ammonia clusters. Thermodynamic properties and frequency analysis

Journal of Molecular Structure (Theochem) 497 (2000) 105–113 www.elsevier.nl/locate/theochem

A quantum chemical study of aniline/ammonia clusters. Thermodynamic properties and frequency analysis J.M. Hermida-Ramo´n*, A. Pen˜a-Gallego, E. Martı´nez-Nu´n˜ez, A. Ferna´ndez-Ramos, E.M. Cabaleiro-Lago Departamento de Quı´mica Fı´sica, Facultade de Quı´mica, Universidade de Santiago de Compostela, Adva das Ciencias s/n, E-15706 Santiago de Compostela, Spain Received 8 March 1999; received in revised form 25 May 1999; accepted 4 June 1999

Abstract The potential energy surface of the aniline/ammonia cluster is analyzed by correlated ab initio molecular orbital methods: MP2 and DFT (B3-LYP functional) with the 6-311G p basis set. Five minima were located at the B3-LYP=6-311G p level, and four minima at the MP2=6-311G p level. The most stable conformation is a consequence of the hydrogen bond between the NH bond of the aniline molecule and the lone pair of the nitrogen atom of ammonia. Other local minima result from the interaction between the aromatic ring of aniline and the hydrogen atoms of ammonia, or from the hydrogen bond through the hydrogen atoms of the aromatic ring and the nitrogen atom of ammonia. Single-point calculations at different levels have been done. From the obtained results the predicted energy for the global minimum is about 24.50 kcal/mol. A comparison between experimental and calculated frequencies suggests that, aside from the most stable dimer, some other minima could be present. Some of the thermodynamic properties of the cluster were calculated from its harmonic frequencies. The analysis of the obtained values seems to confirm the existence of several cluster conformations which affects the experimental results. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Aniline/ammonia clusters; Ab initio calculations; DFT calculations; Intermolecular interactions; Frequency analysis

1. Introduction The study of intermolecular interactions is one of the fields in which quantum chemical ab initio methods have made the largest contribution, both qualitatively and quantitatively, to our knowledge in chemistry. In particular, in recent years these methods have been extensively used in the structure determination of intermolecular complexes. The exact understanding of the aggregate structure is the primary and one of the most important steps to interpret the mole* Corresponding author. Fax: 1 34-981595012. E-mail address: [email protected] (J.M. Hermida-Ramo´n).

cular clusters properties. Using a clear knowledge of the structure one can further pursue the analysis of the aggregate potential surface and obtain more insight into the nature of the cluster formation, which can help us to understand different processes, as the solvation processes and solution dynamics. Among the studies aimed to determine cluster structures, a large number of them concerned with the analysis of clusters containing aromatic molecules. Such isolated clusters between aromatic molecules and small polar [1–3] and non-polar [4–6] solvents have been considered of particular importance, because these complexes can be used as prototypes for the hydrogen bonding

