Crossed beam studies of low energy proton transfer reactions: H2 +(Ar,H) HAr+ from0.4 to 7.8 eV (c.m.)R. M. Bilotta, F. N. Preuninger, and J. M. Farrar Citation: The Journal of Chemical Physics 73, 1637 (1980); doi: 10.1063/1.440345 View online: http://dx.doi.org/10.1063/1.440345 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/73/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A guidedion beam study of the hydrogen atom transfer reaction of stateselected N+ 2 with H2 at collisionenergies ranging from subthermal to 2 eV (c.m.) J. Chem. Phys. 102, 214 (1995); 10.1063/1.469394 Reactions of Ar+, Ne+, and He+ with SiF4 from thermal energy to 50 eVc.m. J. Chem. Phys. 90, 2213 (1989); 10.1063/1.456016 Crossed molecular beam study of the endoergic reaction Hg+I2→HgI+I from threshold to 2.6 eV (c.m.) J. Chem. Phys. 67, 3507 (1977); 10.1063/1.435348 Translational energy dependence of the reaction cross section for Rb + CH3I → RbI + CH3 from 0.12 to 1.6 eV(c.m.) J. Chem. Phys. 61, 4091 (1974); 10.1063/1.1681704 Observed translational energy dependence of the cross section for the Rb + CH3I→RbI + CH3 reaction from0.12 to 1.6 eV (c.m.) J. Chem. Phys. 61, 738 (1974); 10.1063/1.1681955

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Crossed beam studies of low energy proton transfer reactions: H~ (Ar,H) HAr+ from 0.4 to 7.8 eV (c.m.)

R. M. Bilotta, F. N. Preuninger, and J. M. Farrar

Department of Chemistry, University of Rochester, Rochester, New York 14627 (Received 24 March 1980; accepted 8 May 1980)

We present a crossed beam study of the proton transfer reaction Hi (Ar,H) HAr+ over an extended energy range. At the lowest collision energies (-0.4 eV), the reaction appea~s to proceed with substantial interaction among all three atoms, while the dynamics become "direct" in the higher energy regime. Collision induced dissociation of the HAr+ product is observed for collision energies above -2 eV, but products with internal energy in excess of the HAr+ dissociation limit are observed in all cases. These observations are rationalized in terms of the metastability of HAr+ products with rotational energy in excess of the dissociation limit. A surprisal analysis on the product translational energy distributions is also presented.

INTRODUCTION

Interaction between theorists and experimentalists in recent years has led to rapid growth in the area of chemical dynamics. Molecular beam techniques have been demonstrated to be of value in elUCidating the dy­namics of chemical reactions! and the development of laser technology and its applications to problems of chemical interest has expanded our concepts of chemi­cal reactivity.2 The theory of collision dynamics has also experienced a period of growth as more highly re­fined dynamical models and improved computational techniques allow one to calculate more reliable poten­tial energy surfaces as well as allowing more sophisti­cated dynamical calculations to be carried out on these surfaces. 3

The most impressive growth in chemical dynamics has been experienced in the area of the interactions of neutral speCies, but substantial growth in the study of . ion -neutral reaction dynamics has been achieved in re­cent years. Improved experimental techniques have now made the regime of low energy ion-neutral collisions accessible and crossed beam studies of such interac­tions at low energies are yielding important inSights in­to their reaction dynamics. Along with improved experi­mental techniques in ion-neutral systems, theoretical advances in nonadiabatic collision dynamics and in the computation of strongly interacting potential surfaces have led to fundamental advances in our knowledge of ion-neutral interactions. Among the advances in dy­namical calculations, the trajectory surface hopping (TSH) model of Tully' stands as a key advancement in understanding the dynamics of molecular collisions evolving on several coupled potential surfaces. The TSH model provides the mechanism for applying essen­tially classical methods to nonadiabatic collisions.

Quantum mechanical techniques which solve coupled equations on several interacting surfaces have been applied to ion-neutral interactions by Baer. 5-1 While these calculations are for collinear collisions of Ar+ with H2 and Hi with AI', these computations represent one of the first examples of the application of close­coupled techniques to multisurface reactive scattering.

With these advances in experiment and theory, the choice of experimental systems for study becomes

crucial and a key motivation of the experimentalist be­comes choosing systems for which fruitful-comparisons with theory can be made. The reactions of the Hi ion, the Simplest molecular ion, suggest themselves as likely candidates for study, but the proton and charge transfer reactions of this species have received very limited attention in crossed molecular beam studies. Low energy crossed beam studies have been performed only on the systems Hi + He by Herman and co-work­ers, 8,9 Hi + H2 by Wolfgang et al. , !O and most recently the Hi + CO system from this laboratory. 11,12 As we have indicated in our previous work, the kinematic problems which have hampered attempts to examine proton transfer and charge exchange from Hi to heavier species can be eliminated by appropriate experimental techniques.

The ArHi system is of particular importance from several viewpoints. The ion-molecule reaction Ar+ + H2 is among the best studied of all such reactions and has been the object of several theoretical studies. The potential surfaces involved in the Ar+(H2> H)HAr+ reac­tion have been calculated by Roach and Kuntz13 using the diatomics-in-molecules technique and the salient fea­tures of the surfaces leading to Chemical reaction are well understood. In the entrance valley where the (Ar+ -H2) distance is large, the two lowest surfaces cor­responding to Hi + AI' and Ar+ + H2 cross along the H2 vibrational coordinate. This surface crossing yields a seam in the entrance valley of the potential surfaces at RH _ H - O. 8 A. Furthermore, the products HAr+ + H cor­relate to reactants Hi + AI'. Consequently, the Ar+ + H2 system reacts only if the collision system undergoes a nonadiabatic transition to the lowest energy Hi + AI' sur­face.

