Energy distribution among reaction products. IX. F + H2, HD and D2

Chemical Physics 12 (1976) 419-431 0 North-Holland Publishing Company

ENERGY DISTRIBUTION AMONG REACT[ON PRODUCTS. IX. F + H,, HD and D, D.S. PERRY and J.C. POLANYI Department o~Chentistr_v, Univcrsit_vof Toronto. Toronto Ai5S IA I, Camda

Received 19 August 1975

The infrared chemiluminescence technique has been used to obtain detailed rate constants k( v’, R’, T’) (V’, R’. T’ me product vibrational, rotational and translational energies) for four isotopic reactions: (la) I’+ HD -f HF + D (-Ago = 31.1 kcal mole-‘), (lb) 1: + HD - DF + H C-4 = 32.8 kcal mold’), (2) F + Hz -+ Hi-’+ i: (--A& = 3 1.9 kcal mole-’ 1, and (3) I: t Dz -) DF t D [-A@ = 31.8 kwl mole-’ ). The mean fraction of the available energy which becomes vibration and rotation in the molecular product, C@ and (fR>,listed in this sequence for the four reactions is: (la) 0.59 and 0.125; (It: 0.63 and 0.066; (2) 0.66 and 0.083; (3) 0.67 and 0.076. The changes in mean product rotational escitation along the series are correctly predicted by (prior) classical trajectory studies. These studies do not, hcwever, account for (@la < $$lb. The “anomalously” low vibrational excitation for reaction (12) is likely to be linked to the fact that this reaction liberates an energy barely sufficient to populate the (highest) vibrational level, HF( U’= 3); classical mechanics is unsuited to the study of processes near to threshold. The effect on the product vibrational and rotational distributions of variation in the temperature of the molecular reagent in the range from 77-1315 K. has been determined for reactions (la), (2) and (3). The chanses in the mean product distributions are in accord with our earlier linding, based on both theory and experiment, that enhanced reagent translation results in enhanced product translation and rotation, (A7) -(A?? + (AR’>.The detailed rate constant k(o’ = 3) for the HF product of 1: + HD [reaction (la)] showed a marked increase with reagent energy at low energy (77-400 K), levei!ing off at higher reagent energy (2 600 K). This threshold-type behaviour contrasts with that observed in the other systems for highly vibrationally excited product. For (la) the energy release measured off the energy surface, 17~- A& (where Ea is the activation energy) exceeds the energy of HP (II’= 3) by only -0.2 kcd mole-‘. For reactions (2) and (3) I$ - Ati exceeds the energy of the highest-populated u’-level by 2 1 kcal mole-‘. Triangle plots, recording k( V’, R’, T’), are given for both paths of F + HD [i.e., (la) and (lb) p:oceeding in the uxothermic direction] and foi both paths (HF f D and DI: + H, each yielding F + HD) in the endothermic direction.

persurface with the isotopically reIated reactions:

1. introduction The reaction F + HD offers the possibility of attack at either end of the KD molecule: /HF(u’,J’) F ’ HDhDF(u’,f)

+ D, -A@ = 31 .l kcal mole-’ ,(la) + H, - Al4 o = 32.8 kcal mole” .(lb)

Both of these reaction channels have large exothermicities, denoted -4; the small difference between them is due to the difference in zero point energy between HF and DF. The energy released is distributed among the product states, indicated by the vibrational and rotational quantum numbers, u’ and J’. These reactions share the same potentiai-energy hy-

F + H, + HF(v’, J’) + H, -AI$

= 3 1.9 kcal mole”,

(2)

F + D, + DF(u’, J’) + D, -do

= 3 1.8 kcal mole-‘.

(3)

These four reactions and the surface on which they occur have been the subject of intensive theoretical and experimentai investigation. From a theoretica standpoint this group of reactions is of special interest since each reaction involves only eleven electrons. This makes accurate ab initio calculations feasible on-this system, which has therefore become a model of exothermic reaction. Bender et al. [I j have produied ab initio points on the collinear surface, FHK. Polanyi and -: .

420

-D.S. Peny. J.C. Polanji, /I:iwrgy distribution among reaction pmdmts. IX

Schreiber [2] have fitted these points to an LEPS-type function (LEPS denotes the London, Eyring, Polanyi, Sato expressi&& and have investigated the collinear reaction dynamics of F + Hz on the resulting surface -by means of classical trajectories. Experimental investigations of these reactions have been made using the infrared chemiluminescence technique [3-61, reactive scattering of molecular beams [7], chemical laser methods [8,9] , and mass spectrom-etric measurements [IO]. This wealth of experimental data has stimulated theoretical interest, particularly in the form of classical trajectory calculations [6,1 l-161. An information-theoretic approach due to Bernstein and Levine has been successful in representing the mostdetailed rate constants presently available (k(u’,J’) from [5]) in terms of two parameters 1171. The fact that light masses are involved has made these reactions a valuable proving ground for both semiclassical trajectory studies [ 181 and quantum scattering calculations [19-221. In a recent Paper-[231 we reported product energy distributions for the reactions (la) and (lb). The Bernstein-Levine (information-theoretic) theory of branching ratios [24,25] links the product energy-distribution to the branching ratio (i.e., to the relative yields of HF and DF). The theory was found to predict a branching ratio in excellent agreement -with expetiment. However, a more detailed examination of the theoretical predictions, with the aid of classical trajectory results for these reactions [11,16] , raised a question as to the significance of the agreement. In the present work we report in more detail on the product energy distributions of reactions (la) and (lb). The temperature dependence of the energy distributions for reactions (la), (2),and (3) has now been obiained, and is reported here.

