Exchange reactions of hydrogen halides with hydrogenic atoms

~emicalPhysics71(1982)

117-125

North-Holland Publishing Compvly

EXCHANGE REACI’IONS OF HYDROGEN HALIDES WITIf HYDRQGENIC ATOMS

Department of Chemistry. Universi~ Manchesrer MS0 1 QD, UK R&eked

of ~Xanc~~este~~~slituie of Science and Technology.

1 Mvch 1982

CaIcuIatiomontheD+HBr-DBr+HandD+HI + DI + H reactions are reported. A three-dimensional, quantumdynamical approximation is used which involves applying the energy sudden approximation to the entrance channel hamiltonian and the centrifugal sudden approximation to the exit channel hamiltonian. Results of inrem and differcntial cross sections, rate coefficients and rotational distributions are presented. Diatomics-in-molecules potentiai-enelgy

surfaces have been used in the computations. The H-Br-H potential has been cptimised so that the c&x&ted roomtemperature rate coefficient agrees with experiment. This potential has a barrier height of 0.231 eV_ Rate coefficient computations for the four reactions H’ + H”Cl + H’Cl+ H” (H’, H” = H or D) are also reported. These results, for a LEPS surface, agree well with those obtained in quasiclassical trajectory and varktional tznsition state theory ulculations.

1. Introduction Studies of the gas-phase reactions of hydrogen halides have contributed significantly to the understanding of chemical reactions [1,2] _One particular subset of these types of reactions, the exchange reactions of hydrogen halides with hydrogenic atoms, have been the subject of many experimental and theoretical investigations. These reactions are of the for?n H’+XH”+H’X+H”,

(0

where H’ and H” are hydrogen or deuterium atoms and X is 2 halogen atom. Rate coeft%ients for the D f HCl or D f HBr exchange reactions have been measured using EPR [3,4], massspectrometer ES] and laser [6] techniques. Furthermore, molecular-beam experiments of ann,gular distributions have been reported for the exchange reactions of D atoms with HBr, Hl and HCI [7,8]. Many related experiments on the abstraction reaCtiOnS

(n) have also been performed [9-121. Theoretical work on the exchange reactions (a) has included ab iuitio calculations of potential~ner,~ sur0301-0104/82/0000-0000/S

02.75 0 1982 North-Holland

faces for the H-Cl-H [13-1.51 and H-Br-H [16] reaction systems. Semi-empirical potentials have also been proposed for these reactions [ 17-241. Some of these semi-empirical potentials have been used in quasiclassical trajectory (QCT) calculations on the HBr 123,243, Hl [22] and HCI [19--221 reactions. Information theory has been applied [25] to the product distributions of trajectory computaticns [24] on the D + HBr + DBr f H reaction. Transition state theories I’ve also been applied to these reactions [ 121

and variational transition state theory (VTST) calculations of rate coefficients for the four reactions H’ t H”C1+ H’Cl + H”, where H’, H” = H or D atoms, have been performed [26]. Recently, a new three-dimensional (3D) quantumdynamical approximation for exchange reactions of the light-heavy-light type was formulated [27] and used in calculations of vibrational-rotational integral and differential cross sections, and rate coefficients, for the D + HCl -+ DC1 + H reaction [28,29]. Both LEPS [19] and diatomics-in-molecules (DIM) [17,18] potentials were used in these computations. This quantum method involves applying the energy sudden approximation (ESA) to the entrance channel hamiltonian and the centrifugal sudden approximation

118

D. C Gky

/

Exchangemmions

(CSA) to the exit channel hsmi&o&n_ Closecoup& expansions of adiabatic vibmtional functions, multiplied by orbital spherical harmonics for the entrance channel 2nd rotational spheri& h2rmor-k for the e_xit channel, 2re then made, 2nd the rn2tchiug between entrance and exit channel w2vefunctions is performed 2n2lyti&.ly. Here we apply this 3D quantum method to the reactions D+HBr+DBr+H 2nd D+HI-+Dl+H,

