Chemical Physics Letters 456 (2008) 150–155
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IR-photodissociation and photodetachment spectroscopy of Cl (NH3)x (IR: x = 1–4, PD: x = 1) Martin Tschurl, Ulrich Boesl * Technical University of Munich, Chemistry Department, 85747 Garching, Germany
a r t i c l e
i n f o
Article history: Received 31 January 2008 In final form 15 March 2008 Available online 24 March 2008
a b s t r a c t Complexes of ammonia molecules and one chloride ion have been studied by photodetachment and IRphotodissociation spectroscopy. For the smallest anionic complex, the stabilisation energy with respect to the bare chloride ion and vibrational frequencies have been determined. Two bands showed a splitting due to rotational branches, which could be represented by simulation. Rotational constants obtained by former ab initio calculations [P.S. Weiser, D.A. Wild, P.P. Wolynec, E.J. Bieske, J. Phys. Chem. A 104 (2000) 2562] are confirmed and rotational constants of a vibrationally excited state are supplied. IR-photodissociation spectra of clusters with up to four ammonia molecules per chloride ion were recorded. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction A major aim of studying weakly bound charged molecular complexes is to obtain insight into solvation processes. One way of such studies is to perform IR-spectroscopy on the smaller species of such complexes. This supplies valuable information about vibrational properties of the solvated ionic species, enables the comparison with ab initio calculations, and finally leads to well defined structures of these complexes. On the other hand, the study of the micro-solvation properties of a species is governed by the hope that the so-obtained information can be extrapolated to its solution properties. Chloride is the most abundant terrestrial anionic species. It can be found in many biological media and plays an important role in several cell physiological processes [1]. Therefore, it is not astonishing that small complexes consisting of one halogen anion and one or more water molecules are already well examined [2–8]. However, using other solvents than water allows deeper insight into hydrogen bonds and micro-solvation. Ammonia is an interesting system since it plays an important role in our environment as exhaust gas or as degradation product of amino acids. Some studies on halogen–ammonia complexes have already been performed. Markovich et al. [9] investigated the smallest chloride-ammonia complex by using photodetachment photoelectron spectroscopy. Additionally, they used ab initio calculations in order to explore the structures of the anionic and neutral ground state and that of the charge-transfer state of the neutral complex. Weiser et al. [10] studied the same complex by IR-spectroscopy and compared the so-obtained spectra with their MP2 calculations.
* Corresponding author. E-mail address:
[email protected] (U. Boesl). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.03.041
Larger halogen–ammonia complexes were investigated by Frischkorn et al. [11]. Beside rearrangement studies of the complexes after photoexcitation, the authors also performed photodetachment photoelectron spectroscopy on these systems. However, while the studied complexes consisted of iodide with several ammonia molecules, no further experimental results on larger (more than one ammonia molecule) complexes of other halogenide complexes are reported in the literature. Only for F (NH3)x (x = 1–3) does there exist ab initio calculations of Wild and Lenzer [12]. In this Letter, we will present IR-spectra of Cl (NH3)x (x = 1– 4) and a photodetachment spectrum of the smallest complex. 2. Experimental The experimental principle of combining negative ion source, mass selection, selective ion excitation, and neutral/ion separation has been realised by Lineberger and co-workers [13] (see also citations in [14]) many years ago. Our experimental setup, which follows this principle, is presented in detail elsewhere [15,16]. Here, just a brief description of our apparatus will be given. In order to obtain enough amount of the desired species, trace CCl4 vapour was added to a water-free gas flow of ammonia. Chlorine anions were formed by dissociative electron attachment to the CCl4 moiety. The electrons (kinetic energy 0.8 eV) originated from a Nd:YAG laser beam (4th harmonics at 266 nm) focused onto a hafnium wire. The inlet system to the mass spectrometer consists of a fast-working solenoid valve and a 200 lm pinhole. Due to the short opening time of 150 ls and the pressure difference of 1 to 3 bar, a supersonic molecular beam has been generated where cooling of molecular degrees of freedom occurred and weakly bound complexes like the desired chloride-ammonia species were formed. The cold anion beam was skimmed and entered the ion optics of a Wiley–McLaren time of flight mass spectrometer.
