bromine-bromine energy transfer by binary collisions

Chenucal Physics 88 (1984) 261-270 North-Holland, Amsterdam

261

BROMINE-BROMINE ENERGY TRANSFER BY BINARY COLLISIONS

D.L. JOLLY, B.C. FREASIER, N.D. HAMER

Deparrmenr of Chenuslp. Far&v of Mdrran Sludres, Unruerslry of New Sourh Wales. Dunrroon, ACT -7600. Auwaha

and

Sture NORDHOLM

Department of Theorerrcal Chemtsrry, Unruersr~y of S_I dney, NS IV 2006. Aus~ulta

Recewed 30 December 1983. m final form 30 March 1984

The colhs~onel energy transfer between a highly exc~texi bromme molecule and a non-reactwe monatomlc (Ar or Br) or dlaronuc (Br,) medium has been mvestlgated by bmary WaJecrory calculations over a wade range of medium temperatures and mtemal energes of the reactant molecule The efficiency of the energy transfer IS compared wllh expectations based on simple statIstIcal apprortlmatlons used In ummolecular reaction rate theory Large devlattons are found, particularly with respect to the contnbutions made by different types of degrees of freedom and to the dependence on the internal energy of the reactam molecule Transfer to or from vIbratIonal degrees of freedom appears to be very mefflclenr TranslatIonal energy IS most readily transferred The rate coefhclent for energy transfer appears IO decrease with mcreasrng Internal energy In most cases

1. Introduction

Unimolecular reactIons are presently under- stood as a consequence of two more or less m- dependent mechanisms: a verbcal energy transfer process and a horizontal (elastic) decay. For the case of thermally activated reactIons in the gas phase, energy IS transferred to and from a reactant molecule by colhsions with medmm molecules. Thus, an understanding of colhslonal energy transfer is a cornerstone m the development of theones of unimolecular reactlons. The dtfftculty of the analysis of molecular collision events IS such that at present the colhslonal energy transfer theones rely heavily on statisbcal approximations [l-l I]_ The validity of a priori approxunations based on microscopic first principles may then be investl- gated by comparing theoretIcal predictions with expemnental observations, but tfus comparison raises many mterpretaiional dlfflculties. The observed deviations may be due to one or several of a wde range of possible causes. For this reason comparison of approximate theory unth exact or

numerical analysis of simple model systems has become essential in interpretmg errors, discovering new mechamsms and suggesting improved ap- proxlmations

The work reported here IS part of an ongoing program of mvestigatlon into the mechamsms of chemical reacclons by numerical simulation methods Earlier reports have been concerned with the collisional energy transfer and dlssociatlon of bromme (Br?) m argon over a wide range of medmm temperatures and densltles [12-241. In these simulations the essential point has been to Investigate many-body effects and, m particular, the degree to which the molecule-fluid Interaction can be represented as a series of independent bmary collisions. To facilitate this comparison we have developed a binary collision trajectory program and applied It to the Br,-Ar system [14,15]. While we have found signiftcant deviations be-

tween independent binary collision (IBC) and fluid-molecule energy transfer, it IS clear that for reasons of theoretical and numerical simphcity the development of improved theones of bmary colli-

0301-0104/84/$03.00 0 Elsevier Science Publishers B V. (North-Holland Physics Pubhshing Division)

262 D .I_ Jollr er al / Bronrme- hronrrne energr rransfer

ston energy transfer wtll contmue for some time to

have a pnonty. Thus. we are now extending our

IBC calculattons to a wrder range of systems and ~111 report below the results obtained for Br,-Br, colhstons wherein one of the bronune molecules has a well defmed and very htgh Internal energy

whtle the other bromtne molecule and the relative

motion IS In canomcal equthbnum at temperatures 7 = 106. 160. 300 and 1500 K. The Internal energy of the energtzed molecule IS vat-ted over a range of vJt.res centrcd on the drssocratron energy at 45 9

kcal/mol The atm here IS to ftnd out how the energy

transfer efftctency depends upon the temperature

of the medtum and the mtemal energy of the reactant In parttcular. we wash to know how the

observed energy transfer for a dlatomlc medwm molecule compares \vlth that for a monatomtc

medium molecule and wtth the trends and magm-

tudes predtcted by simple stattsttcal theory The

dtatonuc medtum molecule can absorb the energy transferred In the colhslon mto translational. rota- tlonal. or wbratlonal motion; and the brdnchmg ratios descnblng the energy sharlnp among the different degrees of freedom w11l be examtned