(Iv)

using DIM potentials [i 7,18]_ We report vibmtionalrotational product distributions, differential cross sections 2nd rate coefficients for these reactions, with the initial hydrogen halide in the ground vibrational state. We also report rate coefficient computations for the four reactions

than H + Hz 2ppear to be out of re2ch at the present time [34] 2nd thus approximate, but reliable, 3D quantum techniques have some value. It is clearly important, however, to test approximate methods on 2s many systems as possible. Our previous study on the D f HCI + DCI + H reaction [28] was complicated by the fact t.h2t consider2ble uncertainty rem&s about the banier height for this reaction, with theoretid 2nd experimental estimates differing wildly [l&28]. The D + HBr -+ DBr + H reaction has less uncertainty about the barrier height [4,16] 2nd thus is a better candidate for theoretical comparisons with experiment. Section 2 briefly describes our 3D quantum approxirnztion, 2nd 2lso provides details of the potent&lener,gy surfaces used. Section 3 present2 results for the D + HBr 2nd D f HI exch2rrge reactions (III) 2nd (IV) while the calculations on the H’ + C?H” reactions or) are discussed in section 4. Conclusions are in section 5.

2. Details of c2lcul2tions

H+HCI-tHCi+H,

31. Method

D+HCi+DCIi-H,

D+DC+DCI+D.

of hydrogen halihs

03

In these H’CI reactions a LEPS potential-energy surface [19] has been used so that direct comparisons cur be made between our 3D quantum results 2nd previous QCT [19] 2nd VTST [26] computations on these four reactions in which the same LE?S [I9 J surface w2s used. Despite the fact th;it this LEPS surface is thought to be inadequate for these reactions [12, 281, comparisons of this kind shed a useful light on the suitability of the present cprantum technique, and the QCT 2nd VTST methods, for calculating rate coefficients. Predictions of kirretic isotope effects, in p2rticular, aze one of the most severe tests of chemical reaction theories. There bar been comiderable interest recently in the application of 3D quantum techniques to atomdiatom chemical reactions. This is because both theoret&l and experimental result2 su%est that qlrantum effects such as tunneiling [30,3 I] and resonances [32, 331 cc~l be important for these reactions_ Exact 3D quantum calculations on reac
The 3D quantum approximation for atom-diatom exchange reactions of the light-heavy-light type has been described in detail before [27]. Only a brief summary is presented here. It is assumed that the S&iidinger equation can be solved for a single reaction path, with bifurcation into the product abstract& arrangement c’kmnel being neglected. This is expected to be a reasonable approximation for reactions with coUi.nearIy dominated potentialener,~ surfaces 1351. The reaction is divided up into an entnurce (o) channel and an exit (@) channel, each with its own set of natuml co&ion coordinates [36] _In ‘the entice channel, the ESA [37] is applied. This involves replacing the rotational an,+r momentum operator by the eigenv2hre$jG+ 1). A close-coupling (CC) expansion in the basis functions

jz

g, (uo3 qF1te, 0)

is then made, where gn(ud is 2 vibration&y

0)

adiabatic basis function, Yfr is a spherical harmonic, with orbi‘%dangular momentum quantum number I, 2nd 6 is the atom--diatom orientation 2&e_ In the exit ch2nnel we make the CSA [38] which involves repIacing

the orbital angular momentum operator 13 by the eigemalue@f(f + 1). The exit channel close-coupling basis functions are then &‘(Ug) ~@,

0) ,

(2)

where j’ is a rotational angular momentum quantum number. The exit and entrance channels have a common coordinate system [27] with z axis along RF (which is equivalent to rcr for Light-heavy-light sys-

terns). Tire CC equatIo.ns are soIved by using the R matrix propagator method [36]. After setting [39-421 j = 7=7’, the wavefunctions in the entrance and exit channels are matched analytically and boundary conditions are applied to yield the S matrix elements @f.u~~~~, where -theprimes represent the product sty i : and v is a vibrational quantum number. The calcuiations have to be repeated for all magnetic quantum numbers M contributing to cross-section_expressions (see below). The formulae relating the S$$ to differential and integral cross sections in the helicity representation have been derived [27]. We have daR(v, j, rnj + v’, j’, mj*)/dw = (lj4kzj)

(3)

for the differen’ti cross section, in which the initial (mj) and final (mjf) rotational angular momentum projections are along the initial and ikal momenta directions hkd, and hk,y respectively. Here dmj,, is a retluced rotation matrix andJ is the total angular momentum quantum number. The S matrix $$nDgfnf is defmed in body-fured coordinates in which the initial and fina z axes are along & and R, respectively_ This is related to S’${~~ by [27] 3;l;inu,j,n, = ~(3 f l)/(u X F

c(.i

+ I)] !/2(-l)j+W-J-j

- KK!O) C(ljJ - LtOCi’)

X S$$j’G&fn’ .

