An ab initio molecular dynamics study of the SN2

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JOURNAL OF CHEMICAL PHYSICS

VOLUME 118, NUMBER 6

8 FEBRUARY 2003

An ab initio molecular dynamics study of the SN2 reaction FÀ ¿CH3 Cl\CH3 F¿ClÀ Martina Mugnai, Gianni Cardini,a) and Vincenzo Schettino Laboratorio di Spettroscopia Molecolare, Dipartimento di Chimica, Universita` di Firenze, Via della Lastruccia 3, Sesto Fiorentino, Italy and European Laboratory for Nonlinear Spectroscopy (LENS), Via Nello Carrara, Sesto Fiorentino, Italy

共Received 8 May 2002; accepted 12 November 2002兲 The F⫺ ⫹CH3 Cl→CH3 F⫹Cl⫺ reaction has been investigated by ab initio molecular dynamics with the Car–Parrinello method. The Hamprecht, Cohen, Tozer, and Handy exchange-correlation functional produces a stable prereactive complex. Thermal effects at 300 K have been calculated in the Blue Moon ensemble. An appreciable increase in the energy barrier has been obtained at 300 K relative to the 0 K. The averaged potential energy surface at 300 K shows the presence of a stable hydrogen bonded complex. Noncollinear impact trajectories have been examined. The transition state lifetime has been estimated. The energy redistribution among the degrees of freedom following the impact shows that a large part of the energy is localized in the C–F stretch and also in the umbrella bending. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1535212兴

I. INTRODUCTION

pose of the present paper is to implement the ab initio MD treatment of the reaction by including correlation effects explicitly by the density functional approach within the generalized gradient approximation 共GGA兲. On the other side, the reaction under study is characterized by a very small barrier and this poses serious problems in the use of DFT methods that have the tendency to overestimate the TS stability giving a lower barrier than the highest levels of theory, as it has been discussed by many authors.12,28,29 However, Angel and Ervin9 have reported an extensive study of the potential energy surface for this reaction using both a coupled cluster approach, CCSD共T兲/augcc-pVDZ, and density functional theory with the B3LYP 共Ref. 30兲 functional, showing how the latter reproduces all the PES computed at higher levels of theory semiquantitatively. In the first part of the paper it is shown that the exchange correlation functional recently developed by Hamprecht et al. 共HCTH兲 共Ref. 31兲 gives results equivalent to the B3LYP functional and can be considered as a suitable choice for a CP molecular dynamics simulation. Within this approach the results of a finite temperature molecular dynamics simulation will be reported showing that the Blue Moon ensemble exploration of the potential energy surface is able to unravel several interesting features that can escape the standard quantum mechanical approach at 0 K. In particular, it has been found, confirming previous reports,9 that deep minima exist outside the collinear approach corresponding a hydrogen bonded intermediate. This complex has been characterized also at 0 K and can likely be considered as a prereactive intermediate for the elimination reaction. Impact trajectories calculations have been carried out showing that the transition state lifetime strongly depends on the impact geometry and the reaction products are in a vibrationally excited state not only of the C–F stretching mode, but also of

The interest in computational studies of bimolecular nucleophilic substitution reactions in the gas phase by molecular dynamics 共MD兲 with ab initio calculation of the interatomic forces has grown considerably in recent years.1–13 Ab initio MD methods have been demonstrated to be very effective in analyzing issues like finite temperature effects and nonstatistical behaviors6,12–14 of the reactions. The available approaches include the Born–Oppenheimer dynamics,15,16 where the usual quantum mechanical procedures are applied to optimize the wave function at each step of the dynamics, and the Car–Parrinello method,17–21 where classical molecular dynamics and density functional theory are coupled and the wave function follows the nuclear motion adiabatically. In the present paper we will report on a Car–Parrinello MD study of the SN2 reaction F⫺ ⫹CH3 Cl→CH3 F⫹Cl⫺ . This reaction is characterized by a high efficiency and it can therefore be argued that the barrier does not represent the bottleneck of the reaction. The high reaction efficiency will also imply a too short lifetime for the prereactive complex to allow energy equipartition, a key requirement for the application of statistical theories like the Rice–Ramsperger– Kassel–Marcus 共RRKM兲 one. As a matter of fact the reaction has been analyzed by the RRKM theory,22,23 but the nonstatistical behavior24 –26 makes the application of the theory questionable and the results obtained should be taken with due caution.14,27 A study of this reaction with ab initio MD offers the opportunity to overcome these difficulties. Recently, Tachikawa7 reported on a series of almost collinear impact trajectories studied by the Born–Oppenheimer dynamics at the STO-3G level of theory supporting the idea of a nonstatistical behavior for this reaction. Tachikawa’s approach did not consider electronic correlation effects that are known to be important for this kind of reactions. The pura兲