Chapman and PrestonU have used the TSH model of Tully to confirm the nature of reactive collisions in the ArHi system. Their calculations indicate that only those trajectories which approach the entrance channel seam with motion transverse to the reaction coordinate, i. e. , H2 vibrational motion, and cross to the Hz + AI' surface will undergo chemical reaction. Those trajectories which do not cross to the lower surface do not yield chemical reaction.

More recent collinear quantum mechanical calcula-

J. Chern. Phys. 73(4), 15 Aug. 1980 0021·9606/80/161637·12$01.00 © 1980 American Institute of Physics 1637

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1638 Bilotta, Preuninger, and Farrar: Proton transfer reactions

tions by Baer and Beswick1 on the ArH; system are con­sistent with the results of the classical calculations. The quantum calculations which include many vibration­al states of Hi have also been shown to be in good agree­ment with a two-state curve crossing treatment which includes the states Ar++H2 (v=0) and Ar+H2(v=2).

The large body of theory on the ArHi system, with particular emphasis on the role of the ground state Hi + Ar surface in promoting chemical reactivity, suggests that low energy crossed beam studies on the Hi + Ar system will be of value in establishing a connection be­tween experiment and theory. In this paper we present an experimental study of the reaction Hi (Ar, H) HAr+ in the barycentric energy range from 0.4 to 7.8 eV.

EXPERIMENT AL

The apparatus used for these experiments has been described in some detail in earlier work from our labor­atory.12 Briefly, an ion beam formed by impact of 75 eV electrons on hydrogen gas is focused, momentum analyzed, and decelerated to the desired laboratory po­tential with respect to ground. The laboratory energy of the beam ranges from 0.4 to 8.2 eV with FWHM en­ergy and angular spreads of O. 3 eV and 1° to 3°, respec­tively' and beam currents ranging from 5 x10- 10 to 1. 2 X 10-9 A. The ion source is operated in the pressure regime of 10-5 to 10-6 Torr, yielding ions which possess a distribution of populated vibrational states. Impact of 75 eV electrons on H2 will produce a distribution of Hi vibrational states given by Franck-Condon factors for ionization; von Busch and Dunn15 have discussed the appropriateness of describing the rotational populations of Hi produced by single-electron impact in terms of a Boltzmann distribution of rotational energy in the pre­cursor neutral. Using the Franck-Condon factors of ViUarejo16 and an ion source temperature of 100°C, the reactant vibrational excitation is estimated to be 0.89 eV with rotational excitation of 0.03 eVj we have used a value of 0.92 eV for the Hi internal excitation in the kinematic analysiS of our experimental data.

This collimated beam of ions is directed into a large vacuum chamber evacuated to the mid-10-7 Torr region with a liquid nitr~gen trapped oil diffusion pump. A neutral beam, prepared by supersonic expansion of a mixture of 2% Ar in H2 carrier gas, intersects the ion beam at 90°. The supersonic beam is prepared by a differentially pumped source and is modulated at 150 Hz by a tuning fork chopper.

Products of the proton transfer reaction are detected with an energy -analyzer quadrupole mass spectrometer detector which rotates about the collision center in the plane of the beams. The energy range of the analyzer is swept by a ramp generated from a homebuilt multi­channel scaler circuit under control of a minicomputer. Energy resolution is 0.07 to 0.15 eVj calibration of the energy scale of the experiment is accomplished by mea­suring the energy distribution of Hi ions produced at 90° to the ion beam by resonant charge transfer. We esti­mate that the energy scale of these experiments is ac­curate to O. 1 eV.

The compromises associated with constructing an ap­paratus with a reasonable scattering volume (- 3 mm on a side) and a compact energy-analyzer detector with good resolution have forced us to choose a geometry in which the detector viewing angle subtends only a part of the collision zone. This situation introduces an angle dependent viewing factor into our experimental results. This correction can be made to first order by including a multiplicative factor I(e) into our data reduction. This function has the form

and has been included in the data analysis which is pre­sented in the next section.

A schematic diagram of the experimental apparatus is shown in Fig. 1.

RESULTS AND ANALYSIS

Kinematics

The standard kinematic relations between center of mass (c. m. ) speed u and angle e and the corresponding laboratory quantities v, e hold in ion-neutral interac­tions. Because the relative kinetic energy in such sys­tems may be varied so readily, one must include ex­plicitly the fact that at sufficiently high relative ener­gies, the dynamics of the chemical reaction may chan­nel sufficient internal excitation into reaction products to cause them to dissociate. The allowed limits on product stability can be shown most clearly by using the translational exoergicity Q, defined as follows:

Q=E~ -ET'

where E~ and ET are the final and initial translational energies, respectively. The limits on Q may be defined according to the stability zone of products allowed by conservation of energy consistent with the formation of products with internal energy below the dissociation limit D.

We have the following limits on Q:

E 1nt - ~E~ - D$ Q$ - ~E~ + E 1nt ,

where ~E~ is the reaction exothermicity of -1. 3 eV, D is the HAr+ dissociation energy of 3.8 eV, and Elnt is the initial internal energy of Hi, taken to be 1 eV. We thus have the following limits on Q:

-1.5$Q$+2.3 eV.