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There, the anions are accelerated perpendicularly with respect to the primary gas beam. The mass selected anions were irradiated by a second laser beam, which crossed the anion trajectories at the space focus of the time-of-flight mass spectrometer. Depending on which kind of spectroscopy should be applied, laser light in the IRor in the UV-range was used. Tuneable IR-light was generated by difference frequency mixing of the fundamental of a Nd:YAG laser beam (1064 nm) with the output of a dye laser in a heated LiNbO3 crystal. Tuneable UV laser light was obtained from a frequency doubled dye laser beam. Since the interaction of the laser beam with the anions results in both cases in the formation of neutral species, a negative voltage was applied to a grid in front of the detector to separate the parent ions from the neutral species. The voltage was chosen in such a manner that the parent ions still reached the detector. Therefore, normalisation of the neutral signal on the laser power and on the parent ion current was possible. A typical spectrum was obtained by displaying the normalized and integrated neutral current versus the laser wavelength. Calibration of the wavelength was performed by using either the argon lines of an optogalvanic cell or by recording the wavelength of the dye laser beam with a wavemeter.
complex is found where the chloride is bound to one hydrogen atom, while in the neutral cluster a chloride nitrogen bond is preferred. Johnson et al. discussed possible alternative processes taking part at photodetachment, e.g. for complexes such as I N2, I CH3I or I CH3CN [18]. These processes involve formation of molecular dipole bound states, charge transfer to the molecule or ion molecule reactions. In the case of the molecular partner NH3, the dipole moment 1.5 D is too small to allow dipole bound states. In addition, the anion of NH3 is not stable (even not its molecular clusters up to n < 34 [19]), and the process Cl NH3 + hm ? HCl + NH2 occurs at much higher energy [20] than that available with the excitation energies used here. Therefore, alternative processes as discussed in Ref. [18] can be excluded in our case. If dissociative photodetachment takes place, one may derive the stabilisation energy of the anionic complex directly from the onset of the photodetachment spectrum (representing the dissociation threshold of the neutral complex) and the electron affinity of chlorine (29145.43 ± 0.35 cm1 [21]). The onset in the spectrum that is shown in Fig. 1 is not clearly observable but is surely placed below 31700 ± 150 cm1. Therefore, the upper limit for the stabilisation energy of the Cl NH3 complex is 2550 ± 150 cm1.
3. Results and discussion
3.2. The IR-spectrum of ClNH3
3.1. The photodetachment spectrum of ClNH3
The IR-spectrum in the N–H stretching regime of Cl NH3 has already been investigated by Weiser et al. using IR-dissociation spectroscopy [10]. They also performed extensive high level ab initio calculations in order to obtain exact structures, vibrational frequencies and rotational constants of various conformers of the complex. However, reduced resolution did not allow the authors to observe the true shape of the main band at 3150 cm1 and the assignment of two features in their spectrum is tentative. We remeasured the IR-spectrum of Cl NH3 with better resolution (see Fig. 2). Comparison with the spectroscopic behaviour of larger clusters support our assignment, in addition. In the following discussion of the spectral features in Fig. 2, we will include the experimental and theoretical results of Weiser et al. [10]. The spectrum in Fig. 2 is dominated by a doublet around 3121 cm1, which has a weak tail to higher wavenumbers. This tail changes its relative intensity with respect to the doublet at different supersonic beam conditions and therefore is probably due to hot bands. An effect of conformers can be excluded. Further explanations see in the following text.
Markovic et al. [9] determined a vertical detachment energy (VDE) of 4.0 ± 0.15 eV for the smallest chloride ammonia complex. The shift of the VDE with respect to that of the bare chloride (EA = 3,61 eV) is 0.4 ± 0.15 eV (3200 ± 1200 cm1). To obtain a more precise value we recorded a photodetachment spectrum, which is shown in Fig. 1. The spectrum shows a long and steady increase, which extends over 800 cm1. We will follow here the interpretation of our earlier publication on the chloride–benzene complex [17], where we assigned such a long increase in the photodetachment spectrum to excitation of the complex to a dissociative neutral state. In both cases, the structural differences of the anionic and the neutral ground state (see. [9]) lead to vanishing Franck-Condon factors for a transition into the global minimum structure of the neutral species. This is consistent with ab initio calculations [9]. There, a global minimum geometry of the anionic
energy /eV
neutral current / arb. units
3.92 3.93 3.94 3.95 3.96 3.97 3.98 3.99 4.00 4.01 4.02
0 31600 31700 31800 31900 32000 32100 32200 32300 32400 32500
ν / cm -1 Fig. 1. Photodetachment spectrum of Cl NH3. The long and steady increase is most probable due to detachment into a dissociative neutral state. Using this assumption the spectrum supplies the vertical detachment energy of the complex and the stabilisation energy of its anionic form.
