Photodissociation dynamics of benzoic acid

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producing C6H6O fragments has a barrier height of 87.2 kcal/mol, the other CO elimination channel, which produces a C6H5OH fragment, has a barrier height ...
THE JOURNAL OF CHEMICAL PHYSICS 132, 014305 共2010兲

Photodissociation dynamics of benzoic acid Yuri A. Dyakov, Arnab Bagchi,a兲 Yuan T. Lee (李遠哲兲,b兲 and Chi-Kung Ni (倪其焜兲c兲 Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei 10617, Taiwan

共Received 17 August 2009; accepted 24 November 2009; published online 5 January 2010兲 The photodissociation of benzoic acid at 193 and 248 nm was investigated using multimass ion imaging techniques. Three dissociation channels were observed at 193 nm: 共1兲 C6H5COOH → C6H5 + COOH, 共2兲 C6H5COOH→ C6H5CO+ OH, and 共3兲 C6H5COOH→ C6H6 + CO2. Only channels, 共2兲 and 共3兲, were observed at 248 nm. Comparisons of the ion intensities and photofragment translational energy distributions with the potential energies obtained from ab initio calculations and the branching ratios obtained from the Rice–Ramsperger–Kassel–Marcus theory suggest that the dissociation occurs on many electronic states. © 2010 American Institute of Physics. 关doi:10.1063/1.3274624兴 I. INTRODUCTION

Photodissociation of carboxylic acids has been studied extensively due primarily to the generation of the OH radical and its relevance in atmospheric chemistry. Formic acid, HCOOH, the simplest of the organic acids, is the prototype in the series of carboxylic acid molecules. Previous investigations1–8 demonstrated five potential dissociation channels, HCOOH + hv → HCO + OH,

⌬H = 108 kcal/mol,

共1兲

→H + HCOO,

⌬H = 93 kcal/mol,

共2兲

→H + COOH,

⌬H = 103 kcal/mol,

共3兲

→H2 + CO2, →H2O + CO,

⌬H = 8.4 kcal/mol, ⌬H = − 1.4 kcal/mol.

共4兲 共5兲

These studies revealed that reactions 共1兲 and 共2兲 occur on the excited states and that reactions 共3兲–共5兲 result from the ground state. Near 220 nm the dominant process is OH formation via scission of the C u OH bond.3,4 At 222 nm, 70% of HCOOH molecules dissociate to yield OH radicals with the remaining 30% leading to C u H and O u H bond fissions and the production of H atoms.2–4 Large quantum yields for OH product were also found in the photodissociation of acetic acid 共0.55–0.57兲 and propionic acid 共0.15– 0.35兲 at the same wavelength.9 Kumar et al.10 studied the photodissociation of difluoroacetic acid. They found that decarboxylation 关CO2 elimination, analogous to reaction 共4兲兴 is important in thermal dissociation. On the other hand, OH products resulted solely from UV photodissociation. Butler and co-workers11 studied the photolysis of acrylic acid 共H2C v CHCOOH兲 monomers by at 193 nm light. Photofragment velocity distribution meaa兲

Also at Taiwan international graduate program, Academia Sinica, Taiwan. Also at Department of Chemistry, National Taiwan University, Taipei, Taiwan. c兲 Electronic mail: [email protected]. Also at Department of Chemistry, National Tsing Hua University, Hsinchu, Taiwan. b兲

0021-9606/2010/132共1兲/014305/5/$30.00

surements indicate that C u C and C u O bond fissions are the major photodissociation pathways and that molecular decarboxylation and decarbonylation reactions do not occur to a significant extent. In addition to the molecules previously mentioned, a number of other 共saturated and unsaturated兲 carboxylic acids have been examined, including pyruvic acid,12 thiolactic acid,13 acrylic acid,14 propiolic acid,15 and propynoic acid.16 The majority of these studies focused on the detection of the OH radical, not only because the OH radical is one of the important products but because this radical can be detected easily by laser induced fluorescence 共LIF兲. One of the conclusions drawn from these studies is that these acids undergo dissociation to produce OH from an excited state featuring an exit barrier. However, the branching ratio for OH elimination along with other possible dissociation channels is not well understood for these compounds. Benzoic acid is the simplest aromatic carboxylic acid. The production of OH from benzoic acid has been detected using LIF following excitation by ultraviolet 共UV兲 photons.17 However, quantum yields for OH and other possible dissociation channels were not investigated. In our work, we report the photodissociation of benzoic acid in a molecular beam at 193 and 248 nm using multimass ion imaging techniques. In addition to the OH elimination channel, both CO2 and COOH elimination channels were observed. Photofragment translational energy distributions are also reported. Comparisons with potential energies derived from ab initio calculations and branching ratios obtained from the Rice– Ramsperger–Kassel–Marcus 共RRKM兲 calculations are made. II. EXPERIMENT