One of the problems of the usual type of IBC

energy transfer theory IS the need to esttmdte not only the energy transferred per colltston but also the cross sectton for the colltstons transferring Internal energy. Stnce both the cross sectton and

the energy transfer per collusion affect the rate

constant conststent defunttons of these quanttttes are Important In order to tllustrate thus fact. we

report the observed dependence of the energy

change. (.IE). on the Impact parameter of the collision. b

Dlntomlc dlssoaatlon or recomblnntlon rates

are of great tmportance parttcularly tn the area of

atmosphenc chemistry. The body of expertmental

data avatlable has been revtewed recently by Boyd and Bums [16] The theorettcal work has been concentrated on the case of halogen molecules m Inert gases and the bromine dtssoctation/

recombmatton has been studied particularly by

Burns and co-workers [16-211 and by Razner [22]

apart from ourselves [12-151. Our work differs

considerably from that of Burns et al smce thetr

atm is to obtam dtssoctatton or recombinatton rate

coeffictents dtrectly wlule we are mvesttgatmg the

energy transfer mechantsm tn order to provtde the basts for Improved master equations The dtatorruc

reactions are Interesting tn then own tight but also form the natural point of departure m the attempt

to Improve our understandmg of the reacttons of

larger molecules u-t a wrder range of medta. Although the present work IS directly related to

the partrcular problem of acttvatron-deactivation of the thermal unimolecular reaction. there is also wtde Interest tn energy transfer m btmolecular colltstons anstng from work on gas dynamtcs.

molecular beam expenments. and various forms of

spectroscopy. Several mvesttgattons of rotational

[23.24] and vtbrattonal [25-273 energy transfer of

dtatomtc molecules based on stmtlar traJectory calculattons but mottvated by such altemattve m- trrests have appeared tn the recent hterature. Un-

fortunately. the results and interpretattons are not

eastly related to those we shall present below for several reasons The first and foremost ts that the energy ranges rare dtfferent We work at very hrgh

energtes. at or above the dtssoctatton energy in most cases. whtle tnvesttgattons not mottvated by

untmolecular reactton theory work at compara- tt*/ely low excitatton energres Tlus can be expected

to mean that the energy transfer mechamsms are substantially different. At low energtes properly formulated perturbatron theories can be expected

to explam much of the behavtour. For energtes

near the dtssoctatton energy. on the other hand. hard collwons transfemng many quanta of energy

can be expected to dommate, and there IS little

hope for the successful apphcatton of perturbatton

theory. The low-energy calculattons are usually qunntlzed by some sermclasslcal method and the

results reported m the form of state-to-state cross sections Even tf they were avatlable at hrgh en-

ergies. the format of these results make them dtf- ftcult to compare wtth nucrocanonical energy re- laxatton ttmes obtamed in our work. Nevertheless. there must be an mterestmg relationshrp between

the two types of data when obtatned for the same

or for simrlar coiliston partners. We hope that tt WIII be revealed in future work.

2. Method

D L Jolly et al / Bromme- bromrne energy transfer

We have simulated the transfer of energy by a highly energized brornme (target) molecule to a

263

thermalized particle (proJectde) by a binary Inter- action. Three different proJectiIes WIN be consld- ered here: an argon atom, a bromine atom (treated as an inert gas atom without the possibility of chemical bond formation) and a bromine molecule (again treated wthout regard for the possibility of mtermolecular bond formation and exchange)_ We have modeled all of the molecular interactlons by superimposing atom-atom pair potentials origl- nally used by Keck [28]. The argon-argon, argon-bromme and bromine-bromine atomic pair potentials are represented by Lennard-Jones potential functions of the form:

Vu(‘)=4E[(C7/r)12-(a/r)6],

with potential parameter values

l Ar_Ar/kB = 120 K, c8r_Ar/kB = 143 K.