Fig. 2. IR-spectrum of Cl NH3. The strongest band (m2) and the band at highest wave numbers (m1) can be assigned to N–H stretching modes of the complex; both bands show a rotational envelope with P- and R-branch. The bands at 3210 and 3300 cm1 are due to excitation of the second harmonics of N–H bending modes. The nomenclature m1, m2, m3 and m8 follows that introduced by Weiser et al. [10].
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Other transitions can be found at 3211 cm1, 3299 cm1, and a doublet at 3341 cm1. According to the calculations of Weiser et al. [10], the minimum structure of the Cl NH3 complex is that with only one hydrogen bond between the chloride ion and the ammonia molecule (drawn schematically in Fig. 2). Other conformers are not stable and should not play any role in the spectrum that has been measured 150 ls after ion formation. The doublet of maximum intensity lies at the same energy as a band which Weiser et al. assigned to the m2-mode (a0 -symmetry) of the complex. Their ab initio calculations [10] indicate that this mode originates from the symmetric N–H stretching mode of the ammonia molecule and is due to the stretching motion of the ion-bonded proton. The second weak doublet in Fig. 2 at 3341 cm1 coincides with a similar feature in the spectrum of Weiser et al., which they assigned to the m1-mode (a0 -symmetry) of the complex. This mode belongs to the formerly antisymmetric and degenerate N–H stretching mode of NH3 [10] and is due to the symmetric motion of the two non-bonded protons. A second component of the complex should originate from this free ammonia mode due to broken degeneracy. However, this component is expected to be weak in intensity and located close to an area of the spectrum, where difference frequency mixing is not possible due to IR-absorption of water molecules incorporated in the LiNbO3 frequency-mixing crystal. Therefore, this second band could neither be found in our spectrum nor in the spectrum of Weiser et al. [10]. Concerning the residual transitions in the spectrum of Fig. 2, we assign them to the second harmonics of the m3 and m8 modes, which correspond to the degenerate antisymmetric bending mode of ammonia. These second harmonics gain their intensity via Fermi interactions with the N–H stretching modes. This is reasonable since it is well known [22] that in bare ammonia the second harmonics of the antisymmetric bending mode interact with the totally symmetric N–H stretching mode. The combination band m3 + m8 has the wrong symmetry for Fermi interaction with the N–H-stretching modes. In contrast to the N–H stretching modes that are both red-shifted in comparison to the ammonia molecule (m1: Dm = 107 cm1; m2: Dm = 216 cm1), the second harmonics of the bending modes are split around the value of the bending mode of free ammonia. For a rough estimation of the corresponding fundamentals (respectively their shift in comparison to the free ammonia mode), Fermi-shifts are neglected and purely harmonic potentials assumed. From the above band positions one finds the frequencies of 1605 cm1 (m3) and 1650 cm1 (m8); the corresponding shifts are 21 cm1 and 23 cm1. All vibrational data are summarized in Table 1. We will now address the splitting of the two doublets of the N– H stretching modes at 3121 cm1 and 3341 cm1. In both cases this splitting is 9 cm1, which is a reasonable value for the separation of rotational branch maxima. Considering the geometry of the complex and the calculated rotational constants of Weiser et al. [10], the complex can be identified as a near-prolate symmetric top.
