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Reaction cross-sections for the H+HCl(DCl) reaction: a quasiclassical trajectory study
11 June 1999
Chemical Physics Letters 306 Ž1999. 179–186
Reaction cross-sections for the H q HCl žDCl / reaction: a quasiclassical trajectory study c F.J. Aoiz a , V.J. Herrero b, V. Saez , I. Tanarro b, E. Verdasco ´ Rabanos ´
a,)
a
c
Departamento de Quımica Fısica, Facultad de Quımica, UniÕersidad Complutense, 28040 Madrid, Spain ´ ´ ´ b Instituto de Estructura de la Materia (CSIC), Serrano 123, 28006 Madrid, Spain Departamento de Quımica General y Bioquımica, ETSI de Montes, UniÕersidad Politecnica, 28040 Madrid, Spain ´ ´ ´ Received 19 March 1999; in final form 19 April 1999
Abstract The H q HCl and H q DCl reactions have been investigated with quasiclassical trajectory calculations performed on the ab initio G3 potential energy surface of Allison et al. wJ. Phys. Chem. 100 Ž1996. 13575x. The cross-sections for the abstraction and exchange channels have been calculated for collision energies from threshold to 2.4 eV. The role of initial rotation and vibration on reactivity is addressed and the results are compared to experimental measurements and to previous theoretical calculations. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction In spite of the key role played by the HClH reactive system in the development of gas-phase kinetics since the last century Žsee for instance Refs. w1–4x and references therein., there are still fundamental open questions concerning the dynamics of the reaction between hydrogen atoms and hydrogen chloride molecules. This reaction has two exit channels. H q HCl ™ H 2 q Cl H q HCl ™ HCl q H
Ž 1a . Ž 1b .
termed, respectively, abstraction Ž1a. and exchange Ž1b.. The kinetics of the abstraction reaction is known with good accuracy and reliable Arrhenius parame-
) Corresponding author. Fax: q34 91 3944135; e-mail: [email protected]
ters have been derived for the 200–1192 K temperature range from the existing rate constant measurements w5,6x. In contrast, the reactivity of the exchange channel is not well known and important doubts still persist about its barrier height Žsee discussion in Ref. w4x.. Much work has been invested in the construction of an accurate potential energy surface ŽPES. for the HClH system. In 1973, Stern et al. w7x reported a successful empirical surface, GWS PES, of the London–Eyring–Polanyi–Sato ŽLEPS. type. Dynamical calculations on this surface could account for the reaction rates and kinetic isotope effect data and have been used recently w8x for model studies of the effect of rotation and vibration on the reactivity of Cl q H 2 . However, this surface proved to be inadequate for studies of the dynamics of the exchange process. In an attempt to remedy this deficiency, a new surface, called GQQ, w9x was constructed by the Truhlar group. The GQQ PES w9x was based on the
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 4 3 6 - 4
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GSW LEPS surface but included the results of electronic structure calculations with scaled electron correlation for H–Cl–H-type geometries. Further refinements of this surface, including the addition of more ab initio points in order to improve the Cl–H–H bending potential at the saddle point, have recently led to a new version of the PES called G3, released also by the group of Truhlar w4x. In this PES, the HHCl and HClH saddle points correspond to linear geometries whose energies are 0.194 and 0.785 eV, respectively, above the minimum of the HCl asymptotic potential w4x. For the Cl q H 2 reaction, dynamical calculations on the G3 surface predict rate constants w10,11x and differential cross-sections w3x, that are in very good agreement with experiment. Given the relatively low average collision energies of these experiments, they provide information about the region of the PES close to the threshold for reaction. The higher energy region of the PES has been accessed in a series of hot-atom experiments performed on the H q HCl and H q DCl reactive systems. Total reaction crosssections, s RŽ Ecol ., for these reactions were measured by different research groups w12–15x at collision energies higher than 1 eV. Theoretical calculations of s RŽ Ecol . for the two isotopic variants have been reported on the GQQ surface w14,16x. The quantum mechanical calculations of Branchett et al. w16x for the abstraction channel of H q HCl extend from threshold to Ecol ; 0.8 eV. For the highest collision energies studied, the calculated reaction cross-section is similar to the value recently measured by Volpp and co-workers for a collision energy of 1 eV w15x. The quasiclassical trajectory ŽQCT. calculations of Barclay et al. w14x for H q DCl lead for both reaction channels to larger cross-sections than those experimentally measured by the same authors, the discrepancy being most remarkable for the exchange channel at the highest energy Ž Ecol s 2.4 eV., where the calculated cross-section is larger by an order of magnitude than the measured one. To the best of our knowledge, the G3 PES has only been used for an investigation of the effects of pendular orientation on the reactivity for H q DCl at Ecol s 1.85 eV w17x. In the present work, we have taken this new surface for an extensive quasiclassical trajectory study of the reaction cross-sections of H q HCl and H q DCl. The abstraction and the ex-
change channels of the two isotopic variants have been investigated from threshold to Ecol s 2.4 eV and the possible influence of rotational and vibrational excitation of the reagents on the reactivity is analysed. The results are discussed and compared to the experimental cross-sections available from hotatom experiments and to the previous theoretical calculations on the GQQ PES.
2. Method The QCT calculation methodology is basically the same as used in previous works w18,19x and only the specific details, relevant for the present study, are given here. All calculations have been carried out on the G3 surface w4x for H q HClŽ Õ s 0, 1. and H q DClŽ Õ s 0, 1.. For each isotopic variant and vibrational state, the calculations have spanned an interval of collision energies w E1 , E2 x. The upper limit E2 of this interval has been set in all cases equal to 2.4 eV and the lower limit E1 for each case is determined as indicated below. In order to calculate the excitation function, i.e. the collision energy dependence of the total reactive cross-section s RŽ Ecol ., we have followed the same method as in Refs. w11,19,20x. The procedure consists of running batches of trajectories, for each initial vibrational state Õ, of the reactive molecules, whose collision energy is randomly sampled over the energy range considered. Once the value of the collision energy is sampled, the impact parameter b is obtained for every trajectory by b s b b1r2 bmax Ž Ecol .