The multimass ion imaging techniques we employ have been described in detail elsewhere18共a兲,18共b兲 along with information concerning the high-temperature nozzle we use.18共c兲 A brief description is provided here. A molecular beam containing benzoic acid is formed by flowing, ultrapure Ne carrier gas at pressures of 250 Torr through a pulsed nozzle 共coated with graphite兲. The nozzle is filled with a mixture of benzoic acid sample and graphite powder at 65 ° C. Molecules in the

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molecular beam are irradiated by a UV laser beam 共Lambda Physik, Compex 200:20 ns pulse duration兲 and dissociated into neutral fragments. Due to recoil and center-of-mass velocities, the resulting fragments are distributed on an expanding sphere in flight to the ionization region. The fragments are subsequently ionized with a vacuum ultraviolet 共VUV兲 共118 nm兲 laser pulse. The distance and time delay between the VUV and photolysis laser pulses is set such that the VUV laser passes through the center of mass of the dissociation products and generates a line segment of photofragment ions by photoionization. The length of the segment is proportional to the fragment recoil velocity in the center-of-mass frame multiplied by the delay time between the photolysis and ionization laser pulses. To separate different masses within the ion segment, a pulsed electric field is used to extract the ions into a mass spectrometer after ionization. During mass analysis the length of each fragment ion segment continues to expand in the original direction according to its recoil velocity. At the exit port of the mass spectrometer, a two-dimensional 共2D兲 ion detector is used to detect ion positions and intensity distributions. In this 2D detector, one direction represents the recoil velocity axis and the other direction the mass axis. The image of the ion intensity distribution for each mass-tocharge ratio generated from dissociation is a line-shape image. Molecules not dissociated into fragments upon absorption of UV photons remain within the molecular beam. These molecules, which contain large internal energies, move at the molecular beam velocity to the ionization region where they are ionized by the VUV laser pulse. The wavelength of the VUV laser is set at 118.2 nm such that the photon energy is only sufficiently large to ionize parent molecules. The dissociation of parent molecular cations would not occur at energies remaining after VUV laser ionization. However, dissociation can occur following VUV laser ionization for those excited molecules, which had previously absorbed UV photons without having dissociated. The image of the ion intensity distribution from dissociative ionization differs from the image resulting from the dissociation products of neutral parent molecules. Because ionization and dissociation occurred at the same position, the image of dissociative ionization was a 2D projection of the photofragment ion’s three-dimensional recoil velocity distribution. It was very similar to the image from conventional ion imaging techniques. It was a disklike image rather than a line-shape image. The size of the image from the dissociative ionization did not change with the delay time between the pump and probe laser pulses. Interestingly, the ionization of fragments possessing low ionization potentials or large internal energies resulted in dissociative ionization and generated smaller ionic fragments. Ion images from these reactions were disklike and the width changed with the delay time. From the shape of the image and its change in width with delay time, images from the dissociation of neutral molecules and the respective dissociative ionization of excited parent molecules and neutral fragments can be distinguished.

FIG. 1. Photofragment ion images obtained at photolysis wavelength 193 nm. The respective delay times between pump and probe laser pulses are 10 ␮s 共m / e = 45兲, 6 ␮s 共m / e = 50 and 52兲, 10 ␮s 共m / e = 77 and 78兲, and 49 ␮s 共m / e = 105兲.