Thus, for collision energies above approximately 1. 5 eV, reaction products with internal excitation sufficient to dissociate may be formed in reactive collisions. Figure 2 indicates in schematic fashion the allowed "zone of stability" for reaction products. Of special significance is the "hole" near the center of mass where stable products are prohibited because of excessive internal excitation. 17 The magnitude of this hole grows as the collision energy increases and will be exhibited quite markedly in the recoil velocity distributions of HAr+ product.

J. Chem. Phys., Vol. 73, No.4, 15 August 1980

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Bilotta, Preuninger, and Farrar: Proton transfer reactions 1639

COLLISION CENTER

MAGNETIC SECTOR--~

ION OPTICS --......

24001/'.e

25 em

FIG. 1. Schematic diagram of experimental apparatus.

Cartesian contour plots

The representation of experimental angle and recoil energy data in the format of Cartesian flux contour maps has become essentially a standard in ion-neutral scat­tering measurements. Cartesian flUX

18 is defined as

I _ Ic•m• (u, 8) _ I1ab(V, 8) Cart- u 2 - v2

with the (usual) relationships among the pairs (u, 8) and (v, 8) shown in the kinematic diagram of Fig. 2. Con-

t

511104 em/ .. e

DETECTOR

tours of constant Cartesian flux in velocity space, super­imposed on the Newton kinematic diagram appropriate to a particular experiment; provide an important graph­ical representation of the global properties of a given scattering experiment. We have chosen to display our experimental data in this way and Cartesian contour plots of the proton transfer reaction Hi (Ar; H)HAr+ at various energies are shown in Figs. 3 -10.

One can conclude immediately from inspection of the contour plots that the transfer of a proton from Hi to Ar

FIG. 2. Kinematic diagram for the system H2(Ar, H)HAr+ at a collision energy of 3. 8 e V • Circles labeled Qmlll and Q_ define the loci of minimum and maximum values of UHAr+,

respectively, allowed by prod­uct stability and energy con­servation.

J. Chern. Phys., Vol. 73, No.4, 15 August 1980

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1640 Bilotta, Preuninger, and Farrar: Proton transfer reactions

H:(Ar,H )HAr+

Enl =0.45 eV

5 X 104 em/see

200 ....,,~--300

~~~~~~1l~~400 600 700 800 900

FIG. 3. Cartesian contour plot for Hi (Ar, H)HAr+ at 0.45 eV. Q = - O. 23 eV defines the "elastic spectator" circle.

is essentially a direct process. The HAr+ product ap­pears predominantly in the forward hemisphere with re­spect to the incoming Ar projectile. Since it is conven­tional to refer the direction of product formation rela­tive to the Hi primary beam projectile, we refer to such direct stripping products as being formed in the back­ward direction with respect to Hi. While the qualitative label "stripping"t9 is appropriate to the Hi (Ar, H)HAr+ system, our more detailed kinematic analysis of this re­action will show that the proton transfer reaction is more complicated than the simplistic term stripping implies.

The Cartesian contour plots show the circle of con­stant U~Ar+ corresponding to the "elastic spectator"20 mechanism in which the HAr+ product and the H atom may scatter elastically from one another. The Q value for this process is calculated from Qss = (mArmHI mH!mHAr+ -l)ET, where ET is the initial relative kinetic energy.

Despite the graphical appeal of Cartesian contour maps, they are of limited value in a quantitative assess­ment of the angular and energy distributions of reaction products. Tl\e Cartesian representation does have the advantage that it can be generated exactly from experi­mental data with no concern for transformations be­tween laboratory and barycentric coordinates or for dis­persion in the initial conditions of an experiment. Ex-

H; (Ar, H)HAr+

E,el=O.74eV

tractions of the polar barycentric cross section Ic.m,(u, e) can be difficult and ambiguous since the multiplication of the Cartesian flux by u 2 must be accompanied by an average over initial conditions to extract a meaningful barycentric cross section. More elaborate and precise techniques must be used to extract barycentric cross sections from laboratory data which are convolutions of barycentric quantities with dispersion in initial con­ditions as well as finite detector resolution. We discuss a more satisfying procedure for extracting energy inde­pendent cross sections from our data in the next section.

Iterative deconvolution

Fairly sophisticated techniques of kinematic analYSiS, including integration fitting and iterative deconvolution procedures, have been developed by practitioners of neutral beam collision experiments, but such techniques have not been widely applied to ion-neutral reaction dy­namics. In particular, the method of iterative deconvo­lution of barycentric speed and angular distributions from laboratory data, developed by Siska, 21 is particu­larly well suited to our experiments. This procedure extracts the center of mass cross section Ic.m,{u, e) from experimental data by iteratively solving the equation

" v2

11ab(V, e) = L.i II"'U I c•m• (UI, el ) • I I

The summation extends over a grid of Newton kinematic diagrams describing the initial conditions, with the probability of the ith Newton diagram given by fl' The nonseparable barycentric cross section I c.m. (u, e) is extraCted from the data by this procedure with an error of 5% to 7% after three to five iterations.

The deconvolution procedure was carried out over a grid of 25 Newton diagrams, five for each beam. The primary ion beam energy distribution was taken to be a triangular distribution with a FWHM of 0.3 eV. The secondary neutral beam was assumed to have a standard nozzle beam distribution22 in speed, characterized by a Mach number of 15, for a FWHM speed distribution of -10%.

The quality of the deconvolution procedure can be assessed by comparing calculated fluxes with experi­mental data at various lab angles and initial kinetic en-

1100 1000

FIG. 4. Cartesian contour plot at 0.74 eV. Elastic spec­tator circle at Q=-O.38 eV.