2. Experimental The arrested relaxation infrared chemihnninescence technique 1261 was used in these experiments. The apparatus has been described in detail by. Polanyi and Woodall [S] f In this technique, reagents were introduced into~the reaction vessel in diffuse crossed beams. F’ioduc~moJecules were removed rapidly at the hquidnifrogen-cooled walls of the reaction vessel. This mini: 1mi%ed the effect df relaxationprotiesses. The infrared -. _ . ‘. _ Z,‘-

emission from the vibrationally and rotationally excited products was monitored either by conventional grating spectroscopy or by Fourier transform spectroscopy. A multiple reflection Welsh cell [27] increased the collection efficiency by 30 to 50 times. In the experiments involving molecular reagents at

an enhanced temperature, a graphite oven [6,28] with a 1 mm diameter orifice was used. This oven was heated resistively up to 131 S K. In the experiments involving the molecular reagent HD below room temperature, the HD inlet was a 12 mm diameter copper tube cooled by an appropriate slush bath. The HD used in these experiments was prepared by the action of DzO on LiAlH4 in a di-Iz-butyl ether bath 129,301. Three liquid nitrogen traps in series were used to freeze out any DzO or solvent vapour contaminating the HD. Isotopic purity was tested using a Veeco Model SPI-10 monopole mass spectrometer. For every batch of HD produced, the intensity of mass 2 plus the intensity of mass 4 was less than or equal to 3% of the intensity at mass 3. It was therefore concluded that the HD used in these experiments was 97% isotopically pure. For the purposes of experiments at enhanced reagent energy, the HD isotopic purity was monitored massspectrometrically as a function of temperature, and was found to be invariant up to 1400 K. Fluorine atoms were produced by a microwave discharge in CF4 [5]. There is an excited state F*(2P1,2) which lies 1.15 kcal mole-’ above the ground state F(*P3& Although the equilibrium concentration of the excited electronic state, F*(2Pt,$, is only 7.2% at 300 K, Carrington et al. report that the discharge produces 16% F*(2Pr,2) atoms. Tully [31] in a theoretical treatment invol-ving surface crossing has estimated that the F*(2PI,a) state is only 0.14 as reactive as the F(2P,,2) ground state at 300 K. Therefore the F*(2Ft,-J state will account for approximately 2% of the observed reaction for F + H2. If this is also a reasonable estimate of the contribution to the isotopic reactions F f HD and Dz, the F*(2P1,2) state may be neglected. Although the relative reactivity of F*(2Pt,2) increases at lower temperatures, it appears from fig. 6 of Tully’s paper that it will still be less reactive than F(2P~,2) at 107 K, which was the lowest collision temperature used in this work.

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disttibutior! among reaction products. IX

Table 1 Experimental conditions Expt.

Product

Reaction

-

HDI

F+lID

HD2 HD3 HD4 HDS ND6 HD7 HDB HD9

HDlO HDI I HD12 HD13 HD14

F+HD

HF HF

flD17

FIHl HH2 tiH3

F+H2

DDl DD2 DD3 DD4

F+Dz

hlolecular reagent

Flow (JI mole s-’ ) --

Flow (JI mole s-l ) ---

9 4

e) (W

7-+b) UC) __.__-

64

300

300

7

300

300 300

IIF

1.2

7

300

HI’ HI: HF IiF HF HF HF HP HI: HF

1.2 1.3 1.2

29

300

300

8

300

300

DI’ DF DF DF

HD15 HD16

CF4

HF HF HP

1.3 5 5 5 S 5 5 33 4 10 5 - 33 0.1

0.7 0.7

DF

50

DF DF DF

50 50

4

29

17

107

12

193 279 443 718 918 lli8 1315

212

20 20 20 20 20 20

40 104 16 2614 53 53 53

125 125 125 100

282 415 661 834 1004 1187 ;oo

300 300

300

300

300

300

300

279

281

718 1315

618 1219

279 718 1315

1130

300

300

283 645

a) fl is the oven temperature. which is also the rotational temperature. b) T* is the effective collision temperature [32] given by Tc = (ml 7$ + rnz7$/(rnl + m21 where ml and tn2 are the masses of the molecular and atomic reagents respectively, and fl and ?$ are their respective temperatures.

3. Results and discussion 3.1. Room renzperarure results 3.1.1. Vibrutioual distributions A summary bf the experiments performed, and the conditions of each, is given in table 1. The background pressure in the vessel ranged fro? lo-’ torr for the experiments with the lowest molar inflow rates to 3 X

IO4 torr for those with high flows. The product vibrational distributions for both branches of the reaction, F + HD, are shown in fig. I_ Numerical values for the best (mea&g least-relaxed and lowest-flow) experiments are given in table 2. An estimate of the rate into u’ = 0 was obtained by extrapolation of the vibrational surprisal plots 1331 shown in fig. 2. For the most meaningful comparison with the reactions F + H, and F + Di, the results for ihese reac.

422

D.S. Perry, J.C. Polun~&?qg*

.

