The dynamics of the prototype abstraction reaction Cl(2P3/2,1/2)+ H2: A comparison of crossed molecular beam experiments with exact quantum scattering calculations on coupled ab initio

The dynamics of the prototype abstraction reaction

Cl(2P3/2,1/2) þ H2: A comparison of crossed molecular beam

experiments with exact quantum scattering calculations on coupled

ab initio potential energy surfacesw

Nadia Balucani,a Dimitris Skouteris,a Giovanni Capozza,a Enrico Segoloni,a

Piergiorgio Casavecchia,*a Millard H. Alexander,b Gabriella Capecchizc andHans-Joachim Wernerc

aDipartimento di Chimica, Universita di Perugia, 06123 Perugia, Italy.E-mail: [email protected] and [email protected]; Fax: 39 075 585 5606;Tel: 39 075 585 5514

bDepartment of Chemistry and Biochemistry and Institute for Physical Sciences andTechnology, University of Maryland, College Park, Maryland, 20742-2021, USA.E-mail: [email protected]

c Institut fur Theoretische Chemie, Universitat Stuttgart, D-75069 Stuttgart, Germany.E-mail: [email protected]

Received 5th July 2004, Accepted 6th August 2004First published as an Advance Article on the web 25th August 2004

To investigate the relative reactivity of the two spin–orbit states of atomic Cl with molecular hydrogen,we have measured laboratory-frame differential cross sections (DCSs) using an atomic Cl beam with a knownconcentration of the ground (2P3/2) and excited (2P1/2) spin–orbit states. The experimental results are comparedwith a complete determination of the appropriate centre-of-mass DCSs from quantum mechanical scatteringcalculations on the Capecchi–Werner coupled ab initio potential energy surfaces (PESs). The multi-electronic-statequantum scattering prediction differs somewhat from the experimental results. This disagreement is likely due toan underestimation of the degree of rotational excitation of the HCl product, due to residual imperfections in theexit channel of the ab initio PESs. In particular, an increase in the reactivity of the excited spin–orbit state wouldresult in poorer agreement with experiment.

1. Introduction

The reaction of chlorine atoms with molecular hydrogen (andits isotopomers) has played a central role in chemical kineticsand has long served as a test case for bimolecular reaction ratetheories.1 In addition to its fundamental interest, the Cl þ H2

reaction is also the prototype for the reaction of Cl withhydrocarbons, which are of relevance in atmospheric chemis-try. For these reasons, the ClH2 reactive system has beenextensively investigated over many years with a variety ofexperimental techniques and theoretical methods.2–31

Experimental work on the rate constants of the Cl þ H2

reaction and their temperature dependence is very extensive. Acomprehensive summary has been given by Michael and co-workers2 (see also ref. 3), while more recent determinations canbe found in ref. 4. The accepted room temperature rateconstant is 1.4 � 10�14 cm3 molec�1 s�1 with an activationenergy ofB4.59 kcal mol�1 (T ¼ 200–310 K).32 More recently,detailed information on the microscopic reaction dynamics ofCl þ H2/HD/D2 were provided by molecular beam experi-ments coupled to mass spectrometric5,6 or REMPI detection7–9

and by the ‘‘photoloc’’ technique.10

On the theoretical side, significant progress has been made inthe construction of a reliable potential energy surface (PES)

which adequately describes the ClH2 system.11–13 In 1996,Allison et al.12 introduced a global, semiempirical potentialenergy surface (G3 PES) by modifying the GQQ PES ofSchwenke et al.13 The comparison between quantum mechan-ical (QM) and quasi-classical trajectory (QCT) calculations onthe G3 PES with experimental differential cross sections5,10 andrate constants14–16 validated the overall adequacy of this PES.Although the G3 PES represented a significant step forward

in the quantitative modelling of the Cl þ H2 reaction, itsvalidity was questioned by several recent experimental findings,such as the effect of H2 rotational excitation in promoting thereactivity.7 Also, crossed beam experiments found the energydependence of the DCl/HCl branching ratios in the Cl þ HDreaction to be at variance with the predictions of exact QMcalculations on the G3 PES.17

In 2000, a new, fully ab initio PES, based on internally-contracted, multireference, configuration-interaction calcula-tions (IC-MRCI), was published by Bian and Werner (BW).18