~~~m~==800 600 400

J. Chem. Phys., Vol. 73, No.4, 15 August 1980

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Bilotta, Preuninger, and Farrar: Proton transfer reactions

H2 (Ar,H)HAr+

Erel = 2.05 eV

5 x 10 4 em/sec

/ I I

/'

"--

Hi (Ar. H) HAr+

E r,1 =2.86 eV

!5 X 10 4 emilie

H~ (Ar,H)HAr+

E rel .. 3.80eV

..",

1200 1000 800 600 400 200 100

1000

800

~~~~~~~::::600 ::: 400 200

1000 800

1~1i~~600 400 200 100

J. Chern. Phys., Vol. 73, No.4, 15 August 1980

FIG. 5. Cartesian contour plot at 2.05 eV. Elastic spec­tator circle at Q = - 1. 05 e V.

FIG. 6. Cartesian contour plot at 2.86 eV. Elastic spec­tator circle at Q = -1. 47 eV.

FIG. 7. Cs.rtesian contour plot at 3.80 eV. Elastic spec­tator circle at Q., -1.95 eV.

1641

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1642 Bilotta, Preuninger, and Farrar: Proton transfer reactions

Hi (Ar, H)HAr+

H2{Ar,H) HAt

Erel = 5.76 eV

H2(Ar, H)HAr+

Erel = 7.75 eV I I

!5 X 10 4 emilie

~~~900 800 600 400 200

100 180·

1000

J. Chem. Phys., Vol. 73, No.4, 15 August 1980

FIG. 8. Cartesian contour plot at 4.74 eV. Elastic spec­tator circle at Q=-2.43 eV.

FIG. 9. Cartesian contour plot at 5.76 eV. Elastic spec­tator circle at Q=- 2. 96 eV.

FIG. 10. Cartesian contour plot at 7.75 eV. Elastic spec­tator circle at Q=-3.9 eV.

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Bilotta, Preuninger, and Farrar: Proton transfer reactions 1643

100 SO

)( 60 ::J

u.. 40 c: 20 0

en 0 .. -... 0 u

500 .. > 400 -0 300 .. a: 200

100

0 10

Hi(Ar,H) HAt

Erol ·3.S0eV • •• Expt.

Colc.

20 30 0 10 20 V( 104 em/sec)

30

FIG. 11. Experimental Cartesian flux vs results of iterative deconvolution at 3.80 eV.

ergies. Figure 11 shows such a comparison to the data at 3.80 eV, illustrating the quality of the fit to experi­mental data as well as the quality of the experimental data themselves. Such a presentation of experimental data is preferable to showing only the highly smoothed Cartesian contour plots, as traditionally done in ion­neutral scattering experiments.

As noted above, too output of the deconvolution pro­cedure is a pointwise barycentric cross section l •. m. (u, 0) which is not necessarily separable in recoil energy and angle. It has been noted in the literature23 that the bary­centric function is not necessarily separable in u and 0 although such an approximation is a common starting point for integration fitting procedures for kinematic analysis. For visualization of the energy and angular distributions of the proton transfer reaction Hi (Ar, H)HAr" it is useful to average l •. m. (u, e) over u and e to generate the distribution functions p(u) and l( e). In order to assess the partitioning of energy in the proton transfer reactions we have generated the function P(IT)' where f~ = E~I E tata" the fraction of the total available energy which appears in translational energy E~ of the products:

P(j T') = P(E'-rl E tata !)

= E tata! L u-11 •• m • (u, e,) sine, . , The total energy available to the system is given by

E tata! = ET - AE~ + E 1nt ,

where ET is the initial relative translational energy of the reactants, - AE~ is the reaction exothermicity of 1. 3 eV, and E 1nt is the initial internal excitation of the Hi reactant. We have used an average value for E 1nt of 0.92 eV arising from the Franck-Condon distribution of Hi vibrational states produced by electron impact

ionization of H2• We show P(j'-r) distributions derived from our experimental data in Fig. 12 and discuss them at length later in the paper.

The deconvolution procedures also extracts angular distributions averaged over recoil speed. The functions g( e) defined by

at each of the collision energies are shown in Fig. 13 . The direct nature of the chemical reaction is quite ap­parent at the higher collision energies, with the distri­bution peaking more sharply backward (relative to H2) as the energy increases. Of particular interest is the fact that at all but the highest collision energy, reactive­ly scattered products appear at all scattering angles. Despite the dominant backward scattered product at all energies, a substantial "rebound" component appears in the angular distribution with intensity approaching 5% to 10% of the stripping peak. At the two lowest collision energies, the angular distributions become substantially more isotropic, although the direct stripping peak still dominates the distribution.

It should be noted that small inaccuracies in the ener­gy scale (::::0.05 eV) are responsible for moving the angu­lar distribution peaks away from 1800 in the barycentric system. Since this indeterminacy is comparable to our precision in energy measurement, we have not cor­rected the distributions for this small energy scale shift.

