Hermaphroditism in chemical dynamics: the reaction Ba + Cl2 → BaCl + Cl

Volume 18, number

3

CHEIIICAL PHYSICS LETTERS

1 February

1973

HERMAPHRODITISM LN CHEMICAL DYNAMICS: THE REACTION Ba + Cl, + BaCl + .Cl Michael MENZINGER and David J. WREN 0zemistry Depnrtment, birirersity of’ Toronto, Toronto, Ontario, Canada Recehcd

1 November

1972

The reaction Ba + CIa -+ BaCl f Cl proceeds through different clcctronic channels with diame!ricaBy opposite collision dynamics: ground state BaCl(X’I) is formed via a direct interaction as witnessed by fonvard scattering and a strongly inverted internal state distribution. Electronically excited BaCI*(C211) is formed via a long-lived collision complex, indicated by a statistical vibrational distribution. A simple RRK argument explains the differences of lifetimes towards unimolecular decomposition of the collision complexes. A lower limit of the BaC1(XZx3 dissociation energy is placed at 121 kcal/mole.

Most chemical reactions, whose collision dynamics have been studied in the past decade, are moderately exothermic or thermoneutral processes which proceed adiabatically on a single (that is the ground state) potential energy surface [ 11, As the available energy is raised (either by raising the reactant energy or by chasing a highly exotherrnic reaction) additional channels begin to open up with the formation of electronically excited products. The collision dynamics in the various channels depends of source on the shape of the respec&ive potential energy surface(s) and on the energy available. WC wish to report here a case where in a single chemical system - the reaction between Ba atoms and Cl1 molecules - the reaction follows diametrically different dynamical pathways in two electronic channels. The accepted classification of collision dynamics today [l] takes the lifetime of the collision-complex as the main criterion. (a) A reaction is called “direct”, when the complex breaks up within the time it would take the reactants to pass each other without interaction, or within a rotational period of the complex. Center of mass angular distributions show a marked forward-backward asymmetry with respect to the relative velocity

(b) The other extreme is formation of a long-lived collision complex. This means long compared with the characteristic intramolecular (vibrational and rotation,al) relaxation time. The symptom is an anguIar distribution that extlibits forward-backward symmetry in the center of mass, and a statistically equilibrated product state distribution. Intermediate cases between these extremes are afso known [I]. The reaction between barium and ctdorine exemplifies both extremes simultaneously: Ba + Cl2 + BaCI(X2x) Ba + Cl? + (BaCI,)*

f Cl,

(1)

-+ B~Cl*(C2JI) f Cl.

(2)

ilV

generally highly inverted (the starting point for

Jonah and Zare [2] were the first to investigate the chemiluminescence from this reaction, and to identify the electronically distinct channels (1) and (2). In addition, they made the challenging suggestion that radiative two body recombination was an important process in this system. To test tfris hypothesis we have constructed the flow apparatus described below, and the results bearing on the two body recombination process will be published elsewhere [3]_ The flow system consists of a 1” diameter quartz tube inside a cylindrical oven. On the upstream end the tube carries a quartz window and

chemical

a port

vector,

and product~internal

lasers).

state

distributions

are

for admitting

reactant

gases, and the downstream

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‘, ,~oIume 18; number 3

0

CHEMICAL PHYSICS LE-I-I-ERS

2

4

Q-branch 6 8 10

I

14

I R: 0’

LIL

I?

2

4

branch 6

8

15

I

IO_

A

Fig. 1. Tracing of the 5 140 A band of the BaCi(X’C+- &I,,,) Av = 0 transition. Thz assignments are taken from Parker [4]. Ai discussed in the text, the band intensities XC proportional to population numbers. Tie exponential failoff of the vibrational population indicates qualitatively the existence of a statist&l vibrational distribution and positive vibrationnl temperature.

end holds a capacitance manometer stopcock connected to a diffusion

and a large Teflon pump. The pressure

in the reaction tube can be varied by adding buffer gas and/or by throttling the Teflon valve, but all experiments reported here were performed without buffer .gas at pressures below p < 3 mtorr. The oven temperature is monitored by an iron-constantan thermocouple. A pea size lump of barium metal is placed in .the center of the oven, whicfr is then heated to 1’000 f lC!‘K. As the metal evaporates it.reacts with the chlorine admitted at the upstream port through a stainless-steei needle valve and a brigftlt emerald green f&me develops in the center of the oven. The spectrum is recorded with a Spex 3/4 m Czerny-Turner.monochromatdr iri conjunction with a cooled EMI 6256s photon&plier and a strip-chart recorder. .. 432 ‘..‘. ._ ; .’ ,: -I -.. ‘.~ “