This new PES has been used in a variety of treatments ofthe dynamics (QCT,6,19,20 time-independent and time-depen-dent QM6,17,19,21) and the results have been compared withexperiment.6,17

The BW PES and the semiempirical G3 PES predict a similartopology in the region of the barrier, but significantly differenttopologies in the entrance channel.6,17–19 Calculations based onthe BW PES, in contrast to those based on the G3 PES, yieldedcorrect predictions of the DCl/HCl branching ratio measuredby Liu and co-workers17 as well as the effect of H2 rotationalexcitation on the reactivity.6,19 The difference was attributed

w This paper was written as part of the EC Research Training Networkon Reaction Dynamics (HPRN-CT-1999-00007).z Present address: Dipartimento di Chimica I. F. M., I-10125 Torino,Italy; E-mail: [email protected].

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to a more accurate description of the long-range region of theCl–H2 PES.

The BW PES does not include the spin–orbit Hamiltonian.Inclusion of the spin–orbit Hamiltonian will increase thebarrier height on the ground adiabatic spin–orbit surfacerelative to the value on the spin-free PES by 1/3 of thespin–orbit splitting, B0.84 kcal mol�1.33,34 When the effectof spin–orbit coupling on the barrier height is included inthe electronic partition function,22 QM calculations of Cl þH2 thermal rate constants based on the BW PES yield ex-cellent agreement with experiment over a wide range oftemperatures. After the recognition of the importance of thelong-range region,17 several subsequent studies have focusedon it and, in particular, on nonadiabatic couplings in thisregion.23–25

Considerable interest in spin–orbit and nonadiabatic effectsin the Cl þ H2 reaction has been stimulated by experiments ofLiu and co-workers.7–9 These authors inferred that the spin–orbit excited state of the chlorine atom (2P1/2) was morereactive than the spin–orbit ground state (2P3/2), despite thefact that only atoms in the spin–orbit ground state correlateadiabatically with the observed products in their groundelectronic states, HCl(X 1S1) þ H(2S). In other words, the‘‘adiabatic correlation’’ rule, based on the Born–Oppenheimer(BO) approximation and supported by the majority of pastexperimental work,35 apparently does not apply to the Cl þH2

reaction. Such a striking and unexpected result is the motiva-tion for the research reported here.

The study of nonadiabaticity in the related F(2P1/2) þ H2

reaction goes back to early work of Tully,36 with the goal ofinvestigating whether motion on a single PES is sufficient todescribe adequately the reactions of halogen atoms withmolecular hydrogen.37 Subsequently, scattering studies focus-ing on the importance of spin–orbit and/or nonadiabatic effectswere undertaken by numerous groups,38–43 with particularattention on the F(2P3/2,1/2) þ H2 reaction.

38–42 More recently,time-dependent calculations within the centrifugal suddenapproximation have also been performed for F(2P3/2,1/2) þH2/HD/D2.

44 Unfortunately, all these calculations are subjectto various approximations, both in the treatment of thedynamics and/or in the choice of PES and couplings (non-adiabatic, Coriolis, and spin–orbit).

In 1995 Schatz presented the framework for the exactquantum treatment of reactive collisions involving multipleelectronic states.34 Schatz and co-workers then reported aseries of calculations for Cl þ HCl reaction,45 Alexander,Manolopoulos and Werner (AMW) extended the methodologyof Schatz to treat correctly all total angular momenta.46,47a

This method has been used in subsequent quantum studies ofthe F þ H2(HD)47b,c and Cl þ H2 reactions.

26

The exact treatment of AMW involves four three-dimen-sional electronically-diabatic PESs as well as two hypersurfacesthat describe the coordinate dependence of the spin–orbitcoupling. The scattering is then treated fully quantummechanically. For the F þ H2

46 and F þ HD48 reactions, thecalculations of Alexander and co-workers showed that the BOforbidden reaction of the excited spin–orbit state contributed,overall, on the order of only 10–20% of that of the BO allowedreaction of the ground state. This prediction is fully consistentwith experimental work.48

Stimulated by Liu’s experiments, a similar treatment wasapplied to the title reaction by three of the present authors.26,27