Our experiments on the Hi (Ar, H)HAr+ system cover the collision energy range from 0.4 to 7.8 eV and the total energy range from 2.7 to 10.1 eV. Since the dis­sociation energy of HAr+ is estimated to be 3.8 eV, 19

the reaction dynamics may partition sufficient energy into HAr+ internal excitation to cause product dissocia­tion at relative collision energies as low as -1. 5 eV. Since the internal excitation of stable HAr+ products must not exceed the dissociation energy D, we have the following inequalities:

I T

r'b E~2.05eV , 'b

1.0 .'. E~OA5eV 'b

"

5 "

, b.'·'O. •. H '0" ~ 'Q,'b..

P(f') or-+--r-+--r-+-_r-I+-~-+~-4_'~-·.~~-+--'~~ T

1.0

~'

5 i i " i

, ; "'-.

j 0

~.

5

E~4.74eV ,A, , ",~

"

,5

; j

fT • E-i-I Etot

I

5

E~7.75eV

i i

i i

'.~ \., ...

\~,

, I ,5

FIG. 12. P (fS.) distributions deduced from experimental data wherefT is the fraction of the total energy in translation. Ar­rows denote minimum allowed value off'T as dictated by stabil­ity of rotationless HAr+.

J. Chem. Phys., Vol. 73, No.4, 15 August 1980

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1644 Bilotta, Preuninger, and Farrar: Proton transfer reactions

1.0

.5

-- 0.45eV

----- 0.74 eV

2.05 eV

2.86eV

0~-+--4---~-4--~--~--~--+-~~~~~~~ g(8)

3.80eV

.5

8cm. (degrees)

and

When the total available energy of the system exceeds the dissociation energy of the product, the translation­al energy distribution should be depleted for low values of f~, as our data have indicated, and as the p{f~) graphs of Fig. 12 show. Each of these P{f~) graphs is marked with an arrow to show that value of f~ below which stable products should not be- formed. As the total available energy of the system increases, the minimum allowed value of f~ must also increase.

The upper panels of Fig. 12 show P{f~) plotted vs f~ for initial relative energies up to 2.86 eV. Over this range of energies, the distributions are rather Similar, with maxima near t'T""0.15 to 0.20, corre­sponding to very highly internally excited products. A comparison of p{f~) distributions at 0.74 and 2.05 eV shows some depletion of intensity at low f~ beginning to occur in the higher energy experiment, in agreement with expectations regarding the onset of product disso­ciation.

The lower panels of Fig. 12 demonstrate even more clearly the effect of product dissociation on the p{f~) distributions. The distributions themselves maintain essentially constant shape and width as the collision energy increases, but a very dramatic depletion of product intensity at low f~ is beginning to dominate the distributions.

We note here that experimental and computational artifacts lead to a nonzero value for p{f'r) atf~= 1. The distributions shown in Fig. 12 are not corrected for this effect; in a later section of this paper, we will

5.76eV

7.75eV

FIG. 13. Barycentric angular distribution functions g (8) at indicated collision energies.

describe a procedure to remove this high energy "tail," as required for some of our data analysis.

The experimentally determined P{f~) distributions do in fact demonstrate the depletion of low values of f~ as the collision energy increases, but in all cases we ob­serve stable products with f~ values significantly below the minimum f~ predicted by product stability. A small contribution to this effect certainly comes from appara­tus resolution and kinematic smearing effects, but the basic physics of such "superexcited" product formation is dynamical in origin.

The formation of product molecules superexcited be­yond the dissociation limit has been noted in the litera­ture24 ,25 and may be attributed to very highly rotational­ly excited products. Ottinger24 has observed chemi­luminescence from the CO· (A 2lT) product of the reaction C· + O2 - CO· + 0 and concludes that the CO· rotational temperature may be as high as 45000 K. Koski25 has exploited the very high resolution of his apparatus to assess the effect of storing excess energy in product ro­tation in the reaction F· (H2, H)FW. The calculations of that work suggest that HF· in J;?: 40 and v;?: 11 possess­es total energy in excess of dissociation by 0.060 eV and has a lifetime which exceeds the transit time through the detector, nominally 40 IJ.s.

The experimental data reported here suggest that HAr· products possess substantially more excess ener­gy than 0.060 eV; while the P{f~) distributions may still have apparatus resolution effects contained within them, we can make a conservative estimate of the ex­cess energy by examining the displacement of the ob­served maximum in P{f~) from the minimum allowed value of f~ predicted from product stability considera­tions. At a relative energy of 3.8 eV, this criterion predicts an excess energy of 0.6 eV; at ,a relative ener-

J. Chern. Phys., Vol. 73, No.4, 15 August 1980

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Bilotta, Preuninger, and Farrar: Proton transfer reactions 1645

gy of 7.75 eV, this excess energy corresponds to 1. 7 eV. The total rotational energy which must be added to a ground state (v == 0, J = 0) HAr+ product in order to create a metastable product at the indicated value above the HAr+ dissociation limit corresponds to 4.4 eV at a collision energy of 3.80 and 5.5 eV at an energy of 7.75 eV. Using a value for the HAr+ rotational constant of 10.4 cm-1 derived from the scattering data of Weise, 26

we compute that J values of 58 and 65 1i at collision en­ergies of,3. 80 and 7.75 eV, respectively, create a ro­tational barrier of the correct magnitude.

