from the loss of a neutral NO radical from the parent ion. We also observe NO cations at mass 30, suggesting a parallel channel that lets a departing NO+ fragment carry the charge. To investigate the dynamics of the fragmentation process, we measured time-resolved mass spectra using the ionizing 3ω pulses as the pump and the 2ω pulses as the probe. The resulting

Figure 4. Time-resolved ion traces arising from 3ω pump and 2ω probe. The individual one-color signals were subtracted out so that only the transients are plotted. The fits were obtained by deconvoluting an instrument function and assuming single exponential behavior with fit parameters as identified in Figure 5 and listed in Table 2.

mass spectra of different fragment ions show a bewildering array of behaviors, represented in Figure 4 by a set of examples chosen for their representative character. All ion signals spike at time zero, an effect that arises from the overlap of the pump and the probe pulses and from the increased number of combinations in which two-color, multiphoton processes can ionize the molecules. Beyond this spike, many ions show

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Figure 5. Schematic drawing of the kinetic model used to explain the decays observed in the time-resolved mass spectra. Ionization by the pump pulse leads to the formation of energized ions that fragment. Prior to fragmentation the ion may absorb a probe photon (2ω) and thus gain an even higher internal energy. This will change the fragmentation pattern by depleting some fragments while simultaneously enhancing the abundance of other fragments (b). The component in part a results from a significant depletion by the single color alone; thus fewer molecules are available to the subsequent pulse in the two color experiment.

TABLE 2: Baseline Shifts, Decay/Rise Times, and Amplitudes of the Transient Signals in the 3ω + 2ω Pump Probe Experimenta mass (m/z)

amplitude (A)

baseline shift (B)

rise/decay time (τP(E))

118 116 87 (C5H11O+) 71 (C5H11+) 60 (CH2NO2+) 57 (C4H9+) 29 (C2H5+) 27 (C2H3+)

0.11 0.06 0.07 -0.06 -0.03 -0.11 0.05 0.05

-0.11 -0.15 -0.07 0.07 -0.12 0.04 0.02 0.04

5.3 ps (decay) 13.1 ps (decay) 8.1 ps (decay) 8.2 ps (rise) 3.2 ps (rise) 4.0 ps (rise) 2.1 ps (decay) 1.2 ps (decay)

a The values of A and B are normalized to their respective signals with only the 3ω pump pulses.

dynamical processes on picosecond time scales. Some ions, such as the fragments with m/z 87, emerge from the baseline and decay or rise to a negative or positive offset. Others show similar rises or decays but appear to start with either a dip or a positive offset. For example, the ion transients for m/z 57 and 60 both show an instantaneous depletion of the ion currents immediately after time-zero, followed by rises in the ion currents. While m/z 60 remains below the baseline, m/z 57 rises above. The ion transient for m/z 27 has a positive signal immediately after timezero and subsequently decays to a positive offset. Lifetimes of Excited-State Ions. The fact that the two-color ion signals depend on time whereas the two-color photoelectron spectra do not suggests that the temporal evolution in the ion currents is related to ion state dynamics. We have previously observed that if an ion absorbs a probe photon it may result in the depletion of the parent or some of the fragment ions.3 In amyl nitrite, it is the absorption of a probe photon by the initially generated parent ion that gives rise to the transient features in the mass spectra of the ions.