Approach of the H2 molecule splits the degeneracy of theground state (2P) of the Cl atom, giving rise to three PESs.As shown schematically in Fig. 1, the 1 2A0 state (2S1 in lineargeometry) correlates with the electronic ground state of theproducts HCl(X 1S1) þ H(2S), while the PESs of the twoelectronic excited states PESs (1 2A00 and 2 2A0; correspondingto 2P in linear geometry) correlate with HCl products in thelowest electronic excited state (a 3P). Reaction of the spin–

orbit excited state can therefore occur only by non-adiabatictransitions in the entrance channel.The calculations of Bian and Werner determined only the

lowest electronically-adiabatic PES and did not include thespin–orbit Hamiltonian. Two of the present authors (Capecchiand Werner, CW) then extended the MRCI calculations to allthree electronic state with the inclusion of the spin–orbitinteraction.28 The lowest adiabatic CW PES has been recentlyused in QM calculations of Cl þH2 thermal rate constants andwave packet studies of the reaction dynamics.29,30 Very re-cently, wavepacket studies on the CW PES, including diabaticand spin–orbit coupling, have also been reported.31

There are several major differences between the Cl þ H2 andF þ H2 reactions. First, the spin–orbit splitting of the Cl atom(2.52 kcal mol�1) is more than twice as large as that of theF atom (1.05 kcal mol�1). In principle, this should render non-adiabatic effects less probable in the former reaction. However,the barrier height is much higher (4.93 kcal mol�1) for the Cl þH2 reaction. Consequently, at low collision energies the inter-nal spin–orbit energy can act to overcome the barrier. Also, thereaction of Cl with H2 is nearly thermoneutral, with thereaction of Cl(2P3/2) being slightly endothermic (DH1 ¼þ1.03 kcal mol�1) and the reaction of Cl(2P1/2) slightlyexothermic (DH1 ¼ �1.49 kcal mol�1)]. In contrast, the reac-tions of both spin–orbit states of F with H2 are stronglyexothermic.In spite of these differences, the general trend predicted by

the calculations of Alexander, Capecchi, and Werner (ACW)was similar to what was found for F þ H2 as far as the integralcross sections (ICS) were concerned: those for the BO-allowedreaction of Cl(2P3/2) are much larger than those for the BO-forbidden reaction of Cl(2P1/2).

26 The latter channel becomesimportant only at very low collision energy, where the groundspin–orbit state does not have enough energy to overcome thebarrier. As the collision energy increases, the reactivity of theground spin–orbit state rapidly dominates. These results are indirect contrast to the experimental observations of Liu and co-workers,7–9 who found that the reactivity of Cl(2P1/2) increas-ingly dominates as the collision energy increases.To resolve this outstanding discrepancy, further theoretical

and experimental studies are necessary. In the present articlewe report a full account of experimental measurements andtheoretical simulations of the differential cross sections(DCSs), which are a far more detailed probe of the dynamicsthan ICSs, for the title reactions. A portion of this work waspresented recently in a short communication.27

The experiments were carried out by the crossed molecularbeam (CMB) technique coupled with mass spectrometric de-tection and product time-of-flight (TOF) analysis.49 An im-portant feature of the present experimental set-up is thepossibility of generating atomic Cl beam with a known popu-lation of the two spin–orbit states.50 The technique has already

Fig. 1 Schematic of the energetics of the reaction of Cl(2P3/2,1/2) withH2(v ¼ j ¼ 0). The zero of energy corresponds to Cl(2P3/2) þH2(v ¼ j ¼0). As can be seen, the spin–orbit splitting in the Cl atom (2.52 kcalmol�1) is roughly one-half of the height (4.93 kcal mol�1) of the CWPES barrier. All enegies include zero-point corrections. The zero-pointenergy at the transition state was estimated using the vibrationalfrequencies calculated by Bian and Werner (Table II of ref. 18).