These values of J are consistent with angular momen­tum conservation; the data of Giese and Maier27 indicate that the total cross section for the proton transfer reac­tion decreases from 10 to 5 A2 in the energy range from approximately 4 to 8 eV. Estimating a maximum impact parameter b maz from the relation (]= 1Tb~u and using Lmu= /-Lvbmu, we estimate Lmaz values of -110 1i at both collision energies. Thus, the observation of superex­cited HAr+ molecules beyond the dissociation limit is al­lowed by angular momentum conservation. The net ro­tational energy in product molecules increases with in­creaSing collision energy, essentially following the trend for an increasing fraction of the total angular momentum to appear in product rotational excitation as the colli­sion energy increases.

Surprisel analysis

The extraction of P(j~) distributions for the H; (Ar, H)HAr+ system at several relative translational energies extending beyond the dissociation limit of HAr+ product prompts us to systematize our results using the information theoretic analysis of Levine and Bernstein. 28 Using the basic premise of information theory applied to collisions, that all quantum states of reaction products are formed with equal probability, we can synthesize "prior" translational energy distribution of the following form:

po(~) = 1: E~1/2(Etotal - E'T)/ E~tlal or

This prior translational energy distribution is based upon a rigid rotor-harmonic oscillator (RRHO) model for atom plus diatomic molecule products29 and does not include the fact that at high collision energies the p0(j~) distribution is depleted at smallf~ because of collision induced dissociation. Although one could in­corporate such dissociative processes into the prior distribution, it will be more convenient to use the standard RRHO form for the prior distribUtion, incor­porating deviations from the prior distribution into a surprisal term.

Using the RRHO prior distribution for p°(jT) and our experimentally determined P(j~), we have plotted the surprisal I(j~) = -In[P(j~)/P°(j~)] for four initial rela­tive kinetic energies in Fig. 14. As noted in other work,30,31 computational and experimental uncertainties often prevent experimentally determined P(f~) from be-

I (fr)

-I. L--_-'-__ .L..-_--L. __ ...L..-_--'

O. .2 .4 .6 .8 1.0

FIG. 14. Plot of translational surprisall (I H vs 1 T for four collision energies. The P (/H distributions have been re­normalized to unit area for these calculations.

coming zero as f~ approaches unity. A recommended procedure for correcting this difficulty involves sub­tracting the termf~(j~= 1) from experimentally deter­mined distributions. 30 We have made this correction to our P(j~) distributions used in surprisal calculations, noting that the effect is significant only for f ~ ~ O. 7. The surprisal plots at relative energies of O. 45 and O. 74 eV are linear and give slopes of AT = 1. 7 and 1. 9, re­spectively. The fact that the surprisal plots are linear is consistent with the first-moment constraint that (E~) is a constant for a given initial relative energy.

At a relative energy of 3. 80 eV, the surprisal plot begins to show a marked nonlinearity at low values of f~. We have indicated earlier that, rigorously speaking, products formed below f~" O. 38 are Unstable with re­spect to dissociation at a collision energy of 3.80 eV. The observation of reaction products in this "forbidden" region has been explained by the survival of metaEltable, rotationally excited HAr+ products in flight through the detector. A correct treatment of surprisal in these sys­tems must include two additional factors not incorporated into the RRHO prior distribution: collision induced dis­sociation of excited HAr+ depleting p0(j~) at low f~, and rotationally excited products extending the limit on f ~ to lower values than that of rotationless products.

The surprisal plot for proton transfer at 4. 74 eV is qualitatively similar to that at 3. 80 eV, in that the sur­prisal parameter AT is negative for smallf~, i. e., the forbidden region, and positive for f~ ~ 0.4. Collision induced dissociation prohibits products below f~" 0.46 at this collision energy. Since the prior distritu tion does not incorporate collision induced dissociation, it clearly overestimates the probability of forming products at low f~. At the two highest collision energies shown in Fig. 14, the surprisals reach relative minima at I(j~) .. - o. 5 at f~ values equal to or slightly less than their minimum values allowed by product stability. In the regime near product dissociation, the small nega-

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1646 Bilotta, Preuninger, and Farrar: Proton transfer reactions

TABLE 1. Translational energy dis­tribution surprisal parameters.

Collision energy (eV) ?..r

0.45 1.8 O~fTO

0.74 2.1 O~fTO

2.05 2.5 0.3';;f T O

2.86 3.4 0.3(fT O

3.80 3.2 0.4(fTO

4.74 3.3 0.4';'17-( 1

5.76 2.0 0.5"'1700

7.75 1.4 0.6(fH1

tive value of the surprisal indicates that the probability of forming such products is greater than the prior value, i. e., the products have more than a statistical amount of translational energy. However, as f~ be­comes even smaller and products are even more strong­ly prohibited by stability considerations, the surprisal once again becomes positive, as the products possess more than a statistical amount of internal energy, i. e. , the prior once again overestimates the probability of forming products at low f~. This characteristic in­crease in the surprisal at low f~ thus underscores the importance of excess rotational energy in stabilizing products such that they survive through the detector.