:

1

I

I

I

I

dislriixrtion among rcactiok products. IX

I

If’Fig. 1. Relative vibrational populations. (a) -I - F + HD -+ HF(u’) + D. The data of experiments HDl, HD?, HD3, HD4 and HD5 fall within the indicated ranges ---o---F + H2 -, HF(u’) + H, expt. HHl. (b) -A- F + HD -+ DF(u’) + H, expt. HD148 -D- F + HD -+ DF(u’) + H, espt. HDIS, -D- F + HD -+ DF(u’)k H, expt. HD17. -o-. F + D2 + DF(u’) + D, eypt. DDI. The nortialisation points are indicated b) @. All points not explicitly shown lie within ranges ikticated by I. The rates into u’ = 0 were obtained by extrapolation of the surprisal plots (fig. 2).

Fig. 2..Vibrational surprisals [-&I’) = ln(Y(u’)/&‘))] rue shown as a function of the total product energy appearing as viiration,jCV(a) -*F + HD-+ @F(u’)4 D. expt:HDS. -a--- F + Hz + HFCu’)+ H, expt. HHl. --t.b) -*F + HD -+.DF(+-l_ tf, expt. HD17; -+- F + D2 -+ DF(u’)t D, expt. DDl. Parenth&es&di_ca’te extrapolated vatuek. _:

tions taken from the present series of experiments were used. These results were, however, very similar to those of Polanyi and Woodall [S] , and are not meant to supersede them. It should be noted that the present results were calculated from the experimental intensities using the new Einstein transition probabiIities of Sileo and Cool [34] whereas the previous results used less accurate values based on the Heaps and Herzberg expression [5]. The extent of vibrational relaxation of HF and DF in this apparatus has been discussed in detail previously [SJ . The only possible source of significant vibrational relaxation was shown to be collisional deactivation, From fig. 2, it can be seen that the vibrational distributions of both branches of F + HD are nearly constant over a reasonable range of flow conditions. It can therefore be concluded that these distributions are vibrationally unrelaxed. Only at the highest reagent flows can a slighhtvariation be detected. The principal deactivator is believed to be HD. The vibrational distributions of F + HD -+ DF and F + D2 4 DF are essentially the same, but the average fraction of product energy appearing as vibration, ir;>, is slightly lower in the F + HD case due to its greater exothermicity. The most noteworthy feature of the vibrational distributions is the anomalously low rate into u’ = 3 for F + HD + HF as compared to the F + Hz + HF (fig. 1). The-former reaction being a littte less exothermic than the latter, has a total energy available to the products, E& or&y 1.7 kcal mole-l greater than the energy of HF(u’ = 3). This 1.7 kcal mole-’ includes 1.5 kcal mole-’ of reagent translation plus rotation, that is channelled more efficiently into product translation and rotation than into vibration. Product vibration arises predominantiy from energy released in the downhill portion of the energy surface [35]. This energy release is given approximately by -A@ + L’, (where E, is the_activation energy). For F + HD + HF(u’ = 3) the ener,T release measured on the energy surface in this fashion is -0.2 kcal mole” _For F + H, -+ HF(u = 3) the corresponding figure is -i kcal moIe-’ _ For F + HD --t HF(u’ = 3) there are fewer rotational and translational states of the product that are a&ssible than for F + Hz + HF(u’ = 3). This is of importance in determining reaction probability according to statistical or quasi-sti$istical -ththeories.In c‘surprisai the&? the-sup&al, f(u’) ~:-$ntpcu’)/@(u’)] , compares .. .. ..-

D.S. Perry, .i_C. PoIanyi/Ewrgy

distribution

423

ontoug reaction products. IX

Table 2

Product energy distributions (la) F + HD -f -HF

-_I_ (lb)F+HDdDF -

-(2)F+H2~HF HHl

(3)F+Dt*DF DDl

Experiment

HD5

HD17

(fvP)

‘fR’“)

0.588 0.125

0.626 0.066

0.664 0.083b)

0.665 0.076b)

cJi.1")

0.287

0.308

0.260

0.259 (0.04)

k(d) u’ = 0

(0.06)

(0.06)

(0.04)

uf = 1

0.30

0.18

0.28

0.15

u’ = 2

1.00

0.54

1.00

0.52

IJ’= 3

0.14

1.00

0.55

1.00 0.59

u’ = 4 *’

hot

a)

0.61 36.1

34.3

35.0

35.2

(kcal moles’ ) Berry - Chemical laser results [9]

'fv) k(i)

v’ = 0

V’= 1 v*= 2 VI= 3 v’ = 4

0.55

0.59 0.06 0.32 1.00 (0.15 r o.o@

0.13 0.28 0.63 1.00 (0.3 f 0.2$

0.67

0.60

0.06

0.10

0.29

0.24

1.00

0.56

0.63

1.00 (0.4 + 0.2)C)

Muckerman - Classical trajectory results [11(a)(b)] Qd’

‘rk,“’

0.64 0.10

Schreiber - Classical trajectory results

(fv) (fR)

0.67 0.13 --

0.58 0.04

0.58 0.07

0.06

[ 161 0.63 0.06 .___-__.____..-.

