Reaction Cross Sections and Rate Constants for the Cl + H2(D2

Nov 14, 1996 - Experimental and Theoretical Reaction Cross Sections for the H + HCl System. F. J. Aoiz, L. Bañares, T. Bohm, A. Hanf, V. J. Herrero, ...
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J. Phys. Chem. 1996, 100, 18108-18115

Reaction Cross Sections and Rate Constants for the Cl + H2(D2) f HCl(DCl) + H(D) Reaction from Quasiclassical Trajectory Calculations on an ab Initio Potential Energy Surface Francisco J. Aoiz and Luis Ban˜ ares* Departamento de Quı´mica Fı´sica, Facultad de Quı´mica, UniVersidad Complutense, 28040 Madrid, Spain ReceiVed: July 9, 1996X

The collision energy dependence of the reaction cross section and the rate constants as a function of the temperature in the range 200-550 K have been determined for the Cl + H2 and Cl + D2 reactions by quasiclassical trajectory (QCT) calculations on a new ab initio potential energy surface (PES) by Truhlar and co-workers. For the two reactions, there is a fairly general good agreement between the calculated rate constants and the experimental determinations. The kinetic isotope effect, defined as the ratio of the rate constants for both H2 isotopomers at a given temperature, is also very well accounted for. However, the QCT rate constants for the Cl + H2 system are somewhat larger than the measurements, especially at low temperatures, which might indicate that the collinear barrier given by this PES is probably too low.

I. Introduction The dynamics of the Cl + H2 reaction is attracting a great deal of attention in recent times. High-resolution molecular beam experiments,1 as well as the calculation of new potential energy surfaces (PESs) based on ab initio points2,3 together with exact quantum mechanical (QM) scattering4,5 and rate constant6 calculations, are making this system a new benchmark in the field of reaction dynamics. In addition, the Cl + H2 reaction has played an important role in chemical kinetics for nearly a century7 due to its importance in atmospheric chemistry. The extensive number of experimental studies,8-15 including the most recent one by Michael and co-workers,16 have been used to test reaction rate theories, particularly transition state theory, using semiempirical PESs.16,17 However, the relative complexity of the calculations of ab initio potential energy surfaces for this reaction as compared to the simpler H + H2 and F + H2 systems has impaired the reliability of theoretical studies dealing with the determination of reaction cross sections and, from them, thermal rate constants. Persky and co-workers18-22 performed quasiclassical trajectory calculations (QCT) for the Cl + H2 reaction and isotopic variants on a semiempirical LEPS (London-Eyring-PolanyiSato) PES, named by the authors GSW.18 The energy dependence of the reaction cross section, thermal rate constants, and the product energy partitioning were calculated for all the isotopomers of the H2.19-22 The effect of the reagents’ vibrational excitation and of the position of the barrier on the PES on the cross sections and rate constants was also investigated.23 In particular, cross sections (σR), thermal rate constants, k(T), isotopic branching ratios, and the product energy partitioning for the Cl + H219 and Cl + D220 reactions were calculated over a wide range of collision energies, ET, and initial H2(D2) vibrational state V ) 0 and rotational states j ) 0-4(5). Truhlar’s group released two partly ab initio PESs for the H2Cl system,2 hereafter GQ and GQQ, which leave the ClH-H geometries practically unmodified with respect to the GSW, but introduced important changes in the H-Cl-H ones. * Author to whom correspondence should be sent. E-mail: [email protected]. X Abstract published in AdVance ACS Abstracts, November 1, 1996.

S0022-3654(96)02059-X CCC: $12.00

An experimental study by Barclay et al.,24 where the branching ratios of the H + DCl f HD + Cl (abstraction) and H + DCl f HCl + D (exchange) reactions were measured, and a QCT calculation on the GQQ PES by the same authors lead to the conclusion that the exchange channel of the GQQ PES is deficient in the region of high collision energies where the reacting system, en route to exchange, accesses bent intermediate configurations for which ab initio data are lacking. A new PES has been constructed very recently, also by Truhlar’s group (hereafter G3 PES),3 based on the GQQ PES. This PES corresponds to a new global fit made by including new ab initio points to improve the saddle point bend potential. As a result, the barrier becomes slightly higher (7.88 kcal mol-1 in the G3 Vs 7.70 kcal mol-1 in the GQQ), although its position remains almost invariable. The ClHH harmonic bending quantum, pωbend ) 581 cm-1, is, however, considerably smaller than the one for the GQQ PES, which is 712 cm-1, and this may have some repercussion on the energy dependence of the cross sections and rate constants. As a test of this PES, variational transition state theory with optimized multidimensional tunneling (VTST/OMT) and QM rate constants calculated from well-converged cumulative reaction probabilities (for total angular momentum, J, up to 6) have been obtained also by Truhlar’s group.6 These results show a good agreement with experimental k(T) at high temperatures, but tend to yield too high values for T < 500 K. In a previous study, the effect of the reagent vibrational excitation on the dynamics of the Cl + HD f HCl(DCl) + D(H) reaction was investigated by quasiclassical trajectory calculations on the same G3 PES25 at several collision energies. Very pronounced effects were observed in the integral and especially in the differential cross sections when going from V ) 0 to V ) 1. Qualitatively similar results were experimentally obtained for the related Cl + CH4 f HCl + CH3 system.26,27 We report in this work the results of a quasiclassical trajectory calculation of the collision energy dependence of the reaction cross section for initial rotational states j ) 0-5(6) of H2(D2) and the rate constants, which permits the calculation of thermal rate constants in the range of temperatures between 200 and 550 K. The calculations have been carried out for the Cl + H2 and Cl + D2 isotopic variants, and the results are discussed and compared with calculations on other surfaces and with © 1996 American Chemical Society