Ž 2a .
where b is a random number in the w0,1x interval and the maximum impact parameter at a given collision energy Ecol is given by
ž
bmax Ž Ecol . s D 1 y
ED Ecol
1r2
/
Ž 2b .
The parameters D and ED were previously determined by fitting the maximum impact parameter bmax at several collision energies to Eq. Ž2b.. The ˚ and values of these parameters are: D s 2.62 A,
F.J. Aoiz et al.r Chemical Physics Letters 306 (1999) 179–186
˚ ED ED s 0.10 eV for H q HClŽ Õ s 0.; D s 2.84 A, ˚ and s 0.029 eV for H q HClŽ Õ s 1.; D s 2.40 A ˚ and ED s 0.10 eV for H q DClŽ Õ s 0.; D s 2.57 A ED s 0.05 eV for H q DClŽ Õ s 1.. Large values of the maximum impact parameter are required in order to account for the all the reactivity of the abstraction channel. In all cases, the lower limit E1 of the energy interval mentioned in the previous paragraph is made equal to ED . With this sampling of the impact parameter, each trajectory is weighted by 2 Ž v i s bmax Ecol .rD 2 . The initial rotational state j of the molecule was sampled with the weight corresponding to a thermal distribution at a given temperature. With an appropriate re-weighting of a single set of trajectories one can obtain not only an averaged s RŽ Ecol . at each temperature and initial vibrational state, but also the excitation function for each initial rovibrational state. The integration step size in the trajectories was chosen to be 5 = 10y1 7 s. This guarantees a conservation of the total energy better than 1 in 10 5, and 1 in 10 7, in the total angular momentum. The rovibrational initial energies of HCl and DCl were calculated by semiclassical quantization of the classical action, using in each case the asymptotic diatomic potential of the PES Žsee Refs. w11,19x.. Batches of 7.5 = 10 5 trajectories have been calculated, at 300 K for each vibrational state of H q HClŽ Õ s 0, 1., and 5.0 = 10 5 at 300 and at 100 K for each vibrational state of H q DClŽ Õ s 0, 1.. The overall number of trajectories calculated for this work amounts to ; 4 = 10 6 . The averaged s RŽ Ecol . at each temperature and initial vibrational state and the s RŽ Ecol . for each initial rovibrational state were subsequently calculated by the method of moment expansion in Legendre polynomials, as described in detail in Ref. w19x, using the reduced variable: xs
2 Ecol y E2 y E1 DE
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3. Results and discussion Fig. 1 shows the total reaction cross-sections for the two exit channels of the H q HClŽ Õ s 0. system as a function of the collision energy for various rotational states of the HCl molecule. The s RŽ Ecol . for the exchange reaction grows monotonically from ˚ 2 at a threshold at E0 ; 0.6 eV to a value of 1.8 A Ecol s 2.4 eV. The large value of the threshold reflects the high value of the reaction barrier for this channel Ž0.785 eV from the minimum of the HCl reactant valley.. For all the rotational levels significantly populated at room temperature, the rotational excitation of the molecule has a relatively minor effect on the reactivity, at least at collision energies above 1 eV. In the figure, we have only represented levels j s 0,3,6 for the sake of clarity. The abstraction channel has a much lower threshold Ž E0 ; 0.1 eV., according to the much lower height of barrier
Ž 2c .
where D E s E2 y E1. Significance levels higher than 95% could be achieved using 4–8 Legendre moments, ensuring a very good convergence. The error bars, calculated as in Ref. w19x, correspond to "1 standard deviation.
Fig. 1. Reaction cross-section as a function of collision energy Žexcitation functions. for three selected initial rotational states of the HCl molecule Ž js 0,3,6. for the exchange Župper panel. and abstraction Žlower panel. channels of the HqHCl reaction.
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Ž0.194 eV from the minimum of the HCl potential., and the excitation functions for the different rotational levels do not show a monotonic increase, but rather a smooth maximum at Ecol ; 0.75–1.25 eV followed by a gentle decline. For this channel, there are slight differences between the s RŽ Ecol . corresponding to the various rotational levels but they cannot be considered very significant, at least at collision energies below 0.5 eV, given the uncertainties of the calculation. At the maximum, the values ˚ 2. of the cross-sections lie between 0.22 and 0.30 A For collision energies higher than ; 1.25 eV, the reaction cross-sections of the exchange channel are larger than those of the abstraction one. A most interesting feature is the contribution of impact parameters for the two different reactive channels. Whereas the maximum impact parameter bmax for ˚ for the abstraction the exchange channel is ; 1.4 A, ˚ However, the channel it reaches values ; 2.5 A. reaction probability for low b is up to two orders of magnitude larger in the exchange channel w17x. The corresponding excitation functions for H q DCl, are represented in Fig. 2. The s RŽ Ecol , j . for
Fig. 2. Same as Fig. 1 but for the HqDCl reaction.