EBr-&kB = 170 K,

nAr_Ar - 3.42 A, u~~_,\~ = 3.51 A,

us,_ Br = 3.6 A.

(1)

where k, IS Boltzmann’s constant. The brornme-

bromine bond potentml is of the Morse forrn-

V Br-Br(4 = 4{e+P(r - 4 - l}2.

with

(2)

Q/k, = 2 31 x lo4 K,

p= 1_94A-‘, r,=2 28 A.

The relevant atomic masses are Bven by mA, =

39.994 au and mg, = 79.916 au. We are interested in sunulatmg the deactivation

of model molecular bromine. To do this we examine binary events where the internal energy of the target bromine molecule IS of the order of its minimum dissociation energy. We have previously described the techniques used to follow these binary collisions 1141. We will briefly recapitulate the essential features of the calculational methods and theories of these sunulahons.

The states generated by the traJectory calcula-

tions are referred to as dissociated [13] if the bromine bond length is greater than the effective potential barrier distance, rm, defined by

[av,,,(r)/arl T-Tm = 0,

[a%(+a’r] T_T m < 0. (3)

where the effective potential comprises the bond potential plus the angular momentum centnfugal term defined by

KC/,,,(r) = V&Br(T) + i’/2FZ, (4)

where 1 is the angular momentum, p = mBr/2 and mgr IS the bromine atomic mass. It must be noted that I-,,, goes to Infinity as E approaches 0, from above. ConfIgurations are considered bound If the bond length IS less than r,,, and E, < &(r,,).

Two Important constramts are imposed on the sampling of Initial conflguratlons. The target bromine-projectde particle separation is fixed and large enough that any Interaction at 011s separation is of negligible magnitude (~IJ~~_~~ in the present calculations) and secondly, the bromine configuration IS rejected uniess it IS bound accordmg to the defuutlons above. The latter condition relates pnmarily to the bond length but also the the angular momentum. The IBC calculations have been camed out at several fixed initial energies E, of the target bromine. In each case the bond length IS then selected accordmg to the probabrllty density.

g(E,r)=r’[E- V(r)j1’2

X V(r)]“‘dr -‘, 1 (5) where r,(E) and rz( E) are the two distmct solu- tions of

V(r) + Eam’“( E)r,Z/r’= E. (6)

(Note that rz(E) IS a double root.) The quantity Earn”(E)) is the nunimum value of the scaled squared angular momentum, E,, defined by

E, = 1’/2~& (7)

such that the configurations will be bound, I.L unable to surmount the barrier UI Verr_ Nctc hat

26-l D L Jo/l) er OL / Bromme- tromrne energv lratufer

Em’” IS non-zero only when E > 0,. When Earn’, IS

n&-zero the cosine of the angle between the mter-

nal momentum vector p and the bond vector r IS chosen uniformly in the range

fc?E;ln ( E) ‘,’ ’

I - f’[ E- l’(r)] 1 -

This ensures that E, > ET”” In the sampled mole-

cule. Finally the azimuthal angle of p about r IS

chosen randomly and the length of p scaled to give

the total internal energy E The translational mo-

tions of the proJectlIe particle and target bromine

molecule are selected from the thermal dlstnbu-

tlon using standard Monte Carlo procedures to sample from the appropnately scaled gausslan dls- tributlon The velocity of the centre of mass of the proJectlIe plus the target system IS calculated and

subtracted from the velocities of the individual atoms so that the collision IS vIewed in the centre of mass frame. This means that all knetlc energy

refers to motion relative to the centre of mass

We sample impact parameters In the range 0 <

b G b,,. We are pnmanly tnterested In properties

related to the average loss of InternA energy of the

target molecule per collrsion. (A E). m hlch can be ~ntten as an integral over Impact parameter 6.