Since the rotational constant A is very large (8.8 cm1 [10]) in comparison with rotational constants B and C, one expects a rotational pattern similar to that of a linear molecule, i.e. the Q-branch of parallel bands should be very weak in intensity (it vanishes for linear molecules). Fig. 3 represents the result of a rotational fit for an asymmetric top obtained by a home-written computer program for the asymmetric rotor [23]. Despite the limited experimental resolution of the spectrum in Fig. 2, the change of rotational constants B and C upon vibrational excitation and the rotational temperature could be determined. The rotational constants of the Cl NH3-complex in its vibrational ground state were taken from Weiser et al. [10]. Centrifugal distortion was neglected. Variation of the rotational constant A mainly influences the intensity of the Qbranch. Since its intensity in the spectrum is too weak to be observed, the rotational constant A has been kept constant. In Fig. 3a, the rotational line spectrum at a rotational temperature of 80 K is shown, whereas in Fig. 3b, this spectrum is folded by a GAUSSIAN line shape with a width of 2 cm1 corresponding to the laser bandwidth. The experimental band shape is represented in Fig. 3b for comparison. The exact fitting parameters are given in Table 2; values that were not altered are displayed without uncertainty margin. The comparison of simulation and experiment reveals good agreement; in particular, the energy gap of the peak maxima (which is sensitive to temperature changes, e.g. see Fig. 3c) and the ratio of peak intensities (which is mainly sensitive to changes of B and C constants, e.g. see Fig. 3d) are reproduced satisfyingly. In addition, by this comparison a broad band of lower intensity (above mentioned as weak tail) can be identified which cannot be reproduced by any set of parameters and which overlaps the double headed band. Since this fit was enabled by using the rotational constants from the ab initio calculations of Weiser et al. [10], the experimentally obtained spectrum confirms the geometric structure of the complexes derived by their MP2 calculations. In addition, our simulation supplied rotational constants, and thus structural information of the complex while the proton-bonded N–H-stretching mode is excited. The main difference between the spectrum of Weiser et al. [10] and the spectrum in Fig. 2 is the non-existence of the doublet structure and the large width of the dominant band. We attribute this mainly to the above-mentioned additional absorption band overlapping with the m2-band. This feature is considerably more intense in the spectrum of Weiser et al. than in our spectrum. On the other hand, the second weak double structured band near 3350 cm1 has a similar appearance in the spectrum of Weiser et al. and in our spectrum. We therefore exclude strong rotational broadening due to a larger temperature and assign the tail of the m2-band to vibrational hot bands induced by intermolecular vibrations, whose relative abundance depend on supersonic beam conditions. These hot bands are situated on the high energy side of the m2-band. This fact may be explained by an increase of the effective attraction between Cl and NH3, and thus an increase of
Table 1 Position, relative intensity, assignment, and shift (with respect to the corresponding free ammonia mode: symmetric stretching mss, antisymmetric bending masb, antisymmetric stretching mass) of vibrational bands in the spectrum of Fig. 2 m/cm1
Irel
Dm/cm1
Assignment
3116 ± 1 3125 ± 1
1 0.9
m2 -mode; P-branch
3150 ± 15 3211 ± 6 3299 ± 5 3337 ± 3 3346 ± 3
var. 0.06 0.08 0.10 0.08
hot band of intermolecular modes 2 m3-mode 2 m8-mode m1 -mode; P-branch 3341 2 cm1 m1 -mode; R-branch
m2 -mode; R-branch
3121 1 cm1
m1: Non-ion-bound N–H-stretching mode, m2: ion-bound N–H-stretching mode, m3, m8: bending modes [10].
216 ± 1 (mss)
2 (21 ± 6) (masb) 2 (+23 ± 5) (masb) 107 ± 2 (mass)
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B´= 0.138 cm-1 C´= 0.137 cm-1
T = 80 K
b
T = 80 K
3100
3120
3140
3100
B´= 0.138 cm-1 C´= 0.137 cm-1
3140
d
T = 80 K
B´= 0.140 cm-1 C´= 0.139 cm-1
neutral current / arb.units
neutral current / arb.units
T = 40 K
3120
ν / cm -1
ν / cm -1
c
B´= 0.138 cm-1 C´= 0.137 cm-1
neutral current / arb.units
neutral current / arb.units
a
3100
3120
ν / cm
3140
3100
3120
ν / cm
-1
3140 -1
Fig. 3. Rotational simulation and comparison with the experimental spectrum: (a) the line spectrum of the rotational simulation was obtained by using an asymmetric rotor program [23], (b) optimum fit between experimental and the simulated band shape (smooth line); the latter was obtained by folding the rotational line spectrum (a) with a Gaussian line shape of 2 cm1 FWHM, corresponding to the laser bandwidth, and (c)(d) examples of non-optimum fit for smaller temperature or larger rotational constants B0 and C0 .