5008 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 5 0 0 7 – 5 0 1 7 T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

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been used for the study of the Cl þ H2 reaction at a collisionenergy (Ec) of 5.85 kcal mol�1.5,6 Since the theoretical calcula-tions by ACW predicted reactivity of Cl(2P1/2) to be mostsignificant, as compared to the reactivity of Cl(2P3/2), at lowcollision energy,26 we here extend our previous study to twoadditional lower collision energies (3.85 and 4.25 kcal mol�1)which both lie below the zero-point corrected barrier height(4.93 kcal mol�1) for the reaction Cl(2P3/2)þH2(v ¼ j ¼ 0).18,28

We have calculated DCSs for reaction of each of the twospin–orbit states on the coupled CW PESs at the same Ec’s ofthe experiments (3.85, 4.25 and 5.85 kcal mol�1) and for allrotational levels of H2 present in the reactant beam (see below).Since Lee and Liu have also measured DCSs for the reactionsof both Cl spin–orbit states at Ec¼ 5.2 kcal mol�1,8 for a directcomparison, we have also carried out calculations at this lattercollision energy under the conditions of their experiment.

The paper is organized as follows: Section 2 contains detailson the potential energy surfaces and scattering calculations. InSection 3, the experimental method is briefly described and theexperimental results are reported. Experimental results andtheoretical predictions are compared in Section 4. A discussionand conclusion are contained in Section 5 and 6.

2. Theoretical methods and results

A. Potential energy surfaces and quantum scattering

calculations

As already mentioned, the approach of the H2 molecule to a Clatom splits the degeneracy of the 2P state. Two electronic states(2S1

1/2 and 2P3/2 in linear geometry) correlate adiabaticallywith the ground-state atomic reactant (2P3/2) while a third state(2P1/2 in linear geometry) correlates adiabatically with theexcited-state atomic reactant (2P1/2).

51 Of these, only the lowestelectronic state correlates with the electronic ground state ofthe products [HCl(X 1S1) þ H(2S)]. The two other electronicstates correlate with HCl products in their a 3P electronicallyexcited state, which lies considerably higher in energy52 and is,consequently, energetically inaccessible at low to moderatecollision energies. In the absence of spin–orbit coupling andin Cs nuclear geometries, the lowest state (the S1 state) has A0

symmetry, while the second and third state, which correspondto a degenerate P pair in linear geometry) have A0 andA00 symmetries.

The exact quantum description of the Cl þ H2 reactionfollows the formalism presented earlier by AMW.46 Thisdescription requires three potential energy surfaces (PESs)and an accurate description of the couplings (non-adiabatic,spin–orbit, and Coriolis) between them. We refer the interestedreader to the original paper by AMW and several more recentarticles on the title reaction53,54 and will give here only thosedetails directly relevant to the present investigation.

Capecchi and Werner28 used internally-contracted multi-reference configuration-interaction calculations, based onstate-averaged (three-state) complete-active-space, self-consis-tent field (CASSCF) reference wavefunctions with very largeatomic orbital basis sets, to determine the three electronicallyadiabatic Cl þ H2 PESs in the reactant arrangement with Cs

symmetry: 1A0, 2A0, and 1A00. By analysis of the coefficients inthe CI expansion of the ClH2 electronic wavefunctions, the twoPESs of A0 symmetry are transformed to an approximatediabatic basis,33,55 in which the orientation of the p hole onthe Cl atom is fixed with respect to the plane defined by thethree atoms. These diabatic PESs are then merged28 with thesingle BW PES18 in the product arrangement. These PESs aswell as the coordinate dependence of the spin–orbit couplingwere globally fitted to multiparameter forms.28

To treat the reactive scattering dynamics, we use a close-coupled, time-independent method. The scattering wavefunc-tion is expanded in a non-orthogonal set of products of

electronic-vibrational-rotational states for each of the arrange-ment channels.45,46,56 Canonical orthogonalization is then usedto construct the surface eigenfunctions in each sector.57 Aconstant-reference-potential, log-derivative propagator56,58 isemployed to integrate the coupled channel equations. Thecalculations were carried out with the ABC code of Manolo-poulos and co-workers,56 modified extensively46 to include allmultiple-potential-surface aspects.In the helicity representation, the scattering amplitude for

the centre-of-mass (CM) scattering angle y is given in terms ofthe fundamental scattering (S) matrix elements as59

fjaka jk!ssj0k0 ðyÞ ¼1

2iki

X

J

ð2J þ 1ÞdJkaþk;sþk0 ðp� yÞ

� SJ jakajk; ssj0k0ð Þ:ð1Þ

This expression is the extension53 to reactions involving non-zero electronic orbital and spin angular momentum, of thehelicity-frame expressions59,60 used earlier in the study ofreactions in which the only internal angular momentum isthe rotational motion of the diatomic moiety. Here, J is thetotal angular momentum, ja and j are the total electronicorbital angular momentum of the Cl atom and the rotationalangular momentum of the H2 molecule, with projections kaand k along the initial relative velocity vector, j0 and k0 are therotational angular momentum of the HCl product, with pro-jection k0 along the final relative velocity vector, and s and s arethe total spin of the H atom product and its projection alongthe final relative velocity vector. The quantity dk,k0