0166-1280/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00201-8

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interactions of larger species in solution and in biological systems. Aniline is the simplest amine with an aromatic ring. Over the past 10–15 years, different studies of cluster formation between aniline and several solvents have been done [7–12]. In particular, interest was shown in the complexes with polar solvents (NH3, H2O, CH3OH), because hydrogen bonding interactions involving the NH2 group can be established. This fact is important to elucidate the role of this kind of interactions in complexes of aromatic molecules and its influence on vibrational modes, which contributes to the comprehension of the molecular behavior. In particular, the cluster between aniline and ammonia is especially interesting because both molecules having the same functional group, and therefore the question arises about their behavior as donor or acceptor. Moreover, this system suggests the possibility of three distinct intermolecular interactions: the two hydrogen donor/acceptor arrangements of aniline and NH3, the ‘hydrogen bond’ between the ammonia hydrogen atoms and the aromatic ring (NH…psystem) and finally, a polar, multipole moment electrostatic interaction. Recently, two experimental papers [9,10] have discussed the structure, energy and frequencies of the aniline/ammonia cluster. In the first one [9], the authors used the hole burning spectroscopy technique and calculations employing a Lennard–Jones– Coulomb 6–12–1 model potential. From the obtained results, they predict four minima for the aniline/ ammonia cluster, with the global minimum given by the ‘hydrogen bonding’ interaction of NH3 through its hydrogen atoms with the aromatic p-electron system of the aniline ring. This minimum has a binding energy of 22.34 kcal/mol (based on the force field calculations) in accordance with their experimental data (21.79 kcal/mol). In the second study [10], the aniline/ammonia cluster is analyzed employing infrared depletion spectroscopic techniques combined with mass spectrometry. In addition, some ab initio calculations at the HF level and a posterior MP2 optimization were used to confirm the experimental results. Using the infrared spectra, it is inferred a cluster structure determined by the hydrogen bond between the NH bond of the aniline molecule and the lone pair of the nitrogen atom of ammonia. Accordingly, these two recent

experimental works about aniline/ammonia cluster are in disagreement. As mentioned earlier, there are some discrepancies concerning the structure of aniline/ammonia cluster. Besides, the ab initio calculations were performed at the HF level (only one calculation has been performed at the MP2 level), and seems to have been focussed to characterize the conformation predicted by the infrared results. However, the inclusion of the electron correlation can completely change the stability of the different conformations. These reasons motivated us to carry out a more exhaustive exploration of the potential surface of the aniline/ammonia cluster, for the purpose of finding all possible minima in the cluster configurational space and establishing the differences among them, in order to illuminate the disagreement between the experimental studies [9,10]. In the present study, we performed high-level quantum chemical calculations on the aniline/ammonia cluster. Two different methods have been employed to include the electronic correlation: second-order Møller–Plesset theory (MP2) and density functional theory (DFT). To our best knowledge, there are not many studies in the literature about the behavior of DFT in complexes including aromatic rings and polar solvents. Thus, a comparison of the results obtained by quantum chemical methods can help to further evaluate the capabilities of DFT in the study of clusters with molecules containing aromatic rings.

2. Computational procedure The energy minima for the aniline/ammonia dimer were located by optimizing all 3N-6 internal degrees of freedom via ab initio calculations including electron correlation in the form of the second-order MP2 or by DFT using the B3-LYP functional. Optimizations were carried out with the 6-31G basis set augmented with diffuse and polarization functions on the heavy atoms (6-311Gp ). In a previous study [13], one of us found this basis set as an appropriate choice to establish a balance between the computational cost and the reliability of the obtained results in the field of the intermolecular interactions. The corresponding minima for the dimers were characterized from harmonic frequencies and force constants (zero

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as: T DGTdim ˆ DHdim 2 TDSTdim

…3†

T is the change of the vibrational energy upon DEvib dimerization including the change in zero-point vibrational energies and a contribution which reflects the Boltzmann distribution of the vibrational degrees of freedom. DSTvib is the entropy difference upon the dimerization process, which is expressed in terms of the vibrational partition function and temperature [16]. All calculations done in this study were performed employing the gaussian94 software package [17].

3. Results and discussion 3.1. Structure and energy results Fig. 1. Minima predicted by Ferna´ndez and Bernstein [9].

negative force constants for a minimum) calculated at the same level as that used in the optimization. Several single-point calculations were performed with the 6-31111Gpp and 6-31111G…2d; 2p† basis sets, and also a single-point calculation at the MP4=6311Gp level has been done. All the interaction energies (DEe) were corrected for the basis set superposition error (BSSE) with the full counterpoise (CP) method of Boys and Bernardi [14], resulting in a more reliable estimation of the interaction energies …DEeCP †: The CP correction is the sum of the differences in the energies of the constituent monomers in the geometry of the supermolecule with and without the full basis set of the whole aggregate. Aside from the ab initio interaction energies, several thermodynamic properties were determined from the standard expressions of the statistical thermodynamics of ideal gases [15]. Accordingly, the energy of dimerization can be written as: T T ˆ DEe 1 DEvib 2 3RT DUdim