Rosenberg et al. Our model for explaining the temporal evolution of the ion currents is shown schematically in Figure 5. Absorption of 3 × 3ω (pump laser) ionizes amyl nitrite to an ionic state with considerable internal vibrational energy. Because this internal energy exceeds the thresholds for generating the fragments, any of the one-color ionization pathways can give rise to mass spectra with many fragments such as the one shown in Figure 3. To explain the different types of transients, Figure 4, we suggest that they are comprised of two separate types of behaviors, illustrated in parts a and b of Figure 5. First, in Figure 5a, the relative sequencing of the 3ω and 2ω pulses may change the baseline signal because each pulse by itself may (a) deplete the number of neutral ground state molecules and (b) cause differing amounts of dissociation to specific fragments. This effect gives rise to step functions at time zero, with step values B that can be either positive or negative. Second, in Figure 5b, the parent ion P+, which by itself produces a fragment Fi with an intensity of ci, can absorb a 2ω probe photon. This inserts an additional 3 eV of energy into the molecule, which can change the fragmentation pattern. Out of the excited state, fragment Fi may be generated with an intensity of c|* that may be either larger or smaller than the original intensity ci. Therefore, the absorption of a probe photon will effect either an increase or a decrease, A, of the signal of fragment Fi. The parent ions have, however, a lifetime that is determined by the sum of all the rates of the fragmentation processes to the individual fragment masses. Therefore, the effect of the probe photon decays with a rate that reflects the lifetime of the parent ions. The measurement of the transients in the mass spectrum thus is a measurement of the lifetime of the amyl nitrite parent ion generated by the pump laser pulse. Fitting all the transients to the types of behavior illustrated in Figure 5 allows us to extract the baseline offsets B, the amplitude of the signal modulation A, as well as the lifetimes of the parent ions, τP(E). Table 2 lists the parameters obtained in these fits, which are included in Figure 4 as solid lines. We note that measured lifetimes range from about 1 to 13 ps. Clearly, any given parent ion can have only one lifetime, and an ensemble of parent ions with a range of internal energies will feature a collective lifetime that represents an average over individual lifetimes. The reason why the lifetimes appear to depend on the fragment mass is because parent ions generated with different internal energies will react to different fragments. Thus, a measurement of a particular fragment selects a set of parent ions with an unknown but specific range of internal energies. We did notice that oftentimes an alternative fit with the incorporation of a sub-40-fs second exponential or even in some cases with 10-20-fs time zero shifts gave slightly better agreement with the experimental data. A behavior of this kind has been noted by Fuss and co-workers20 and has been attributed to ultrafast internal conversion processes. Given the nature of our laser pulses, the focus of this work being on slower processes in ions and the fact that a very reasonable fit is obtained with a single exponential and a fixed time-zero we disregarded any information that may lie hidden in the alternative fitting procedure. Table 2 reveals a general pattern: the smaller fragments have faster rise/decay times. This is reasonable because we surmise that cations born with a higher energy react faster and are more likely to have sequential reactions that produce smaller fragments. On the other hand, those cations that are born with little internal energy will react slower and the reaction sequence will stop after the formation of the larger fragments. We also observe that the smaller fragments all have positive A constants. This is reasonable because the probe pulse inserts energy into the

Lifetimes of Internally Excited Amyl Nitrite Cations molecule, so that additional fragmentation pathways leading to smaller fragments open up. All transient signals can be fit to a single exponential form, suggested by Figure 5 and Table 2. This indicates that no other absorption processes are at work: apparently, only the parent ion and none of the fragment ions absorbs the probe photon. This can be understood because it is likely that the initially generated parent ion can absorb a photon to a dissociative surface that splits off an NO fragment, much like the neutral molecule does. This leads to fragments with m/z 87, explaining its positive amplitude A. On the other hand, the likely first dissociation product of the parent ion without photoexcitation is likely the fragment through NO2 loss, i.e., the ion with m/z 71. Both of these fragmentation pathways agree with the calculated changes in the bond lengths shown in Table 1, which supports that, a large amount of vibrational energy is deposited in the [C4H9CH2-ONO]+• and [C5H11O-NO]+• bonds. Photoexcitation of the parent ion with the 2ω pulse therefore reduces the fraction of molecules forming m/z 71, leading to the negative value of the A parameters. Importantly, the rise and decay times of the m/z 87 and 71 therefore gives the lifetime of the parent ions that generate those fragments. It is also understandable now that no further excitation processes come into play: Neither the alkoxy nor any of the hydrocarbon radicals can absorb the probe photon. The background signal from the 2ω alone is very small. Therefore there is no dynamics resulting from 2ω ionization. The step components come about from the different number of ground state molecules. That is, apparently when 2ω comes before 3ω, there are fewer molecules for 3ω to ionize. That is not to say that the 2ω needs to ionize a lot of molecules - there can be other processes that destroy the parent, in particular the 2-photon excitation to the repulsive surface, which would lead to effective loss of NO quite. We note that, while our experiment allows us to determine the lifetimes of the amyl nitrite ions and while we observe that the lifetime depends on the internal energy of the originally generated ion, we cannot deduce quantitatively the dependence of the lifetimes on the energy because we do not know the range of parent energies that give rise to different fragments. One way to obtain that information would be to deploy an experiment with photoelectron-photoion coincidence (PEPICO) detection.21 By selectively observing ions that are coincident with electrons of a specific energy it would be possible to study the decay of ions with well-defined internal energy. Finally, we point out that ions 118 and 116 must arise from a small fraction of molecules that are present in the beam as dimers or higher order clusters. These dimers can quickly dissociate on account of their internal energy, or they can react with by transferring a H-atom from the neutral to the radical cation of amyl nitrite to form m/z 118. Elimination of an H2 molecule would give rise to m/z 116. The decay and rise times of those mass peaks therefore reflects a more complicated interplay of reaction paths involving dissociation, elimination, and H-atom transfer. While it is possible to fit the time dependence to simple exponential forms, it is not possible to derive much information about those competing pathways. 4. Summary Our study has shown that the lifetimes of highly energetic ions can be studied using ultrafast time-resolved pump-probe techniques. In amyl nitrite, a rich variety of transient types of signals can be reduced to a small number of parameters, including the lifetime of the parent ion subsequent to ionization.