J is a Wignerrotation matrix element.61 The CM angle refers to the Cl atombeam, which we choose to define the vertical axis in a conven-tional Newton diagram. The vibrational quantum numbers ofthe H2 and HCl diatomics are assumed included in thisexpression, but are explicitly suppressed, for simplicity. Final-ly, the quantity ki in the denominator of the right-hand-side isthe initial wavevector.The differential cross section is given by the absolute value

squared of eqn. (1). In the experiments to be described theprojection quantum numbers are not selected. Since none ofthe final states (j0,v0,k0,s) are resolved, we simulate the full-rotational-state resolved DCS by summing over all final statequantum numbers and averaging over the initial-state projec-tion quantum numbers, to obtain

dsja j!j0=do ¼1

ð2ja þ 1Þð2j þ 1ÞX

kakk0s

fjakajk!ssj0k0 ðyÞ�� 2: ð2Þ

In the simulation of our experiments we sum over all finalrotational quantum numbers. Integral cross sections (ICS) canbe determined either by integration of eqn. (2) over all angles,or, more directly, in terms of the S-matrix elements.46

The numerical scattering calculations are controlled by anumber of parameters: Kmax (the maximum value of the totalprojection quantum number), jmax (the maximum H2 or HFrotational quantum number included in the channel basis),Emax (the maximum vibration-rotation energy of any stateincluded in the channel basis), and rmax and Ns (the maximumvalue of the hyperradius and the number of sectors used in thenumerical solution of the close-coupled equation). Table 1 liststhe parameters used in these, and in our previously pub-lished,26,27,53 calculations on the Cl þ H2 system. In addition,

Table 1 Summary of parameters which define the scattering

calculationsa

J jmax Kmax Emax/eV rmax/a0 NS

0.5–26.5 15 3.5 1.7 12 100

a See text for the definition of these parameters.


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the sum over the total angular momentum in eqn. (1) waslimited to J r 26.5.

To compare with our experiments scattering calculationswere carried out for three initial collision energies: Ec ¼ 3.85,4.25, and 5.85 kcal mol�1. The total energy corresponding to agiven initial collision energy depends on the internal energy ofthe initial state

Etot ¼ Ec þ ejavj. (3)

Consequently, since the simulations of the experiments, pre-sented in this paper and described in the next Section, requirefive values of the initial rotational quantum number of the H2

molecule (j ¼ 0–4) and two values of the electronic angularmomentum of the Cl atom (ja ¼ 1/2 and 3/2), a completesimulation of the experiments requires scattering calculationsat a total of 30 different total energies.

For a further comparison with Liu’s determination of DCSs,the scattering calculations were also performed at the Ec of thatexperiment.8 In this case, only two rotational states of H2 aresignificantly populated, j ¼ 0 and 1, and the calculations havebeen restricted to those values.

B. Calculated integral and centre-of-mass differential

cross sections

The QM collision energy dependence of the integral cross-sections calculated on the CW coupled PESs for each initial j ofH2 and spin–orbit states of Cl is shown in Fig. 2. The earlier,

single-electronic-state simulations of the title reaction6,19 foundthat the reactivity is strongly enhanced by increasing rotationalexcitation of the H2 with a noticeable decrease of the effectivereaction threshold with increasing j. An identical effect is seenhere in the multi-state calculations. We do observe, however,that the enhancement is greater for reaction of Cl in its ground,as compared to excited, spin–orbit state.Figs. 3–5 present integral reactive cross sections for produc-