0.67 0.10 ..._._~.~_ __

0.64 0.08 ___.-.._-.-~__-~~~~

a) The avenge total energy available to the products is Riot = - Afl+ Ea + #RRT+ RT. The middle two terms represent the average rextive collision energy. The last term is the average reagent rotationd energy. The quantities Cfv), (fRand $T> represent the respective fractions of Eiot that appear as product vibration, rotation and translation. The activation energies were mken to be 1.7,1.8,1.6 and 2.0 kcal mole-’ for reactions (la). (lb), (2) and (3) respectively [9]. b) Result of Polanyi and Woodall [Sl. Theseauthors obtained a signific;;ntly less-rotationally-ielaxed distribution for F + D2 and hence a more-dependable Cfk,.In order that Cfk, for F + H2 and F + DZ shall be comparable, we have taken both from ref. [S] . (The (@ for F + Hz obtained in the present work, using Sileo and Cool’s 1341 transition probabilities, was 0.076.) )‘ Estimated by a less accurate method than the oth‘er values 19). d) These results on Surface II!, for F +‘HD(J= 0) and F f Hz(J = 1) have been recalculated using the zero-point vibrational eneraas a reference [ 1 l(b)] * e’ Results on Surface t [ t l(a)] _

424

D.S. Pew, J.C. Poianyi/Energydistributionamong rcactiotlproducts XI

thebbserved probability of a vibrational level, P(u’), to the statistical prbbabihty of that level, @(u’)T, for a total energy EiOldistributed randomly in a closed system. Since the vibrational surprisal plot (fig. 2) calculated on this basis for F f Hi + HF is linear, we can obtain a predicted value for flu’ = 3) = 0.23 for F + HD -+ HF by extrapolating the surprisat plot linearly from u’ = 1 and 2. This is lower than the corresponding value of 0.30 for the reaction F + Hz * HF, but is considerably in excess of the measured value for F + HD -) HF which is 0.09. It appears likely that there are special dynamic requirements which must be met if a reactive encounter F + HD + HF is to yield U’=3. The “special requirement” would be expected to be linked to the “special” situation that u’ = 3 for F t I-ID + HF is only just accessible, i.e., the reactive cross-section function S&u’ = 3) is being explored near to its threshold. A simpIe and plausible (but hypothetical) “special requirement” would be that the reactive encounter must take place through a geometry that separates the products without the intervention of secondary encounters [35] that could rob the newly-formed HF of its (incipient) vibrational excitation, and hence contribute to the product population in u’ < 3. Avoidance of secondary encounters could be achieved by the presence in the reaction products of a minimum translational energy, and/ or by separation in a bent configuration so that the excursions of the H in the newly-formed FH molecule do not bring it into close proximity with the retreating D atom. Berry [9] has obtained vibrational distributions for both branches of the reaction F + HD using a chemical laser technique. These results (table 2) are in reasonable agreement with the present work with the exception of the relative rate of F + HD + DF(u’ = 4) for which he used a less accurate method and obtained an approximate value lower than (0.5X) that of the pre-

’ The statistical probability ?(o’) was calculated by eq. (4) of 1231, which includes an explicit summation over esact vibrational and rotational energy levels obtained from the Dunham expansion. A different P’(v’) would be obtained if allowance were made for the spread in tdtal product energy arising from the breadth of the reagent energy distribution. This effect could be significant for V’close to the thermodynamic limii. Our failure to include it might account for the nonJir+ity of the surpris31plot for F +,HD + HF. \Ye are : -grateful to The referee for pointing this out.

sent work. The fact that the vibrational surprisal plots of Berry’s results form straight lines - excluding the uppermost level in each case - lends support to the extrapolation procedure used here for obtaining relative rates into u’ = 0. For the HF product, his measured rate into u’ = 0 is the same as the one obtained here by extrapolation of the vibrational surprisal plot (fig. 2). However, for the DF product, Berry’s data fall on a slightly less steep surprisal plot than do the present data, which results in his measured rate into DF(u’ = 0) being twice the value obtained here by extrapolation. Muckerman [ 1 I ] has reported classical trajectory results on three LEES surfaces for the system F f HD (table 2). The predictions on all three surfaces are qualitatively correct in that they channel most of the product energy into vibration, and deposit more rotational excitation in the HF product than the DF. Only on surface III are near-quantitative values of fy> predicted. However, even for surface 111C&>is predicted to be larger for the HF product than for the DF product, rather than the reverse as found experimentally. Classical trajectory calculations on an LEES surface employed in this laboratory, which had been selected to produce tire experimental $,J for F + Hz [6] , gave the observed value of for F + HD +- DF but a slightly high value for F + HD * HF (table 2 and ref. [16]). This discrepancy, which is also to be found in Muckerman’s results, is due to the fact that the channel F + HD + HF(u’ = 3) is close to threshold. In classical trajectory studies the continuum of product energy states eliminates threshold effects. Further discrepancies between classical theory and experiment stem from the fact that the trajectory studies (at least on LEES surfaces) tend to give rise to too narrow prqduct vibrational distributions. Semiclassica! trajectories or quantum scattering calculations may be necessary to predict the behaviour of rates into levels which are (or which are classically predicted to be) sparsely populated. 3.1.2. Rotational distributions The experimental product rotational distributions are shown in fig. 3 and fig. 4. These were extrapolated to obtain the initial rotational distributions [5,36]. The peak of the initial rotational distribution [the “unrelaxed distribution” at the right of each N(J’) plot ] is uncertain to approximately f one J’ level. Resolution of the two rotational peaks was achieved by repeatedly recording the relevant region of the spectrum over a

D.S. Perv, J.C. Pota+&nergy

425

distribution among reaction products. IX

0

04

12

08

eV eV

08

2

4

6 SW

8

IO 12 14 16

Fig. 3. Relative rotational populations for the reaction F + HD --+HF(u’. J’) + D. (The arrows indicate the thermodynamic limits for rotational excitation.) dExpt. HDS. fl= 300 K. --------Truncation of the above to obtain initial populations. Espt. HD13, ti = 1300 K.