the exchange channel show also a monotonic increase over the Ecol range studied and those for the abstraction reaction have a maximum at Ecol ; 0.75 eV. The threshold energies are slightly larger than those for H q HCl and the reactivity is also found to be independent of the rotational excitation at high enough collision energies. For collision energies higher than ; 1.25 eV, the cross-sections for exchange become larger than those for abstraction. Besides these important qualitative similarities there are some differences worth noting. In the exchange channel, the reaction cross-sections for H q DCl are systematically smaller by a factor of about two than those for H q HCl, and in the abstraction channel the post maximum decline in s RŽ Ecol . is much more pronounced for the deuterated isotopomer. As mentioned above, the transition state for the G3 surface is collinear for the two exit channels w4x. Molecular rotation has often been found to play a significant role in reactions with a collinear barrier w8,11,18,19x. At low collision energy the excitation of the first few quanta can sometimes inhibit reactivity due to an ‘orientation effect’ of the PES, whereas high rotational excitation can lead to a higher reaction probability due to the increase in the energy available Ž‘energy effect’.. In the present case, the influence of rotation is found to be relatively small for all values of j significantly populated at room temperature, due most probably to the little reorientation effect of the PES and the relatively small value of the rotational quantum, at least compared with the high collision energies at which the exchange reaction takes place. Fig. 3 shows the effects of molecular vibration on the reaction cross-sections averaged on initial rotational states at Trot s 300 K. For the two isotopic variants and for the two exit channels, vibrational excitation is seen to enhance reactivity considerably, but the effect is more marked for the abstraction channel, where the threshold is clearly lower and the reaction cross-section larger for the reactions with Õ s 1 molecules, over the whole energy range. The influence of vibrational excitation on the s RŽ Ecol . is especially pronounced in the post-maximum region for the abstraction channel of the H q DCl reaction, where the cross-sections for reaction with DClŽ Õ s 1. are more than five times larger than those for reaction with DClŽ Õ s 0.. For the exchange channel, the
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HCl or H 2 products. The measurements allowed the estimation of the cross-section for the abstraction ˚ 2 . and a cross-section for the reaction Ž s R s 2 " 1 A combined processes of reactive exchange and energy ˚ 2 . which were indistinguishtransfer Ž s s 13 " 3 A able in these experiments. In a recent work, Volpp and co-workers w15x determined the reaction cross-section for the abstraction channel at an average collision energy of 1.0 eV also using hot hydrogen atoms, produced in this case in the 248 nm photolysis of H 2 S, and vacuum ultraviolet ŽVUV. laser-induced fluorescence ŽLIF. of the Cl Ž2 P3r2 . product. The cross-section value
Fig. 3. Effect of the vibrational excitation on the cross section for each of the two channels of the HqHCl Žtop. and HqDCl Žbottom. reaction. Solid lines, calculation for rotationally average cross-sections at 300 K for Õ s 0; dotted lines, calculation for Õ s1.
threshold does not vary significantly with vibrational excitation and the reaction cross-sections for Õ s 1 are only larger by ; 60% than those for Õ s 0. For the hot-atom experiments of interest to this study, which sample the region of collision energies far from the threshold, the contribution of excited Õ s 1 molecules to the overall reactivity is very small, since the internal state populations of the molecules correspond to T ( 300 K, and the increase in the cross-section associated with vibrational excitation is not enough to compensate the low population of the vibrationally excited states. In Fig. 4, the reaction cross-sections of the present work are compared with experimental data and with previous calculations on the GQQ PES. The system H q HCl studied experimentally by Valentini and co-workers w12,13x at an average collision energy of 1.6 eV, using hot H atoms generated by 266 nm photolysis of HI and coherent anti-Stokes raman spectroscopy ŽCARS. for the detection of the
Fig. 4. Upper panel: Reaction cross-section as a function of collision energy for the abstraction channel of the HqHCl reaction. Solid line: Present QCT calculation on the G3 PES. Dashed line: QM calculations of Ref. w16x on the GQQ PES. Square and triangle: Experimental results ŽRefs. w12x and w15x, respectively.. Middle panel: Reaction cross-section for the abstraction channel of the HqDCl reaction. Solid line: Present QCT calculations on the G3 PES. Dashed line: QCT calculations on the GQQ PES w14x. Triangles: Experimental results from Ref. w14x. Lower panel: Reaction cross-section for the exchange channel of the HqDCl reaction. Solid line: Present QCT results on the G3 PES. Dashed line: QCT results on the GQQ PES w14x. Triangles: Experimental results from Ref. w14x.
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˚ 2, provided by these authors was s R s 0.34 " 0.05 A 2 ˚ for the reacwith an upper limit of 0.02 " 0.01 A tion leading to ClU Ž2 P1r2 .. The QCT cross-sections represented in the upper panel of Fig. 4 correspond to a thermal Ž300 K. distribution of internal states, since the two hot-atom experiments just mentioned were carried out in reaction vessels with room temperature HCl molecules. For the sake of rigour, the distribution of collision energies should also be taken into account in the comparison. The collision energy spread of these experiments is not given explicitly in the publications, but taking into account the reported experimental conditions, it should be approximately w21x 0.35 eV for the experiment of Valentini and coworkers w12,13x and 0.28 eV for the experiment of Volpp and co-workers w15x. An inspection of the figure shows that this convolution is not necessary in the present case, since the cross-section is practically flat over a collision energy range much larger than the width of the collision energy distributions. The agreement between the experimental crosssection reported by Brownsword et al. w15x at Ecol s 1 eV and the present QCT cross-section is reasonably good, the experimental value being only slightly higher than the calculated one at the same energy. In contrast, at Ecol s 1.6 eV, the QCT result of s R is more than eight times smaller than the cross-section measured by Aker et al. w12x and lies clearly below the large experimental error bar. The QM calculations of Branchett et al. w16x for H q HCl on the GQQ PES have also been represented in the upper panel of Fig. 4. This QM value of s RŽ Ecol . has a somewhat higher threshold than the QCT excitation function on the G3 PES and, for collision energies beyond 0.5 eV, the QM cross-sections are higher than the classical ones, but on the overall, the differences are not too large. Considering that the barrier for the abstraction reaction on the G3 PES is slightly higher than that on the GQQ one, the lower QCT threshold is most probably due to the absence of zero point energy constraints inherent to the quasiclassical treatment. Branchett et al. w16x performed their calculations for HCl Ž j s 0–3. and found also a very weak dependence of s RŽ Ecol . on rotational excitation. The H q DCl isotopic variant of the reaction was investigated experimentally by Polanyi and co-
workers w14x. The isotopic labelling and the alternative detection of D or Cl atoms via resonance enhanced multiphoton ionization ŽREMPI. made possible the discrimination between the products of the two reactive channels, and the use of various photolytic precursors of H atoms allowed the study of the 1–2.4 eV collision energy range. The experimental results are shown in the two lower panels of Fig. 4. In these experiments, especial care was taken in order to prevent HrD isotopic scrambling. Under the experimental conditions reported in Ref. w14x Ž p 0 d s 100 Torr mm, nozzle temperature ; 300 K, probe laser at ; 6 nozzle diameters., the rotational temperature of the reacting DCl molecules should be 20–30 K. The QCT reaction cross-sections for H q DCl reaction from threshold to 2.4 eV are also displayed in the two lower panels of Fig. 4 together with the results of previous trajectory calculations by Barclay et al. w14x over the 1–2.4 eV energy range on the GQQ PES. The present cross-sections have been calculated for a rotational temperature of 30 K, in order to compare with the approximate temperature of the experiment, but, as indicated above, the QCT cross-sections are nearly independent of the rotational excitation of DCl. In the article of Barclay et al. w14x, the initial rotational state Žpresumably j s 0. is not specified but, given the very weak dependence of s RŽ Ecol . on j observed also on the GQQ PES w16x, the comparison is meaningful. As can be seen, the experimental data for the abstraction reaction are in very good agreement with the results of the present QCT calculation. The QCT s RŽ Ecol . values of Barclay et al. w14x are systematically larger than ours and than those from experiment, and the difference increases with collision energy. For Ecol s 1.8 eV the classical s R on the GQQ PES is 2.5 times larger than that on the G3 PES whose value coincides with the experimental point at this energy. The experimental and theoretical results about the exchange channel are represented in the lower panel of Fig. 4. In this case, the discrepancies between experiment and calculations are more pronounced. Within the considerable dispersion and large error bars of the measured points, the experimental reaction cross-section shows a flat or slightly decreasing tendency over the 1–2.4 eV collision energy range.