(4)

For the degeneracy averaged integral reaction cross section, the sum rule [43] for Clebsch-Gordon coefficients C(Ji - S2.QO)is used to sum over mj and the series rule [43] is used to sum over J. We then obtain

the very simple expression

The angular momentum summation thus arises through the flf expansion In the entrance channel and it is not necessary to repeat the calculations for many angular momentum parameters such as J. This simplification leads to very sIgniiicant savings in computer time. Once the oR(v, j + u’, j’) have been calculated for a range of collisional energies it is stralghtforward to compute rate coefficients [27]. At room temperature, molecules such as HBr exist in low j states which are fairly close in energy. The ESA should thus be valid for the entrance channel. For the exit channel, however, product molecules can be populated in hi&j’ states and thus the CSA is more appropriate. From the computatior& point of view, the present method is attractive because, in contrast to the non-reactive case, relatively small I values are needed for reactions to occur and thus the basis-set expansions (1) and (2) are quite small [2X] _Furthermore, only a small number of M values is needed for reactions on collinearly dominated potentialenergy surfaces [30,4]. The present theory is more accurate than the in& r&-order sudden approximation (IOSA) for reactions [45,46] in which the CSA and ESA are applied together in both entrance and exit channels_ In calculations on D + HCI -+ DC1+ H, however, a special formulation of the IOSA [47] gave good agreement with integral reactive cross sections obtained using the method described above. 2.2. Potemiid-energv surfaces In the present calculations on the D + HBr (u = 0, J) znd D i- III (u = 0,j) exchange reactions (III) and (IV) semi-empirical DIM potential-energy surfaces of Last and Baer are used [17,18]. The energy of the threeatom HXH’ system is expressed as a sum of the DIM energy Eo and a supplementary term W which incorporates contributions from threecentre molecular electror?icintegrals which are not taken into account in the traditional DIM method. To calculate the DIM

energy, Eg, of the XII2 system in a minimal basis set, six diatomic potential curves are needed: Hz(rZ’), H2(3X$ HX(iZ+J, HX(?Z+), HX(%I) and HX&). These potential curves are chosen to be the modified

Morse (Uxd and anti-&lorse (GA) potentials internuclear distance R

U&;(R) = &G (R)[G(R) VA(R) =vDeC(R) G(R) = exp[-a(R

in the

- 21 Y(R) ,

(6)

[G(R) f 31 V(R) , - Rej

V(R) = exp [-b (R - R&

(71

,

@I

z

(9)

where De is the dissociation enera, Re is the equilibkm distance, and q, CIand b are coefficknts. The supplementary term JVis expressed as W = Z(S~‘SHX

t SHH’SH’X + SHXSH’X) ,

(10)

Fii. 1. hKni3nun paths, V, of the DIM potential-energy surfaces A and B for H-Br-H, plotted as a fuwtion of reaction coordimre u.

where SHH’, .Ss’x and SHX are overlap integrals and Z=(g/R,)

exp[-a(R~x

- RH*x)*] COS% .

