Theoretical Study of Neutral and Cationic Complexes Involving Phenol

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Reference

Theoretical Study of Neutral and Cationic Complexes Involving Phenol

TRAN, Fabien, WESOLOWSKI, Tomasz Adam

Abstract

Geometry and interaction energy in complexes of the Ph-L type (L = Ar, N2, CO, H2O, NH3, CH4, CH3OH, CH3F) involving neutral or cationic phenol were determined using the density functional theory formalism based on the minimization of the total energy bifunctional and gradient-dependent approximations for its exchange-correlation and nonadditive kinetic-energy parts. For the neutral complexes the calculated interaction energies range from 1 kcal/mol for the Ph-Ar complex to about 10 kcal/mol for Ph-NH3. The interactions are stronger if the cationic phenol is involved (up to 25 kcal/mol). It is found, except for neutral Ph-Ar, that the hydrogen-bonded structure is more stable than the -bound one. Calculated interaction energies (De) correlate well with the experimental dissociation energies (D0).

TRAN, Fabien, WESOLOWSKI, Tomasz Adam. Theoretical Study of Neutral and Cationic Complexes Involving Phenol. International Journal of Quantum Chemistry , 2005, vol. 101, no. 6, p. 854-859

DOI : 10.1002/qua.20346

Available at:

http://archive-ouverte.unige.ch/unige:3281

Disclaimer: layout of this document may differ from the published version.

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Theoretical Study of Neutral and

Cationic Complexes Involving Phenol

FABIEN TRAN, TOMASZ A. WESOŁOWSKI

Department of Physical Chemistry, University of Geneva, 30, quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland

Received 30 September 2003; accepted 2 April 2004

Published online 3 November 2004 in Wiley InterScience (www.interscience.wiley.com).

DOI 10.1002/qua.20346

ABSTRACT:Geometry and interaction energy in complexes of the Ph–L type (L⫽ Ar, N2, CO, H2O, NH3, CH4, CH3OH, CH3F) involving neutral or cationic phenol were determined using the density functional theory formalism based on the minimization of the total energy bifunctional and gradient-dependent approximations for its exchange- correlation and nonadditive kinetic-energy parts. For the neutral complexes the calculated interaction energies range from 1 kcal/mol for the Ph–Ar complex to about 10 kcal/mol for Ph–NH3. The interactions are stronger if the cationic phenol is involved (up to 25 kcal/mol). It is found, except for neutral Ph–Ar, that the hydrogen-bonded structure is more stable than the␲-bound one. Calculated interaction energies (De) correlate well with the experimental dissociation energies (D0). © 2004 Wiley Periodicals, Inc. Int J Quantum Chem 101: 854 – 859, 2005

Key words:density functional theory; subsystems; van der Waals complexes;

hydrogen-bonded complexes; phenol

I. Introduction

A

great deal of experimental and theoretical work has been devoted to characterize the complexes formed by phenol (C₆H₅OH) and ligands such as Ar, N₂, H₂O, etc. Depending on the state of the phenol (ground or excited; neutral or cationic) and on the ligand, the structure of the formed complex can be of the van der Waals type, with the ligand bound to the ␲system of the aromatic ring, or of the hydrogen-bonded type with

the ligand attached to the OH group of the phenol.

A van der Waals␲-bound structure is preferred in complexes involving neutral phenol and a spherical ligand like rare-gas atoms. If the ligand is situated above the aromatic ring, the London dispersion forces dominate as in similar complexes involving benzene and rare-gas atoms. Complexes involving cationic phenol and/or ligand with a permanent electric multipole are more likely to be found in the hydrogen-bonded structure.

In this work, we report calculations on the structure and energetics of Ph–L complexes formed by phenol (Ph) (neutral or cationic) and such ligands (L) as, Ar, N₂, CO, H₂O, NH₃, CH₄, CH₃OH, and

Correspondence to:F. Tran; e-mail: Fabien.Tran@chiphy.unige.ch

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CH₃F. The calculations were performed using the density functional theory (DFT) [1–3] formalism based on the minimization of the total energy bifunctional E[␳1,␳2] [4, 5]. Minimization ofE[␳1,␳2] is performed by solving Kohn–Sham-like one-electron equations: Kohn–Sham (KS) equations with constrained electron density (KSCED). The applied method has been shown to be a well-adapted method to study weakly bound complexes like, for example, the benzene dimer [6] or complexes involving carbazole [7], and to give results superior to the traditional KS formulation of DFT [8].