F.J. Aoiz et al.r Chemical Physics Letters 306 (1999) 179–186
In contrast to this behaviour, both the present and previous w14x QCT calculations carried on the G3 and GQQ PESs respectively, show a monotonic increase in s RŽ Ecol . that leads, for the higher Ecol sampled, to much larger cross-sections than those experimentally determined. The overall agreement is better for the calculations on the G3 PES, but the two points measured at Ecol - 1.24 eV are better accounted for by the cross-sections calculated on the GQQ surface. Two distinct microscopic pathways have been identified in the dynamics of this reactive channel. An ‘end-on’ mechanism in which the H atom attacks directly the Cl molecular end, and an insertion mechanism, relevant at higher energies, in which the attack of the atomic hydrogen takes place between the Cl and D atoms. Barclay et al. w14x attribute the rapid rise of the theoretical cross-section with Ecol , responsible for the large high energy discrepancy with the measurements, to the fact that the calculations on the GQQ PES lead to an ‘excess’ of insertion trajectories that increases quickly with growing collision energy. On this surface, the insertion mechanism is clearly predominant for collision energies higher than ; 1.5 eV. The importance of the insertion mechanism is certainly smaller for the calculations on the G3 PES, as shown in a recent QCT work by Aoiz et al. w17x where it was found that at Ecol s 1.85 eV, the ‘end on’ pathway is still prevalent. On the other hand, and although the G3 excitation function deviates globally less than the GQQ one from the experimental data, it fails to reproduce the measurements. For Ecol ) 2 eV, the QCT crosssections are still too high, and this discrepancy points to remaining inaccuracies in the potential for the bending geometries, which are gradually accessed with increasing Ecol . On the other hand, for Ecol lower than 1.5 eV, the measured values are markedly higher than the calculated ones which suggests that the barrier for exchange may be too high on the G3 PES. 4. Summary and conclusions Quasiclassical trajectory calculations of total reaction cross-sections for the two exit channels of the H q HCl and H q DCl reactions have been performed on the recently released G3 potential energy
185
surface. The calculations extend from the threshold up to a collision energy of 2.4 eV and show that rotational excitation has a relatively minor effect on reactivity, and that vibrational excitation lowers the threshold and increases the reaction cross-section in all cases. The results are compared to experimental data from various ‘hot-atom’ experiments and to theoretical calculations by other groups on the former GQQ PES. The comparison shows good agreement with the most recent experimental results and with previous QM calculations on the GQQ PES and suggests that the abstraction channel Žleading to HH q Cl and to HD q Cl for the two respective isotopic variants. is now well understood and that the too large experimental cross-section reported by Aker et al. w12x at a collision energy of 1.6 eV is probably wrong. In contrast, for the exchange channel there remain some discrepancies with the experimental data available. The only experimental cross-sections available for this channel correspond to the H q DCl isotopomer. The present QCT cross-sections calculated on the G3 surface show a better global agreement with experiment than those from previous calculations on the GQQ PES but they still do not reproduce the experimental data satisfactorily. On the other hand, the measured points are affected by large error bars and do not show a definite trend. Clearly, further experiments and calculations are needed in order to shed more light on the reactivity of the exchange channel.
Acknowledgements This work has been supported by the DGICYT of Spain under Grant PB95-0918-C03.
References w1x M. Bodenstein, S.C. Lind, Z. Phys. Chem. 7 Ž1907. 168. w2x R.E. Weston Jr., J. Phys. Chem. 83 Ž1979. 61. w3x M. Alagia, N. Balucani, L. Cartechini, P. Casavecchia, E.H. van Kleef, G. Volpi, F.J. Aoiz, L. Banares, D.W. Schwenke, ˜ T.C. Allison, S.L. Mielke, D.G. Truhlar, Science 273 Ž1996. 1519. w4x T.C. Allison, G.C. Lynch, D.G. Truhlar, M.S. Gordon, J. Phys. Chem. 100 Ž1996. 13575. w5x J.C. Miller, R.J. Gordon, J. Chem. Phys. 75 Ž1981. 5305.