(9)

The Importance of ,.I gl\en b value in the dz- termmatlon of (A E) IS proportlonnl to the mdgnl-

tude of the Integrand Thus we have. to optmxe our accuracy. sampled the b values m accord with a probablhty density P(b) \\hIch IS a simple ap- provlmatlon of the expected functIonal form of

this mtegrand. Thus we have used

P(b) = Cb eup( - TIJ”b’/cu). 00)

where C IS the normahvng constant, and cx is an emplncally chosen constant. For an ensemble of N

traJectones the impact parameters were therefore chosen to be the inverse of the cumulative proba-

bility distribution function, j,bP(s)ds:

b,= { -(n/T”‘)ln[l -Q(t-+)/N]}‘r-

r=l ,.. . N. 01)

where

Q = 1 - exp( - T1flb,f,;,,/a) (12)

Each trajectory is then weighted by l/P(b) to obtam the averages over b This type of procedure IS referred to as importance sampling and is dts-

cussed generally by Hammersley and Handscomb

[29] and m more detail m a prewous paper [14] The exphclt deternunatlon of the 6, reduces the vanance of 6. thereby decreasing statIstIcal uncer- tainty.

The tr;?lectory dynamics algorithm for sohmg

Newton’s equations of motion has been prevtously described [12] and IS based upon a predlctor-cor- rector method developed by Gear [30] for solving higher-order dlfferentlal equations The procedure

ubes d vanable time-step for maxImum efflclency II-I solvmg the dIfferentlal equations As In our

earlier work lengths WIII be given m units of

Ok- -\r = 3.42 A and energies In units of E<,~_,,~ =

0 2385 hcal/mol

3. Results

In this sectIon we WIII present the results whtch

bear most directly on the energy transfer mecha- nism of these IBC traJectones Tables l-3 contain InformatIon about the average loss per colhsion of Internal energy of the target Br, molecule. As m prevrous papers In this series, we ~111 defme the

Internal energy change, (AE), as E, - E,, where E, and E, are the lmtlal and fInal internal energes of the target bromine molecule, respectively

(A E), is tabulated as a function of impact param-

eter, b. to measure the range of the energy trans-

fernng mteractton. For all temperatures, most slg- niflcant internal energy changes have occurred for

b < 3oq,_ 4r. As expected, the range of sigruflcant

mteractton IS temperature dependent wtth larger b

values becoming more slgmflcant with decreasing

temperatures At all temperatures, the most effi- cient transfer seems to take place for b m the

D L loll) et aI / Brommr- bromrne energ, transfer 265

The change m the Internal energy of the bromme reactant as a function of b for various proJectlIe molecules when kaT/~~,_~~ = 1 33 and E, = ISOr,,_ +_

Table 1 Table 3 The change in the Internal energy of the bromme reacxaru as a function of b for various proJectlIe molecules when A eT,/cAr_ Ar = 12 5 and E, = 18Oc,,_,,

b range (A&)

Ar - Br, Br .+ Br, Br, -, Br,

000-025 10 5 15 3 15 8 0 25-O 50 11 8 15 8 18 2 0 50-O 75 108 144 15 3 0 75-l 00 100 13 2 14 3 loo-125 78 117 14 8 125-l so 52 97 133 I 50-l 75 24 76 120 I 75-2 00 11 42 94 2 00-2 25 05 31 76 2 25-2 50 01 1.7 38 2 50-2 75 01 04 19 2 75-3 00 00 00 08 3 00-3 25 02 0 00-3 25 2.1 41 64

nelghborhood of u,,_ Ar The strength of the mternal energy transfer for Br, collidmg wth Br, IS generally greater than for a monatomlc species colhdmg with Br,. The bromme atomic proJectlIe IS more effuzlent at energy transfer than the atomic argon proJectlIe. This trend IS more pronounced at lower temperatures. The energy rate constant &, IS

Table 2 The change III the rntcmal energy of the bromme reactant as a function of h for various proJectlIe molecules when I, ~T/E,,,_~~ = 2 5 when E, = 180~,,~_,,~

b range (AE)