tion of HCl(v ¼ 0,j0) by reaction of H2(v ¼ 0,j ¼ 0–4) at Ec ¼3.85, 4.25, and 5.85 kcal mol�1. Cross sections are shown forreaction of both Cl(ja ¼ 3/2) and Cl (ja ¼ 1/2). We also observe,as remarked earlier by ACW, that the BO allowed reactiondominates except at the lowest collision energies. In the case ofthe experiments at collision energies below the zero-pointcorrected barrier, reaction of the lowest H2 rotational levelscan proceed only by tunnelling. The reaction of the spin–orbitexcited state, although BO forbidden, will have a lower effec-tive barrier (Fig. 1). At the lower two collision energies (3.85and 4.25 kcal mol�1; Figs. 3 and 4) and up to j ¼ 2, thetunnelling damping of the BO allowed reaction becomes largeenough that the BO forbidden reaction, with a lower tunnellingbarrier, becomes dominant. However, once the collision energyhas increased to 5.85 kcal mol�1 (Fig. 5), the BO allowed

Fig. 2 Quantum reactive integral cross sections (ICS) as a function ofinitial collision energy, Ec, for the reaction of (a) H2(v ¼ 0,j ¼ 0), (b)H2(v ¼ 0,j ¼ 1), (c) H2(v ¼ 0,j ¼ 2), (d) H2(v ¼ 0,j ¼ 3), (e) H2(v ¼ 0,j ¼ 4). Solid and open symbols designate, respectively, cross sectionsfor reaction of Cl(2P3/2) and Cl(2P1/2). The continuous and dashed linesare drawn through the symbols for Cl(2P3/2) and Cl(2P1/2), respectively,to simply guide the eye.

Fig. 3 Quantum reactive integral cross sections (ICS) plotted as afunction of final HCl rotational quantum number at Ec ¼ 3.85 kcalmol�1 for the reaction of (a) H2(v ¼ 0,j ¼ 0), (b) H2(v ¼ 0,j ¼ 1), (c)H2(v ¼ 0,j ¼ 2), (d) H2(v ¼ 0,j ¼ 3), (e) H2(v ¼ 0,j ¼ 4). The filledsquares and open diamonds, designate, respectively, cross sections forreaction of Cl(2P3/2) and Cl(2P1/2).


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reaction dominates for all initial H2 rotational levels. We referthe reader to the paper by ACW26 for a comparison betweenintegral cross sections determined by the complete calculationstreatment, including all quasi-diabatic potential energy sur-faces and the simpler, treatment, based on only the lowestelectronically-adiabatic PES.

The corresponding CMDCSs, summed over all HCl productrotational levels, are shown in Figs. 6–8. For the reaction ofboth Cl(2P3/2) and Cl(2P1/2), the DCSs are strongly backwardpeaked for all Ec’s and j’s, although the degree of backwardpeaking is somewhat less for the Cl(2P1/2) reaction.

3. Experimental methods and results

The scattering experiments were carried out in a universalcrossed molecular beam apparatus described in detail else-where.49 Briefly, two well collimated supersonic beams of thereagents are crossed at 901 under single-collision conditions ina large scattering chamber with background pressure in the10�7 mbar range. The angular and velocity distributions of thereaction products are recorded by a rotatable, triply-differen-tially pumped, ultra-high-vacuum (10�11 mbar) electron-impact-ionization quadrupole mass-spectrometer detectorusing time-of-flight (TOF) analysis.

The supersonic atomic chlorine beams were generated by ahigh-pressure radio-frequency (rf) discharge beam source,which has been used successfully in our laboratory for over a

decade to generate intense supersonic beams of a variety ofatomic and radical species.49,50,62 The source is similar indesign to that developed by Sibener et al. to produce atomicoxygen beams.63 A high level of rf power was fed, through anLC circuit made to resonate around 14 MHz, into a plasmacontained in a quartz nozzle (diameter f ¼ 230 mm) cooled bylow electrical conductivity water. Due to the circuit design, theplasma is located behind the orifice of the nozzle permitting avery high degree of molecular dissociation (up to 98%).Because of the high plasma temperature reached when a pureCl2–rare gas mixture is used, we operated by discharging gasmixtures that also included molecular oxygen. The plasmatemperature is thereby reduced to B1000 K, so that it ispossible to operate at relatively high pressure (B300–400 mbar) without losing beam stability. The conditions ofthe experiments performed at Ec ¼ 5.85 kcal mol�1 arereported in ref. 5.The conditions of the new experiments were set to explore

fully the origin of the discrepancies visible when comparingprevious experimental results at Ec ¼ 4.25 kcal mol�1 with thesimulations from QM scattering calculations on the BW PES.6

To do so, it is necessary to improve the kinematics. These are,unfortunately, inherently unfavorable, because of the largemass of HCl compared to the departing H atom and by thesmall product translational energy [the maximum translational

Fig. 4 Same as Fig. 3, except at Ec ¼ 4.25 kcal mol�1.