Electronic mail: [email protected]

0021-9606/2003/118(6)/2767/8/$20.00

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© 2003 American Institute of Physics

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J. Chem. Phys., Vol. 118, No. 6, 8 February 2003

Mugnai, Cardini, and Schettino

TABLE I. Bond lengths and bond angles at different levels of theory. Distances 共Å兲

HCTH

F–C H–C H–F

1.399 56 1.098 29 2.038 39

Angles 共deg兲

HCTH

F–C–H H–C–H

108.7857 110.1479

CH3 F BLYP-PW 1.4261 1.0984 2.0501

BLYP6-311⫹⫹G(d,p) 1.4166 1.0984 ¯

BLYP-PW

BLYPa

108.176 110.735

108.4361 110.4862

Distances 共Å兲

HCTH

CH3 Cl BLYP

BLYPa

Cl–C H–C H–Cl

1.783 34 1.093 22 2.370 49

1.815 09 1.089 50 2.389 04

1.829 1.093 ¯

Angles 共deg兲 Cl–C–H H–C–H

Experiment 1.382 1.095 ¯ Experiment ¯ 110.4 Experimentb 1.776 1.085 ¯

HCTH

BLYP

BLYPa

Experiment

108.5453 110.3260

108.057 110.848

108.1 110.8

108.6 ¯

a

Reference 12. Reference 62.

b

normal modes involving the hydrogens and, among these, the umbrella mode. II. METHOD

All the calculations have been performed by ab initio molecular dynamics in the Car–Parrinello formulation using the CPMD code.32 The system has been simulated in a cubic box of 25 a.u. side and considered isolated by the method proposed by Hockney.33 Troullier–Martins pseudopotentials34 have been adopted along with a plane wave expansion with a 70 Ry cutoff that allows the geometrical parameters to converge better than 3%. The HCTH exchangecorrelation functional recently proposed by Hamprecht et al.31,35 has been used for most of the calculations but, for comparison purposes, some results obtained with the more common BLYP 共Refs. 30, 36兲 functional have also been reported. The transition state 共TS兲 structure has been computed by constrained minimization followed by a geometry optimization performed with a quasi-Newton method 共BFGS兲 共Ref. 37兲 starting from an initial Hessian computed by a finite difference method. The minimum energy profile has been obtained by an annealed dynamics starting either from the transition state or from ion and molecule at large intermolecular separation. Average finite temperature results have been obtained in the Blue Moon ensemble38,39 keeping the C–Cl or C–F distance constrained at various values. For each computed point a preliminary thermalization has been performed by velocity scaling followed by a production run of at least 10 000 steps of 5 a.u. keeping the system in contact with a thermal bath at 300 K by the Nose–Hoover chain method.40,41 The free energy along the reaction path has been computed integrating the mean constrained force.38,39,42,43 The electronic distribution along the reaction path has been analyzed using both the Wannier centers6,44 – 46 and the electron localization functions 共ELF兲.47– 49 The Wannier centers

have been used to evaluate polarization effects along the reaction path while the ELF has been used to give an intuitive representation of the charge distribution at selected phase space points. III. RESULTS AND DISCUSSION A. Preliminary calculations

Preliminary calculations were carried out using both the BLYP 共Refs. 30, 36兲 and the HCTH 共Refs. 31, 35兲 functionals. The former is the most commonly adopted in Car– Parrinello simulations and served as a reference, the latter has recently been shown to give reasonably accurate results in simulations of SN2 reactions.12,13,29 As it can be seen from Table I both functionals satisfactorily reproduce the geometry of the isolated molecules. The well known tendency6,12,13,28 of the BLYP functional to overestimate the

FIG. 1. Minimum energy profile calculated with the HCTH 共solid line兲 and BLYP 共dashed line兲 functionals.