…1†

the enthalpy of dimerization is given by: T T ˆ DUdim 2 RT DHdim

…2†

and the Gibbs free energy of dimerization is defined

Fig. 1 shows the four minimum energy structures predicted by Ferna´ndez and Bernstein [9] using twocolor mass resolved excitation (MRES) and hole burning (HB) spectroscopy, and by model potential energy calculations. The interaction energies obtained by the force field calculations for these minima are 22.34, 22.33, 22.06 and 22.06 kcal/mol for I, II, III and IV, respectively. From MRES spectroscopy the interaction energy for the complex is found to be 21.79 kcal/mol. The MRES and HB results predict that two different isomers are present in the aniline/ ammonia cluster. The first one is assigned to minima I and II (not distinguished experimentally). The second one corresponds to minimum III, and for structure IV there are no experimental features related to it. Nakanaga et al. [10], however, obtained values and intensities of NH frequencies from infrared depletion spectroscopy complemented by ab initio calculations. From these data the authors predicted a structure for aniline/ammonia cluster similar to IV-D in Fig. 2 whose interaction energy is 26.58 kcal/mol. In Fig. 2 the minima obtained at the B3-LYP/6311G p level are shown and Fig. 3 gives the stationary points found at the MP2=6-311G p level. Ab initio methods including electronic correlation are used in order to take into account effects produced by the dispersive forces. This kind of interactions can play an important role in this cluster due to the presence of the aromatic ring. The starting

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Fig. 2. Minimum energy structures found for the aniline/ammonia cluster at the B3-LYP=6-311Gp level.

Fig. 3. Stationary points for the aniline/ammonia cluster located at the MP2=6-311Gp level.

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Table 1 Interaction energies and thermodynamic properties at 298 K for the different minima of the aniline/ammonia cluster (kcal/mol) B3-LYP=6-311Gp

DEe DEeCP Do DUdim DHdim DGdim

MP2=6-311Gp

I-D

II-D

IV-D

V-D

VI-D

III-M

IV-M

V-M

VI-M

21.14 20.83 20.20 1.03 0.43 5.02

21.23 20.95 20.35 0.91 0.32 4.65

25.47 24.50 23.06 22.34 22.94 4.15

21.43 20.81 0.10 1.20 0.60 6.47

21.23 20.63 0.18 1.35 0.76 6.16

25.97 23.35 21.92 20.67 21.85 5.26

27.32 24.47 22.85 22.25 22.84 4.21

23.14 20.96 20.13 1.01 0.42 5.19

23.03 20.87 20.04 1.11 0.51 5.23

configurations employed in the different optimizations were taken from literature and also several conformations were chosen according to the chemical criteria. As shown in Figs. 2 and 3, the correlated calculations do not predict similar structures to the conformations found by Ferna´ndez and Bernstein [9]. The closest structures to the minima I and II (see Fig. 1), with its hydrogen atoms pointing toward the ring, are I-D and II-D at the B3LYP/6-311Gp level and I-M and II-M at the MP2=6-311Gp level. In contrast to I and II, the two DFT conformations present only one hydrogen atom pointing toward the ring, which is located close to the carbon atom opposite to the NH2 group and not on the middle of the ring. Therefore, this fact is contrary to the existence of the ‘hydrogen bonding’ between all hydrogen atoms of ammonia and the p-system of the aniline. The MP2 calculations corroborate this observation: the conformations close to I-M and II-M are found as transition states dropping to minima IV-M and III-M, respectively. Both levels of calculation predict minima similar to conformer IV (IV-D and IV-M). Also, the minima characterized by the interactions between the nitrogen atom of ammonia with the meta-hydrogen and the para-hydrogen of aromatic ring are given by the two correlated methods (V-D, V-M, VI-D and VI-M). In contrast, the minimum denoted as III-M appears only at the MP2 level. For this configuration a hydrogen bond ammonia/aniline (proton donor/proton acceptor) is obtained (similar to structure III in Fig. 1). With regard to DFT method, this structure collapses to a minimum IV-D. In general, it can be noted that there are very important differences in the ab initio minima with respect to the conformations obtained by Ferna´ndez and Bernstein [9]. Table 1 shows the energies for the minima obtained