Ar 4 Br, Br 4 Br, Br, c-) Br2

0 00-o 25 124 179 15 9 0 25-o 50 146 164 15 3 0 so-o 75 12 3 15 0 159 0 75-100 110 152 175 100-125 73 124 146 125-l 50 44 82 126 150-l 75 15 38 58 175-200 05 25 39 2 Ml-2 25 00 07 21 2 25-2 50 00 1.5 06 2 50-2 75 00 00 07 2 75-3 00 00 00 01 000-300 24 41 61

b range

0 00-O 25 0 25-O 50 0 50-O 75 0 75-l 00 100-125 1 25-15@ 1 50-l 75 1 75-2 00 ZOO-225 0 00-2 25

<ar>

Ar d Br,

16 3 164 146 106 63 21 0.2 01 00 42

Br e Brz Br, + Br,

179 23 8 16 1 185 15 1 177 120 17 4 84 15 1 41 102 09 42 00 18 00 05 50 77

defmed as

I%, = cj(AE)/( E, - 2k,T), (13)

where ti IS the hard sphere colhslon frequency

ij = (SlTk,T/jI)‘%~,,. (14)

r; being equal to the proJectde-bromine reduced mass

ji = 2nl,nlBr/(I~lp + 2n1,,), 05)

where nlP Is the total mass of the proJectlIe_ We have tabulated k, for a number of mitral energies, E,, and a number of medium temperatures for the Ar, Br, and Brl proJectlIes in tables 4-6 respec- tlvely. There are a few general trends worthy of comment The rate of Internal energy transfer generally mcreases with Increasing temperature and generally increases with decreasmg mltial Internal energy. (Although this IS not categoncally true for

k J/E/C 4r = 12.5.) The energy transfer rate IS usually greater for the Br, proJectlIe than for the atormc proJectrIe, although agam this is not true at the highest temperature tabulated.

In the case of the molecular proJectlIe It IS also of Interest to know Into which modes of molecular motion the energy L.s being transferred by a colhsion. To examine the detaJs of this energy disposal we have tabulated a number of branching ratios. In table 7 we examine the quantity (AE),, /(AE) summed over all b as a function

266 D L Jot!, er al / Bromtne - bronrrne energy mmsfer

Table 4

&, as a functton of E, and T for Ar 4 Br2 The results utth mtemal cnerges marked utth a t m&de tralectones which have

produced dtssoctattons To convert iE from reduced to SI urn::: (m3 s-‘) multrply by 1 847x IO-”

40 80 120 180 200 200; 220 2207 250 25Oi 280 28Oi

0 74 09 07 OS 08 06 06 04 03 03 02

0 85 09 07 08 08 07 07 04 03 03 02

1 33 11 08 08 09 OS 09 05 05 04 03

2 50 26 IS 15 11 I I 13 12 12 09 08 07 06

12 50 66 48 40 52 60 70 65 70 64 70

Table 5

X a as a functton of C and T for Br - Br, The results \rtth mtemal enrrgtes marked utth A i Include trqectones shtch have produced drssoctattons To comert it from reduced to SI umts (m’ s-t) multtply by I 847x lO-‘7

40 80 120 180 200 NOT 220 2207 250 2507 280 2807

0 88 17 1 I I2 14 I I I I 07 07 06 05

1 33 17 I2 I 1 I2 12 13 09 08 07 06

2 50 IS 14 14 16 I4 I5 II I 1 09 09

I2 50 63 45 39 53 55 65 62 72 57 68

Table 6

iF AS a functton of E, and T for Br, - Br2 The results \rrth mtsmal energws marhed tbrth a i Include tralectones ahrch have

produced drssocrattons To convert i E from reduced to SI umts (m’s_‘) multtply by 1 847~ IO-”