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An ab initio molecular dynamics study of an SN2 reaction

J. Chem. Phys., Vol. 118, No. 6, 8 February 2003 TABLE II. Stationary points energy referred to the reactants. ⌬ 1 labels the TS energy relative to the prereactive minimum. The experimental results refer to data obtained by RRKM theory 共Ref. 23兲. ⫺

F ¯CH3 Cl 关 F¯CH3 ¯Cl兴 共kJ/mol兲 共kJ/mol兲



FCH3 ¯Cl 共kJ/mol兲



⌬1 共kJ/mol兲

MP2a QCISDa QCISD共T兲a G2共⫹兲b MP2c CCSDc CCSD-Tc CCSD共T兲c PES共F,Cl兲d HF/3-21⫹G(d) e W1f HCTHf HCTH120f B3LYP DZP⫹difg B3LYP TZ2P⫹difg B3LYP TZ2Pf⫹difg

⫺66.10 ⫺67.27 ⫺69.28 ⫺65.27 ⫺62.42 ⫺63.80 ⫺65.98 ⫺66.10 ⫺66.23 ⫺66.11 ⫺64.55 ⫺52.96 ⫺64.51 ⫺64.01 ⫺67.32 ⫺66.31

⫺48.36 ⫺52.21 ⫺58.36 ⫺52.80 ⫺43.51 ⫺46.10 ⫺52.80 ⫺53.34 ⫺48.36 ⫺59.00 ⫺54.14 ⫺49.99 ⫺63.34 ⫺61.63 ⫺66.19 ⫺64.56

⫺172.38 ⫺184.51 ⫺181.75 ⫺171.79 ⫺165.64 ⫺183.21 ⫺178.23 ⫺177.94 ⫺172.50 ⫺189.95 ⫺136.60 ⫺156.18 ⫺163.42 ⫺178.36 ⫺173.38 ⫺169.00

17.74 15.06 10.92 12.46 18.91 17.69 13.17 12.76 17.86 7.11 12.09 2.97 1.13 3.01 1.13 1.76

HCTH

⫺62.51 ⫺58.20 Experimenth

⫺154.10

4.31

Frequencies 共cm⫺1兲

Barrier ⌬ 1 (kJ/mol)

100 200 300 Average a

Reference 5. Reference 63. c Reference 3. d Reference 58. b

33.89 28.87 24.27 29.01 e

Reference 64. Reference 52. g Reference 50. h Reference 23. f

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TABLE III. Bond lengths and bond angles at stationary points of the reaction.