III. RESULTS

Fragments of mass-to-charge ratio m / e = 39, 45, 50, 52, 77, 78, and 105 were observed from the photodissociation of benzoic acid at 193 nm using a 118.2 nm photoionization laser beam. Figure 1 depicts the photofragment ion images. Fragments of m / e = 45, 77, 78, and 105 have line-shape images. The line-shape images suggest that the photofragments result from the dissociation of benzoic acid. The images of fragments m / e = 50 and 52 are disklike. However, the widths of the disk change with the delay time. Instead of dissociative ionization from undissociated parent molecules, they must originate from the dissociative ionization of heavy fragments. From the widths of the disklike image, it can be determined that the photofragments are from the dissociative ionization of fragment C6H6. This is confirmed by our previous study, which found that benzene with a large amount of internal energy can be easily cracked into m / e = 52, 50, and 39 fragments upon VUV photoionization.19,20 The images suggest the following reactions: C6H5COOH + h␯共UV兲 → C6H5共m = 77兲 + COOH共m = 45兲,

共6兲

→C6H6共m = 78兲 + CO2共m = 44兲,

共7兲

→C6H5CO共m = 105兲 + OH共m = 17兲.

共8兲

The intensity of fragment m / e = 39 is very small. We only observed it in time of flight mass spectra. No image of m / e = 39 was recorded. The VUV photon energy of 118.2 nm is 10.5 eV, which is smaller than the ionization energies of fragments, CO2 and OH. As a result, we are unable to observe these two fragments. The photofragment translational distributions obtained from the images are illustrated in Fig. 2. The total fragment translational energy distributions obtained from heavy fragment C6H5 and from light fragment COOH match well with translational energies larger than 4 kcal/mol, confirming reaction 共6兲. The distributions do not compare well with translational energies less than 4 kcal/ mol. The intensity of fragment m / e = 77 is larger than that of fragment m / e = 45 in this region. This is partially due to the secondary dissociation of heavy fragment C6H6 关i.e., C6H6共m = 78兲 → C6H5共m = 77兲 + H兴 and partially due to the secondary dissociation of COOH with large internal energy

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FIG. 3. Photofragment ion images obtained at photolysis wavelength of 248 nm. The delay times between pump and probe laser pulses are 7 ␮s 共m = 77 and 78兲 and 51 ␮s 共m / e = 105兲.

tained from the normalization of these ion intensities by the ionization cross section for each fragment at this VUV wavelength 共118.2 nm兲. Unfortunately, we do not have the ionization cross sections for these fragments at 118.2 nm. However, these ion intensities provide a rough estimate of the relative importance of these dissociation channels. The photodissociation of benzoic acid at 248 nm was also investigated. Fragment ions of m / e = 77, 78, and 105 were observed. The photofragment ion images are shown in Fig. 3. The image for m / e = 77 is disklike and its width does not change with the delay time. It represents the dissociative ionization of the undissociated excited parent molecules. The ion images for m / e = 78 and 105 are line shape. They result from reactions 共7兲 and 共8兲. The corresponding photofragment translational energy distributions are shown in Fig. 4. IV. DISCUSSION

FIG. 2. Photofragment translational energy distributions for reactions 共6兲–共8兲 obtained at photolysis wavelength of 193 nm. For reaction 共6兲, the open circles represent the distribution obtained from fragment m / e = 45 and the solid squares represent the distribution obtained from fragment m / e = 77.

The isomers of benzoic acid on the ground state, possible dissociation channels, and the relative positions of various electronic states from previous ab initio calculations21 are summarized in Fig. 5. There are two energy-minima structures for benzoic acid in the ground state. One has a planar structure and the other a nonplanar geometry in the COOH functional group. The first structure is more stable than the second 共relative energy of 6.6 kcal/mol兲. A barrier

关i.e., COOH共m = 45兲 → CO2 + H兴. Both secondary dissociations make the intensity of m / e = 77 larger than that of m / e = 45 in the lower translational energy region. Figure 2 also shows that the released translational energy is large for reaction 共7兲. The maximum translational energy is as high as 80 kcal/mol. The large translational energy release is consistent with the potential energy from ab initio calculation 共see below兲, which shows that the heat of reaction is small and the exit barrier height is large. On the other hand, the average translational energies released from reactions 共6兲 and 共8兲 are small. The small translational energies also agree with the potential energy from ab initio calculation 共see below兲, which shows that the heat of reaction is large and there is no exit barrier for these two channels. Table I summarizes the ratio of photofragment ion intensities. Branching ratios for the various reactions can be obTABLE I. Photofragment ion intensity ratios.