(11)

Here g is an adjustable parameter, (Yis set to 1, RHX and R&X are the HX and H’X distances respectively and 6 is the WXH’ angle [17,18]. The potential surface parameters used in one set of calculations on D t HBr and D f HI are given in table 1_ These parameters have been proposed by Last [4X], with the exception of the adjustable parameter g which is taken to be the parameter used in our pretiOILScalculations on D + HCl 1281 (g = 0.182). This potential for HBrH is cal!ed DiM surface A. As is discussed in section 3, the calculations with this DIhf surf&e A gave a room-temperature rate coefficient for D + HBr much higher than that obtained in an EPR experiment [4]. Emmeter g was aiso optimised for HBrH so *&at the calculated rate coefficient for the D + HBr exchange reaction (III) agreed with experiment [4] (see section 3). This optimised potential has g = 0.22 and is denoted D!M surface B. Fig. 1 presents the potentiahner,~ profiles, along the reaction coordinate u 1361 for the H-Br-H DIM potentials A and B. In both cases the minimum porecTable 1 Dihl potential-cner,vy

tial-energy paths are collinear, and the potentials become very repulsive for non-collinear geometries. The barrier heights are 0.148 and 0.237 eV for DIM surfaces A and B respectively. For the H-I-H DIM surface the barrier heighht is 0.127 eV_

3. Results for D + HBr and D + HI Calculations on the D + HBr (v = 0, i) and D + HI (u = 0,~‘) exchange reactions (III) and (iv) were performed withi = 3, this being the most highly populated HBr and HI state at room temperature. Vibration-rotation reaction integral and differential cross sectiors were computed for a range of initiaI tmnslational energies Etrans o-j from threshoid up to 0.295 eV for HBr and 0.255 eV for HI. The usual variations in numbers of basis functions and R mat&. sectors were performed to check the convergence of the results, and the numerical parameters required are very sir&u to those described in detail for the closely related D + HCI reaction on the DIM surface [2S].

surfac: panmcrers for XHz (X = Br or 1)

Hz HBr HI 2) See cq. (24) of ref. [ 181.

0.17447 0.1439 0.1174

1.0291 0.957 0.947

0.018 0.012 0.011

1.4016 2.673 3.032

0.394 0.32i 0.321

1.6 1.28

D. C C&y

Fig. 2 presents

/ Exchange

the total integral reactive cross sec-

remxions

of

hydrogen

121

halides

Table 2 Reaction cross sections &Cl, 3) for D + HJ3r -+ DBr + Ii on DJX surface B. Numbers in parentheses are powers of ten

ti0Il.S

(12)

0.045

0.40 (-4) 0.31 (-3) 0.58 (-2)

0.075

for the D + HI (u = 0, j = 3) exchange reaction on the DIM surface and the D + ‘HBr (u = 0,j = 3) exchange reaction (III) on DIM surfaces A and B. Also presented, for comparison, are the oR(0,3) for the D + HCl (u=O, i = 3) exchange reaction calculated previously. On this scale, cross sections with magnitude less than 0.010~ are omitted_ It can be seen that the D f Hl oR(0,3) are much the largest, with a “threshold” of 0.03 eV. The threshold is defmed as the energy at which oR(0,7) becomes larger than O.Ola$ The threshold for D + HBr on DIM surface A is 0.05 eV, while that for DIM surface II is 0.13 eV. The difference between these two HBr values is approximately equal to the difference in barrier heights for surfaces A and B (0.089 ev). Note that the oR(0,3) for D + HBr on DIM surface B are smaller than those for the D + HCl reaction. The DEM D + HCl surface has not yet been optimised, however, as inconsistencies remain in the experimental data for this reaction lo]. Table 2 presents our calculated uk (0,3) for the

0.125 0.175

0.245

0.61 (-1) 0.38 (+O)

0.295

0.74 (i0)

D t HBr reaction on DIM surface B. Since this surface has been optimised, we hope these results might be useful for comparisons with other methods fcr calculating cross sections, particularly those which can incorporate tunnelling features. 3.2. Rate coefficients Rate coefficients, k,, are obtained by MaxwellBoltzmann averaging over the oR(O, ~1 using the procedure described in ref. [27], with j held fixed since the ESA is applied. The ko for D + Hl and D + HBr on DIM surfaces A and B are presented in fig. 3. It can be seen that the D + HBr rate coefficient for surface A is about an order of magnitude larger than that for surface B. Thus rate coefficients for these ligh-heavylight reactions are very sensitive to small changes in the three-centre integral term of eqs. (10) and (11).

‘1-“I 15. 200

250

300

T/K Fig. 2. Toti integral reactive cross sections oR(0,3) for the D + HI, D + HCl and D + HBr exchange reactions. The D + HBr results for DIM swfacas A and 3 are shown.