1 February

1973

This arrangement seems to give intenser emission than the molecular beam experiment [2]. Spectral resolution could therefore be increased to 0.2 A. We see additional structure, that is superimposed on the continuous spectrum reported by Jonah and Zare. Details will be published elsewhere [3]. Here w’e concentrate only on the X2x’ + C2 !Iai2 band of BaCl at 5140 A, a tracing of which is shown in fig. 1. The advantage of analyzing this band, rather than the band originating from the lower ‘I11i2 state of the spirr-orbit doublet, lies in the fact that the shape of the potential energy curves does not change much during this transition. This strongly favors the Av = 0 over the AV f 0 transitions. This makes the interpretation straightforward, since now the vibrational population is closely proportional to the emission intensity of a band. The only complication stems frotn the overlap of the Q and R branches. Fig. 1 contains the band assignments due to Parker [4], ;adicating that the P-Q overlap occurs from the Q(3-3) band onwards. This marks also the point at which the intensity distribution be&ins to deviate from a purely statistical exponential she (see fig. 2). For the present purposes (a) we neglect this interference from the R branch, and jb) we assume the peak height to be proportional to the integrated band intensity. Fig. 2 is a Boltunarm-plot for the determination of the vibrational temperature. An almost statistical distribution is evident, although a single vibrational temperature is not sufficient to represent the data. Indeed, energy and angular momentum restrictions preclude a pure Boltzmann-distribution, as has been shown by phase space calculations [S], but the monotonically decreasing distribution strongly suggests a vibrational!y equilibrated, long-lived collision complex. Bernstein et al. [6] at Wisconsin and Her-m [7] at Berkeley have measured the angular distributions, and Hershbach et al. [8] at Harvard have determined the velocity vector distribution of BaCl by crossed molecular beam techniques involving mass spectrometric detection. Their relevant results are briefly: (1) the BaCl product is predominantly scattered forward ir the center of mass and (2) a high fraction of the exothermicity is found as internal product excitation (i.e., the internal energy distribution is strongly inverted). The apparent contradiction with the chemiluminescence results becomes plausible in the light of the _ :. ..

‘,.

Volume 18, number 3

t Februxy

CHEhIICAL PHYSICS LETTERS

1973

Fig. 2. Boltzmann plot of Ule vibrational population. Esscnti;llly sratistical vibration distribution is characterized by vibrational temperatures TJO-2) = 2120 i 60’K for 1’= O-2, T,(S-i i) = 1400 5 100°K for 1’= 3-l 1 and T,(il-17) = 800 I ISO’K for u= 11-16.

finding i2] that probably more than 90% of the total reaction give: ground-state products and only the remaining small fraction reacts on the upper surface. This means that the molecular beam experiments see primarily the forward scattered ground-state products, which are formed via a direct mechanisin. We have here the striking case ot‘a reaction which is direct on the ground-state surface (complex lifetime 7 < 4 X 1O-t3 set), and involves a long-Iived complex (7 9 4 X IO-l3 set) on the excited-state surface. It is this difference in comples lifetimes that we are trying to understand. Wolfgang [9] has viewed the dynamics via direct interaction and long-lived complexes and transitions between these extremes from the point of view of unimoIecular breakup of a collision complex with total energy E and dissociation threshold Eo. In terms of simple RRK theory [9. 101 the lifetime of a molecule with s effective vibrational degrees of freedom, an excitation energy E and a decomposition threshold E. is given by

“IEa +C12

Fig. 3. Potential energy versus reaction coordinate. energy values are given in table 1.

Tile

433 .:

Volume 18, number 3 .Table 1

E(kcal/moIe) Eo(kcaJ/moIe) E - Eo(kcaI/molc)

BaC12

BaCl;

165*5 112r3

60+25

53 + 8

-2 c 7a) s:7b)

7.8 9.7 12.64

16 48 95

(s++2)RTV=(E*-E;)) R = A’/A

2.05 5 7.5

a) From E-Eo-Te(BaCI*). b) F rom application of the equipartiiion theorem, see text. c) hlin, mcd, max value: correspond to the upper central and lower confidence iimits of E. E* and E-Eo, respectively.