The Cl + H2(D2) f HCl(DCl) + H(D) reaction

J. Phys. Chem., Vol. 100, No. 46, 1996 18109

experimental measurements. In particular, the comparison with the quantal rate constants for Cl + H2 on the same PES provides a means to check the range of validity of QCT calculations. II. Methods The general method for the calculation of the quasiclassical trajectories has been described previously (see refs 28-30 and references cited therein). The usual way in the QCT calculations to determine the collision energy (ET) dependence of the reaction cross section, σR(ET), i.e excitation function, consists in running batches of trajectories, each of them at a given collision energy and internal quantum state of the reagent (see, for instance, for the title reaction, refs 19, 20). However, in the present calculations, as in previous works,31,32 in order to improve the computational efficiency, the collision energy of the trajectories was sampled randomly within the interval [E1, E2] for each one of the rotational states of H2 and D2. The lower limit E1 of the energy interval lies below the threshold for reaction. Once a collision energy has been chosen within the mentioned interval, the impact parameter is obtained by sampling randomly between zero and a maximum value, bmax(ET), given by

( )

bmax(ET) ) D 1 -

ED ET

1/2

(1)

2R

[

1

E2 - E1 2

M

]

+ ∑cnPn(x) n)1

(2)

where the reduced variable x is given by

x)

2ET - E2 - E1 E2 - E1

(3)

and R is the Monte Carlo estimate of the integral E2

SNR

1

N

R ) 〈σR(ET)〉∆E ) ∫E σR(ET) dET ≈ πD2∆E

(4)

where N is the total (reactive and nonreactive) number of trajectories, ∆E ) E2 - E1, and the sum of the weights of the reactive trajectories (wi), SNR, is given by NR

SNR ) ∑wi

(5)

i)1

The coefficients of the Legendre expansion, cn, of eq 2 are calculated as the Monte Carlo average of Legendre moments, N

cn )

∞

k(T) ) ∑pV,j(T) k(T;V,j)

(7)

j)0

where pV,j(T) are the Boltzmann’s statistical weights of the H2(D2) rotational states, including the 3:1(1:2) nuclear spin weights, such that ∑jpV,j(T) ) 1. A detailed account of the procedure, including the calculation of errors, is given in ref 31. For the temperature range of the present study, 200-500 K, rotational numbers up to j ) 5 have been included for H2 and up to j ) 6 for D2. In all cases, the upper limit E2 of the collision energy interval considered was 0.8 eV. All the calculations were performed for the ground vibrational state of the molecules and the 37Cl isotope mass. Batches of 50 000 trajectories were run for each rotational state. The checks of conservation of energy and of angular momentum and the selection of initial states were the same as in previous works.29,30 III. Results and Discussion

where D and ED are previously obtained by fitting the values of the maximum impact parameters found by running small batches of trajectories at several selected collision energies to the line-of-the-centers expression of eq 1. The parameters ED and D are chosen so that no reactive trajectories occur for a given ET at impact parameters even somewhat smaller than the values of bmax(ET) given by eq 1. With this kind of energy dependent sampling of the maximum impact parameter, each trajectory is weighted by wi ) bmax2/D2. The σR(ET) were subsequently calculated by the method of moments expansion in Legendre polynomials as

σR(ET) )

The series is truncated by using the statistical SmirnovKolmogorov test. The rate constants for selected rotational states of the reactants, k(T;V,j), are obtained from the corresponding excitation functions, σR(ET), by thermal averaging with the Maxwellian distribution at a given temperature. The thermal (averaged on initial j) rate constant can be written as

2n + 1 -1 R 2n + 1 SNR ∑wiPn(xi) ) 〈Pn〉 2 2 i)1

(6)