193 nm 248 nm a

Fragment

C 6H 5

C6H6共+C4H4 + C4H2兲

C6H5CO

Ion intensitya Ion intensitya

1 ⫾ 0.1

1 ⫾ 0.1 0.5⫾ 0.2

0.08⫾ 0.008 1 ⫾ 0.1

Ion intensities have been corrected for the effects of fragment velocities.

FIG. 4. Photofragment translational energy distributions for reactions 共7兲 and 共8兲 obtained at photolysis wavelength 248 nm.

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FIG. 5. Transition states, dissociation products for various dissociation channels, and the adiabatic energies and characters of S1, S2, T1, and T2. Adopted from Ref. 22.

height of 11.6 kcal/mol was found on the isomerization pathway between these two structures. The S1 state arises from an electronic excitation located in the C v O group and it is of 1n␲ⴱ character. The adiabatic excitation energy from the ground state S0 to the first excited state S1 is 91.5 kcal/mol. The S2 state is 1␲␲ⴱ in character and the adiabatic excitation energy is 100.7 kcal/mol. The adiabatic excitation energy of the first triplet T1 state is 74 kcal/mol and originates from the ␲ → ␲ⴱ excitation in the aromatic ring. The T2 state is of 3 n␲ⴱ character and has a relative energy of 90.0 kcal/mol. The calculated vertical excitation energies from the ground state to the three lowest excited singlet states are as follows: 113.2, 117.1, and 130.5 kcal/mol along with their respective oscillator strengths 0.0002, 0.015, and 0.18. Room temperature absorption spectra show two absorption bands. One band from 290 to 260 nm with the maximum absorption at 273 nm 共104.9 kcal/mol兲 and the other band from 260 nm to a wavelength shorter than 210 nm, with the maximum absorption at 220 nm 共130.2 kcal/mol兲.22 In comparison with the calculation, they can be assigned to the excitation to the S2 and S3 states, respectively, although the calculated vertical excitation energy of the S2 state is overestimated. No fluorescence was observed from the S1 excited state. Benzoic acid in rigid glass 共at 77 K兲 was found to show only phosphorescence and at a high quantum yield,23 indicating that an intersystem crossing to the lowest triplet state occurs very efficiently in benzoic acid. Sensitized phosphorescence excitation spectroscopy was used to observe the electronically excited states of benzoic acid in supersonic jets.24 Two sharp bands at 35 923 and 35 943 cm−1, respectively, were assigned to the origins of the excitation from the ground state of two rotational isomers of benzoic acid to the S1共 1␲␲ⴱ兲 excited state. Actually, they are S1共 1n␲ⴱ兲 instead of S1共 1␲␲ⴱ兲 according to the previous ab initio calculation21 described in previous paragraph. Laser desorption followed by jet cooling has been utilized to identify the S0 → S1 absorption spectrum of benzoic acid in the gas phase.25 The S0 → S1 band origin was determined to be 35 960 cm−1 and the rate for intersystem crossing to the triplet state 共as determined from the absorption linewidth兲 was found to be 1.2⫻ 1012 s−1. These two experimental values of S1 band origins are not very consistent and they are both higher than that from ab initio calculations. Unlike that for the photodissociation of formic acid, only a few experimental and theoretical investigations have been performed on the photodissociation of benzoic acid. Early

FIG. 6. Potential energies of isomers, transition states, and dissociation products for H, OH, and COOH elimination channels on the electronic ground state.