Theory level

C–H 共Å兲

HCTH MP2a CCSD共T兲b PES共F,Cl兲a HCTHc HCTH-120c

1.086 1.078 1.080 1.078 1.091 1.090

Theory level

C–H 共Å兲

HCTH MP2a CCSD共T兲b PES共F,Cl兲a HCTHc HCTH-120c

1.080 1.069 1.072 1.069 1.086 1.086

Theory level

C–H 共Å兲

HCTH BLYP

1.094 ¯

MP2a CCSD共T兲b PES共F,Cl兲a HCTHc HCTH-120c

1.082 1.086 1.082 1.099 1.099

F⫺ ¯CH3 Cl C–Cl 共Å兲 1.883 1.837 1.853 1.831 1.903 1.931 关 F¯CH3 ¯Cl兴 ⫺ C–Cl 共Å兲

2.099 2.106 2.121 2.108 2.098 2.077

C–F 共Å兲

H–C–Cl 共degs兲

2.557 2.511 2.502 2.521 2.565 2.496

107.1 108.1 107.6 108.1 ¯ ¯

C–F 共Å兲

H–C–Cl 共degs兲

2.152 1.997 2.030 1.995 2.190 2.208

98.8 95.9 96.3 96.1 99.2 100.0

C–Cl 共Å兲

F–C–H 共degs兲

1.434 1.471

3.345 3.223

108.9 108.0

1.413 1.417 1.410 1.431 1.436

3.178 3.188 3.198 3.528 3.358

109.1 108.9 109.3 108.7 108.7

FCH3 ¯Cl⫺ C–F 共Å兲

a

Reference 4. Reference 3. c Reference 52. b

carbon–halogen bond distance can be noted. This is to a good extent corrected by the HCTH functional.12,13,29 The energy profile along the reaction path has been calculated using the two functionals and using, as usually, r(C–Cl) – r(C–F) as the reaction coordinate. In agreement with previous reports,12,13,28,29 the BLYP functional is unable to predict a stable prereactive complex and the reaction proceeds directly to the postreactive complex. The BLYP functional is unable to produce an energy barrier even when coupled with diffuse Gaussian basis sets 共DZP,TZ2P,TZ2Pf兲.50 The calculated energy profiles are represented in Fig. 1. It can be seen that the HCTH functional predicts a stable ion–dipole complex. The energy barrier 共4.31 kJ/mol兲 is small but larger than predicted by the B3LYP functional.50 Comparison with experiments is problematic in the present case. In fact, the available estimates of the barrier 共29.01⫾5.02 kJ/mol兲 共Refs. 22, 23兲 are based on RRKM calculations and are not reliable for the reasons discussed above. As a matter of fact, calculations based on the highest levels of theory predict a barrier in the range of 12 kJ/mol. MP2 calculations, that are known to overestimate the barrier, also predict a value much smaller 共17–18 kJ/mol兲 than the RRKM estimate.22,23 The performance of the HCTH functional on the energy barrier, albeit probably too low as shown in Table II, where a comparison with other calculations is reported, appears to be reasonable to carry out ab initio molecular dynamics simu-

lations aimed at a semiquantitative description of the reaction dynamics. As a matter of fact, ab initio dynamics calculations have been carried for the present reaction only at the HF 3-21G level.7 It is of interest to include correlation effect in the treatment. For the symmetric Cl⫺ ⫹CH3 Cl reaction, ab initio correlated dynamic calculations have been carried only at the MP2 level11 using a small basis set and more recently a molecular dynamics calculation13,51 has been reported with the DFT approach adopted in the present work. Before discussing the results obtained from finite temperature and trajectory calculations, it is useful to report briefly on structural properties at stationary points of the reaction. The results are summarized in Table III and compared with other available calculations. It can be noted that the present HCTH calculations are much closer to higher level of theory calculations than reported by Parthiban et al.52 using the same functional. Differences with Parthiban et al.52 calculations should be ascribed to the more extended basis set used in the present work. The charge flow during the reaction is evident in the two-dimensional plot of the density isosurfaces of the stationary points reported in Fig. 2. It can be seen that in the

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FIG. 4. Dipole moment of CH3 Cl and CH3 F and induced dipole moment on the F⫺ and Cl⫺ ions along the reaction path. The positions of the pre关 F⫺ ¯CH3 Cl兴 ⫺ and postreactive 关 Cl⫺ ¯CH3 F兴 ⫺ complexes are labeled by vertical arrows.

F⫺ ¯CH3 Cl complex the electronic charge is still highly localized in the C–Cl bond. This is not the case anymore in the transition state where the isosurfaces around the halogens reduce. There is a consequent increase of the charge on the methyl group and a strengthening of the C–H bond that is monitored by the increase of the C–H stretching frequency by 30 cm⫺1. In Fig. 3 the F–C–H bond angle variation as a function of the reaction coordinate is reported. It can be seen that the Walden inversion, corresponding to an angle of 90°, occurs for a value of 0.36 Å of the reaction coordinate, i.e., appreciably to the right of the transition state. This is expected from the Hammond postulate53 establishing that in exother-

mic reactions the energetics and the geometrical properties of the transition state will resemble those of the reactants. Strong polarization effects occur along the reaction path. These are best represented reporting the electric dipole moment of the various species as a function of the reaction coordinate. The dipole moments have been obtained by assigning the electrons to a set of doubly occupied orbitals obtained by the maximally localized Wannier functions method.44,45 This method has been used with increasing success to study chemical reactions12,13,29,54,55 and to calculate infrared absorption spectra56,57 and bond properties.46 The results are shown in Fig. 4. Polarization effects are particularly strong for the CH3 Cl species at the prereactive complex position, where the dipole moment is much larger than found in the Cl⫺ ⫹CH3 Cl symmetric substitution reaction12 as a consequence of the higher penetration of the fluoride ion in the methyl umbrella.