II. Theory and Computational Details

In the KSCED approach, the total energy of a system composed of two subsystems of densities␳1

and␳2is represented by the bifunctional [4, 5]

E关␳1,␳2兴⫽Ts关␳1兴⫹Ts关␳2兴⫹Tsnadd关␳1,␳2兴

⫹1

2

冕冕

^共␳¹^共^r^兲^⫹^␳²^共^r^兩^r^兲兲共␳^⫺^r¹^共^⬘兩^r^⬘兲^⫹^␳²^共^r^⬘兲兲^drdr⬘

⫹Exc关␳1⫹␳2兴⫹

冕

^v^ext^共^r^兲共␳¹^共^r^兲^⫹^␳²^共^r^兲兲^dr^⫹^Vⁿⁿ^{, (1)}

where

Tsnadd关␳1,␳2兴⫽Ts关␳1⫹␳2兴⫺Ts关␳1兴⫺Ts关␳2兴 (2) is the orbital-free nonadditive kinetic-energy bifunctional and all the other terms are deﬁned as in the traditional KS scheme [2]. As in the case of the exchange-correlation functionalE_xc[␳], the exact orbital-free form ofT_s^nadd[␳1,␳2] is unknown and any practical calculation relies on approximations for T_s[␳]. Partitioning the electron density makes it possible to perform the minimization of the total energy following a stepwise procedure in which the energy is minimized with respect to either␳1or␳2

[9]. Similar steps as those used to derive the KS equations [2] lead to the following equations for the one-electron orbitals␺i,J(J⫽1, 2) used to construct the electron density of subsystemJcomposed ofN_J electrons [4, 5]:

冉

^⫺¹²^ⵜ²^⫹^v^eff,J^共r兲

冊

^␺î,J^共r兲^⫽^⑀î,J^␺î,J^共r兲, ⁽³⁾

where

veff,J共r兲⫽␦Tsnadd关␳1,␳2兴

␦␳J共r兲 ⫹

冕

^␳¹^共^r^兩^⬘兲^r^⫺^⫹^r^␳^⬘兩²^共^r^⬘兲^dr⬘

⫹␦Exc关␳1⫹␳2兴

␦␳J共r兲 ⫹vext共r兲 (4)

and

␳J共r兲⫽

冘

i⫽1 NJ

兩␺i,J共r兲兩². (5)

We used the generalized gradient approximation (GGA) of Perdew and Wang (PW91) [10] forE_xc[␳] and, following the conjointness conjecture of Lee et al. [11], we used a reparametrized version [12] of the enhancement factor of the exchange part of the PW91 functional for the three components of the nonadditive kinetic energy T_s^nadd[␳1, ␳2] [Eq. (2)].

This approximation for T_s^nadd[␳1, ␳2] has appeared to be the most accurate one among the GGA approximations (see Ref. [13] and references therein).

The chosen GGA approximations in E[␳1,␳2] were recently shown to lead to very accurate interaction energies for a large set of van der Waals complexes for which benchmark ab initio results were available [8].

The KS calculations of isolated phenol Ph and ligand L were performed using the PW91 functional for the exchange-correlation energy. The calculations were carried out using two different orbital basis sets: the ﬁrst basis set (basis set I) is triple zeta valence with polarization (TZVP) [14] and the second basis set (basis set II) was developed by Partridge [15]. The number of basis functions used for the construction of the electron density ␳J of a molecule in the complex is the same as that used for the isolated case (the basis functions centered on the atoms of the molecule of interest); hence no basis set superposition error [16] had to be cor- rected. Our recent tests of the dependency of the KSCED energies on the basis set [17] indicate that basis set II leads to interaction energies that deviate from the basis set limit by at most 0.08 kcal/mol.