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w6x G.Y. Adusei, A. Fontijn, J. Phys. Chem. 97 Ž1993. 1409. w7x M.J. Stern, A. Persky, F.S. Klein, J. Chem. Phys. 58 Ž1973. 5697. w8x J.B. Song, E.A. Gislason, Chem. Phys. Lett. 237 Ž1998. 159. w9x D.W. Schwenke, S.C. Tucker, R. Steckler, F.B. Brown, G.C. Lynch, D.G. Truhlar, J. Chem. Phys. 90 Ž1989. 3110. w10x S.L. Mielke, T.C. Allison, D.G. Truhlar, D.W. Schwenke, J. Phys. Chem. 100 Ž1996. 13588. w11x F.J. Aoiz, L. Banares, J. Phys. Chem. 100 Ž1996. 18108. ˜ w12x P.M. Aker, G.J. Germann, J.J. Valentini, J. Chem. Phys. 90 Ž1989. 4795. w13x P.M. Aker, G.J. Germann, K.D. Tabor, J.J. Valentini, J. Chem. Phys. 90 Ž1989. 4809. w14x V.J. Barclay, B.A. Collings, J.C. Polanyi, J.H. Wang, J. Phys. Chem. 95 Ž1991. 2921.
w15x R.A. Brownsword, C. Kappel, P. Schmiechen, H.P. Upadhaya, H.R. Volpp, Chem. Phys. Lett. 289 Ž1998. 241. w16x S.E. Branchett, S.B. Padkjaer, J.M. Launay, Chem. Phys. Lett. 208 Ž1993. 523. w17x F.J. Aoiz, B. Friedrich, V.J. Herrero, V. Saez J.E. ´ Rabanos, ´ Verdasco, Chem. Phys. Lett. 289 Ž1998. 132. w18x F.J. Aoiz, V.J. Herrero, V. Saez J. Chem. Phys. 94 ´ Rabanos, ´ Ž1991. 7991. w19x F.J. Aoiz, L. Banares, T. Dıez-Rojo, V.J. Herrero, V. Saez ˜ ´ ´ Rabanos, J. Phys. Chem. 100 Ž1996. 4071. ´ w20x F.J. Aoiz, L. Banares, V.J. Herrero, V. Saez I. ˜ ´ Rabanos, ´ Tanarro, J. Phys. Chem. A 101 Ž1997. 6165. w21x W.J. Van der Zande, R. Zhang, R.N. Zare, K.G. MacKendric, J.J. Valentini, J. Phys. Chem. 95 Ž1991. 8205.
Chemical Physics Letters 306 Ž1999. 179–186
Reaction cross-sections for the H q HCl žDCl / reaction: a quasiclassical trajectory study c F.J. Aoiz a , V.J. Herrero b, V. Saez , I. Tanarro b, E. Verdasco ´ Rabanos ´
a,)
a
c
Departamento de Quımica Fısica, Facultad de Quımica, UniÕersidad Complutense, 28040 Madrid, Spain ´ ´ ´ b Instituto de Estructura de la Materia (CSIC), Serrano 123, 28006 Madrid, Spain Departamento de Quımica General y Bioquımica, ETSI de Montes, UniÕersidad Politecnica, 28040 Madrid, Spain ´ ´ ´ Received 19 March 1999; in final form 19 April 1999
Abstract The H q HCl and H q DCl reactions have been investigated with quasiclassical trajectory calculations performed on the ab initio G3 potential energy surface of Allison et al. wJ. Phys. Chem. 100 Ž1996. 13575x. The cross-sections for the abstraction and exchange channels have been calculated for collision energies from threshold to 2.4 eV. The role of initial rotation and vibration on reactivity is addressed and the results are compared to experimental measurements and to previous theoretical calculations. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction In spite of the key role played by the HClH reactive system in the development of gas-phase kinetics since the last century Žsee for instance Refs. w1–4x and references therein., there are still fundamental open questions concerning the dynamics of the reaction between hydrogen atoms and hydrogen chloride molecules. This reaction has two exit channels. H q HCl ™ H 2 q Cl H q HCl ™ HCl q H
Ž 1a . Ž 1b .
termed, respectively, abstraction Ž1a. and exchange Ž1b.. The kinetics of the abstraction reaction is known with good accuracy and reliable Arrhenius parame-
) Corresponding author. Fax: q34 91 3944135; e-mail: [email protected]
ters have been derived for the 200–1192 K temperature range from the existing rate constant measurements w5,6x. In contrast, the reactivity of the exchange channel is not well known and important doubts still persist about its barrier height Žsee discussion in Ref. w4x.. Much work has been invested in the construction of an accurate potential energy surface ŽPES. for the HClH system. In 1973, Stern et al. w7x reported a successful empirical surface, GWS PES, of the London–Eyring–Polanyi–Sato ŽLEPS. type. Dynamical calculations on this surface could account for the reaction rates and kinetic isotope effect data and have been used recently w8x for model studies of the effect of rotation and vibration on the reactivity of Cl q H 2 . However, this surface proved to be inadequate for studies of the dynamics of the exchange process. In an attempt to remedy this deficiency, a new surface, called GQQ, w9x was constructed by the Truhlar group. The GQQ PES w9x was based on the
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 4 3 6 - 4
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GSW LEPS surface but included the results of electronic structure calculations with scaled electron correlation for H–Cl–H-type geometries. Further refinements of this surface, including the addition of more ab initio points in order to improve the Cl–H–H bending potential at the saddle point, have recently led to a new version of the PES called G3, released also by the group of Truhlar w4x. In this PES, the HHCl and HClH saddle points correspond to linear geometries whose energies are 0.194 and 0.785 eV, respectively, above the minimum of the HCl asymptotic potential w4x. For the Cl q H 2 reaction, dynamical calculations on the G3 surface predict rate constants w10,11x and differential cross-sections w3x, that are in very good agreement with experiment. Given the relatively low average collision energies of these experiments, they provide information about the region of the PES close to the threshold for reaction. The higher energy region of the PES has been accessed in a series of hot-atom experiments performed on the H q HCl and H q DCl reactive systems. Total reaction crosssections, s RŽ Ecol ., for these reactions were measured by different research groups w12–15x at collision energies higher than 1 eV. Theoretical calculations of s RŽ Ecol . for the two isotopic variants have been reported on the GQQ surface w14,16x. The quantum mechanical calculations of Branchett et al. w16x for the abstraction channel of H q HCl extend from threshold to Ecol ; 0.8 eV. For the highest collision energies studied, the calculated reaction cross-section is similar to the value recently measured by Volpp and co-workers for a collision energy of 1 eV w15x. The quasiclassical trajectory ŽQCT. calculations of Barclay et al. w14x for H q DCl lead for both reaction channels to larger cross-sections than those experimentally measured by the same authors, the discrepancy being most remarkable for the exchange channel at the highest energy Ž Ecol s 2.4 eV., where the calculated cross-section is larger by an order of magnitude than the measured one. To the best of our knowledge, the G3 PES has only been used for an investigation of the effects of pendular orientation on the reactivity for H q DCl at Ecol s 1.85 eV w17x. In the present work, we have taken this new surface for an extensive quasiclassical trajectory study of the reaction cross-sections of H q HCl and H q DCl. The abstraction and the ex-
change channels of the two isotopic variants have been investigated from threshold to Ecol s 2.4 eV and the possible influence of rotational and vibrational excitation of the reagents on the reactivity is analysed. The results are discussed and compared to the experimental cross-sections available from hotatom experiments and to the previous theoretical calculations on the GQQ PES.