FIG. 3. Behavior of the F–C–H angle as a function of the reaction coordinate calculated with the BLYP 共dashed line兲 and HCTH 共solid line兲 functionals.

FIG. 5. Energy profile along the reaction path at ⬇0 and ⬇300 K computed in the Blue Moon ensemble. 共Energies relative to the isolated reactants at 0 K.兲

FIG. 2. Density isosurfaces at the stationary points of the reaction.

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J. Chem. Phys., Vol. 118, No. 6, 8 February 2003

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FIG. 6. 共Color兲 Thermal energy surface as a function of the reaction coordinate r(C–Cl) – r(C–F) and as a function of r(F–H1 ) – r(F–H2 ) 共before the TS兲 and of r(Cl–H1 ) – r(Cl–H2 ) 共after the TS兲. The color scale labels the energy values.

B. Thermal effects

The thermal effects have been calculated in the Blue Moon ensemble at about 300 K constraining the C–Cl or C–F bond length at a fixed value. Each simulation 共24 points along the profile兲 has been performed for a number of time steps ranging between 4000 and 20 000. The energy profiles at 300 and 0 K are compared in Fig. 5. The thermal effect at 300 K is substantial in the present case and the energy barrier more than doubles compared to that at 0 K reaching a value of 9.11 kJ/mol. Significant thermal effects on the energy barrier have already been reported for other SN2 reactions.6,51 Sampling in the Blue Moon ensemble offers the advantage of a more extended exploration of the potential energy surface. In fact, apart from the constraint on the carbon– halogen distance, all other degrees of freedom are free. The potential energy surface before the TS is shown in Fig. 6共a兲 as a function of the reaction coordinate and of the r F–H1 – r F–H2 coordinate, representing the displacement of the incoming ion from the symmetry axis. It can be seen that at large carbon–halogen distances secondary minima are present for an off-axis position of the F⫺ ion 共high values of r F–H1 – r F–H2 ). These correspond to a close approach of the fluoride ion to one of the hydrogens and therefore to the formation of a hydrogen bond. A hydrogen bond formation is confirmed by the movies of the explored configurations and by the behavior of the F–C–H bond angles. These latters are shown in Fig. 7, where it can be seen that when the hydrogen bond is formed the three F–C–H bond angles become very different and the fluctuation around the mean value becomes very large. A typical H-bond structure has been quenched and characterized at 0 K obtaining structural and energetic properties close to those reported by Angel et al.9 for the intermediate of the elimination reaction. In fact at 0 K a F–H bond dis-

tance of 1.669 Å and a F–C–H bond angle of 164.5° are obtained to be compared with the values of 1.621 Å and 173.5°, respectively, reported by Angel et al.9 The structure of the H-bond complex has been further characterized by computing the ELF that are reported in Fig. 8, where the isosurfaces with f ⫽0.2, 0.4, 0.6, 0.8 are cut by the two planes defined by the F–C–H and F–C–Cl groups. This clearly shows the typical feature of a H-bond, as previously observed for similar systems.12 The energy of the hydrogen bonded complex is lower than the SN2 prereactive minimum, as already reported by Angel et al.9

FIG. 7. F–C–H and H–C–H angles as a function of the constrained C–F and C–Cl distances. Error bars indicate the fluctuations.

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FIG. 8. 共Color兲 Hydrogen bonded complex. Left: density isosurfaces. Right: ELF isosurfaces plotted with f values of 0.2, 0.4, 0.6, 0.8. r(C–Cl) – r(C–F). The ELF isosurfaces have been drawn with the GopenMol program 关L. Laaksonen, J. Mol. Graphics 10, 33 共1992兲兴.