III.1. Energy Dependence of the Reaction Cross Sections. The excitation functions for the Cl + H2 and Cl + D2 reactions calculated on the G3 PES between threshold and 0.8 eV are shown in Figure 1. In all cases, the reaction cross section increases smoothly after the threshold. For the two isotopic variants, the reagents’ rotational excitation has a negative effect on the reactivity from threshold up to the highest collision energy calculated in this work. An increase of the H2(D2) rotational quantum number j, up to j ) 5, results not only in larger threshold energies but also in lower values of the cross sections at a given ET. The isotopic substitution of H2 by D2 causes a decrease in the reactivity at a given collision energy. Nevertheless, the negative effect of the diatom rotation on the reactivity is, in general terms, milder for the reaction with D2. Table 1 lists the calculated threshold energies as a function of the j state of the H2(D2) diatom. The threshold value increases with j until j ) 5, where it levels off, and, for a given j, the threshold energy of the respective excitation function is sensibly higher for the Cl + D2 reaction as compared with the Cl + H2 one. The QCT calculations carried out by Persky on the semiempirical GSW PES19,20 predict a very similar behavior with both collision energy and initial j for the reactions with the two isotopomers. However, at the highest collision energies calculated in those works, the reaction cross section is practically independent of j, whereas in the present calculations, even at the highest collision energies calculated (0.8 eV ) 18.44 kcal mol-1), the cross section clearly decreases with j for the two isotopic variants. The threshold values for a given j are always greater in the G3 PES in comparison with those in the GSW ones, in accordance with its higher barrier. There are some accurate QM scattering calculations of the total reaction cross sections for the title reaction. Launay and Padkjaer4 performed close-coupling three-dimensional converged QM calculations on the GQQ PES at a series of collision energies and for the Cl + H2 (j ) 0) reaction. These QM results are in good agreement with the present calculations on the G3 PES, although the reactivity seems to be slightly lower on the GQQ PES, especially at collision energies above 0.5 eV. Truhlar’s group33 has performed accurate converged QM

18110 J. Phys. Chem., Vol. 100, No. 46, 1996

Aoiz and Ban˜ares

Figure 1. Total reaction cross section as a function of collision energy (excitation function) calculated by QCT on the G3 PES for the Cl + H2 (V ) 0,j ) 0-5) (top) and Cl + D2 (V ) 0,j ) 0-6) (bottom) reactions. The error bars represent one standard deviation of the calculation.

TABLE 1: Threshold Energies (in eV) for the Cl + H2 (W ) 0, j ) 0-5) and Cl + D2 (W ) 0, j ) 0-6) Reactions Calculated on the G3 PES Cl + H2

Cl + D2

j

present work

Perskya

0 1 2 3 4 5 6

0.149 ( 0.014 0.176 ( 0.008 0.209 ( 0.021 0.239 ( 0.019 0.248 ( 0.022 0.232 ( 0.020

0.143 0.160 0.186 0.208 0.208

a

present work

Perskyb

0.201 ( 0.008 0.212 ( 0.008 0.232 ( 0.016 0.259 ( 0.014 0.274 ( 0.016 0.279 ( 0.020 0.269 ( 0.020

0.182 0.204 0.217 0.234 0.234 0.234

Reference 19. b Reference 20.

scattering calculations at several collision energies and initial j ) 0-3 for the two isotopic variants studied here on the G3 PES. The quantal behavior with j is analogous to the classical one; that is, the cross section decreases as j increases, at a given total energy. For the Cl + H2 reaction, the calculations at ET ) 0.260 eV and j ) 0 and ET ) 0.245 eV and j ) 1 are in quite good agreement with the QCT results. However, at j ) 2 and ET ) 0.216 eV, which lies very close to the classical threshold, the quantal σR is substantially larger than the classical one, indicating that, as in other systems,31,34 the role of rotation in the very vicinity of the threshold is different in the QM case, perhaps due to a rotational enhancement of tunneling. A general