where Y is the frequency of intramolecular energy transport,.usually of the order Y x 1013 set-l [lo]. Fig. 3 shotis the reaction coordinates for the two electronic channels. Although the relevant energies, in particdar the electronic term value T, of the BaCI; complex and the bond energies [ 1 l-l 51 are not or only approximately known, we believe the figure to be at least semi-quantitatively correct. The E, E’, E. and E; values (the asterisk represents the excited species) recorded in table 1 have been obtained as follows. 2 =D~(BaC12) - D$Cl,) f eR where Dz(BaC1,) = 2 17 i 4 kcal/mole is the atomization energy [ 131 of BaCl,, $(Clz) = 57 kcal/niole the dissociation energy [l l] of Cl? and en x 5 kcal/mole is the’ sum of reactant internal and translational enercgy. &, is taken from ref. [ 131, and I?-Ei is given as E”--Ez = E - E,, - T,(BaCl) where T,(BaCl) = 55 kcal/mole is the electronic term value of BaCI(C21i,,,). The only unknown quantity, the electronic term value of BaCIi, Te(BaCI;) has bee11 estimated as T,(BaCl;) = 105 t 2.5 kcal/;nole. yielding E’ = E - T (BaCl;) ? 60 -+ 30 kcal/mole. The (F-E,) = .-2 + 7 = 2; kcal/mole value [labelled (a) in table I] discomfortingly scatters around zero, but a better estimate, labelled (b), may be obtained from the .vibrational temperature ?“v and an application of the equipartition theorem. Accordingly, the total available energy E* - Ei - (I?,!) is distributed equally between vibrations and rotations of the transition state. We assign an average energy RT, per vibrational mode and

e&T, p&active rotation: :-

‘.

.

I February

CHEMICAL PHYSICS LETTERS

1973

-LQ’),

where r is the number of active rotations and (I?,.) the average exit rotational barrier. With s=3, r=I for a tight complex! and (ER,) = 2.4 kcal/mole from a curve crossing model and TV= 2 100°K (the temperature corresponding to the lowest I,-levels, where the P-branch does not overlap) we obtain (E*- Ei) = 8.7 kcal/mole. This value is used in the calculation. Setting the “effective” number of oscillations equal to the total number, s=3, and assuming that the characteristic frequencies u are the same for BaCI, and BaClz, we can compare the relative lifetimes A = [E/(E-E,)]-~-l w h ic h are recorded in table 1. Also given are the ratios of relative lifetimes R =A*/A for the excited and the ground-state complex. The wide error limits of the energetics are responsible for the large spresd of lifetime ratios, as indicated by the minimum, median, and maximum values. The significant result is the distinctly longer dissociative lifetime of BaCli relative to the RaCl, complexf. The physical reason for this is clearly the drastic (= sixfold) decrease of excess energy (E-Eo) + (E* -Eg) compared to the moderate decrease of total excitation E + E” in going from ground-state to excited-state BaCl,. This is equivalent to the transition from direct to complex mechanism with decreasing collision energy in systems with appreciable binding energy [ 1, 91. A more reliable estimate of the absolute timescale than that obtained by simply setting LJ’= 1Or3 set-* in eq. (3) follows from explicit consideration of rotational and vibrational periodsAssuming the force constants in BaC12 and in BaCl [ 11, 121 to be comparable [ 131, the vibrational period is estimated 7, = 1.2 X lo-l3 sec. A curve crossing model [I] indicates rhat the angular momentum of relative motion is large, typically = 200 tl. With a reasonable geometry of the highly excited complex (treating BaC12 as a quasi-diatomic molecule with an rms distance Pa-C12 equal to 3/4 of the crossing radius) this gives a rotational period of rR = 4 X I O-l3 sec. The time for reactants to pass each other without interaction is = Ll.5 X IO-l3 sec. These two quantities

f If one uses the data in refs. [ 12, 151 rather than the more recent ones for evaluating the relevant energies, the lifetime ratios become R=2.5 fmin), 5 (med), 2.5 (max).

characterize the duration of the direct Bn + Cl, inter. action, particularly as they practically coincid-k. Obviously the = 3 vibrational periods (for p=l the first excited level) ‘equivalent to this timespan are insufficient for the complex to equilibrate internally. BaCI; survives = 5 times longer or = 25 X lo-l3 set, and c 20 vibrational and = 5 rotational periods - sufficient time for vibrational and rotational randomization. Although successful in rationalizing the “hermaphroditic effect” the present calculation does not attempt to explain the extremely long ccmplex lifetimes (r > 1O-9 set) implied by the relativeiy prominent radiative recombination process proposed by Jonah and Zare [ 11. To that end further experiments are required, as well as a more detailed theoretical model involving presumably transitions between electronic states of the complex and centrifugal effects [16] in unimolecular rate theory. The dissociation energies of BaCI(X2C) quoted in the literature scatter widely: Vedeneev et al. [ 121 give 62 t 5 kcal/moie, Hildebrand [ 131 recommends