theoretical calculations26 showed that the energy of the transition state for decarboxylation 关reaction 共7兲兴 is 62 kcal/mol. This energy falls to 31.5 kcal/mol for a benzoic acid-water complex. Recent theoretical calculations21 give the potential energy profiles for C u C and C u O bond fissions as well as decarboxylation from different electronic states, which are summarized in Fig. 5. The C u O bond cleavage leads to fragment products, C6H5CO and OH, in the ground state. This dissociation channel can occur on the ground state without an energy barrier or it can originate from the triplet T2 state 共with a barrier height of 102.3 kcal/mol兲. Nascent OH product state distributions from the photodissociation of benzoic acid have been measured using techniques employing LIF at different UV excitation wavelengths.17 By comparison of the OH product appearance threshold obtained from experimental measurement and the dissociation thresholds of various electronic states from calculations, the T2 state is proposed to be the dissociative state for OH elimination channel. The same theoretical calculations show that the heat of reaction to generate fragments, C6H5 and COOH, in the ground state is 109 kcal/mol. It can occur from the triplet state 共with a barrier of 121 kcal/mol兲 or from the ground state 共without an energy barrier兲. We also performed ab initio methods to calculate geometries and energies of various isomers, transition states, and dissociation products in the ground electronic state. In the calculations, the geometries were optimized at the hybrid density functional B3LYP/ 6-31Gⴱ level and the energies were calculated using the G3 model chemistry scheme. The results for various dissociation channels are summarized in Figs. 6 and 7. Hydrogen atom elimination from various molecular positions is energetically possible dissociation channels. Dissociation thresholds for C u H bond cleavage in aromatic rings are in the range of 113.9–117.4 kcal/mol, depending on the position of the C u H bond. These thresholds are all close to the 248 nm photon energy. The elimination of hydrogen from OH requires less energy than does C u H bond fission from the aromatic ring. These H atom elimination channels do not have an exit barrier, as shown in Fig. 6. The barrier height for the secondary dissociation C6H5COO 共after O u H bond fission兲 → C6H5 + CO2 is as large as 119 kcal/mol. It only becomes possible at 193 nm. The threshold

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FIG. 7. Potential energies of isomers, transition states, and dissociation products for CO, H2O, and CO2 elimination channels on the electronic ground state.

for OH elimination is only 106.8 kcal/mol. Secondary dissociation following OH elimination to produce C6H5 + CO has a large barrier height 共131.8 kcal/mol兲 and a large heat of reaction. On other hand, COOH elimination has a relatively low threshold 共108.2 kcal/mol兲. The pathways of other dissociation channels, including CO, H2O, and CO2 eliminations, are shown in Fig. 7. They are all energetically allowed at both 248 and 193 nm. For CO elimination, the channel producing C6H6O fragments has a barrier height of 87.2 kcal/mol, the other CO elimination channel, which produces a C6H5OH fragment, has a barrier height of 95.2 kcal/mol. Water elimination also has two pathways. One has a very high barrier 共112 kcal/mol兲 as well as a large heat of reaction 共109.8 kcal/mol兲. These values are close to the 248 nm photon energy. Therefore, it is not likely to occur at 248 nm. The barrier height and heat of reaction of the other water elimination pathway are only 81.4 and 73.1 kcal/mol, respectively. It can occur at both photolysis wavelengths. Compared to CO and H2O elimination, CO2 elimination has a very low barrier height 共71 kcal/mol兲. Our RRKM calculations on the electronic ground state find that CO2 elimination is the dominant channel. The relative branching ratios are 90% and 10% for the CO2 and H2O elimination channels at 193 nm. They become 65% and 35% at 248 nm. Our experimental results reveal that OH elimination channel is important at 248 nm. This is consistent with the previous study. However, our results find that CO2 elimination is also important at this wavelength. Since our RRKM calculation suggests that the branching ratio of OH elimination on the ground state is very small, this channel must occur on the excited state. On the other hand, RRKM calculation also predicts that CO2 and H2O elimination channels are both important for the dissociation occurring on the ground state at this wavelength. Since we do not observe the products corresponding to H2O elimination, therefore, it is not likely that CO2 elimination occurs on the ground state. As the photolysis wavelength changes from 248 to 193 nm, OH elimination becomes less important. The major channels are CO2 and COOH elimination. Because RRKM calculations point to CO2 elimination as the dominant channel on the ground state at 193 nm, the observation of large ion intensities for m / e = 77 共C6H5兲 and m / e = 45 共COOH兲 sug-