period of l-2 hours at slow scanning speeds, and averaging the results. No secondary peak was obtained in N(J’) of DF(u’ = 4) indicating that the product which carries the initiat rotational excitation is obscured by the tail of the Bottzmann peak (produced in every case, \\

J’ _3 Fig. 4. Relative rotational populations for the reaction F f HL -+ DF(u’, J’) + H. (The arrow has the same meaning as in fig. 3.) Expt. HD17.e = 300 K. --------Truncation of the above to obtain initial populations.

v’=Z(k~

=054

I--

Fig. 5. ‘%iangIe piots” for both branches of the F + HD reao tion, showing the distributions of vibrational, rotational aid translational energy among the reaction products. Quantisation is ignored in joining contours of equal detailed rate constant, k(V',R', T').The ordinate is the product vibrational energy. V’; the abscissa is the product rotational energy, R'.Since the total available energies, Eiot, are almost constant (at 34.3 and 36.1 kcal mole-‘) the translational energy, T’, can be obtained by difference and is indicated by the dashed lines. The total rate constants given for each vibratior$ level are kf[&(u’) 1.= x&‘, J’). (The symbol, kf, denotes a rate constant’in the fqrward, i.e., exothermic. direction.)

-426

--

LX‘ Perry.J.C. Yo~at~yifhergy distribution amongreactionproducts.IX

--. by rotational relaxation); An extreme change in the location of the best-guess initial N(J’) for DF(u’ = 4) ; (fig. 4) by ZZ units of J’, from j’ = 3 up to p = 7 alters (f&I froti 0.062 to 0.07 1. Fig. 5_shows the initial vibrational-rotational ciistributions in the form of triangular contour plots. From these pI#s (and from table 211it can be seen that for the reaction F + HD, the HF product has nearly twice as much rotational excitation as does the DF product. A full discussion of this phenomenon and its significance for the Bernstein-Levine theory of branching ratios [24,2S] hasbeen given in a previous paper [23] . Variations iti product rotational excitation were dis- cussed in terms of a very simple repulsive model that appeared to give some insight into the variation of rR) with mass-combination in the isotopic series FH*D, FH*H, FD*D and FD-H (the dot is the locus of the product repulsion, the molecular product is at the left; the intermediates are listed here in the sequence of decreasing (&>) [23]. On Muckerman’s surface I [ 1 la,b] (the only surface for which directly comparable data are given), the product rotational excitations found theoretically for the four isotopically related reactions (la,b,2,3) follow the patterns observed experimentally (table 2). Schreiber’s classical trajectory results [16] give quantitatively the product rotational excitations for each branch of F + HD: the results for F t H2 and D2 are close to the experimental values but not quite so well predicted (table 2). The sequence of diminishing rotational excitation (@ for FH*D > FH*H > FD.D > FD.H) once again a#ees qualitatively with experiment.

vibration into product vibration;see, e.g., ref. [dj), it was concluded that all of the emission observed was due to reaction with reagents in their ground vibrational state. (Ref. [6], page 265, gives evidence that an . even greater percent of vibrationally excited D2 makes only a minor contribution to the overall rate of F + D, + DF), The effective collision temperature 132) is given by T* = ()?I~Lr? + mz~)l(ml + mu), where 79 and @ are temperatures of the hot and cold reagents and ~1 and m2 the masses of the hot and cold reagents respectively. Due to the mass combinations involved in these experiments, f is less than but close to the oven temperature, q (see table 1). The average energy available to the products is then (E&I = -do

+ E, + $RT* t Rc,

where E, is the activation energy (l-6-2.0 kcal mole-’ [9,37] ; precise values used are listed in table 2, footnote a) and R is the gas constant. All enhanced-reagent-energy experiments were performed within the range of conditions which gave arrested vibrational relaxation for room temperature reagents. Using a combined shock-tube laser-induced fluorescence technique, Bott has found the vibrational relaxation of HF by Hz (38,391 and of DF by D2 [39, 403 to be approximately independent of temperature, for temperatures in the range 300 K to 1000 ELThis is a proximately the range of collision temperatures s work. In view of this, the experimental (dinthi conditions which arrest vibrational relaxation at room temperature should also arrest it when the Hz or D2 is at an enhanced temperature.

3.2. Enhanced reagent energy 3.2.1. Experimental conditions The product ener@ distributions of the three reactions (I$j F t HD + HF, (2) F + H2 -+ HF, and (3), F t D2 -S:PF have been studied under the range of reagent conditions indicated in table 1. The effect of heating the molecular reagent in the graphite oven was td etiance the reagent vibrational, rotational and translationai-enerdes. Since the fraction of the hot reagent iri’,the fiisf excitkd vibrationa level was only 0.870, I.So/irid:3.1% for Hz, HD and D2 respectively at 1315 _5 (the,l@est temperature used}, and since no HF(V’~ = 4) dr .DF@ =_.s)emission was observtid (despite the expectationaf efficient trar&r of enhanced reagent .--:~.. . ,_ -: ..

3.2.2. Effect of enhnc2d r&nt energy on product vibrationaldistributions The relative rates of reaction into each accessible vibrational leve! are shown as a function of oven temperature - i.e., molecular-reagent temperature - in fig. 6, for the reactions F + HD + HF, ti + Hz -f HF and F + Dz + DF. The threshold behaviour of F 4 HD + HF(u’ = 3) has been obtained by varying the molecular reagent temperature from 77 K to 1300 K. For comparison, the average_totai energy, EL,, available to the products is shown in fig. 6a for this reaction, as well as the energy of HF(u’ = 31, The rate of F t HD -+ HF i&o u’ = 3 inc&ses siibsiantyly at low temperatures but then-.