2. Method The QCT calculation methodology is basically the same as used in previous works w18,19x and only the specific details, relevant for the present study, are given here. All calculations have been carried out on the G3 surface w4x for H q HClŽ Õ s 0, 1. and H q DClŽ Õ s 0, 1.. For each isotopic variant and vibrational state, the calculations have spanned an interval of collision energies w E1 , E2 x. The upper limit E2 of this interval has been set in all cases equal to 2.4 eV and the lower limit E1 for each case is determined as indicated below. In order to calculate the excitation function, i.e. the collision energy dependence of the total reactive cross-section s RŽ Ecol ., we have followed the same method as in Refs. w11,19,20x. The procedure consists of running batches of trajectories, for each initial vibrational state Õ, of the reactive molecules, whose collision energy is randomly sampled over the energy range considered. Once the value of the collision energy is sampled, the impact parameter b is obtained for every trajectory by b s b b1r2 bmax Ž Ecol .
Ž 2a .
where b is a random number in the w0,1x interval and the maximum impact parameter at a given collision energy Ecol is given by
ž
bmax Ž Ecol . s D 1 y
ED Ecol
1r2
/
Ž 2b .
The parameters D and ED were previously determined by fitting the maximum impact parameter bmax at several collision energies to Eq. Ž2b.. The ˚ and values of these parameters are: D s 2.62 A,
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˚ ED ED s 0.10 eV for H q HClŽ Õ s 0.; D s 2.84 A, ˚ and s 0.029 eV for H q HClŽ Õ s 1.; D s 2.40 A ˚ and ED s 0.10 eV for H q DClŽ Õ s 0.; D s 2.57 A ED s 0.05 eV for H q DClŽ Õ s 1.. Large values of the maximum impact parameter are required in order to account for the all the reactivity of the abstraction channel. In all cases, the lower limit E1 of the energy interval mentioned in the previous paragraph is made equal to ED . With this sampling of the impact parameter, each trajectory is weighted by 2 Ž v i s bmax Ecol .rD 2 . The initial rotational state j of the molecule was sampled with the weight corresponding to a thermal distribution at a given temperature. With an appropriate re-weighting of a single set of trajectories one can obtain not only an averaged s RŽ Ecol . at each temperature and initial vibrational state, but also the excitation function for each initial rovibrational state. The integration step size in the trajectories was chosen to be 5 = 10y1 7 s. This guarantees a conservation of the total energy better than 1 in 10 5, and 1 in 10 7, in the total angular momentum. The rovibrational initial energies of HCl and DCl were calculated by semiclassical quantization of the classical action, using in each case the asymptotic diatomic potential of the PES Žsee Refs. w11,19x.. Batches of 7.5 = 10 5 trajectories have been calculated, at 300 K for each vibrational state of H q HClŽ Õ s 0, 1., and 5.0 = 10 5 at 300 and at 100 K for each vibrational state of H q DClŽ Õ s 0, 1.. The overall number of trajectories calculated for this work amounts to ; 4 = 10 6 . The averaged s RŽ Ecol . at each temperature and initial vibrational state and the s RŽ Ecol . for each initial rovibrational state were subsequently calculated by the method of moment expansion in Legendre polynomials, as described in detail in Ref. w19x, using the reduced variable: xs
2 Ecol y E2 y E1 DE
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3. Results and discussion Fig. 1 shows the total reaction cross-sections for the two exit channels of the H q HClŽ Õ s 0. system as a function of the collision energy for various rotational states of the HCl molecule. The s RŽ Ecol . for the exchange reaction grows monotonically from ˚ 2 at a threshold at E0 ; 0.6 eV to a value of 1.8 A Ecol s 2.4 eV. The large value of the threshold reflects the high value of the reaction barrier for this channel Ž0.785 eV from the minimum of the HCl reactant valley.. For all the rotational levels significantly populated at room temperature, the rotational excitation of the molecule has a relatively minor effect on the reactivity, at least at collision energies above 1 eV. In the figure, we have only represented levels j s 0,3,6 for the sake of clarity. The abstraction channel has a much lower threshold Ž E0 ; 0.1 eV., according to the much lower height of barrier
Ž 2c .
where D E s E2 y E1. Significance levels higher than 95% could be achieved using 4–8 Legendre moments, ensuring a very good convergence. The error bars, calculated as in Ref. w19x, correspond to "1 standard deviation.
Fig. 1. Reaction cross-section as a function of collision energy Žexcitation functions. for three selected initial rotational states of the HCl molecule Ž js 0,3,6. for the exchange Župper panel. and abstraction Žlower panel. channels of the HqHCl reaction.