Coming back to the 300 K energy surface of Fig. 6共a兲, it can be noted that the minima are isolated by an additional high barrier from the SN2 channel. Furthermore, the transition state for the elimination is so high in energy that it cannot be reached in our simulations at 300 K. As it can be seen in Fig. 6共b兲, also in the C–Cl constraint case, corresponding to the backward reaction, the Cl atom swings away from a collinear position, but always within the umbrella space at least for the explored values of the constraint. So in this case it is not possible to speak of an actual H-bond. The free-energy profile reported in Fig. 9 has been obtained by integrating the mean force along the Blue Moon profile. A barrier of 1.805 kJ/mol is obtained. It can be remarked that, as usually for SN2 reactions, the free energy is smaller than the thermal energy due to the entropic contribution. C. Impact trajectories

Useful information on the dynamics of gas phase reactions can be obtained from impact trajectories studies. Since, as discussed above, the calculated barrier height is too low compared to highest levels of theory estimates, the kinetic energy of the incoming ion needed to overcome the barrier will likewise be too low. This, however, will not modify the qualitative description of the dynamics of the reaction. For the reaction of interest in the present work, trajectories studies have been reported adopting an analytic potential energy surface58 and more recently by Tachikawa7 using the Born–Oppenheimer molecular dynamics but only at the STO-3G level and for a nearly collinear impact geometry. In the present work we have carried a number of impact studies at selected geometries to investigate the effect of noncollinear impact trajectories and the energy redistribution following the collision. Compared to the previous report by Tachikawa,7 the barrier height is lower by about 3 kJ/mol but the electronic correlation effects are taken into account. The impact direction of the incoming F⫺ ion was always in a Cl–C–H plane 共a symmetry plane of the CH3 group兲 but deviations from the symmetry axis and the collinear impact were allowed either in the direction of the hydrogen atom 共m-type trajectories兲 or in the opposite direction 共 p-type trajectories兲. The incoming ion was set at an initial distance of 4 Å from the carbon atom and shot in the direction of the carbon atom with a velocity corresponding to a translational temperature of 150 K. A random distribution of the velocities

of the atoms of the system was used corresponding to a temperature of 300 K. The explored trajectories were extended for angles relative to the symmetry axis ranging from 0° to 30° for the m-type trajectories and from 0° to 90° for the p-type trajectories. A trajectory at 180° was also explored and found to not lead to any reaction. In some cases the initial distance of the F⫺ ion from the carbon was set at 6 Å 共using a larger simulation cell to prevent images interactions兲 to verify that the initial distance did not affect the results of the impact studies appreciably. It has been found that the SN2 reaction occurred only when the impact angle was in the range 0°–15° or 0°– 60° for the m and p-type trajectories, respectively. The lifetime of the transition state has been estimated as the time lack between the breaking of the C–Cl and the formation of the C–F bond. The breaking and the formation of the two bonds have been taken at points along the trajectory where the bond length becomes longer or shorter, respectively, than the sum of the covalent radii 共1.970 and 1.665 Å for C–Cl and C–F, respectively兲. The results are shown in Fig. 10 and Table IV. Although this definition of the lifetime can be quite arbitrary, it can give an useful qualitative indication. The obtained lifetimes are very short, in the same range of those estimated by Tachikawa7 for the pre- and postreactive complexes. The present results are well in the range of the values observed for a series of bimolecular reactions.59 It can be seen that for the p-type trajectories the breaking of the C–Cl bond occurs at shorter times with increasing the

FIG. 9. Free energy as a function of the reaction coordinate r(C–Cl) – r(C–F).

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An ab initio molecular dynamics study of an SN2 reaction

J. Chem. Phys., Vol. 118, No. 6, 8 February 2003

FIG. 10. TS lifetime for impact trajectories as a function of the impact angle. Circles and squares refer to p and m-type impacts, respectively.