similar agreement between QM and QCT results is found for the Cl + D2 reaction, but in this case, there is a better accordance between both methods near the threshold at the three j’s studied. The negative influence of rotation on the reactivity has been extensively described for different reactions and explained in terms of dynamical models.31,35,36 The subject has been thoroughly discussed by Song and Gislason in a very recent paper37 for the F + H2 reaction, where the strongly collinear M5 PES was used.38 Although the more recent surfaces for that particular system greatly depart from the M5 PES and the effect of rotation is known to be very different for the F + H2 reaction when the more accurate surfaces are used,32,39-41 the conclusions given in ref 37 are strictly applicable to the title reaction since its potential surface is collinearly dominated as in the case of the M5 PES. The general idea is that the forces outside the barrier tend to steer the reactants into the cone of acceptance in absence of rotation. Initial rotation would hinder this steering, leading to a decline of σR with j for the first rotational quanta, thus diminishing the possible orienting effect of the PES. These effects are augmented if the PES is, as in the present case, collinearly dominated. It has been pointed out37 that an additional falloff at even higher j is due to the fact that trajectories approach obliquely to the cone of acceptance along γ ) 0 or 180° (γ being the Jacobi angle between R, the distance between the incoming atom and the center-of-mass of the diatom, and r, the internuclear distance of the diatom), increasing the chances of hitting the repulsive wall centered around γ ) 90°. A similar behavior with rotation was also found in QCT calculations for the D + H2 reaction,31 although in that case the negative effect of rotation was overcome at lower collision energies (0.5-0.7 eV) and at smaller values of j. The effect is more dramatic for the title reaction basically for two reasons: (a) the character of the potential energy surface, which is sensibly less orientating in the case of the Cl + H2 system, and (b) the different kinematics of the two systems, i.e., the relative A-BC reduced mass is larger for the chlorine reaction. At a given relative energy, the approach to the cone of acceptance for the reaction of Cl with H2 is much slower compared to the rotation of the diatom than in the case of the D + H2 system. Therefore, the probability for the attacking atom to be disoriented in route to the cone of acceptance is larger in the case of the reaction with Cl. An important issue is whether the lower zero-point energy of the heavier deuterium molecule might explain the smaller reactivity of the chlorine atoms with D2 in comparison with H2. In the top panel of Figure 2, the excitation functions for both reactions at j ) 0 and j ) 3 are plotted against the total energy. As can be seen, the total energy threshold is slightly smaller for the reaction with D2 at initial j ) 0, and the evolution of the cross section with total energy is very similar for the reactions with the two isotopomers. To further assess this effect, the excitation functions for the two isotopic variants have been calculated from trajectories starting with the diatoms in the minimum of the potential energy, i.e. with no internal energy, and are displayed in the bottom panel of Figure 2. As can be seen, in the absence of zero-point energy, the reactivity of the two systems is essentially the same from the threshold to the highest calculated energy. The comparison of the excitation functions for initial j ) 3 plotted against the total energy (see top panel of Figure 2) indicates that the rotation is clearly more unfavorable, at a giVen total energy, for the Cl + H2 reaction. Again, this can be explained in terms of the competition between the approaching velocity to the cone of acceptance and the

The Cl + H2(D2) f HCl(DCl) + H(D) reaction

J. Phys. Chem., Vol. 100, No. 46, 1996 18111 thresholds also increase with j, this effect is more pronounced at low temperatures. At T ) 200 K, the rate constant for Cl + H2 (V ) 0,j ) 0) is about 160 times larger than that for j ) 3, but the difference in these rate constants at T ) 500 K has been reduced to a factor of about 7. The corresponding rate constants for the Cl + D2 reaction are always smaller than those for the Cl + H2 system; nevertheless their values decrease less markedly with initial j, in accordance with the σR(ET) behavior. Thermal rate constants k(T) for both reactions were obtained between 200 and 550 K from the k(T;V)0,j) after the appropriate weighting with the distribution of rotational states of the H2(D2) molecules. In this case, a multisurface correction factor (see for instance refs 19, 40 and references cited therein), accounting for the assumption that nonadiabatic processes do not contribute to the reaction, is included in order to make the results directly comparable with the experiments. This factor is calculated using the following expression:

f ) [2 + exp(-∆E/kBT)]-1

Figure 2. (Top) Comparison of the total energy dependence of the reaction cross section for the Cl + H2 (V ) 0,j ) 0,3) (solid lines) and Cl + D2 (V ) 0,j ) 0,3) (dashed lines). (Bottom) Reaction cross section as a function of the collision energy for the Cl + H2(D2) (j ) 0) reactions calculated from trajectories with no initial internal energy of the diatom (i.e. without zero-point energy).

rotation of the diatom. In simple terms, and neglecting the orbital relative motion, the decrease of R, ∆R, as the molecule rotates by ∆γ, at a given collision energy, ET, and initial rotational quantum number, j, is given by

IBC ET ETre4 µBC2 ∆R 2 ) ) ∆γ µA,BCErot j(j + 1)p2µA,BC

( )

(8)

where IBC is moment of inertia of the diatom, µi are reduced masses, and Erot ) j(j + 1)p2 is the rotational energy. The comparison of ∆R/∆γ for the two isotopic variants of the reaction yields

() ∆R ∆γ

) ClH2

( )( )

µH2 µCl,D2 µD2 µCl,H2

1/2

∆R ∆γ

(9) ClD2

The quotient of the reduced masses is ∼0.7, indicating that as the Cl atom approaches the diatom, the probability of disorientation caused by rotation is higher in the case of the H2. This simple argument explains why the effect of rotation is milder for the reaction with D2. III.2. Rate Constants. The excitation functions represented in Figure 1 have been used to calculate state-selected rate constants as a function of temperature for each of the initial j, k(T;V)0,j). The values obtained are listed in Table 2 and represented in Figure 3. For a given temperature, the rate constants decrease rapidly with rotational excitation. Since the