Fig. 3. Rate coefficients ko for the D + HI and the D + HBr reaction on DIM sufzces shown (open circle) is an experimental [4] D + HBr + DBr + H rate coefficient at T =

exchange reaction A and B. Also value for the 295 K.

122

D.C Chy /Exchange reacnbnsof &drogen halides

As was mentioned in section 2, the parameter g of eq. (11) was varied in our rate coefficient computations until the calculated ko gave good agreement with experiment. Wthg = 0.22 (surface B) the caIcuIated rate coefficient is 1.16 X lo-l4 cm3 molecule-’ s-l at T = 295 K whiIe the vabre obtained from the EPR experiment [4] is (i .3 t 0.4) X 1O-l4 cm3 molecule-l s-‘. The barrier height for the optimised DIM surface B is 0.237 eV. This falls within the estimate of 0.130.48 eV made by Botschwina and Meyer on the basis of their PNO CEPA ab inItio computations on the H-Br-H system [16] _ The tirhenius parameters, obtained by a least-squares fit to the function kg = A exp(-E,/kT)

(13)

between 200 and 300 K are A = I.95 X 10-l’ cm3 molecule -1 s-1 and E, = 0.131 eV for the D + HBr reaction on DIM surface B. Clearly, more extensive experimental rate coefficient measurements over a wider temperature range wiII be useful to determine parameters such as these so as to test further if the DIM surface B is optimum. Our value for Ea is well below the e!ectronic and vibrationahy adiabatic barrier heights of 0.237 and 0.166 eV respectively, suggesting that tunnelling is ixnportult for the D f HBr room-temperature rate coefficient. This was ah.0 the conclusion of the D + HCI study [28] _ To our knowledge, there have been no experimentaI measurements on the D f HI exchange reaction rate coefticient, and thus we could not optimise the DIM surface for this particular reaction. 3.3. rl!rsrlar disrriburions Xlolecuiar-beam experiments of an,&ar distributions (difftxentid cross sections) for the exchange reactions of D atoms with HBr, HI and HCI have been sported by McDonald and Herschbach [7]. In these experiments, the hydrogen halide was at 250 K while tl:;! incident D bearr was at 2800 K. This corresponds to zn initial translational energy of ==0.39 eV. In every cr?se, strong backward peaking of the difi;rcntial cross sections was obtained in the experiments [7]. In ail of our calculations on the D + HI ar:d D + HBr exchange reactions with the DIM surLI<~s,we also obtained strong backward peaking in me deferential cross sections, which are very insensi-

Fii. 4. Calculated

to*M reactive

difierential cross section for

the D + HBr exchan.serextion 0.245 eV (unbroken line). tained in a molecular-beam distributions are normali& obtain absolute values for 0.610; sr-I.

on DIM surface B at J?&& = A!so shown is the distniution obexperiment [7] (shad& area). The to the vaIue at 8~ = 180°. To the calculations, multiply by

tive to E$i_ This was aIso true for the D + DC1 c&culations [28]. Fig. 4 shows our calculated differential cross section for the I) + HBr exchange reaction with DIM surface B and @;& = 0.245 eV. The scattering angIe, @D,on the diagram is the angle between the product DBr and the incident D atom. Also plotted is ‘he experimental distribution, which is seen to agree well with the caIcuIation. Unfortunately,. we cotdd not perform calculations at the high@;& value of 0.39 eV. As was discussed in our previous work [27,28], if the potential is isotropic for light-heavy-light reactions then the angular distribution is also isotropic. However, both the experiments and calculations give strongIy anisotropic angular distributions, and the good agreement between the calculations and experiment strongly suggests that the angular characteristics of the H-I-H and H-Br-H DIM potentials are realistic. Since the bending potentials away from collinearity are very repulsive in these DIM surfaces, our findings provide good evidence to suggest that the true surfaces wiU aIso have very repulsive bending potentials. Limited ab initio computations [16] on H-Br-H provide evidence to support this view. These were also the fmdings in our D + HCl study [28]. 3.4. Rotational distributions Detailed rotational product distributions have not yet been measured for reactions such as D + HBr * DBr + H, but with the recent advances in Iaser tech_niques [49] such experiments might be possible in the future. Fig. 5 shows our calculations of these quanti-