with both methods employed here. As shown in the Table, the global minimum is the structure IV (IV-D and IV-M) with energy of about 24.50 kcal/mol. The energy obtained by Nakanaga et al. [10] for this configuration, 26.58 kcal/mol, is much larger than our result. However, in their calculations Nakanaga et al. have not mentioned the BSSE; hence we checked their energy data by means of an optimization and a posterior CP correction using the same level (MP2/6-31G pp) as they had employed, obtaining a corrected energy for IV-M of 24.78 kcal/mol. Consequently, an erroneous value is given by Nakanaga et al. As shown in Table 1, and as have been reported elsewhere [18], it is necessary to correct the BSSE in MP2 calculations, since at this level the BSSE is meaningful. This error is less considerable using DFT method with the B3-LYP functional. With regard to the second most stable minimum (III-M), in spite of the fact that it is much more stable than the other minima (except minimum IV-M) this conformation is only found at the MP2=6-311Gp level. When a DFT method is employed, this structure collapses to minima IV-D, although the optimization process with a DFT method points out that the region close to the conformation III-M is very flat. The rest of minima have energies close to 21.00 kcal/mol, although the structures I-(D, M) and II-(D, M) are more stable than V-(D, M) and VI-(D, M). The energies for conformations I-M and II-M are 22.43 and 21.51 kcal/mol, respectively. The differences with respect to the DFT values follow directly from the fact that they correspond to transition states of the two most stable minima. DFT and MP2 single-point calculations with the 6-31111Gpp basis set in all found minima have been done. The interaction energies obtained were:

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Table 2 Scaled intermolecular frequencies for the different stationary points of the aniline/ammonia cluster (cm 21) (Frequency scaling factors: 1.0013 (B3-LYP=6-311Gp ); 1.0485 (MP2=6-311Gp ). Obtained from Ref. [19]) B3-LYP=6-311Gp