impact angle. Most likely, in the noncollinear impact the molecule is forced to rotate around the heavy Cl atom and this produces a distortion of the molecule that facilitates the C–Cl bond breaking. As it can be seen from Fig. 10 the transition state lifetime increases regularly with the impact angle for p-type trajectories. It is also seen that m-type trajectories are more unfavorable for the reaction. As it can be seen from Table IV the average value of the C–F bond length following the impact is considerably larger than the equilibrium value, suggesting that a significant amount of the energy may be stored in the C–F stretching mode. As a matter of fact, the kinetic energy of the fluoride atom after the impact shows regular oscillations corresponding to a frequency around 800 cm⫺1. Considering the anharmonicity constant of 8 cm⫺1 for the C–F stretching vibration60,61 it can been deduced that the C–F stretching mode is excited in the ␯⭓5 vibrational state. This is in good agreement with estimates reported by Tachikawa.7 In Fig. 11 the energy distribution for a collinear impact closest to the situation discussed previously by Tachikawa7 has been reported. It can be noted that immediately after overcoming the barrier a large part of the kinetic energy is transferred to the hydrogens 共and in particular to the umbrella motion兲 contrary to Tachikawa’s7 findings. This can be due either to the different initial conditions or to the length of the trajectories. It can be

TABLE IV. Parameters obtained from impact trajectories. 具C–F典 labels the average C–F bond distances after the reaction. Impact angle C–Cl breaking C–F formation T.S. lifetime 具C–F典 distance 共degs兲 共ps兲 共ps兲 共ps兲 共Å兲 m30 m22.5 m15 m7.5 0 p15 p30 p45 p60 p90 p180

0.199 47 0.180 20 0.191 08 0.163 03 0.145 12 0.140 77 0.133 51

Not Not 0.257 85 0.208 02 0.217 20 0.192 54 0.181 41 0.185 28 0.193 01 Not Not

effective effective 0.058 38 0.027 82 0.026 12 0.029 51 0.036 29 0.044 51 0.059 50 effective effective

1.632 37 1.473 67 1.507 73 1.454 74 1.471 02 1.492 51 1.515 27

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FIG. 11. Kinetic energy distribution for the collinear impact trajectory. Continuous line, F atom; dashed line, Cl atom; dot-dashed line, sum for the three hydrogens.

noted that an appreciable energy transfer to the hydrogens has been previously reported for a similar reaction by Raugei et al.6 IV. CONCLUSIONS

In the present work the SN2 reaction F⫺ ⫹CH3 Cl→Cl⫺ ⫹CH3 F has been studied by the Car–Parrinello molecular dynamics. The charge flux along the reaction coordinate has been discussed and the thermal effects have been evaluated in the Blue Moon ensemble. In addition impact trajectories studies have been performed. Preliminary calculations have shown that the HCTH exchange-correlation functional is a reasonable choice to study the present reaction with the Car– Parrinello method, beyond the approach of statistical theories. As a matter of fact the HCTH functional is able to produce a stable prereactive complex with an improved energy barrier compared to the B3LYP functional.50 The thermal effects at 300 K are remarkable and the energy barrier increases to 9.11 kJ/mol. Full exploration of the potential energy surface in the Blue Moon ensemble was able to detect additional minima outside the collinear approach of the F⫺ ion, corresponding to hydrogen bonded complexes that are stable also at 300 K. The hydrogen bonded complexes have been quenched and characterized at 0 K obtaining results comparable with previous reports.9,14 Considering the complexity of the potential energy surface it was found of interest to carry trajectories studies with noncollinear impact geometries. A definition of the TS lifetime as a function of the impact geometries has been attempted. The energy redistribution following the impacts has been analyzed. In agreement with Tachikawa7 the C–F stretching mode is excited in a vibrational level with ␯⭓5. However, the present work shows that an appreciable amount of energy is transferred to other vibrational modes as well. Strong polarization effects along the reaction path have been monitored by studying the dipole moment of the different species. ACKNOWLEDGMENTS

The authors would like to thank Professor M. Parrinello for making the QMDCP program 共Ref. 32兲 available. A special

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thanks is due to Dr. Simone Raugei for the MT pseudopotentials to be used with the HCTH functional and to Dr. Marco Pagliai for helpful discussions. This work was supported by the Italian Ministero dell’Universita` e della Ricerca Scientifica e Tecnologica 共MURST兲, and by the European Union 共Contract No. HPRI-CT-1999-00111兲. The authors would like to thank the CINECA supercomputer center, where part of the calculations were carried out, for a generous allocation of computer time. 1

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