DC. C&Y /Exchange

123

reactions of hydrogen halides Table 3 Rate coefficients at T= 295 K for H’ + H”C1 reactions. are cm3 molecule-’ s-l X lo-‘* Reaction

Method presefit

claxsiul trajectory

variational transition state theory (ICW/MCPSAG)

1.77 0.20 1.47 0.74

1.7oco.3 0.25~0.08 1.01~0.18 1.2 +0.2

1.51 0.21 1.10 0.83

.*

J

Fig 5. Rotational product distributions for the D + HEir exchange reaction at threedifferent tia&ationaI energies: Ef3 = 0.175 eV and Eg = 0.245 eV (DIM surface B), and E$ = 0.265 eV (DIM surface Afi TogObtainibsolute cros$sectionsa multiply the results for El, Ez and E3 by 0.007&& 0.035ao and 0.097& respectively.

ties for the D + HBr reaction on the DIM surface B, for two selected values of @;&_ These distributions are defined by P(u,i+

l/J’)

= &u,j+

v’J’)l&u,~+

a’,]=) ,

where (fi’,i”> is the most highly populated product state for given initial state (u,~). It can be seen that these distriiutions are unimodal, with a slight increase in J='as the translational energy is increased. Also shown in fig. 5 is the rotational distribution at E$& = 0.265 eV for D + HBr with DIM surface A. This distribution shows about twke as much rotational excitation as that for DIM surface B with the very close translational energy of @;& = 0.245 eV. Thus the rotational distributions are also very sensitive to the three-centre integral term (10) in the potential-energy surface. The DIM surface A has a smaller barrier height than surface B and thus more energy is available to enter the product rotational modes in surface A. Clearly, experiments on the detailed rotational distributions for these reactions will yield data that will be very useful in calibrating potentialenergy surfaces..

4. Calculations

on the H’CI reactions

Rate coefficient calculations were performed on the four H’CI reactions defined in eq. (V). The LEPS surface of Valencich et al. [19] was used in these computations. These rate coefficients are displayed in table 3 for the temperature 295 K. Also shown in table 3 are the quasiclassical trajectory results of

Units

Hi.HCl+ HCI+H H+DCI-XCI+D D+HCld DCliH D+DCi* DCl+D

Valencich et al. [19] and the variational transition state theory results of Garrett et al. [26]. These transition state theory calculations were performed with the ICVT/MCPSAG procedure which refers to an improved canonical variational theory with a MarcusColtrin-path semiclassical adiabatic ground-state transmission coefficient [26]. It can be seer? that the rate coefficients obtained with these three very Werent methods show agreement to within a factor of two for all four reactions. This is a very satisfactory agreement, and is partly due to the fact that tunnelling is not important for these reactions ai this temperature [28]. It would be of interest if a similar comparison could be done for these reactions using the DIM surface for which tunnelling is more important [28]. In all three methods of calculation, the H + HCI reaction has the largest rate coefficient, while the H + DC1 reaction has the smallest_ In table 4 we present our calculated Arrhenius parameters which are obtained by a least-squares fit of eq. (13) to the quantum rate coefficients between 200 and 300 K. The H + HCl and H + DC1 reactions have very similar A factors while the ~5~of the H + DC1 reaction is 0.053 eV higher than that of the H + HCI reaction. Table 4 Calculated

Arrhenius

parameters

Reaction

A (cm3 molecule-’

H+HCl H+DCl D+HCl D+DCl

1.14 1.01 1.19 6.33

x x x x

lo-‘0 lo-‘0 lo-‘” IO-”

between 200 and 300 K s-l)