MP2=6-311Gp

I-D

II-D

IV-D

V-D

VI-D

I-M

II-M

III-M

IV-M

V-M

VI-M

10.2 15.9 48.1 61.9 100.5 177.7

7.9 16.8 52.3 59.0 79.8 164.9

27.8 36.6 44.0 146.6 233.2 251.1

29.2 34.0 46.6 77.3 133.2 173.3

22.6 29.3 33.8 74.9 129.8 154.9

261.9 17.1 42.8 112.0 121.6 209.9

2102.0 30.3 48.7 68.7 91.8 150.0

21.1 67.6 132.5 173.0 178.9 225.6

27.8 56.0 73.4 166.0 208.4 267.4

18.8 28.5 41.6 103.9 149.2 156.4

17.3 30.2 33.8 103.0 145.6 147.0

20.75, 20.87, 24.38, 20.84, 20.62 kcal/mol for ID, II-D, IV-D, V-D and VI-D at the B3-LYP=6-31111Gpp level; and with MP2 method the III-M, IV-M, V-M and VI-M conformations had energies of 23.37, 24.50, 21.00 and 20.92 kcal/mol, respectively. A single-point calculation at the MP2=6-31111G…2d; 2p† level was done in the IV-M minimum; the obtained energy was 24.77 kcal/mol. It seems clear from these data that increasing the basis set has not too much influence over the energy values. In other words, it can be assumed that the 6-311Gp basis set gives a good prediction of energies for this complex. To check the influence of higher order effects in the cluster stability a single-point calculation at the MP4=6-311Gp level was performed in the IV-M geometry. The obtained energy of 24.29 kcal/mol, similar to MP2 and DFT results, suggests a low influence of high order effects. 3.2. Frequency bands and thermodynamic properties In Table 2 are shown the scaled [19] intermolecular frequencies for the different stationary points calculated with the ab initio methods. According to the results from HB spectroscopy obtained by Ferna´ndez and Bernstein [9], there are two conformations for aniline/ammonia cluster with different series of intermolecular frequencies. The frequency values found for the first of these conformations were 18 and 32 cm 21, and for the second one only a value, 8 cm 21, was obtained. Furthermore, using vibrational frequencies of the excited electronic state, the authors predict a vibrational frequency of about 90–100 cm 21 for the ground state of both conformations, which is

assigned to the stretching vibration of the intermolecular bond. The comparison between these experimental data and the frequencies shown in Table 2 suggests that either the V-(D,M) or the VI-(D,M) structure corresponds with the first experimental conformation, since there is a good agreement between the experimental and ab initio frequencies (although the DFT results have a larger deviation than the MP2 data). As regards the another experimental conformation, it seems to accord with either the I-D or the II-D structure (for this assignment the IM and II-M frequencies have not been taken into account). From the given data no distinction between I-D and II-D, and also between V-(D,M) and VI(D,M), can be done. The IV-(D,M) and III-M structures have higher frequencies than those experimental frequencies determined by Ferna´ndez and Bernstein [9], and no evidences corresponding to these minima can be found in their experimental results. However, the experimental aniline/ammonia interaction energy obtained by these authors (21.79 kcal/mol) is more negative than the ab initio values of the four conformations that we have identified from the experimental frequencies. This discrepancy might be due to the fact that this energy is the result of an average over the energies of all conformations, which might be an evidence related with the presence of III-M and IV(D,M) conformers. The scaled [19] vibrational frequencies and their intensities in the NH stretching region are given in Tables 3 and 4, respectively. As can be seen in Tables 2 and 3, and according to the study of Scott and Radom [19], different frequency scaling factors are used depending on whether low of high frequencies are taken into account. The analysis of these data

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Table 3 Scaled vibrational frequencies in the NH stretching vibration region for the different stationary points of the aniline/ammonia cluster (cm 21) (Frequency scaling factors: 0.9614 (B3-LYP=6-311Gp ); 0.9434 (MP2=6-311Gp ). Obtained from Ref. [19]) B3-LYP=6-311Gp I-D

II-D

MP2=6-311Gp IV-D

Aniline monomer a: 3413; 3506 3416 3415 3290 3510 3508 3477 Ammonia monomerb: 3328; 3460; 3460 3320 3320 3325 3447 3447 3450 3453 3452 3451 a b

V-D

VI-D

3409 3501

3408 3500

3325 3452 3453

3325 3452 3453

I-M

II-M

III-M

IV-M

Aniline monomer a: 3351; 3454 3346 3349 3339 3259 3440 3452 3442 3420 Ammonia monomerb: 3309; 3462; 3462 3289 3297 3278 3292 3437 3441 3422 3438 3438 3445 3442 3439

V-M

VI-M

3346 3448

3346 3448

3296 3445 3446

3296 3446 3446

Experimental values: 3422, 3508 cm 21. Ref. [12]. Experimental values: 3337, 3337, 3444 cm 21. Ref. [20].