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Ž0.194 eV from the minimum of the HCl potential., and the excitation functions for the different rotational levels do not show a monotonic increase, but rather a smooth maximum at Ecol ; 0.75–1.25 eV followed by a gentle decline. For this channel, there are slight differences between the s RŽ Ecol . corresponding to the various rotational levels but they cannot be considered very significant, at least at collision energies below 0.5 eV, given the uncertainties of the calculation. At the maximum, the values ˚ 2. of the cross-sections lie between 0.22 and 0.30 A For collision energies higher than ; 1.25 eV, the reaction cross-sections of the exchange channel are larger than those of the abstraction one. A most interesting feature is the contribution of impact parameters for the two different reactive channels. Whereas the maximum impact parameter bmax for ˚ for the abstraction the exchange channel is ; 1.4 A, ˚ However, the channel it reaches values ; 2.5 A. reaction probability for low b is up to two orders of magnitude larger in the exchange channel w17x. The corresponding excitation functions for H q DCl, are represented in Fig. 2. The s RŽ Ecol , j . for
Fig. 2. Same as Fig. 1 but for the HqDCl reaction.
the exchange channel show also a monotonic increase over the Ecol range studied and those for the abstraction reaction have a maximum at Ecol ; 0.75 eV. The threshold energies are slightly larger than those for H q HCl and the reactivity is also found to be independent of the rotational excitation at high enough collision energies. For collision energies higher than ; 1.25 eV, the cross-sections for exchange become larger than those for abstraction. Besides these important qualitative similarities there are some differences worth noting. In the exchange channel, the reaction cross-sections for H q DCl are systematically smaller by a factor of about two than those for H q HCl, and in the abstraction channel the post maximum decline in s RŽ Ecol . is much more pronounced for the deuterated isotopomer. As mentioned above, the transition state for the G3 surface is collinear for the two exit channels w4x. Molecular rotation has often been found to play a significant role in reactions with a collinear barrier w8,11,18,19x. At low collision energy the excitation of the first few quanta can sometimes inhibit reactivity due to an ‘orientation effect’ of the PES, whereas high rotational excitation can lead to a higher reaction probability due to the increase in the energy available Ž‘energy effect’.. In the present case, the influence of rotation is found to be relatively small for all values of j significantly populated at room temperature, due most probably to the little reorientation effect of the PES and the relatively small value of the rotational quantum, at least compared with the high collision energies at which the exchange reaction takes place. Fig. 3 shows the effects of molecular vibration on the reaction cross-sections averaged on initial rotational states at Trot s 300 K. For the two isotopic variants and for the two exit channels, vibrational excitation is seen to enhance reactivity considerably, but the effect is more marked for the abstraction channel, where the threshold is clearly lower and the reaction cross-section larger for the reactions with Õ s 1 molecules, over the whole energy range. The influence of vibrational excitation on the s RŽ Ecol . is especially pronounced in the post-maximum region for the abstraction channel of the H q DCl reaction, where the cross-sections for reaction with DClŽ Õ s 1. are more than five times larger than those for reaction with DClŽ Õ s 0.. For the exchange channel, the
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HCl or H 2 products. The measurements allowed the estimation of the cross-section for the abstraction ˚ 2 . and a cross-section for the reaction Ž s R s 2 " 1 A combined processes of reactive exchange and energy ˚ 2 . which were indistinguishtransfer Ž s s 13 " 3 A able in these experiments. In a recent work, Volpp and co-workers w15x determined the reaction cross-section for the abstraction channel at an average collision energy of 1.0 eV also using hot hydrogen atoms, produced in this case in the 248 nm photolysis of H 2 S, and vacuum ultraviolet ŽVUV. laser-induced fluorescence ŽLIF. of the Cl Ž2 P3r2 . product. The cross-section value
Fig. 3. Effect of the vibrational excitation on the cross section for each of the two channels of the HqHCl Žtop. and HqDCl Žbottom. reaction. Solid lines, calculation for rotationally average cross-sections at 300 K for Õ s 0; dotted lines, calculation for Õ s1.
threshold does not vary significantly with vibrational excitation and the reaction cross-sections for Õ s 1 are only larger by ; 60% than those for Õ s 0. For the hot-atom experiments of interest to this study, which sample the region of collision energies far from the threshold, the contribution of excited Õ s 1 molecules to the overall reactivity is very small, since the internal state populations of the molecules correspond to T ( 300 K, and the increase in the cross-section associated with vibrational excitation is not enough to compensate the low population of the vibrationally excited states. In Fig. 4, the reaction cross-sections of the present work are compared with experimental data and with previous calculations on the GQQ PES. The system H q HCl studied experimentally by Valentini and co-workers w12,13x at an average collision energy of 1.6 eV, using hot H atoms generated by 266 nm photolysis of HI and coherent anti-Stokes raman spectroscopy ŽCARS. for the detection of the
Fig. 4. Upper panel: Reaction cross-section as a function of collision energy for the abstraction channel of the HqHCl reaction. Solid line: Present QCT calculation on the G3 PES. Dashed line: QM calculations of Ref. w16x on the GQQ PES. Square and triangle: Experimental results ŽRefs. w12x and w15x, respectively.. Middle panel: Reaction cross-section for the abstraction channel of the HqDCl reaction. Solid line: Present QCT calculations on the G3 PES. Dashed line: QCT calculations on the GQQ PES w14x. Triangles: Experimental results from Ref. w14x. Lower panel: Reaction cross-section for the exchange channel of the HqDCl reaction. Solid line: Present QCT results on the G3 PES. Dashed line: QCT results on the GQQ PES w14x. Triangles: Experimental results from Ref. w14x.