~uT.r+r-A~ E,

40 80 120 180 200 2OOi 220 22Oi 250 250t 280 280~

0 88 31 23 22 25 21 21 I4 11 12 06

1 33 35 23 22 25 23 24 16 12 I4 07

2 50 76 53 40 2s 27 30 29 30 21 17 17 11 II 50 72 51 40 55 59 66 58 61 56 54

Table 7

The branchrng ratto, (A E}, ,/(A E) summed over ali b for Br: 4 Brl The results \rttb mtcmal emerges marked wrth d i mclude

tra,ectones H htch have produced dtssoctattons

40 80 120 180 200 2mT 220 220-i 250 250~ 280 280t

0 88 06 06 06 06 06 06 07 06 0.7 06

I 33 06 06 06 06 07 07 07 06 07 06

2 50 06 06 06 06 07 07 07 07 07 07 0’ 06

1250 07 07 07 07 07 07 07 07 0.7 07

D L Jolly et al / Browme- brotnrne energy transfer 267

Table 8 The branching ratlo. (A E,&,,/( A E) bummed over all b for Br, - Brz. The results with mtemal energxs marked with a i mclude trayxtones uhxh have produced dissociations

‘WC,,- Ar E,

40 80 120 180 200 2007 220 220T 250 25% 280 280;

088 04 04 04 04 0.3 03 03 04 03 04 1 33 04 04 03 03 03 03 03 03 03 03 2 50 04 04 03 03 03 03 03 03 03 03 03 03

1250 03 03 03 03 03 03 03 03 03 03

of temperature and imttal internal energy. (AE), “, IS the change m the sum of the centre of mass kinetic energtes of the proJecttIe and target par- ticles This branchmg ratto vaned from 0.6 to 0.7 with larger values at hrgher temperatures and m- ternal energies. Thts indicates that most of the energy drsposal was through the kmettc energy of the translatronal matron.

We can also look at the change m the rotational energy of the proJecttie parttcle by exammmg the branchmg ratto, (A E,),,,,,/(A E), where (A E,,)

IS the change m the scaled squared angular momentum.

EA = 1’/2pre’. (16)

For the small mternai energies (relattve to the target molecule) which the proJecttIe attams from the uuttal thermalizatton procedures this quantity ( EA) IS numerically equivalent (wtthm 1%) to the quantrty we would ordrnarrly associate with the average rotattonal energy, E,,,. of the projectile molecule

E,,,, = (1’/2pr’), . 07)

The subscript E indrcates a mrcrocanomcal aver-

age at internal energy E. In table 8 we fmd that thrs branchmg ratio vanes from 0.3 to 0.4 It decreases for mcreasmg Internal energy and temperature.

We fmally calculate a vrbrattonal energy branching ratto = ((AE),,,, - (AE,),,O,)/(AE). where (A E),,, is the increase m the internal energy of the proJectile. Except at the very highest temperature thts branchmg ratto decreases as a functton of temperature for a flxed internal energy for the target molecule. We fmd m table 9 that thus branching ratto IS comparattvely small bemg typically = 0.03. The vrbratronal branching raho m- creases as the temperature and/or internal energy mcreases. The three branchmg ratros must sum to umty by energy concervatton. In vrew of the fact that the rotational energy 1s not constant and EA does not coincide with E,,, except m the low energy limtt we must a!low for the possibthty of some maccuracy in the deternunauon of the vrbratronal energy branchmg ratto. However, It is cer- tautly small by comparison wtth the translattonal and rotattonal branching ratios. In tables 7-9 we have displayed the three branchmg rattos wtth and without tralectories which terminate with drssocta-

Table 9 The branchmg ratlo ((A E),,, - (A EA&,)/( AE). summed over all h for Br? - Br2 The results HII~ mremal ensrgws marhed wth a T mclude Iryectones which have produced dlssoclatlons

AT/~A,-A, E, 40 80 120 180 200 2OOt 220 22Or 250 25OT 280 28Ot-

0 88 004 004 004 004 003 003 003 004 003 004 1 33 004 004 003 003 003 003 003 003 003 003 2 50 004 004 003 003 003 003 003 003 003 002 003 003

12 50 003 003 003 003 003 003 003 003 002 003

3-68 D L_ Jol!r er al / Bromne- bronrrne energ transfer

tron. The branchtng ratros do not seem to depend strongly on the drssociative character of the trajec- tortes.