ing vibration of NH2 group in conformers I-M or II-M. As noted earlier from the ab initio results of Table 1, minimum IV-(D, M) is the most stable conformation. Yet, application of the zero-point vibrational energy (ZPE) to minima results in a decrease of the energy differences between the global minimum and the other minima. This effect is transferred to the thermodynamic properties studied here. It must be emphasized, however, that the entropic contribution to the dimerization process significantly decreases the difference in free energies, the result being a similar stability of the different conformations. This fact will be reflected in the Boltzmann population ratios. Thus, the population ratios are 2:1 (IV-D:II-D) and 5:1 (IVM:V-M) at 298.15 K. Therefore, a presence of different minima would be expected, which seems to

seems to confirm the predictions of Nakanaga et al. [10]: these authors found a very strong band at 3354 cm 21 and a strong band at 3479 cm 21 in the infrared spectrum of the aniline/ammonia cluster, and assign these bands to the two stretching vibrations of the NH2 group of an aniline molecule contained in a complex similar to IV-(D,M). Besides this, another weak absorption bands at 3429, 3438, 3460 and 3499 cm 21 are found; which are assigned to the NH stretching vibrations of the NH3 because the authors suppose that there is only one cluster conformation. Nevertheless, according to the data collected in Tables 3 and 4, it can be suggested that some of these aforementioned bands are yielded by the stretching vibrations of the different conformations of the aniline/ammonia cluster. Thus, the band at 3499 cm 21 might be due to the antisymmetric stretch-

Table 4 Intensity of the vibrational frequencies in the NH stretching vibration region for the different stationary points of the aniline/ammonia cluster (km/mol) B3-LYP=6-311Gp I-D

II-D

MP2=6-311Gp IV-D

Aniline monomer: 12.4; 12.7 14.4 14.3 455.3 13.6 13.6 37.9 Ammonia monomer: 1.9; 2.6; 2.6 7.6 5.2 3.4 27.8 23.3 6.5 2.0 1.8 7.5

V-D

VI-D

8.9 10.7

8.9 10.7

2.5 3.6 4.0

2.6 3.5 3.8

I-M

II-M

III-M

Aniline monomer: 13.4; 15.6 17.9 14.8 14.9 16.0 16.6 16.0 Ammonia monomer: 0.8; 7.4; 7.4 2.1 0.9 19.3 4.8 24.2 30.8 3.8 3.9 5.3

IV-M

V-M

VI-M

332.7 52.5

9.8 13.4

10.0 13.6

5.2 10.6 12.3

1.5 7.6 9.8

1.6 7.6 8.9

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corroborate the above-mentioned hypothesis about the mean energy of the cluster. Finally, with regard to the DFT–MP2 discrepancies, the most important difference between them is the disagreement in some of the obtained structures. In contrast to the DFT method, the possible H…psystem bonds in the I-M and II-M conformations are clearly determined by the effect of N…H interactions; corresponding these structures to transition states of IV-M and III-M minima. No minimum similar to IIIM in DFT results is found, which seems to be due to DFT method to produce an intermolecular interaction between the hydrogen atoms of the aniline NH2 group and the nitrogen atom of ammonia that is stronger at medium distances than MP2 interaction. These features can be explained by the different behavior at large and middle distances of DFT and MP2 methods.

4. Conclusions Based on our exploration results, the potential energy surface for the aniline/ammonia cluster is rather complex: it contains four (MP2) or five (DFT) minima, and transition states more stable than some minima. The most stable minimum results from a hydrogen bond through the NH bond of the aniline molecule and the lone pair of the nitrogen atom of ammonia. Conformers determined by dispersion interactions, with the NH3 molecule close to the aromatic ring and the hydrogen atoms pointing toward the ring, have low stabilization energy (around 21.00 kcal/mol). Another type of minima with energies close to 21.00 kcal/mol is found. These minima appear from the hydrogen bond between the hydrogen atoms of the aromatic ring and the nitrogen atom of the ammonia molecule. It is illustrated how the BSSE affects the prediction of the energy on the obtained conformations, and also the differences between the DFT and MP2 methods. As it has seen, Nakanaga et al. [10] have not allowed for this effect, affording an important error in their result of the energy value of the most stable minimum. The two correlated methods employed give similar energy results. However, the character of the stationary points is different depending on the employed method. This contrast seems to be due to differences