105 kcal/mole, Jonah and Zare [I] place a lower limit at > 1 10 kcaljmole and Gaydon [ 141 quotes Do” = 115 C 9 kcal/mole. Jonah and Zare’s estimate [2] was obtained from energy conservation tit.5

R = D;(BaCl)

- @Cl?)

+ eR > (/ZV),.,

where eR is the reactant energy and (Iw)~,,, the observed short wavelength limit of the BaCI(X+-C) emission. The inequality approaches an equality when a detectable fraction of products contains all the exothermicity, and when the observed (hv), corresponds to the transition from the corresponding upper state Y’ level to the v”=O level of the lower state. This latter condition is clearly violated in the present case? due to Franck-Condon restrictions favoring the &=O transitions, and an improved estimate of oi(BaCl) is to a given possible. The (Iw), value corresponding (~‘1~“) transition has to be augmented by the vibrational energy ev(v’3 of the final state and the above. equation has to be modified to:

A$(BaCl)

I February 1973

CHI:MICAL PHYSICS LETTERS

Volume IS, number 3

2 D;(Clz) - ‘+ f (hi’),

f e&“‘).

In our case, the hi&&t observed iransicicn is the (P’, t”‘) = ( 17.17) band at 5 1 19 .& corresponding [4] to (WS,,, = 55.6 kcal/mole. The vibrational energy ev( 17) = 13.1 kcal/molc is calculated from w, and aexe values [ 11, 121, and eR = 5 kcal/moIe. With this the lower limit of the dissociation energy becomes Di(BaCl) Z 12 1 kcal/mole in good agreement with

Gaydon’s value [ 141. We would like to thank Professors R.B. Bernstein, for making their results available to us prior to publication. This work has been supported by the NRC and by the Research CarporaR. Herm and D.R. Hershbach

tion.

References Ill J.L. Kinsey. in: Kcaction kinetics, cd. J.C. Polanyi (Butterworth,

London

1972) ch. 6.

121 C.D. Jcnah and R.N. Zax, Chcm. Phys. Letters 9 t1971) 65.

[3i hl. Menzinger and D. Wren. to be published. La1A.E. Parker. Phys. Rev. 46 (193:) 301. [51 J.C. Light, Discussions Faraday Sot. 44 (1967)

L4: W.H.Wong. Can. J. Chem. 50 (1972) 633. 161 J.A. Iiaberman, K.G. Anlauf. R.B. Bernstein and FJ. van Itallic. Chcm. Phys. Letters 16 (1972) $42. 171 S.-11. Lin, C.A. hlimr and R.R. Hcrrn. to be published. 181 D.R. Fic‘rshbxh and H.J. Locsch. private communica!ior.. [91 R. \i’olfgng, Accounts Chcm. Res. 3 (1970) 48: Z. Hcrmnn, A. Lee and R. Wolfgang. J. Chem. Phys. 5 1 (1969) 452. K. Laidler. Chemicd kinetics (M&raw-Hilt. New York. 19G5). G. Herzberg, Spectra of diatomic molcculcs (Van Nostrand. Princeton 1967).

V.I. Vcdeneev, L.B. LurvicB, V.N. Kondzatiev, V..4. hledvcdcv and Y.L. Frankwitch, Bond encrgics, ionizstion potentials and electron affinities (St. Sfartin’s Press. New York, 1966). L131 D.L. Iiildebrand, J. Chcm. Phgs. 52 (1970) 5751. [IdI A.G. Gaydon. Dissociation cnergicsand spectraof diatomic molcculcs (Chapnan snd Hall, London; 1968). [15i V.G. Ryabova and L.V. Gurvich, Tepiophisika Vyoskikl~ Temp. 3 (1965) 652 [En&h irand. Hi$ Temp. 3 (1965)

6041. 1161 S.A. Snfron, N.D. Weinstein and D.R. Hrrshbach. Chem. Phys. Letters 12 (1972) 564; D.L. Bunker, J. Chcm. Phys. 57 (1972) 332.

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