3. Discussion and conclusion

Before drscusstng the contents of the tables. It

may be useful to recall bnefly what was knovvn prtor to thus vvorh. We know that statistical theories of energy tr,msfer such as the ergodrc colhston theory [7.10] based on the assumptton of mtcro- c,momcJ rektxatron tn each “kinetrc theory-’ type

of colhs~on overesttmate the energy transfer rate by typically half an ordsr of magnttude and for small systems such xs Br,-Ar by an order of magnitude [31]. There IS evtdence from our stmula- ttonb that rl large part of the devtatton ts due to the overestrmdtton of the colhston frequency. I e. ;1 small subset of relattvely strong colhstons transfer most of the energy tf we use the st~nd.trd detun- tions of colhsron cross srctrons from theorrrs 01

trxtslattomtl reld\atton [;I] The problem IS th,tt

the st,rttsttcA theones such ,rs the ECT (or the prior dtstrrbutron In the rnformatron theoretuxl approach of Levine xtd co-worhcrs [32]) clre prt- martly theorrcs of final stcltr br,mchtng ratios xrd not total cross sectrons Hovvevrr. compxrson wtth ekprrtment or stmul&on often involves both branching rJtros and total cross secttons The crude estrmatrs of the latter often used rn crude statrstt-

CJI theory may then be J stgntfrcdnt cause of dcvtdtton between theory and obscrvatton There

dre JISO theoretad rrclsons to beheve that. due to short collwon duratton. potenttal energy IS less .rvJil.ible for transfer thJn Linetic energy [ 1 I] Thts

would lewd to the predtctton th,rt vtbr,rtton,tl energy trdn\ters less efftctentlv th.tn rotJtronJl en-

ergy as has indeed been observed 111 JII our strnuhr-

trons on the Br,-Ar system [I?-151 Other m&ha- ntsms yet to be rdenttfrrd m.ty. ot course. also

contrtbute to thts observatton. Tables 1-j show a number of notevkorthy feet-

turcs On the barn of the ECT theory [7.10.31] we

would expect (AL> to rrw by a factor of = 1.5 JS

\ve change the medrum molecule from Ar to Br,. This IS m rough xcord with \v*hJt IS observed In

our CAxtlrtttons. However. the results for the

Br2-Br system show that part of thus rise is due to the mass of the medium molecule and the strength of tts interaction with the reactant molecule. Com- panng the Br,-Br and Br2-Br-, (AE), values, the nse is perhaps by a factor of 1.2 but not the factor 1.5 of the ECT theory for small Impact parameters. The average (AE), for larger b reflects the

dtfferent ranges of the tnteractton. The (AE) value

for the full range of b reflects both energy transfer

efftctency at small b and the range of tnteractton The average energy transferred per colhston increases slightly wtth mcreastng temperature for small Impact parameters but decreases for large

Impact parameters Thus the range of the tnterac-

tton decreases wtth rncreasmg T. The muural ex- planatron for thts IS that at low T the attracttvr part of the reactant-medtum molecule tnteractron

IS ,tble to pull m trqsctortes of relclttvelp large b to mabe more effrctent contact between the two

molecules As the reMwe translattonal veloctty

Increases the effect of the attractwe part of the molecule dtmtntshes If we let & be the effective

rddtus of tnterxtion. e g. chosen so that energy

tr,.rnsfer due to traJectones wtth b > b IS sm,.tll ( = 5% or less). then vve have

& = 2 l(T= 160 K). 19(300 K). 1.5(1500 K)

for Br,-Ar.

i? = 2 6(160 K). 24300 K). 1.7(1500 K).

for Brl-Br. And

b = 3 0( 160 K). 2 6(300 K). 2_3( 1500 K).

for Brl-Br, The rxtge of the tnterxtton drops by almost J factor of two ,.rs we go from T = 160 K to T= 1500 K.