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energy the products can attain is given by Etot ¼ Ec � DH1 þEi, where DH1 is the enthalpy of reaction: slightly positive(endothermic) in the case of reaction of Cl(2P3/2) and Ei is theinternal energy of the reactants].

Guided by these considerations, we used a slow beam ofatomic chlorine (with Ne as seeding gas) and fast molecularhydrogen beams, which were achieved by heating the gas. Forthe experiments performed at Ec ¼ 3.85 and 4.25 kcal mol�1,we used a nominal rf power of 310 W in a 2.75% Cl2 �2.75%O2–Ne mixture at 350 mbar pressure. The Cl beam peakvelocity and speed ratio (SR) were 1615 m s�1 and 6.9,respectively, as measured from single-shot TOF analysis. Theatomic chlorine beam was skimmed by a boron nitride skim-mer (f ¼ 0.96 mm) and further collimated by a rectangular slit.The angular divergence of the beam was 2.31.

In the present investigation it is crucial to know the relativepopulation of the spin–orbit states of Cl in the beam. When a rf(or other electric) discharge is used to produce an atomicplasma, multiple electronic and fine structure levels are popu-lated. Supersonic expansion is quite efficient in quenching mostof the excited states; however, the 2P1/2 spin–orbit excited stateformed in the plasma is inefficiently quenched as shown byStern–Gerlach magnetic analysis.50 The ratios of the 2P1/2 to

2P3/2 populations were determined to be 0.22 � 0.03 whenusing Ne as the seeding gas (Ec¼ 3.85 and 4.25 kcal mol�1) and0.15 � 0.03 when using He (Ec ¼ 5.85 kcal mol�1).50

The beam of H2 was produced by supersonic expansion ofneat H2 at a stagnation pressure of 2.5 bar through a 100 mmstainless steel nozzle resistively heated at a nominal tempera-ture of 650 and 730 K, respectively, for the experiments at Ec ¼3.85 and 4.25 kcal mol�1. The peak velocity of the H2 beamswas 3820 m s�1 (SR ¼ 12) and 4020 m s�1 (SR ¼ 11),respectively. The angular divergence of both beams was 5.71.Unfortunately, even though the supersonic expansion is

usually accompanied by substantial rotational relaxation, be-cause of the large rotational spacing, the relaxation of theheated H2 beam is inefficient, so that levels up to j ¼ 4 aresignificantly populated. The presence of excited H2 rotationallevels in the beams counteracts the advantage of working atlow Ec, since H2 rotational excitation strongly promotes thereaction of the spin–orbit ground state. In addition, to simulatethe experimental results, the QM calculations need to beperformed for each initially populated H2 rotational level,from j ¼ 0 to 4. Since the calculated integral and differentialcross sections are slightly different for each initial rotationallevel, an accurate simulation depends on knowing the relativerotational level populations in the n-H2(j) beams.We have not directly measured the rotational state popula-

tions of H2 in our beams and so must resort to an estimate. Weuse two different procedures: First, we extrapolated the

Fig. 6 Quantum CM differential cross sections (DCS), summed overall HCl product rotational and vibrational levels at Ec ¼ 3.85 kcalmol�1 for the reaction of (a) H2(v ¼ 0,j ¼ 0), (b) H2(v ¼ 0,j ¼ 1), (c)H2(v ¼ 0,j ¼ 2), (d) H2(v ¼ 0,j ¼ 3), (e) H2(v ¼ 0,j ¼ 4). The continuousand dashed lines designate, respectively, the differential cross sectionsfor reaction of Cl(2P3/2) and Cl(2P1/2).