gests that COOH elimination does not occur on the ground state. According to previous calculations21 the possible excited states for OH and COOH elimination are T2 and T1 state, respectively. In summary, we find that many electronic states are involved in the photodissociation processes of benzoic acid. At this moment, we do not have clear evidence to identify the electronic state for each dissociation channel. On the other hand, the experimental observation shows that the dissociation properties of benzoic acid at 248 nm are quite similar to those for other carboxylic acids, i.e., elimination of OH is the major channel. However, the photodissociation properties at 193 nm show significant differences from that of most of the carboxylic acids studied at longer wavelengths. The minor channel is OH elimination and the major channels are CO2 and COOH elimination. H. Su, F. Kong, W. Fang, and R. Liu, J. Chem. Phys. 113, 1891 共2000兲. S. R. Langford, A. D. Batten, M. Kono, and M. N. R. Ashfold, J. Chem. Soc., Faraday Trans. 93, 3757 共1997兲. 3 D. L. Singleton, G. Paraskevopoulos, and R. S. Irwin, J. Phys. Chem. 94, 695 共1990兲. 4 M. Brouard, J. P. Simons, and J.-X. Wang, Faraday Discuss. Chem. Soc. 91, 63 共1991兲. 5 M. Brouard and J. O’Mahony, Chem. Phys. Lett. 149, 45 共1988兲. 6 T. Ebata, T. Amano, and M. Ito, J. Chem. Phys. 90, 112 共1989兲. 7 K. W. Lee, K. S. Lee, K. H. Jung, and H. R. Volpp, J. Chem. Phys. 117, 926 共2002兲. 8 K. Saito, T. Kakumoto, H. Kuroda, S. Torii, and A. Imamura, J. Chem. Phys. 80, 4989 共1984兲. 9 D. L. Singleton, G. Paraskevopoulos, and R. S. Irwin, J. Photochem. 37, 209 共1987兲. 10 A. Kumar, H. P. Upadhvava, and P. D. Naik, J. Phys. Chem. A 108, 6257 共2004兲. 11 D. C. Kitchen, N. R. Forde, and L. J. Butler, J. Phys. Chem. A 101, 6603 共1997兲. 12 S. Dhanya, D. K. Maity, H. P. Upadhyaya, A. Kumar, P. D. Naik, and R. D. Saini, J. Chem. Phys. 118, 10093 共2003兲. 13 K. K. Pushpa, H. P. Upadhyaya, A. Kumar, P. D. Naik, P. Bajaj, and J. P. Mittal, J. Chem. Phys. 120, 6964 共2004兲. 14 H. P. Upadhyaya, A. Kumar, P. D. Naik, A. V. Sapre, and J. P. Mittal, J. Chem. Phys. 117, 10097 共2002兲. 15 A. Kumar, H. P. Upadhyaya, P. D. Naik, D. K. Maity, and J. P. Mittal, J. Phys. Chem. A 106, 11848 共2002兲. 16 A. Kumar and P. D. Naik, Chem. Phys. Lett. 422, 152 共2006兲. 17 Q. Wei, J. L. Sun, X. F. Yue, S. B. Cheng, C. H. Zhou, H. M. Yin, and K. L. Han, J. Phys. Chem. A 112, 4727 共2008兲. 18 S. T. Tsai, C. K. Lin, Y. T. Lee, and C. K. Ni, Rev. Sci. Instrum. 72, 1963 共2001兲; C. K. Ni and Y. T. Lee, Int. Rev. Phys. Chem. 23, 187 共2004兲; Y. Morisawa, Y. A. Dyakov, C. M. Tseng, Y. T. Lee, and C. K. Ni, J. Phys. Chem. A 113, 97 共2009兲. 19 S. T. Tsai, C. K. Lin, Y. T. Lee, and C. K. Ni, J. Chem. Phys. 113, 67 共2000兲. 20 S. T. Tsai, C. L. Huang, Y. T. Lee, and C. K. Ni, J. Chem. Phys. 115, 2449 共2001兲. 21 J. Li, F. Zhang, and W. H. Fang, J. Phys. Chem. A 109, 7718 共2005兲. 22 V. Talrose, E. B. Stern, A. A. Goncharova, N. A. Messineva, N. V. Trusova, and M. V. Efimkina, “UV/Visible Spectra” in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, edited by P. J. Linstrom and W. G. Mallard 共National Institute of Standards and Technology, Gaithersburg MD兲, http://webbook.nist.gov, retrieved June 3, 2009. 23 H. Baba and M. Kitamura, J. Mol. Spectrosc. 41, 302 共1972兲. 24 S.-i. Kamei, H. Abe, N. Mikami, and M. Ito, J. Phys. Chem. 89, 3636 共1985兲. 25 G. Meijer, M. S. de Vries, H. E. Hunziker, and H. E. Wendt, J. Phys. Chem. 94, 4394 共1990兲. 26 J. Li and T. B. Brill, J. Phys. Chem. A 107, 2667 共2003兲. 1 2