The rate constclnt of energy transfer

mg to IBC theory (at ION denstty)

AF = j\&_

IS accord-

(IS)

where i, IS thz rate constant for energy transfer dt umt denstty of medunn molecules (II,, = 1) as

defined 111 eq (13) Tables 4-6 show that II,

Increases wrth T. but thts tncreclse IS usually due to the T’d” dependence of the colltston frequency [see

eq (14)) The rate constant decreases with rncreas-

D L Joltj et al / Bronrme- bromme energy transfer 269

mg mternal energy E of the reactant molecule. This trend IS clearer at low T than at 1500 K

where it might be more accurate to say that kE dtsplays only “noise-like” dependence on the In-

ternal energy. Note that according to statisttcal thcones such as ECT theory [7,10]. krE should be

approximately independent of E. It may seem countermtutttve that the ii, should decrease wtth IncreasIng E. but the expenmental evtdence con-

csmmg the energy dependence of &, seems to be unclear [33.34]. and our current understandmg of non-statistical energy transfer 1s meager.

Fmally. tables 7-9 show the branchmg rattos

for the deposttton of the transferred energy Into the three types of degrees of freedom of the medium bromine molecules In the Br2-Br, calculations. The most Important point IS tmmedtately apparent_ the vtbrattonal mode receives only 3% of

the energy while translattonal and rotational modes

receive about two thuds and one thtrd of the total. respectively These branchmg ratios are not very sensitive to either temperature or internal reactant energy. The translatronal branching ratro IS slrghtly

larger at high T and E A mrcrocanomcal relaxa-

tion assumption as used In the ECT theory [7.10] would lead to branching rattos of approxtmately 3/7. 2/7 and 2/7 for the translattonal. rotattonal and vibrational energy. respectwely. The IECT

theory In wluch the potenttal energy IS conserved due to the short colhsron hfetrme [ll] would yteld correspondrng branching ratros of approvtmately

l/2. l/3, and l/6. The IECT predtcttons tahe us

tn the right dtrectton but do not go far enough The vrbrattonal energy IS a smaller and the transla-

ttonal energy a larger fraction of the total The energy transferred to the rotattonal portton of the proJectlIe may seem large by normal expectattons

(cf refs [23-27,351) but we note that the bmding

energy of the target Br, IS htgh The rotattonal

energy IS of the order of 20 kcal/mole and only d small fractton of this (= 10%) IS transferred Into proJecttIe rotation (from all sources) per collusion.

It is clear that the classtcal model of Br?--Br,

colhstonal energy transfer contmued to display the kmd of strong deviattons from microcanomcal relaxation assumptions found m the Br,-Ar slmu- lattons and suspected to be a wtdespread phenom- enon. The present models are. of course, not m

detarled agreement wtth the cxpenmental systems they represent, but they are the kind of stmphfred models that chemists would hke to be able to use

We take the vtew that one should gtve priortty to a

search for stmple and general mechanisms which would be unhkely to depend very strongly on the detatls of the potenttal energy surface. Neverthe- less, we must acknowledge the posstbthty of great senstttvtty to features of the mtra- and mtermolecular potentials. Work IS underway to ex-

amine this possrbihty m the present class of models The question of the consequences of short range forces associated wtth chemtcal bondmg and

reactive rearrangement processes is of parttcular

interest Meanwhile. we have some dramatic illus- trations of non-stattsttcal energy m simpler models to reflect upon The challenge of the future IS to

fmd simple descnpttons for the mechantsms

responstble. The present numencal data confirm and ampltfy several plausible charactertstlcs of the energy transfer. They should be of some atd m the development of new theory and could. of course. also be used as “emprrtcal” Input into para-

metertzed representattons of colhstonal energy transfer

Acknowledgement

We thank ProFessor R J Bearman and The Australian Research Grants Scheme for support of this work. We would also lthe to thank the referee for 111s helpful comments on the rrutlal manuscrtpt

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bromine-bromine energy transfer by binary collisions

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