D.S. Perry, JL

Pokanyi/lherp)

distribution

among reaction products. IX

(Etmr) (kc@mole-I)-

I.

.4

’

427

I

’

F+HD-HF(v’) z F+H,-+HFh”) 3 F+D2- DFW

10

I

l

’ A

-

T,“(K)--

(E’,,,) (kcai mole-934

,

IO _ A,

36 I

(b) ;+Da-f

I

38 I

-&“(KkI-

DF (“‘1

Fi_g.7. The average fraction of product ener,g appearing as vibration, Cj$, as a function of the oven temperature fl. levels out to a value, k(u’ = 3) = 0.2 1, which is much less than the value of k(u’ = 3) = 0.55 for the reaction

Fig. 6. Relative rates into the product vibrational levels are shown as a function of temperature. (a) The rates are normahsed to k(u’ = 2) = 1. The values of &lot, the total energy availabte to the products, appIy to the molecular reagent indicated. -sF + HD - HF(u’) + D this work-The energy of u’ = 3 is indicated on the fi and U?‘iot)scales by an arrow. -uF + Ha -+ HFto’) + H, this work. ---a--- F + Ha + HF(u’) + H, Coombe and Pimentel’s chemical kser results [8b] for u’ = 3 (upper curve) and u’ = 1 (lower curve). , (b) The rates are normal&d to k(u’ = 3) = 1. The values of Etot are those appropriate to F f Da. -AF + Da d DF(u’) + D, this work. ---A--- F +-Ds A DFtu’) + D, Coombe and Pimentel’s chemicaI laser results [8bl for Y’= 21

F + Hz + HF [for which k(u’ = 3) is independent of temperature]. In comparing k(u’ = 1) for these two reactions, it is seen that at room temperature this rate is nearly the same but at higher temperatures it is substantially greater for F + Hz + HF than for F + HD + HF. For all three reaction, WV>decreases monotonically with temperature (fig. 7). This is due both to the increase in the relative rate into the low vibrational levels (fig. 6) and to the increase in the average totai energy available to the products; i.e., decreases both absolutely and (still more) as a fraction of EL,. Using chemical laser methods, Coombe and Pirnentel [8b] have studied the temperature dependence of the vibrational distributions of F + Hz and F + D2. Their results, shown in fig. 6, are in poor agreement with the present work. It should be noted that the chemical laser work for F + D2 depended entirely on the “equal gain temperature” technique, which Coombe and F’iiental state involves higher uncertainty than the “zero gain” method used in mosf of their F + H2 work: The behaviour of F + Hz + HF($ = I) is the only case in which there is agreement (the agreement here is good). Coombe and Pimentel’s finding that the relative rate of F t D, * DF(u’ = 2) de&eases.with.temperature

428

0.S: Perry. J.C. Polar~yi/kizcrgy

distribution among reaction products. IX

-(fig: 6b) is anomalous in view of the behaiiour of F + Hz. It was suggested by these authors that the differing rotational occupancies of Hz and D, might be a factor. In the present study the behaviour of F + Hi and F + D2 is found to be simihu, implying that the differing rotational occupancies do not have a pronounced effect on k(u).

T

3.2.3. Ejyecb of enhanced reagent energy on prodrtct

zO

rotational-vibrationa!

IO

0 IO

IO

distributions

0; :

The experimental

product rotational-energy distributions for the 1315 K experiments are shown in figs. 3,8 and 9. For all three reactions,.higher rotational states are populated than at room temperature. The rotational enhancement is particularly pronounced for F + Dz. This can be seen clearly from fig. 9, even though the products of the F + D2 experiments were substantially rotationally relaxed. Together these experiments (3.2.2 and 3.2.3) indicate that an increase in reagent translation, AT, (and rotation, AR) gives rise to an increase in product translation, AT’, and rotation, AR’. This result is in accord with the generalisation proposed previously, AT 3 AT’ + AR’.

(4)

The generalisation was based on experimental and theoretical studies (trajectory computations on LEPS surfaces) of the reactions Cl + HI d HCl+ I (experiment,

F+HZ-,

HF(v;J’)+H v’=S

2

4

6

s--

8

IO

12

14

16

Fig. 8. R&tire rotational popuIations for the rtiction F +.H2 --LHI%‘, J’) + H. ii P = 279 K, ekpt. HHI. -# 1 f 1315-K. expt. HH3.

_

,Pb

1. ,r’

‘;.

v’=2

4 0 IO v’=l

~

4

8

12 16 .J’ +

20

24

28

Fig. 9. Relative rotational populations for the reaction 1; + D2 -+ IX%‘, J’) + D. 300 K, data of Polanyi and Woodall [S 1. 1315 K, expt. DD3.

[28] ; theory [41]), F + HCl j HF f Cl (experiment and theory, [6]), H + Cl2 --, HCl + Cl [6] and H + F2 -* HF + F (experiment [42] , theory [43] ), as well as in an earlier study of F + D2 * DF + D (61. In the present work the effect of reagent rotation cannot be disccunted [8cJ ; in the studies of Cl + HI, H + CI2 and H f F2, AT was achieved without AR since it was the atomic reagent that was heated. Wilkins [ 131 has used the classical trajectory technique on an LEPS surface to study the product energy distribution of the reaction F + Hz as a function of reagent temperature. His findings are in excellent agreement with the present experimental results: (a) the relative rate into u’ = 3 is independent of temperature, (b) the rate into u’ = 1 increases moderately with temperature, (c) there is an increase in rotational excitation with . temperature, (d) as temperature increases fV> decreases, @ increa.ses, and (&> increases slightly. Jaffe’ and Anderson [12] made a trajectory study of the reaction _Ft Hz. Ding et al. [6] made a study of F + D2. Both trajectory studies used LEPS surfaces, and examined the effect on product energy-distribu.