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˚ 2, provided by these authors was s R s 0.34 " 0.05 A 2 ˚ for the reacwith an upper limit of 0.02 " 0.01 A tion leading to ClU Ž2 P1r2 .. The QCT cross-sections represented in the upper panel of Fig. 4 correspond to a thermal Ž300 K. distribution of internal states, since the two hot-atom experiments just mentioned were carried out in reaction vessels with room temperature HCl molecules. For the sake of rigour, the distribution of collision energies should also be taken into account in the comparison. The collision energy spread of these experiments is not given explicitly in the publications, but taking into account the reported experimental conditions, it should be approximately w21x 0.35 eV for the experiment of Valentini and coworkers w12,13x and 0.28 eV for the experiment of Volpp and co-workers w15x. An inspection of the figure shows that this convolution is not necessary in the present case, since the cross-section is practically flat over a collision energy range much larger than the width of the collision energy distributions. The agreement between the experimental crosssection reported by Brownsword et al. w15x at Ecol s 1 eV and the present QCT cross-section is reasonably good, the experimental value being only slightly higher than the calculated one at the same energy. In contrast, at Ecol s 1.6 eV, the QCT result of s R is more than eight times smaller than the cross-section measured by Aker et al. w12x and lies clearly below the large experimental error bar. The QM calculations of Branchett et al. w16x for H q HCl on the GQQ PES have also been represented in the upper panel of Fig. 4. This QM value of s RŽ Ecol . has a somewhat higher threshold than the QCT excitation function on the G3 PES and, for collision energies beyond 0.5 eV, the QM cross-sections are higher than the classical ones, but on the overall, the differences are not too large. Considering that the barrier for the abstraction reaction on the G3 PES is slightly higher than that on the GQQ one, the lower QCT threshold is most probably due to the absence of zero point energy constraints inherent to the quasiclassical treatment. Branchett et al. w16x performed their calculations for HCl Ž j s 0–3. and found also a very weak dependence of s RŽ Ecol . on rotational excitation. The H q DCl isotopic variant of the reaction was investigated experimentally by Polanyi and co-
workers w14x. The isotopic labelling and the alternative detection of D or Cl atoms via resonance enhanced multiphoton ionization ŽREMPI. made possible the discrimination between the products of the two reactive channels, and the use of various photolytic precursors of H atoms allowed the study of the 1–2.4 eV collision energy range. The experimental results are shown in the two lower panels of Fig. 4. In these experiments, especial care was taken in order to prevent HrD isotopic scrambling. Under the experimental conditions reported in Ref. w14x Ž p 0 d s 100 Torr mm, nozzle temperature ; 300 K, probe laser at ; 6 nozzle diameters., the rotational temperature of the reacting DCl molecules should be 20–30 K. The QCT reaction cross-sections for H q DCl reaction from threshold to 2.4 eV are also displayed in the two lower panels of Fig. 4 together with the results of previous trajectory calculations by Barclay et al. w14x over the 1–2.4 eV energy range on the GQQ PES. The present cross-sections have been calculated for a rotational temperature of 30 K, in order to compare with the approximate temperature of the experiment, but, as indicated above, the QCT cross-sections are nearly independent of the rotational excitation of DCl. In the article of Barclay et al. w14x, the initial rotational state Žpresumably j s 0. is not specified but, given the very weak dependence of s RŽ Ecol . on j observed also on the GQQ PES w16x, the comparison is meaningful. As can be seen, the experimental data for the abstraction reaction are in very good agreement with the results of the present QCT calculation. The QCT s RŽ Ecol . values of Barclay et al. w14x are systematically larger than ours and than those from experiment, and the difference increases with collision energy. For Ecol s 1.8 eV the classical s R on the GQQ PES is 2.5 times larger than that on the G3 PES whose value coincides with the experimental point at this energy. The experimental and theoretical results about the exchange channel are represented in the lower panel of Fig. 4. In this case, the discrepancies between experiment and calculations are more pronounced. Within the considerable dispersion and large error bars of the measured points, the experimental reaction cross-section shows a flat or slightly decreasing tendency over the 1–2.4 eV collision energy range.
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In contrast to this behaviour, both the present and previous w14x QCT calculations carried on the G3 and GQQ PESs respectively, show a monotonic increase in s RŽ Ecol . that leads, for the higher Ecol sampled, to much larger cross-sections than those experimentally determined. The overall agreement is better for the calculations on the G3 PES, but the two points measured at Ecol - 1.24 eV are better accounted for by the cross-sections calculated on the GQQ surface. Two distinct microscopic pathways have been identified in the dynamics of this reactive channel. An ‘end-on’ mechanism in which the H atom attacks directly the Cl molecular end, and an insertion mechanism, relevant at higher energies, in which the attack of the atomic hydrogen takes place between the Cl and D atoms. Barclay et al. w14x attribute the rapid rise of the theoretical cross-section with Ecol , responsible for the large high energy discrepancy with the measurements, to the fact that the calculations on the GQQ PES lead to an ‘excess’ of insertion trajectories that increases quickly with growing collision energy. On this surface, the insertion mechanism is clearly predominant for collision energies higher than ; 1.5 eV. The importance of the insertion mechanism is certainly smaller for the calculations on the G3 PES, as shown in a recent QCT work by Aoiz et al. w17x where it was found that at Ecol s 1.85 eV, the ‘end on’ pathway is still prevalent. On the other hand, and although the G3 excitation function deviates globally less than the GQQ one from the experimental data, it fails to reproduce the measurements. For Ecol ) 2 eV, the QCT crosssections are still too high, and this discrepancy points to remaining inaccuracies in the potential for the bending geometries, which are gradually accessed with increasing Ecol . On the other hand, for Ecol lower than 1.5 eV, the measured values are markedly higher than the calculated ones which suggests that the barrier for exchange may be too high on the G3 PES. 4. Summary and conclusions Quasiclassical trajectory calculations of total reaction cross-sections for the two exit channels of the H q HCl and H q DCl reactions have been performed on the recently released G3 potential energy
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surface. The calculations extend from the threshold up to a collision energy of 2.4 eV and show that rotational excitation has a relatively minor effect on reactivity, and that vibrational excitation lowers the threshold and increases the reaction cross-section in all cases. The results are compared to experimental data from various ‘hot-atom’ experiments and to theoretical calculations by other groups on the former GQQ PES. The comparison shows good agreement with the most recent experimental results and with previous QM calculations on the GQQ PES and suggests that the abstraction channel Žleading to HH q Cl and to HD q Cl for the two respective isotopic variants. is now well understood and that the too large experimental cross-section reported by Aker et al. w12x at a collision energy of 1.6 eV is probably wrong. In contrast, for the exchange channel there remain some discrepancies with the experimental data available. The only experimental cross-sections available for this channel correspond to the H q DCl isotopomer. The present QCT cross-sections calculated on the G3 surface show a better global agreement with experiment than those from previous calculations on the GQQ PES but they still do not reproduce the experimental data satisfactorily. On the other hand, the measured points are affected by large error bars and do not show a definite trend. Clearly, further experiments and calculations are needed in order to shed more light on the reactivity of the exchange channel.
Acknowledgements This work has been supported by the DGICYT of Spain under Grant PB95-0918-C03.
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