(10)

where ∆E is the energy splitting between the two fine-structure states of chlorine, 2P3/2 and 2P1/2, taken as 110 meV, kB is the Boltzmann constant, and T is the temperature. A thermal population in both spin-orbit states is also assumed. The results are listed in Table 3 and represented in Figures 4 and 5, where they are compared with the experimental data available for these reactions,8-16 with the QCT rate constants of Persky on the GSW PES,19,20 and with the recent QM results of ref 6. The experimental rate constants listed in Table 3 are calculated from the Arrhenius fits reported in every experimental work, and the parameters of these fits are included in the table as footnotes. As depicted in Figure 4, the present QCT rate constants calculated on the G3 PES are in very good agreement with the measurements, especially at temperatures above 300 K. Below this temperature, the calculated rate constants are somewhat larger than the experimental ones. In contrast, the quantal rate constants calculated on the same PES6 are systematically larger than the classical ones. Given the good agreement in the σR(ET) for initial j ) 0 between QM and QCT calculations, the main differences in the thermal rate constant values should be due to the discrepancies in the σR(ET) values near the threshold for initial j g 1. Similar effects were also observed in the D + H231 and OH + H234 reactions with rotational excitation in the H2 molecule. In both cases, as j increases, there is a neat enhancement of tunneling; that is, whereas the classical thresholds increase with j (up to j ) 6), the quantum dynamical threshold remains practically unchanged as j increases. In addition, a common feature of both QM and QCT calculations is the decrease of reactivity with increasing j, as commented on in the previous section. The QCT rate constants calculated by Persky on the GSW PES19 are larger than the ones calculated on the G3 PES, in accordance with the lower value for the collinear barrier of the GSW PES (7.7 kcal mol-1) and, thus, in worse agreement with the experimental data (see Table 3). For the reaction of Cl with D2, the classical k(T) are practically coincident with the experimental data from 250 to 550 K (see Figure 5). The determination of the two lowest temperature k(T) by Miller and Gordon14 (at 203 and 227 K) seems to be in much worse agreement with the calculations. However, the authors14 pointed out that the strong deviation from Arrhenius behavior, which is in strong contrast with similar results for the Cl + H2 reaction,12 is probably due to a competing process occurring with D2 that is absent in the reaction with H2. The QCT rate constants calculated by Persky on the GSW PES,20 shown in Figure 5, are also larger than the ones calculated on

18112 J. Phys. Chem., Vol. 100, No. 46, 1996

Aoiz and Ban˜ares

TABLE 2: Specific Rate Constants for the Cl + H2 (W ) 0, j ) 0-5) and Cl + D2 (W ) 0, j ) 0-6) Reactions as a Function of Temperature Calculated on the G3 PESa Cl + H2 Reaction T (K)

j)0

j)1

j)2

j)3

200 250 300 350 400 450 500 550

3.20 ( 0.98(-15) 2.31 ( 0.48(-14) 9.04 ( 1.33(-14) 2.46 ( 0.27(-13) 5.32 ( 0.45(-13) 9.84 ( 0.66(-13) 1.63 ( 0.09(-12) 2.48 ( 0.11(-12)

8.31 ( 1.57(-16) 7.94 ( 1.07(-15) 3.71 ( 0.38(-14) 1.15 ( 0.09(-13) 2.74 ( 0.18(-13) 5.47 ( 0.29(-13) 9.62 ( 0.42(-13) 1.54 ( 0.06(-12)

1.19 ( 0.65(-16) 1.67 ( 0.47(-15) 1.01 ( 0.18(-14) 3.76 ( 0.47(-14) 1.03 ( 0.10(-13) 2.29 ( 0.16(-13) 4.39 ( 0.25(-13) 7.56 ( 0.36(-13)

2.01 ( 1.56(-17) 4.07 ( 1.63(-16) 3.15 ( 0.78(-15) 1.39 ( 0.23(-14) 4.35 ( 0.53(-14) 1.07 ( 0.10(-13) 2.22 ( 0.16(-13) 4.08 ( 0.24(-13)

T (K)

j)4

j)5

200 250 300 350 400 450 500 550

8.32 ( 6.17(-18) 1.89 ( 0.79(-16) 1.59 ( 0.43(-15) 7.54 ( 1.44(-15) 2.48 ( 0.35(-14) 6.39 ( 0.70(-14) 1.38 ( 0.12(-13) 2.63 ( 0.18(-13)