D.S. fcrr~. J.C Polan~~i/hzerg?.distribution among reaction products. IX

429

tion of a change in reagent temperature. Both yielded results in full accord with (d) above. Blais and Truhlar f 151 used a semi-empirical valence-bond surface to Cal&ate classical trajectories for the reaction F + D2. In contrast to the surfaces previously mentioned, this surface has a 4 kcal mole-’ well in the.approach channel. The calculations on this surface predict that the relative rates into both u’ = 2 and u’ = 4 increase with collision energy. The present findings (which incIude rotational as well as translational excitation of the reagents) show a similar behaviour of u’ = 2, but u’ = 4 is found to be approximately constant with temperature. The increase of IJ’= 4 with collision energy in Blais and Truhlar’s study could be associated with the well in the entrance channel (as noted above), since LEPS surfaces which lack such a well exhibit a net shift to lower vibrational excitation when the collision energy is enhanced. 3.24. Detailed endothermic +D-+F+HDarzdDF+H+F+HD

HF(v’. J’)+D+ F+HD ENDOTHERMIC

R’

(kcol mole?+

rates for the reactions HF

It has been shown [44,45] that detailed exothermic rate constants of the type summarised in fig. 5 can be used to obtain a good estimate of the corresponding detailed endothermic rates. These endothermic rate constants (fig. 10) refer to a given total reagent energy. E’tot, distributed variously among the vibrational, rotational and translational degrees of freedom of the reagents for the endothermic reaction. For both endothermic reactions, HF f D + F t HD and DF + H + F f HD, the rate of reaction depends dramatically on the distribution of I!& among the reagent degrees of freedom. The maximum rate occurs for the highest vibrational level consistent with the total energy. This is in accord with the proposition (for a review see [46,47]) that reagent vibration is the most effective form of motion in promoting “substantially endothermic” reactions. The meaning of the designation “substantially endothermic” is discussed in an appendix to the present paper. Because the vertical ridge on the triangle plot occurs at higher R’ in fig. IOa than in fig. lob, we conclude that rotation is relatively more effective in promoting the endothermic reaction HF + D (at a constant total energy) than it is in promoting the reaction DF + H. The ridge marks the optimal reagent rotational energy for reaction. Though it occurs at higher reagent rotational energy for HF + D than for DF + H, it corres-

R’ (kcol mole-’ )d

Fig. 10. ‘Triangle plots” (cf. fig. 5) for the endothermic reactions: -1 (a) HF(u:, J:) f D - 1: + HD, E;,t = 34.3 kcal mole_, @) DF(u , J ) + H-t 1: + HD, Eiot = 36.i kcal mole . Contours indicate the values of reagent vibrational (V’), rotational (R’) and translational (T’) energies (ignoring quantisation) which correspond to equal detailed endothermic rate constants. The total reagent energies are constant at Ei,t (=T’ + Y’ + I?‘). Broken &ago@ lines correspond to equalvalues of _ T’. The quantities k, shown for eachvibrational-quantum number, v’, represent the sum of the endothermic rates over the various rotational states of that vibraiional level. The normaliition is such that kr = 1 for the vibrational level most populated by the exothermic reaction.

ponds to similar reagent rotational quantum number numbers in the two cases.

.

.43u. :

D.S. I’erty. J.C. ?‘oknyifEnerg_vdistributionamong reactionprodrtcts.0’

AcknowIedgement bne of us (DSP) thanks the National Research Coun&l‘of Canada for a scholarship. JCP thanks the Canada Council for the award of a Killam Memorial Scholarship. The work described here was supported by a grant from the National Research Council of Canada.

of roughly comparable masses; it is excessively stringent for the mass-combination L + H H (Ls light, H i heavy), and could be insufficent for a mass combination H +H L (depending on the actual mass disparity between Hand L).

References [l] (a) C.F. Bender, P.K. Pearson, S.V. O’Neiland H.F.

Appendix It would be of value to have an approximate guide to the meaning of the designation “substantially endothermic”. For the case that the exchange reaction involves transfer of an H atom the BEBO method [Bond Energy Bond Order method: H.S. Johnston, Gas phase reaction rate theory (Ronald Press, New York, 1966)] permits a calculation of the minimum endothermicity required in order that the crest of the endothermic barrier lie along the coordinate of separation; i.e., have coordinates r-$3*> r**o, where rs*O is the extension at the barrier&t of tl?e bond be& broken relative to its equilibrium separation, and r$O is the corresponding quantity for the bond being formed. We have computed this minimum endothermicity for all combinations of a substantial range of BEBO parameters [p =0.8-i .OS, 4 = 0.8-l .05, (De)3 = 65-I 10 kcal mole-t, ~3~= 1.752.75 II-‘, A& = 0.70-0.80 A-l; the-endothermicity was varied from O-15 kcat mole-’ by holding the dissociation energy of the bond being formed constant, (II,_)2 = 90 kcal mole-‘, and varying (De)1 from 90105 kcal mole-l. The symbolism is that of Johnston, lot. cit.]. Using this substantial range of values for p and 4 (the most important of the variables), it was found that an endothermicity of2 IO kcal mole-* was sufficient to ensure that the barrier crest lay along the coordinate of separation on the unscaIed surface. We interpret “substantially endothermic” on the basis of this limited evidence as meaning 3 10 kcal mole-’ endothermic. In applyingthis inteipretatioh it should be borne in mind-for all marginal cases that the barrier location is more properly measured on the scaled surface, i.e., the mass cdmbination can be a significant element in determiningthe preferred dynamics [B.A. Hodgson and J.C. Polanyi,_J. Che?. Phys. 5.5 (1971) 47451. The 10 kcal rnoh? endothermicity criterion applies to the reaction