J. Phys. Chem. A, Vol. 114, No. 26, 2010 7025 The transients are of single exponential character, suggesting no absorption of the probe photons by any species other than the parent ions. Lifetimes in the range of several picoseconds have been observed for ions with total internal energies of up to 3.7 eV. The lifetimes depend sensitively on the total internal energy of the ion, resulting in a trend that shows smaller fragments with faster time scale transients. The tendency for higher energy parent ions to produce smaller fragments also manifests itself in the ionization experiments with different pump laser wavelengths. Systematically varying the ionization wavelength in a photoelectron-photoion coincidence (PEPICO) study could allow the itemization of the lifetimes as a function of internal energy. Acknowledgment. C.Z.B. acknowledges financial support from The Danish Council for Independent Research and Natural Sciences. The Brown part of the project was supported by the Division of Chemical Sciences, Geosciences, and Biosciences, the Office of Basic Energy Sciences, the U.S. Department of Energy by Grant No. DE-FG02-03ER15452 as well as the Army Research Office, Grant No. W911NF-08-C-0100, administered through Ryon Technologies, Inc. References and Notes (1) Dantus, M.; Rosker, M. J.; Zewail, A. H. J. Phys. Chem. 1988, 89, 6128. (2) Stolow, A. Annu. ReV. Phys. Chem. 2003, 54, 89. (3) Rusteika, N.; Brogaard, R. Y.; Sølling, T. I.; Rudakov, F. M.; Weber, P. M. J. Phys. Chem. A 2009, 113, 40. (4) Taylor, D. P.; Goode, J. G.; LeClaire, J. E.; Johnson, P. M. J. Chem. Phys. 1995, 103, 6293. (5) LeClaire, J. E.; Anand, R.; Johnson, P. M. J. Chem. Phys. 1997, 106, 6785. (6) Johnson, P. M.; Anand, R.; Hofstein, J. D.; LeClaire, J. E. Electron Spectrosc. Relat. Phenom. 2000, 108, 177. (7) Ho, J.-W.; Chen, W. K.; Cheng, P.-Y. J. Chem. Phys. 2009, 131, 134308. (8) Untch, A.; Weide, K.; Schinke, R. Chem. Phys. Lett. 1991, 180, 265. (9) Hippler, M.; Al-Janabi, F. A. H.; Pfab, J. Chem. Phys. Lett. 1992, 192, 173. (10) Mestdagh, J. M.; Berdah, M.; Dimicoli, I.; Mons, M.; Meynadier, P.; d’Oliveira, P.; Piuzzi, P.; Visticot, J. P.; Lardeux-Dendonder, C.; MartrenchardBarra, S.; Soep, B.; Solgadi, D. J. Chem. Phys. 1995, 103, 1013. (11) Finke, H.; Spiecker, H.; Andresen, P. J. Chem. Phys. 1999, 110, 4777. (12) Castle, K. J.; Kong, W. J. Chem. Phys. 2000, 112, 10156. (13) Ji, M.; Zhen, J.; Zhang, Q.; Chen, Y. J. Chem. Phys. 2009, 130, 174314. (14) Rosenberg, M.; Sølling, T. I. Chem. Phys. Lett. 2010, 484, 113. (15) Yue, X.-F.; Sun, J.-L.; Zhou, C.-H.; Cheng, S. B.; Yin, H.-M.; Han, K. L. Chem. Phys. Lett. 2008, 452, 14. (16) Kim, B.; Thantu, N.; Weber, P. M. J. Chem. Phys. 1992, 97, 5384. (17) Schick, C. P.; Dion, C. F.; Bernstein, E. R. J. Chem. Phys. 1997, 106, 3512. (18) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision E.01; Gaussian, Inc.: Wallingford, CT, 2004. (19) Schultz, J. C.; Houle, F. A.; Beauchamp, J. L. J. Am. Chem. Phys. 1984, 106, 3917. (20) Fuss, W.; Schmid, W. E.; Trushin, S. A. Chem. Phys. Lett. 2001, 342, 91. (21) Baer, T. Int. J. Mass Spectrom. 2000, 200, 443.

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