1.33 ( 1.87(-17) 2.57 ( 1.90(-16) 1.95 ( 0.87(-15) 8.60 ( 2.56(-15) 2.69 ( 0.56(-14) 6.68 ( 1.03(-14) 1.41 ( 0.16(-13) 2.62 ( 0.24(-13)

Cl + D2 Reaction

a

T (K)

j)0

j)1

j)2

j)3

200 250 300 350 400 450 500 550

1.07 ( 0.28(-16) 1.44 ( 0.27(-15) 8.49 ( 1.16(-15) 3.10 ( 0.32(-14) 8.32 ( 0.68(-14) 1.82 ( 0.12(-13) 3.45 ( 0.18(-13) 5.87 ( 0.26(-13)

5.97 ( 1.22(-17) 8.93 ( 1.35(-16) 5.65 ( 0.65(-15) 2.17 ( 0.20(-14) 6.08 ( 0.45(-14) 1.38 ( 0.08(-13) 2.68 ( 0.14(-13) 4.65 ( 0.20(-13)

1.89 ( 0.56(-17) 3.53 ( 0.72(-16) 2.59 ( 0.39(-15) 1.11 ( 0.13(-14) 3.36 ( 0.30(-14) 8.11 ( 0.59(-14) 1.66 ( 0.10(-13) 3.02 ( 0.15(-13)

5.79 ( 1.46(-18) 1.41 ( 0.24(-16) 1.22 ( 0.15(-15) 5.86 ( 0.57(-15) 1.93 ( 0.15(-14) 4.97 ( 0.31(-14) 1.07 ( 0.06(-13) 2.02 ( 0.09(-13)

T (K)

j)4

j)5

j)6

200 250 300 350 400 450 500 550

1.75 ( 0.97(-18) 5.23 ( 1.57(-17) 5.25 ( 1.02(-16) 2.81 ( 0.39(-15) 1.01 ( 0.10(-14) 2.79 ( 0.22(-14) 6.39 ( 0.41(-14) 1.26 ( 0.07(-13)

6.49 ( 6.30(-19) 2.31 ( 2.19(-17) 2.62 ( 2.11(-16) 1.54 ( 0.75(-15) 5.96 ( 1.60(-15) 1.74 ( 0.35(-14) 4.15 ( 0.57(-14) 8.55 ( 0.60(-14)

7.05 ( 6.51(-19) 2.35 ( 2.11(-17) 2.55 ( 1.98(-16) 1.46 ( 0.69(-15) 5.51 ( 1.15(-15) 1.59 ( 0.42(-14) 3.75 ( 0.68(-14) 7.68 ( 0.99(-14)

Numbers in parentheses represent powers of 10. The multisurface factor discussed in the text was not included.

the G3 PES, although the differences between the two sets of QCT calculations are smaller than those found in the reaction with H2. A remarkable agreement is found for both reactions between the calculated rate constants and those corresponding to the Arrhenius fits given by Kumaran et al.16 (footnotes h and k of Table 3; short-dashed lines in Figures 4 and 5). However, these fits were done by using three sets of experimental determinations corresponding to very different temperature ranges: one individual determination at 296 K and measurements in the temperature ranges between 699 e T e 1217 K and 1769 e T e 2939 K. The absence of direct experimental determinations in the range of temperatures between 200 and 550 K calculated in this work, with the only exception being the one at room temperature, forces us to take this comparison with some precautions. Additionally, Kumaran et al.16 produced global Arrheniuslike “best fits” using all the experimental data available in the literature for both reactions in the temperature range between 200 and 2939 K for Cl + H2 and 255 and 3020 K for Cl + D2 (see eqs 10-12 of ref 16). These fits, along with the present QCT calculations on the G3 PES and those by Truhlar and coworkers,6 are depicted in Figure 6. The present k(T) values slightly overestimate the data from the experimental fits in the range of temperatures considered in this work for the Cl + H2

reaction, whereas the differences are within the error bars for the reaction of chlorine atoms with D2. Therefore, it seems that the classical rate constants calculated on the G3 PES for the reaction with H2 are somewhat larger than the experimental “average”. The QM rate constants calculated by Truhlar and co-workers6 for the Cl + H2 reaction are larger than both the QCT ones calculated on the same PES and the experimental “average”. Thus, one might possibly conclude that the G3 PES has a too low barrier. In fact, Harding43 has performed ab initio calculations using orbitals obtained by three-electron, three-orbital complete-activespace (CAS) self-consistent-field (SCF) calculations, estimating the correlation energy by multireference configuration interaction wave function including all single and double excitations from CAS, and also including an estimate of the effect of quadrupole excitations by the Davidson method. The resulting height of the collinear saddle point is Vq ) 9.6 kcal mol-1 as compared to Vq ) 7.88 kcal mol-1 for the G3 PES and Vq ) 7.7 kcal mol-1 for the GSW PES. Harding’s calculations yield a somewhat broader bending potential (a Cl-H-H νb ) 501 cm-1, Vs νb ) 581 cm-1 for the G3 PES) at the collinear saddle point. In addition, the imaginary frequency at the collinear saddle point is smaller than that of the G3 PES (νi ) 1408i Vs νi ) 1520i). This would imply that the barrier of the G3 PES is too thin, a deficiency that has been observed previously in