The KSCED calculations were performed using the modiﬁed version of the deMon program into which the KSCED formalism was implemented [18]. The results presented in this work were obtained after four “freeze-and-thaw” iterations [9].

NEUTRAL AND CATIONIC COMPLEXES

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 855

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III. Results and Discussion

The results obtained after geometry optimization for the interaction energies and intermolecular distances are reported in Tables I and II, respectively.

Table I shows that, for most of the complexes, the results obtained for the interaction energyD_e with the two basis sets are similar. Nevertheless, we can see a difference of the order of 1 kcal/mol between the two basis sets for the three cationic complexes involving Ar (proton-bound structure), H₂O, and NH₃, and this means that for these complexes the quality of basis set I is not sufﬁcient to obtain reli- able values ofD_e. Therefore, the use of basis set II seems to be necessary, particularly for the cationic Ph–Ar complex. If we consider the intermolecular

distances (Table II), we can see that the largest difference between the two basis sets is of about 0.2 Å for cationic Ph–Ar in the proton-bound structure.

No signiﬁcant effects of the basis set change were found for the other complexes. In the following part, only the results obtained with basis set II will be discussed.

For the neutral Ph–Ar complex, it is found that the ␲-bound structure [Fig. 1(a)] is energetically favored compared to the planar proton-bound structure [Fig. 1(c)] (1.33 kcal/mol for␲-bound and 1.00 kcal/mol for proton-bound), which is in agreement with the analysis of the experimental results by Mu¨ller-Dethlefs and collaborators [19, 20] who detected only the van der Waals␲-bound structure, but did not exclude the existence of a proton-bound structure. The value of 1.33 kcal/mol compares well with the experimental value of 1.04 kcal/mol TABLE I ______________________________________

Calculated well depthsD_e(with basis sets I and II) and experimental (exp) dissociation energiesD₀of neutral and cationic Ph–L complexes.

Complex Structure D_e(I) D_e(II) D₀ (exp) Ph–Ar proton-bound 0.87 1.00

␲-bound 1.30 1.33 1.04^a Ph^⫹–Ar proton-bound 1.37 2.53

␲-bound 1.27 1.77 1.53^a Ph–N₂ proton-bound 2.51 2.24 1.24^b Ph^⫹–N₂ proton-bound 6.23 5.90 4.69^b Ph–CO proton-bound-C 3.46 3.39 1.88^b

proton-bound-O 1.84 1.59

Ph^⫹–CO proton-bound-C 8.31 8.76 6.93^b proton-bound-O 4.84 4.31

Ph–H₂O proton-bound 7.04 7.37 5.60^c

␲-bound 3.11 3.29

Ph^⫹–H₂O proton-bound 18.97 19.87 18.54^c Ph–NH₃ proton-bound 9.59 9.93

Ph^⫹–NH₃ proton-bound 23.72 24.86 Ph–CH₄ proton-bound 1.71 1.86

␲-bound 1.51 1.51

Ph^⫹–CH₄ proton-bound 4.64 5.20

␲-bound 2.50 2.55

Ph–CH₃OH proton-bound 7.55 7.71 6.11^c Ph^⫹–CH₃OH proton-bound 20.70 21.28 21.40^c Ph–CH₃F proton-bound 4.61 4.86 4.40^d Ph^⫹–CH₃F proton-bound 13.55 13.99 11.24^d Values are expressed in kcal/mol. See Figures 1–3 for the structures.

aRef. [21].

bRef. [25].

cRef. [28].

dRef. [43].

TABLE II _____________________________________

Calculated intermolecular distancesR(Å) (with basis sets I and II) of neutral and cationic Ph–L complexes.