Ea (ev) 0.106 0.159 0.112 0.113

i24

D.C_ C&p / Exchange reactions of hydrogen halides

This is almost exactly equal to the differemzes in HCL 2nd DCl vibrational energies (0.051 ev). Garrett et 2l. [26] also fitted Arrhenius p2mmeters to their rate coefficients for a higher temperature range (4?9610 K). Their Ea factors increased according to (H+HCl)<(D+HCl)<(D+DCl<(H+DCl) which is the same relationship found in our quantum calculatiorr for the temperature range ZOO-300 K. The results enabIe us to test how well the present quantum method satisiies detailed balance_ The equilibrium constant for the D + CM + DC1 + H reaction on the LEES surface is 5.38 a? 295 K. Our caIcul2tion gives 7.35 while the QCT result is.38 [I 9]= Thus, our method slightly overestimates the equilibrium constrmt, while the reverse is true in the QCT calculations. Since we apply different approximations to the entrance 2nd exit channels in our method, detailed balance c2n only be satisfied fortuitously. One major approximation we do make is the ener,T sudden procedure of considering just one initi2lj value in computing rate coefficients. in our Calculation, the most probabIe j value at room temperature is-chosen which isj = 3 for HCI and i = 4 for DC1. To give some indiication concerning the sensitivity of the rate coefficient to initial_i, calculations on the D + HCI - DC1 + H reaction were performed at an identic2lvalueof.@;~~(0.111eV)withj=0,32nd 5. The oR(O, j) obtained were 0.80& 0.9&i and l.l&,$ forj = 0,3 and 5 respectively, and are seen to increase withj. Avera_@ng these three oR(O,j) with the Boltzm2nn distribution gives 0.99& Thus, by settingj = 3 we are probably giving a slight underestimate to the rate coefficient that would be obtained by separately considering 2ll contributlngj states to the rate coefficient. This effect of intiti2lj will be more pronounced for H + DC1 --f HCI + D tllan D + HCl + DC1 f H since higher j states c2n be populated for DC1 than HCI at 2 given ?emperature. It is thus likely that a slight improvement in the calculated equilibrium constant would be obtained by performing separate CIOSSsection calculations for all possible j states. Such a calculation would be too expensive with our computation2l facilities however.

5. Conclusions

CalcuMions of integral 2nd differential cross sections, rate coef55ents and rotational distributions have been performed on the D + HBr +- DBr + H 2nd D + iHI + DI + H exchange reactions. A 3D quantumdynamical method has been used which involves applying the ener_gy sudden apprortiation to the entrance channel harniltonian 2nd the centrifugal sudden rlpproximation to the exit channel hamiltoniul. The computations have been performed using diatom&-in-molec-ales potential-energy surfaces [17, 181. In the Mse of the D + HBr reaction, the DIM surf2ce h2s been optimised so that the calculated roomtemperature rate coefficient agreea with experiment [4]. The optimised potential-energy surface has an electronic btier height of 0.237 eV. The study shows that rate coef5cients and rotational distributions are very sensitive to the magnitudes of terms representing the contribution from three-centre molecular integrals to the H-Br-H potential ener,oy. The differential cross sections are backward peaked for bo+h D + HBr and D + HI and the good agreement with experiment provides strong evidence to suggest that the true potential-ener,z surfaces for the H-Br-H and H-I-H systems are very repulsive away from the collinear geometry. This was also the conclusion of 2 previous study on D f HCl in which the same quantum -method was used [28] _Furthermore, the results suggest thzt iunnelling is important for the room-temperature D + HBr rate coefficient, which was also the finding in the D + IICl investigation [2X]. Rate coefficient calcd2tions are also reported for the four reactions H f HCI + HCI + H, H f DC1 + HC1+D,D+HC1+DC1i-HandD+DCl+DCl+D. A LEES 1191 potential-energy suzface has been used in these computations. Good agreement is obtained with quasiclassicat trajectory [IS] 2nd variational transition state theory [26] results for all four reactiOnS.

Acknowledgement The calculations were performed on the CDC 7600 computer of the University of MancheSter Regional Computer Centre and the CRAY-1 computer of the

D. C Uary / Exchange reactions of hydrogen halides

SERC Laboratory, Daresbury. I am pleased to acknowledge a grant of computer time from the Science and Engineering Research Cound. I am also grateful to Dr. I. Last for providing a copy of his DIM potential, znd for forwarding the parameters of the H-Br-H and H-I-H potentials before publication.

References !l] [2] f3] [4] [S] [6] [7] [8]

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