The energy dependence of AT is rather interesting, particularly at lower energies. As the collision energy decreases below the threshold for product dissociation, the surprisal plot becomes linear, i. e., we may repre­sent the surprisal as I(j~) = Ao + AT f'T' Table I tabulates AT for our experiments in the "allowed" range of f~ where AT is positive. As the collision energy decreases, AT decreases toward zero, suggesting that the proton transfer reaction product behaves in a more "statisti­cal" fashion at low energies. Evidently, proton trans­fers at low energies are most effective in generating a microcanonical distribution of product internal energies. The parameter AT appears to maximize near 5 eV with a decrease as the collision energy increases further. A more correct model of the prior distribution including collision induced dissociation, as well as modeling the constraint of detecting rotationally excited products be­yond the dissociation limit, is required before one can proceed further with a surprisal analysis on this sys­tem in the higher energy regime. 32

DISCUSSION

The foregoing analysis of the Hz (Ar, H)HAr+ system over the energy range from 0.4 to 7.8 eV demonstrates that the reaction may be classified according to the glo­bal term "direct." The reaction product translational and angular distributions show, however, that the sim­plistic "spectator stripping" mechanism, while of clear qualitative utility in classifying the reaction, cannot ex­plain the details of the reactive scattering. An elabora­tion of the spectator stripping mechanism to include

elastic scattering of the products from one another is an improvement to the model, but the overall energetics of the reactive system require that product dissociation be included in the description of reactive scattering, even at fairly low collision energies.

The observation of very high product rotational excita­tion is an interesting phenomenon extracted from the low energy behavior of p(j~). The product excitation ob­served in our experiments, while totally consistent with angular momentum conservation and disposal, is some­what surprising in view of the substantially lower exci­tation seen by Koski and collaborators25 in the F+ (H2, H)HF+ system. Although these investigators pre­dicted that some reactive systems should store sub­stantially larger amounts of energy in product rotation than they observed, one might not expect to see such an effect in a hydrogen-containing product, since em­cient quantum mechanical tunneling through the angular momentum barrier should reduce the lifetimes of such rotationally metastable species. Since the molecular reactant in our studies (Hi) is formed under nonequilib­rium conditions, its rotational excitation may contrib­ute to the overall transformation of initial angular mo­mentum into product rotational excitation.

The increasing importance of product rotational exci­tation as the relative collision energy increases has been noted in the infrared chemiluminescence experiments of Polanyi and co-workers33 and has been modeled by these workers using classical trajectory calculations. The F + D2 system is particularly interesting in that the mass combination H + LL also describes the Hi + Ar sys­tem; the F + D2 system demonstrates a marked con­version of excess reagent translational energy into product rotation, with a smaller fractional increase in product translation. A comparison of trajectory studies on the Ar+ + D2 reaction at two collision ener­gies (0.22 and 2.2 eV) demonstrates that 90% of the 2 eV increase in reactant translation appears in product translation and rotation. 34

The explanation of the enhanced product translation and, particularly, rotation stems from the ability of re­actants with excess energy to sample the "corner" of the potential surface. 35 In the case of F + D2, collisions which reach the corner correspond to a compressed D2 bond with the F-D distance essentially its value in the isolated product. Release of the repulsive energy as the products separate, particularly in a bent configura­tion of the three particles, leads to substantial rotation­al excitation and accompanying translational energy re­lease. The Hi + Ar system will likely demonstrate the same effect in which the high translational energy of re­actants' coupled in this case with nearly 1 eV of vibra­tional energy, will allow trajectories to reach the corner with a compressed Hz bond length. The fact that the proton transfer in the Hi + Ar system resembles a strip­ping reaction supports the notion that the nascent products leave the corner of the surface and move into the exit valley in a bent configuration which imparts substantial rotational excitation to the products.

The internal excitation of Hi may also playa role in the overall form of product energy and angular distriw tions

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Bilotta, Preuninger, and Farrar: Proton transfer reactions 1647

and the energy dependences of these quantities. The calculations of Baer, 5-7 although collinear in nature, indicate that the adiabatic surfaces for state-selected reactants

H2(v) + Ar - HAr+(v)+ H

for low vibrational quantum numbers v do not possess local minima along the reaction coordinate. However, for higher values of v, Baer's surfaces as a function of reaction coordinate do possess rather significant basins in the strong interaction region, i. e., that part of the potential energy surface where proton transfer occurs. These basins are barely perceptible for v = 1 but are very much in evidence for v==: 3. Such a local minimum along the reaction coordinate for proton trans­fer would be expected to make the reaction dynamics more "complex" at low energies, as the three interact­ing particles experience an attractive encounter which exceeds a rotational period. Both the angular and ener­gy distributions extracted from our data are consistent with a more long-lived attractive collision encounter as the relative collision energy decreases. The angular distributions for proton transfer are clearly dominated by backward scattering at all energies, but a significant forward "plateau, " corresponding to "rebound" type col­lision, is present in all the angular distributions below 7.8 eV and is especially apparent at the lowest colli­sion energies.

The surprisal analysis of the translational energy dis­tributions also lends evidence to the argument that a significant attractive interaction among all three react­ing atoms eXists, particularly at low energies. The tendency of the translational surprisal AT to approach a small positive value at low collision energies sug­gests that chemical reaction at these energies may lead to a microcanonical distribution of product energies.

While the conclusions of a theoretical study of Hi + Ar based upon collinear surfaces must be viewed with some caution, the present results lend support to some of the results of those computations, in particular the presence of a substantial attractive interaction along the reaction coordinate. Of great interest is the hypothesis that this attractive interaction is a function of the vibrational state of Hi. The role of H~ vibrational excitation in deter­mining product state distributions is a second question of some interest generated by the theory and this ques­tion' as well as the dynamics of the charge transfer re­action Hi (Ar, H2)Ar+ at low energy, is currently under investigation in our laboratory.

ACKNOWLEDGMENTS

This research was supported in part by the U. S. Department of Energy. Support of the Petroleum Re­search Fund, administered by the Chemical Society, and by the Research Corporation are also gratefully acknowledged. We also wish to acknowledge stimulat­ing diSCUSSions with Professor Richard Bernstein. Professor Peter Siska provided us with a copy of his iterative deconvolution program as well as helpful com­ments regarding its implementation. We also acknowl­edge Professor John Muenter for cheerfully providing access to his Power Supply Lending Library.