Complex Structure R R(I) R(II) Ph–Ar proton-bound OH–Ar 2.77 2.70

␲-bound ␲–Ar 3.25 3.24 Ph^⫹–Ar proton-bound OH–Ar 2.62 2.39

␲-bound ␲–Ar 3.14 3.10 Ph–N₂ proton-bound OH–N 2.12 2.16 Ph^⫹–N₂ proton-bound OH–N 1.90 1.92 Ph–CO proton-bound-C OH–C 2.13 2.13 proton-bound-O OH–O 2.17 2.20 Ph^⫹–CO proton-bound-C OH–C 1.93 1.92 proton-bound-O OH–O 1.91 1.92 Ph–H₂O proton-bound OH–O 1.86 1.84

␲-bound ␲–O 3.20 3.18 Ph^⫹–H₂O proton-bound OH–O 1.67 1.65 Ph–NH₃ proton-bound OH–N 1.85 1.83 Ph^⫹–NH₃ proton-bound OH–N 1.66 1.64 Ph–CH₄ proton-bound OH–C 2.45 2.39

␲-bound ␲–C 3.27 3.31 Ph^⫹–CH₄ proton-bound OH–C 2.19 2.11

␲-bound ␲–C 3.11 3.11 Ph–CH₃OH proton-bound OH–O 1.84 1.83 Ph^⫹–CH₃OH proton-bound OH–O 1.64 1.63 Ph–CH₃F proton-bound OH–F 1.97 1.95 Ph^⫹–CH₃F proton-bound OH–F 1.73 1.73 For the proton-bound structures,Ris the distance between the H atom of the OH group of Ph and the indicated atom of L; for the ␲-bound structures, R is the vertical distance between the␲-plane of Ph and the indicated atom of L. See Figures 1–3 for the structures.

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forD₀[21]. In the cationic case, the planar proton- bound structure [Fig. 1(c)] (2.53 kcal/mol) is more stable than the␲-bound one [Fig. 1(b)] (1.77 kcal/

mol). This result agrees well with the conclusion of Solca` and Dopfer [22–24] who deduced, the proton- bound structure to be the global minimum and the

␲-bound one to be a local minimum based on a combined analysis involving infrared spectra and ab initio MP2 calculations. The experimental value of 1.53 kcal/mol [21] for the dissociation energy, assigned to the ␲-bound structure [22–24], compares well with our value of 1.77 kcal/mol forD_e. For the complexes involving N₂the calculations lead to the values of 2.24 kcal/mol and 5.90 kcal/

mol in the planar proton-bound structure [Fig. 1(d)]

for the neutral and cationic cases, respectively.

These calculated values ofD_eare comparable to the experimental values for D₀ [25] (1.24 kcal/mol for neutral and 4.69 kcal/mol for cationic). The differences between these values can be attributed to the zero-point energy (ZPE), which for the proton- bound structure can have values as large as 2 kcal/

mol, depending on the ligand L [26 –28]. The planar proton-bound structure has often been suggested

by experimental and theoretical works to be the global minimum both in the neutral [20, 29 –31] and cationic cases [22, 24, 29, 30, 32].

For neutral and cationic Ph–CO complexes the global minimum geometry is the proton-bound structure with the C atom of CO pointing in the direction of the OH group of the phenol [Fig. 1(d)].

This in agreement with the experimental and theoretical results of Mu¨ller-Dethlefs and collaborators [20, 25, 30]. Again, when compared to the experi- mentalD₀values [25], the differences can be attributed to ZPE.

Among the Ph–L complexes, the one involving H₂O has been one of the most studied by both theoretical and experimental methods (see Refs.

[26 –28, 33– 40] for some representative papers). The KSCED calculations predict, both for the neutral and cationic complexes, the proton-bound structure [Fig. 2(a)] to be the global minimum. The plane of H₂O is approximately perpendicular to the plane of Ph, as it has already been concluded from previous calculations (see, e.g., Refs. [34, 36]). The calculated interaction energies D_e (7.37 kcal/mol for neutral and 19.87 kcal/mol for cationic) agree well with the FIGURE 1. Equilibrium geometries derived from

KSCED calculations. (a) Neutral␲-bound Ph–Ar; (b) cationic␲-bound Ph–Ar; (c) neutral or cationic proton- bound Ph–Ar; (d) neutral or cationic proton-bound Ph–N₂or Ph–CO.

FIGURE 2. Equilibrium geometries derived from KSCED calculations. (a) Neutral or cationic proton- bound Ph–H₂O; (b) neutral␲-bound Ph–H₂O; (c) neutral or cationic proton-bound Ph–CH₄; (d) neutral or cationic␲-bound Ph–CH₄.