Table 2 Rotational constants and temperature of Cl NH3 of the best fit
vibration which does not involve motion of the intermediate proton.
Vibrational state
A/cm1
B/cm1
C/cm1
T/K
v(m2) = 0 v(m2) = 1
8.8 8.8
0.136 0.138 ± 0.001
0.135 0.137 ± 0.001
80 ± 20
The corresponding simulated spectrum is displayed in Fig. 3. The rotational constants A, B(v = 0), C(v = 0) have been taken from [10].
the intermolecular vibrational frequency when vibrationally exciting the intermediate proton, as supposed by Weiser et al. [10]. The argument that intermolecular motions are responsible for these hot bands is supported by the observation, that no hot bands of the m1-band appear in our spectrum nor in the spectrum of Weiser et al. This band is induced by the nonbonded proton NH-stretching
3.3. The IR-spectra of Cl (NH3)x (x = 1–4) The spectra of all four complexes are shown in Fig. 4. They exhibit a large blue-shift of the m2-band and a weak blue-shift of the m1-band with increasing cluster size. This blue-shift reduces the original red-shift of these Cl NH3 modes with respect to the free ammonia modes. The m2-mode of Cl NH3 exhibits the largest redshift, which obviously decreases rapidly with increasing cluster size. On the other hand, the 2 m3 band near 3210 cm1 shows nearly no shift at all, while the 2 m8 band near 3300 cm1 exhibits a slight red-shift. The separation of the second harmonics of these two bending modes m3 and m8 therefore decreases slowly for increasing cluster size.
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ν ss
NH3 (liquid)
2ν asb
νass
neutral current / arb. units
n=4
n=3
n=2
n=1
3100
3150
3200
3250
3300
3350
3400
ν / cm-1 Fig. 4. IR-spectra of Cl (NH3)x. For increasing cluster sizes the N–H stretching modes exhibit a blue-shift reducing their original red-shift in Cl NH3 with respect to the free ammonia N–H stretching modes. The separation of the two N–H bending modes is decreasing slightly. Band positions and band intensities approximate the liquid ammonia spectrum involving the symmetric stretching (mss), the antisymmetric bending (mass) and the antisymmetric stretching mode (mass) [22–24].
At the top of Fig. 4, frequencies of the symmetric stretching mode mss, the antisymmetric stretching mode mass and the second harmonics of the antisymmetric bending mode masb of liquid ammonia are indicated. Due to the differences of the corresponding values taken from the literature [24–26], frequency ranges instead of single values are given. Note that stretching mode frequencies of liquid ammonia are smaller than of gas phase ammonia by about 100 cm1, while the antisymmetric bending modes are nearly unchanged. The change of band positions with increasing cluster size reflects the decreasing influence of the ion on the ammonia molecule with increasing cluster size and the mode frequencies become more similar to the corresponding values of liquid ammonia. This situation is marked by dashed lines in Fig. 4. The bands at 3300 and 3210 cm1 approximating the second harmonics of the antisymmetric bending mode of ammonia 2 masb support our assignment of these bands to the bending modes m3 and m8 which have been calculated by Weiser et al. [10]. Concerning band intensities, the comparison of all the spectra of Fig. 4 reveals a relative intensity of the modes 2 m3, 2 m8 and m1 that increases for increasing cluster sizes with respect to the intensity of the m2 mode. Here, a similar tendency with respect to liquid ammonia is observed as for the vibrational frequencies. In the IRspectrum of liquid ammonia the symmetric stretching mode is very weak [24] or medium intense [25], while the most dominant band in the N–H stretching region is due to the antisymmetric
stretching mode [24–26]. The intensity of the second harmonics of the antisymmetric bending mode is described as weak [24] to medium [25,26]. From these similarities of Cl (NH3)n clusters with increasing cluster size and of liquid ammonia one may deduce structural information. In both scenarios of ‘interior states’ (the anion is embedded between solvent molecules) and of ‘one-sided subclusters’ (the anion sits on top of a network of solvent molecules), the decreasing influence of the chloride on the ammonia molecule will result in a blue shift of the H-bound N–H-stretching frequencies in direction of the unperturbed ammonia value. Here the corresponding frequencies of liquid rather than of gas phase ammonia are valid. Of course, the m2 frequency will only approach but not reach the symmetric N–H stretching frequency, since it is connected to the chloride-bonded proton motion. In the case of ‘interior states’, a maximum