The Cl + H2(D2) f HCl(DCl) + H(D) reaction

J. Phys. Chem., Vol. 100, No. 46, 1996 18113

Figure 4. Comparison of thermal rate constants from experiment and theory for the Cl + nH2 f HCl + H reaction (see Table 3). The solid line with error bars is the results of the present QCT calculations on the G3 PES. In this case, the multisurface factor mentioned in the text was included. The dashed line corresponds to the QM results of Truhlar et al.6 The short-dashed line corresponds to the Arrhenius fit of the experimental results as given in ref 16. The open symbols are for experimental data as follows: circles, ref 8; squares, ref 10; triangles, ref 12; diamonds, ref 13.

Figure 3. Arrhenius plot of the specific rate constants, k(T;V)0,j), calculated from the excitation functions of Figure 1 from 200 to 550 K for the reaction of chlorine atoms with hydrogen (deuterium) molecules (without including the multisurface factor; see text): (upper panel) Cl + H2; (lower panel) Cl + D2. The error bars represent the estimated error of the calculations.

extended LEPS surfaces,3 and this may lead to an overestimation of tunneling. If the actual PES for this system would have those properties (larger and wider collinear barrier than the G3 PES), the calculated quantal and classical rate constants would be substantially smaller than the ones obtained on the G3 (or GSW) PES, thus in better agreement with the experimental results and, also, leading to a better agreement between QM and QCT results. As mentioned in ref 3, none of these calculations take into account the spin-orbit coupling. This coupling is expected to strongly mix the three states in the asymptotic region and, to a much lesser extent, in the vicinity of the barrier, but, nevertheless, it would lead to an effective increase of the barrier height. The same effect has been recently discussed by Stark and Werner for the F + H2 reaction.44 Figure 7 displays the kinetic isotopic ratio of the rate constants, kCl+H2/kCl+D2 as a function of the temperature calculated on the G3 PES. For comparison purposes, the results calculated by Persky on the GSW PES19,20 are also shown. The experimental results represented by the symbols correspond to refs 14 and 42, and the thick dashed line is the result of dividing the Arrhenius fits reported by Kumaran et al.16 obtained from their experimental data. There is a general good agreement between the different results, and only at the highest temperatures do the experimental ratios seem to be somewhat lower than the theoretical ones.

Figure 5. Comparison of thermal rate constants from experiment and theory for the Cl + nD2 f DCl + D reaction (see Table 3). The solid line with error bars is the results of the present QCT calculations on the G3 PES. The small triangles connected by a dashed line are the QCT results of Persky on the GSW PES.20 In both cases, the multisurface factor mentioned in the text was included. The shortdashed line corresponds to the Arrhenius fit of the experimental results as given in ref 16. The open circles are experimental data from ref 14.

IV. Conclusions Quasiclassical trajectory (QCT) calculations for the Cl + H2 and Cl + D2 reactions have been carried out on an ab initio potential energy surface (PES) in order to determine the energy dependence of the reaction cross sections for selected initial rotational quantum numbers and rate constants in the temperature range between 200 and 550 K. A negative effect on the reactivity with rotation has been found for the reaction with the two isotopomers in the whole range of collision energies and initial rotational quantum numbers j investigated in this work. The different reactivity between the two isotopic variants of the reactions has been explained in terms of the differences in the zero-point energy of the diatoms. The present results on the new ab initio G3 PES are compared with experimental determinations, recent approximate QM rate

18114 J. Phys. Chem., Vol. 100, No. 46, 1996

Aoiz and Ban˜ares

TABLE 3: Thermal Rate Constants k(T) (cm3 s-1) for the Cl + nH2 and Cl + nD2 Reactions as a Function of Temperature Calculated on the G3 PES and Taking into Account the Multisurface Factor (See Text) (Numbers in Parentheses Represent Powers of 10) Cl + H2 Reaction T (K)

QCT;G3 PES

QM;G3 PESa

200 250 300 350 400 450 500 550

5.99 ( 1.50(-16) 4.59 ( 0.76(-15) 1.86 ( 0.22(-14) 5.20 ( 0.47(-14) 1.14 ( 0.08(-13) 2.13 ( 0.13(-13) 3.56 ( 0.18(-13) 5.46 ( 0.23(-13)