ISee, for example, R. B. Bernstein, Adv. At. Mol. Phys. 15, 167 (1979).

2S. Kimel and S. Speiser, Chem. Rev. 77, 437 (1977). 3Atom-Molecule Collision Theory, edited by A. B. Bernstein

(Plenum, New York, 1977).

4J . C. Tully and R. K. Preston, J. Chern. Phys. 55, 562 (1971).

5M. Baer and J. A. Beswick, Chern. Phys. Lett. 51, 360 (1977).

bM. Baer, Mol. Phys. 35, 1637 (1978). 7M. Baer and J. A. Beswick, Phys. Rev. A 19, 1559 (1979).

SF. Schneider, U. Havemann, L. Ziilicke, V. Pacak, K. Birkinshaw, and Z. Herman, Chern. Phys. Lett. 37, 323 (1976).

9V. Paciik, U. Havemann, Z. Herman, F. Schneider, and L. Ziilicke, Chern. Phys. Lett. 49, 273 (1977).

10J. R. Krenos. K. K. Lehmann. J. C. Tully. P. M. Hierl. and G. P. Smith. Chern. Phys. 16, 109 (1976).

IIF. N. Preuninger. R. M. Bilotta. and J. M. Farrar. J. Chern. Phys. 71. 4166 (1979).

12R. M. Bilotta. F. N. Preuninger. and J. M. Farrar. J. Chern. Phys. 72. 1583 (1980).

13p. J. Kuntz and A. C. Roach. J. Chern. Soc. Faraday Trans. 268. 259 (1972).

14S. Chapman and R. K. Preston. J. Chern. Phys. 60. 650 (1974).

15F. von Busch and G. H. Dunn, Phys. Hev. A 5, 1726 (1972). IbO. Villarejo. J. Chern. Phys. 48. 4014 (1968). I7This effect has been discussed in detail in T. M. Mayer.

B. E. Wilcomb, and R. B. Bernstein. J. Chern. Phys. 67, 3507 (1977). with respect to Hg+ 12- HgI + I.

IS R. Wolfgang and R. J. Cross, Jr .• J. Phys. Chern. 73, 743 (1969) .

19A • Henglein. K. Lacmann, and G. Jacobs, Ber. Bunsenges. Phys. Chern. 69. 279 (1965).

200. R. Herschbach. Appl. Opt. Suppl. 2. 128 (1965). 21p. E. Siska. J. Chern. Phys. 59. 6052 (1973). 22J. B. Anderson. R. P. Andres. and J. B. Fenn, Adv. Chern.

Phys. 10. 275 (1966). 23K. T. Gillen. A. Rulis. and R. B. Bernstein, J. Chern.

Phys. 54, 2831 (1971). 24J. Simonis and Ch. Ottinger, Phys. Rev. Lett. 35. 924

(1975). 25C. A. Jones. K. L. Wendell. and W. S. Koski. J. Chern.

Phys. 67. 4917 (1977). 2bH._P. Weise. Ber. Bunsenges. Phys. Chern. 77, 578 (1973). 27C. F. Giese and W. B. Maier, J. Chern. Phys. 39, 739

(1963). 28See• for example. R. B. Bernstein, and R. O. Levine. Adv.

At. Mol. Phys. 11. 216 (1975). 29A lack of reliable spectroscopic information on HAr+ has

motivated us to use the RRHO approximation for pO (lB. A comparison of the RRHO treatment with a direct count for isoelectronic HCI shows that at a total energy of 2.7 eV. the RRHO approximation is accurate to ~ 25% over the range 0", f'T",0.6. RRHO overestimates pO (IT) by as much as a factor of 2 in the region O. 8", IT'" 1. O. This is to be ex­pected since the energy in internal degrees of freedom is very small. The net effect of this overestimation of po (IT) at highlT is to reduce the value of the surprisal by 0.2 to 0.7 in the range O. 4 '" fT '" 1. O. The lack of spectroscopic data on HAr+ as well as the difficulty of precise determination of measured P (tTl near tT = 1 makes a more detailed treatment of pO (tT) for HAr· seem unjustified.

30A. Ben-Shaul. R. O. Levine. and R. B. Bernstein, J. Chern. Phys. 57, 5427 (1972).

31F. F. Crim and G. A. Fisk, J. Chern. Phys. 65, 2480 (1976). 32Parenthetically. we note that the "transfer of momentum"

constraint developed by Levine and co-workers [A. Kafri. E. Pollak. R. Kosloff, and R. D. Levine. Chern. Phys. Lett. 33, 201 (1975)] does not provide an improved represen-

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1648 Bilotta, Preuninger, and Farrar: Proton transfer reactions

tation of translationsl surprisal in these systems. We can­not find a physically meaningful parameter € of their model which improves over a simple linear surprisal calculation. At low energies in particular, one does not expect such a transfer of momentum constraint to be valid.

33A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi,

and J. L. Schreiber, Faraday Discuss. Chem. Soc. 55, 252 (1973).

34p. J. Kuntz and A. C. Roach, J. Chem. Phys. 59, 6299 (1973).

35p. J. Kuntz, in Dynamics of Molecular Collisions, edited by W. H. Miller (Plenum, New York, 1976), Part B, p. 53.

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