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experimental values [28] forD₀(5.60 kcal/mol for neutral and 18.54 kcal/mol for cationic).

To our knowledge no experimental data are available for the interaction energy of Ph–NH₃and Ph–CH₄complexes. The Ph–NH₃complex [proton- bound structure, Fig. 3(a)] (see Ref. [41] for a very recent theoretical work on this complex) has the largest values of D_e among the complexes studied in this work, and this both for the neutral (9.93 kcal/mol) and cationic (24.86 kcal/mol) complexes.

At the opposite end, the Ph–CH₄ [Figs. 2(c), (d)]

complex constitutes one of the most weakly bound with a value of 1.86 kcal/mol for the neutral case and a value of 5.20 kcal/mol for the cationic case, both in the proton-bound structure. The neutral Ph–CH₄ complex has two energetically nearly equivalent structures: 1.86 kcal/mol for the proton- bound structure and 1.51 kcal/mol for the␲-bound one (see Table I). ZPE is probably larger for the proton-bound structure than for the ␲-bound;

therefore the␲-bound structure cannot be excluded to be the global minimum based on our calculations, as it is suggested for spherical ligands like rare-gas atoms or CH₄[24].

CH₃OH and CH₃F are the largest among the considered ligands in the Ph–L complexes. These two systems are found to be the most stable in the proton-bound structure. Figure 3(b) shows that the O atom of CH₃OH interacts with the OH group of Ph to form a hydrogen bond (conﬁrmed experimen-

tally by Westphal et al. [42] for the neutral complex). The structures of neutral and cationic Ph–

CH₃F complexes are shown in Figs. 3(c) and (d), respectively. For this system, the F atom of CH₃F interacts with the OH group of Ph to form a hydrogen bond. The experimental dissociation energies for these two complexes (Refs. [28] and [43] for Ph–CH₃OH and Ph–CH₃F, respectively) agree well with the KSCED results, but nevertheless an under- estimation is expected for the cationic Ph–CH₃OH complex if ZPE would be added to the experimental value.

IV. Conclusions

In this work we obtained equilibrium geometries and interaction energies in a series of intermolecular complexes involving phenol in its neutral or cationic state.

As the structure of these complexes is concerned it was found that for all complexes, except for neutral Ph–Ar, the hydrogen-bonded structure is more stable than the ␲-bound one. This is in agreement with the picture emerging from experimental and ab initio results reported in the literature.

As the energetics of the studied complexes is concerned, we analyzed the magnitude of the well depthD_eat minimum energy structure. This quan- tity is not always directly available experimentally as the experimentally available dissociation energies D₀ differ from D_e by the magnitude of ZPE, which can be expected to fall in the 1–2 kcal/mol range [26 –28] for the studied complexes. An exact estimation of ZPE is not possible with our imple- mentation of the KSCED method, especially since about 30% of ZPE is of intramolecular origin [26 – 28]. In our set of intermolecular complexes, we calculated interaction energies falling in the 1–25 kcal/mol range, and, taking into account ZPE, a good correlation between experimentalD₀and calculated D_e is obtained. This indicates that the applied method is applicable for these type of complexes.

Moreover, only few ab initio studies relevant to the complexes investigated in this work have been reported in the literature. Because the applied ab initio method is usually MP2 (which does not account for all electronic correlation effects) with basis sets of medium quality, our systematic analysis can provides a useful reference.

FIGURE 3. Equilibrium geometries derived from KSCED calculations. (a) Neutral or cationic proton- bound Ph–NH₃; (b) neutral or cationic proton-bound Ph–CH₃OH; (c) neutral proton-bound Ph–CH₃F; (d) cationic proton-bound Ph–CH₃F.

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ACKNOWLEDGMENT

This work is part of the project 200020-100352 of the Swiss National Science Foundation. The avail- ability of the computer resources at the Swiss Cen- ter for Scientiﬁc Computing in Manno is greatly acknowledged. The authors are grateful to Dr. Otto Dopfer for helpful discussions and providing us with experimental data prior to publications.

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