8.77(-16) 6.34(-15) 2.52(-14) 6.94(-14) 1.51(-13) 2.80(-13) 4.64(-13) 7.05(-13)

QCT;P77b

exptl; WH68c

5.76(-15) 3.47(-15) 2.31(-14) 1.47(-14) 4.12(-14) 1.30(-13) 8.92(-14) 1.63(-13) 4.15(-13)

T (K) exptl;WDMCO77e exptl;MG81f exptl;KS82g 200 250 300 350 400 450 500 550

3.83(-16) 4.12(-15) 2.01(-14) 6.21(-14)

3.52(-16) 3.54(-15) 1.65(-14) 4.97(-14) 1.13(-13) 2.15(-13) 3.60(-13)

1.59(-14) 5.17(-14) 1.25(-13) 2.48(-13)

exptl; LMPSW77d 3.82(-16) 3.56(-15) 1.57(-14) 4.54(-14) 1.01(-13) 1.87(-13) 3.08(-13)

exptl;KLM94h

1.83 ( 0.27(-14) 5.03 ( 0.75(-14) 1.10 ( 0.17(-13) 2.08 ( 0.31(-13) 3.51 ( 0.53(-13) 5.47 ( 0.82(-13)

Cl + D2 Reaction T (K)

QCT;this work

200 250 300 350 400 450 500 550

2.57 ( 0.64(-17) 3.33 ( 0.60(-16) 1.93 ( 0.27(-15) 6.96 ( 0.76(-15) 1.86 ( 0.16(-14) 4.07 ( 0.29(-14) 7.70 ( 0.47(-14) 1.31 ( 0.07(-13)

QCT;P78i

exptl;MG83j

4.42(-16) 2.39(-15)

3.18(-16) 2.07(-15) 7.89(-15) 2.15(-14) 4.70(-14) 8.77(-14)

2.11(-14) 8.55(-14)

exptl;KLM94k

1.97 ( 0.39(-15) 6.97 ( 1.39(-15) 1.86 ( 0.37(-14) 4.09 ( 0.82(-14) 7.82 ( 1.56(-14) 1.35 ( 0.27(-13)

a Reference 6. b Reference 19. c k ) (2.0 ( 0.5) × 10-11 exp[-(2165 ( 96)K/T]; ref 8. d k ) (2.66 ( 0.42) × 10-11 exp[-(2230 ( 60)K/T]; ref 10. e k ) (5.5 ( 0.5) × 10-11 exp[-(2375 ( 100)K/T]; ref 11.f k ) (3.65 ( 0.28) × 10-11 exp[-(2310 ( 20)K/T]; ref 12. g k ) (6.0 ( 0.5) × 10-11 exp[-(2470 ( 100)K/T]; ref 13. h k ) 4.78 × 10-16 T1.58 exp[-1610K/T] ((15%); ref 16. i Reference 20. j k ) (2.42 ( 0.17) × 10-11 exp[-(2810 ( 20)K/T]; ref 14. k k ) 9.71 × 10-17 T1.75 exp[2092K/T] ((20%); ref 16.

Figure 7. Ratio of the rate constants for the Cl + nH2 and Cl + nD2 reactions as a function of the temperature (kinetic isotope effect). Solid line: present work. Dotted line: QCT results by Persky on the GSW PES.19,20 Thick-dashed line: result of dividing the Arrhenius fits to the experimental data on ref 16. Open circles: experimental results from ref 14. Open squares: experimental results from ref 42.

and the present calculations, the fact that at low temperatures the QCT rate constants are slightly larger than the experimental ones indicates that the height of the collinear barrier might be underestimated. This hypothesis seems to be corroborated by the QM calculations of the rate constants on this surface. In particular, the comparison between approximate QM rate constants and the present results, both on the same surface, shows that the classically obtained rate constants are smaller in the range of temperatures between 200 and 550 K, and as such, they provide a lower bound approximation to the more accurate QM ones. As in the case of other reactions with H2, the discrepancies between QM and QCT results can be related to an overestimation of the reaction thresholds with rotational excitation of the reagents in the classical case. Acknowledgment. We are most indebted to Prof. D. G. Truhlar and T. C. Allison for sharing with us the code of the G3 PES prior to its publication and for communicating to us their quantum calculations. This work has been financed by the DGICYT of Spain under Grant PB92-0219-C03. References and Notes

Figure 6. Arrhenius plot of the QCT thermal rate constants (solid line with error bars, present QCT results on the G3 PES; dashed line, QM results of Truhlar et al. for the Cl + H2 reaction6) and the “best” overall fit (with error bars) of the experimental data as given in ref 16 (short-dashed line) for the Cl + H2(D2) reactions.

constants calculated on the same surface, and previous QCT calculations carried out on other semiempirical PESs. Although there is a very good agreement between the experimental results

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