number of protons is bound to the chloride and the influence of the ion is distributed over a finite number of ammonia molecules. The decrease in particular of the m2 frequency would then level out at a cluster size for which the possibilities of the chloride to bind ammonia clusters is saturated. Ab initio calculations are necessary to determine how many such hydrogen-bonds are possible and if this agrees with experimental results. In the case of small fluoride clusters, such ‘interior states’ are found in ab initio calculations by Wild and Lenzer [12]. They also calculated IR-spectra and found much stronger shifts of the H-bound N–H-stretching frequencies than observed for the m2-mode in Fig. 4. On the other hand, ‘one-sided subclusters’ are assumed for small iodideammonia complexes according to an estimation of Frischkorn et al. [11]. Obviously, the size of the ion governs which type of so-called micro-solvation takes place. Since the size of the chloride ion lies between iodide and fluoride, we want to consider further arguments following Frischkorn et al. [11]. Generally, the structure of the complexes reflects the balance of halide solvent and solvent– solvent interaction. The shift of the vertical detachment energy resembles the stabilisation energy of the attached solvent molecule. Markovich et al. [27] obtained a stabilisation energy of 760 meV for Cl H2O, while for the water dimer a dissociation energy of 160 meV has been found [28]. For Cl NH3, the stabilisation energy lies below 400 meV (see Fig. 1) and a dissociation energy of 79 meV was found for the ammonia dimer [29]. Since both pairs of values show a similar ratio, one might expect similar geometries of the corresponding complexes. Ab initio calculations of Cl (H2O)2 that were compared with the IR-dissociation spectrum of this complex [30] show that a network of water molecules is formed. This leads one to the assumption that one-sided subclusters also are formed in the case of small Cl (NH3)x complexes. However, only theoretical structures and their comparison with spectroscopic results will finally help to solve the question which type of micro-solvation occurs in chloride ammonia complexes. 4. Conclusion While the photodetachment spectrum of Cl NH3 allowed for investigation of the stabilisation properties of the complex, the IR-spectra of Cl (NH3)x (x = 1–4) supplied information about the vibrational frequencies of the complexes. The long onset of the photodetachment spectrum is attributed to the detachment into a dissociative neutral state. Thus, the shift of the vertical detachment energy of the cluster with respect to that of chlorine equals the stabilisation energy of the complex and is determined to be 2550 ± 180 cm1. The IR-spectrum of the smallest complex is in good agreement with a previous spectrum published by Weiser et al. [10]. However, a refined assignment can now be given. The dominant peak and another band in the spectrum of the complex show a splitting which we assign to two rotational branches. Rotational constants could
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be determined by using the simulation program of an asymmetric rotor. The simulated spectrum is in good agreement with the experimental one and confirms the calculated rotational constants published by Weiser et al. [10]. Addressing the spectra of larger complexes, we observe that the spectra of larger clusters become more similar to that of liquid ammonia concerning the frequency as well as the relative intensity of the vibrational bands. This is an indication for the decreasing influence of the chloride ion on the vibrational modes of ammonia. Arguments involving the energies of the solvent–solvent and the solvent–ion interaction as used by Frischkorn et al. [11] for the I (NH3)x complexes would support the assumption of one-sided subclusters Cl (NH3)x (x = 1–4). However, for secure structural predictions ab initio calculations are indispensible. Acknowledgements The authors are grateful to Dr. H. Selzle of the Technical University of Munich for providing his asymmetric rotor program. This work has been supported by the DFG (German research society). References [1] J. Darnell, H. Lodish, D. Baltimore, Molecular Cell Biology, fifth edn., Freeman, New York, 2004. [2] J.H. Choi, K.T. Kuwata, Y.B. Cao, M. Okumura, J. Phys. Chem. 102 (1998) 503. [3] S.S. Xantheas, J. Phys. Chem. 100 (1996) 9703. [4] P. Ayotte, C.G. Bailey, G.H. Weddle, M.A. Johnson, J. Phys. Chem. A 102 (1998) 3067. [5] M.S. Johnson, K.T. Kuwata, C. Wong, M. Okumura, Chem. Phys. Lett. 260 (1996) 551.
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