Schaefer HI, Science 176 (1972) 1412. (b) C.F. Bender, B.J. Garrison and H.F. Schaefer III, 1. Chem. Phys. 62 (1975) 1188. [2] J.C. Polanyi and J.L. Schreiher, Chem. Phys. Lett. 29 (1974) 319. [3] J.C. Polanyi and D.C. Tardy, J. Chem. Phys. 51 (1969) 5717. [4] N. Jonathan, C.M. Melliir-Smith and D.H. Slater, Mol. Phys. 20 (1971) 93. IS] J.C. Polanyi and K.B. Woodall, J. Chem. Phys. 57 (1972) 1574. 161 A.hI.G. Ding, L.J. Rirsch, D.S. Perry, J.C. Polanyi and J.L. Schreiber, Faraday Disc. Chem. Sot. 55 (1973) 252. [7] (a) T.P. Schafer, P.E. Siska, J.N. Parson, F.P. Tully, Y.C. . Wong and Y.T. Lee, J. Chem. Phys. 53 (1970) 3325. (b) Y .T. Lee, Physics of Electronic and Atomic Collisions 7 (1972) 359. [8] (a) J.H. Parker and G-C. Pimentel, J. Chem. Phys. 51 (1969) 91. (b) R.D. Coombe and C.C. Pimentel, J. Chem. Phys. 59 (1973) 251. (c) R.D. Coomhe and G.C. Pimentel, J. Chem. Phys. 59 (1973) 1535. [9] M.J. Berry, J. Chem. Phys. 59 (1973) 6229. [lo] (a) A. Persky, J. Chem. Phys. 59 (1973) 3612. (b) A. Persky, J. Chem. Phys. 59 (1973) 5578. (c) F.S. Kfein and A. Persky. J. Chem. Phys. 61 (1974) 2472. [ 1 l] (a) J-T. hluckerman, J. Chem. Phys. 54 (1971) 11.55. (b) J.T. hluckerman;J. Chem. Phys. 56 (1972) 2997. (c) J.T. hfuckerman, J. Chem. Phys. 57 (1972) 3388. [ 121 R.L. Jaffe and J.B. Anderson, J. Chem. Phys. 54 (1971) 2224. 1131 R.L. Wilkins, J. Chem. Phys. 57 (1972) 912. 1141 R.L. Jaffe, J.M. Henry and J.B. Anderson, J. Chem. Phys. 59 (1973) 1128. [15] N.C. Blais and D.G. Truhlar, J. Chem. Phys. 58 (1973) 1090.

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D.S. PUT. J.C. PolanvijEnergy distriburion among reaclion products.IX R.D. Levine and R.B. Bernstein, hlolecular rcaction dynamics (Oxford University Press, 1974) i. 209; Accts. Chem. Res. 7 (1974) 393. [18] F.A. Whitlock and J.T. Muckerman, J. Chem. Fhys. 61 (1974) 4618. 1191 S.F. Wu, B.R. Johnson and R.D. Levine, Mol. Phys. 25 (1973) 839. 120) (a) G.C. Shatz, J.M. Bowman and A. Kuppermann, J. Chem. Fhys. 58 (1973) 4023. (b) J.M. Bowman, G.C. Schatz and A. Kuppermann, Chem. Phys. Lett. 24 (1974) 378. [21] J.T. Adams, R.L. Smith and E.F. Hayes, J. Chem. Fhys. 61(1974) 2193. [22] hl.J. Redmon and R.E. Wyatt, to be published in Lnternational Journal of Quantum Chemistry, Symposium 9 (1975). [23] D.S. Ferry and J.C. Folanyi, Chem. Fhys., 12 (1976) 37. [24] R.D. Levine and R. Kosloff, Chem. Fhys. Lett. 28 (1974) 300; R.D. Levine and R.B. Bernstein, Chem. Fhys. iett. 29 (1974) 1. 1251 R.B. Bernstein and R.D. Levine, J. Chem. Fhys. 61 (1974) 4926. [26] K.G. Anlauf, P.J. Kuntz, D.H. Maylotte, F.D. Facey and J.C. Folanyi, Disc. Faraday Sot. 44 (1967) 183. [27] (a) H.L. Welsh, C. Gumming and E.J. Stansbury, J. Opt. Sot. Am. 41(1951) 712. (b) H.L. Welsh, E.J. Stansbury, J. Romanko and T. Fetdman, J. Opt. Sot. Am. 45 (1955) 338. [28] L.T. Cowley, D.S. Home and J.C. Folanyi, Chem. Phys. Lett. 12 (1971) 144. 129) A. Fookson, F. Pomenntz and E.H. Rich, J. Research N.B.S. 47 (1951) 31. 1301 D.S. Perry, Ph.D. Thesis, University of Toronto, Toronto, Canada (1975).

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