between DFT and MP2 methods in the behavior of large and middle range interactions. Comparison of ab initio intermolecular frequencies with the experimental values obtained by Ferna´ndez and Bernstein [9] gives no evidences for the existence of conformation IV (the most stable minimum), which seems to confirm the observation of these authors. However, it is likely that the binding energy obtained by Ferna´ndez and Bernstein was the result of an average over the binding energies of the different conformers (including the most stable minimum). With regard to the ab initio results of Nakanaga et al., the same conclusions as these authors can be drawn in the present paper. Nevertheless, the weak bands assigned by Nakanaga et al. [10] to NH3 vibrations can also be assigned to vibrations from another cluster conformations (different than IV structure). We conclude from the obtained energy and frequency results that a conformation like structure IV-(D, M) is the global minimum, but that another conformations of the aniline/ammonia cluster have influence in the properties of the complex. This hypothesis seems to be corroborated by the thermodynamic properties of the different minima. Acknowledgements The authors wish to thank Roberto Rodrı´guezFerna´ndez for his help as system manager of our computer facilities. Time allocation for calculations was provided by the Centro de Supercomputacio´n de Galicia (CESGA). E.M.-N. and A.P.-G thank Xunta de Galicia and the Segundo Gil Da´vila Foundation, respectively, for their grants. References [1] A.W. Garret, T.S. Zwier, J. Chem. Phys. 96 (1992) 3402. [2] S. Li, E.R. Bernstein, J. Chem. Phys. 97 (1992) 792. [3] J. Wanna, J.A. Menapace, E.R. Bernstein, J. Chem. Phys. 85 (1986) 1795. [4] T. Brupbacher, A. Bauder, J. Chem. Phys. 99 (1993) 9394. [5] P.I. Nagy, C.W. Ulmer II, D.A. Smith, J. Chem. Phys. 102 (1995) 6812. [6] S. Sun, E.R. Bernstein, J. Phys. Chem. 100 (1996) 13348. [7] E.J. Bieske, M.W. Rainbird, A.E.W. Knight, J. Chem. Phys. 94 (1991) 7019. [8] J.M. Smith, X. Zhang, J.L. Knee, J. Chem. Phys. 99 (1993) 2550.

J.M. Hermida-Ramo´n et al. / Journal of Molecular Structure (Theochem) 497 (2000) 105–113 [9] J.A. Ferna´ndez, E.R. Bernstein, J. Chem. Phys. 106 (1997) 3029. [10] T. Nakanaga, K. Sugawara, K. Kawamata, F. Ito, Chem. Phys. Lett. 267 (1997) 491. [11] T. Nakanaga, K. Kawamata, F. Ito, Chem. Phys. Lett. 279 (1997) 309. [12] P.K. Chowdhury, K. Sugawara, T. Nakanaga, H. Takeo, J. Mol. Struct. 447 (1998) 7. [13] J.M. Hermida-Ramo´n, M.A. Rı´os, J. Phys. Chem. A 102 (1998) 2594. [14] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553. [15] L.A. Curtiss, D.J. Frurip, M. Blander, J. Am. Chem. Soc. 100 (1978) 79. [16] R.G. Gilbert, S.C. Smith, Theory of Unimolecular and Recombination Reactions, Blackwell Scientific Publications, Oxford, 1990.

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[17] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, N.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. AlLaham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, V. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, V. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, in Gaussian 94, Revision C.3. Gaussian, Inc. (1995). [18] K. Szalewicz, S. Cole, W. Kolos, R. Barllet, J. Chem. Phys. 89 (1988) 3662. [19] P. Scott, L. Radom, J. Phys. Chem. 100 (1996) 16502. [20] T. Shimanouchi, Tables of molecular vibrational frequencies. Consolidated volume I. US Department of Commerce, 1971.