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experimental determination of Pollard et al.64 for beamsobtained under similar expansion conditions. Secondly, aftercalibrating the thermocouple which reads the nozzle tempera-ture in a pure helium expansion, we were able to derive the H2

internal energy from the amount of the translational energy ofthe H2 beams measured from TOF measurements.65 Theresults of the two methods are similar. The rotational distribu-tions we have used in the simulations of our experiments arereported in Table 2. Of course these are only estimates. Werecall that the rotational energy of the j ¼ 1, 2, 3 and 4 levels is0.34, 1.01, 2.03 and 3.38 kcal mol�1,66 respectively (theseinternal energies are substantial compared to both the reactionbarrier and the heat of reaction).

The laboratory angular distributions, N(Y), of the HClproducts were obtained by taking at least five scans of 100 scounts at each angle. The nominal angular resolution of thedetector for a point collision zone is 11. The secondary target

H2 beam was modulated at 160 Hz with a tuning fork chopperfor background subtraction. Even though 35Cl is about threetimes more abundant than 37Cl, we detected the scatteredproducts at a mass to charge ratio (m/z) of 38 (H37Cl), thusavoiding the detection of products at a m/z ratio intermediatebetween the intense peaks of the two atomic chlorine isotopes(35Cl and 37Cl).Velocity distributions of the HCl products were obtained at

selected laboratory angles using a cross correlation TOFtechnique with four 127-bit pseudorandom sequences. High-time resolution was achieved by spinning the TOF disk, locatedat the entrance of the detector, at 393.7 Hz, corresponding to adwell time of 5 ms channel�1. The flight length was 24.6 cm.Counting times varied from 30 to 60 minutes depending uponsignal intensity.Figs. 9–11 display the laboratory angular distributions from

the Cl þ H2 reaction at the three values of Ec investigated,together with the corresponding Newton diagrams. The errorbars of the experimental distributions represent �1 standarddeviation. Product TOF distributions at selected laboratoryangles are shown in Figs. 12–14. The solid line in Figs. 9–14represents the angular and TOF distributions obtained fromQM scattering calculations (see below); the separate contribu-tions from the two Cl spin–orbit states are also shown asdashed and dotted lines.

4. Comparison between experimental results and

theoretical simulations

The theoretical differential cross sections are calculated in thecentre-of-mass (CM) coordinate system. Therefore, in order tocompare these DCSs directly with the experimental data, wehave to convert them into the laboratory (LAB) system ofcoordinates. Due to the finite experimental resolution (i.e.,finite angular and velocity spread of the reactant beamsand angular resolution of the detector) the CM-LAB


Table 2 Estimated H2 rotational populations in the supersonic beams

(see text)

Ec/kcal mol�1 j ¼ 0 j ¼ 1 j ¼ 2 j ¼ 3 j ¼ 4 j Z 5

3.85 0.08 0.52 0.14 0.22 0.02 0.02

4.25 0.07 0.46 0.14 0.26 0.04 0.03

5.85 0.08 0.49 0.14 0.24 0.03 0.02

Fig. 9 HCl product laboratory angular distributions at Ec ¼ 3.85 kcalmol�1. The solid lines represent the angular distribution obtained fromQM scattering calculations. The separate contributions from thereactions of Cl(2P3/2) (dashed lines) and Cl(2P1/2) (dotted lines) areshown. The corresponding canonical Newton diagram is also shown.vCl and vH2

are the laboratory beam velocity vectors,YCM indicates thelaboratory location of the CM angle in the LAB frame. The circle inthe Newton diagram delimits the maximum speed that HCl(v0 ¼ 0)can attain if all the available energy for the reaction of Cl(2P3/2) withH2(v ¼ 0,j ¼ 0) is channelled into product translation.


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transformation is not single-valued. Consequently, we prefer touse a forward convolution routine. This approach removes anypossible ambiguity associated with the derivation of the best-fitCM functions.

The theoretically derived final HCl j0 rotational distributionswere converted into final relative translational energy distribu-tions, Pj(E

0t), and then to CM speed distributions, Pj(u), for

each initial j of H2, with Pj(u) treated as continuous functions.The theoretical reaction endoergicity (which is slightly largerthan the experimental value) was used to convert the HClrotational distributions obtained in our scattering calculationsinto final relative translational energy distributions. Thischoice has an influence on the simulation, but we believe itto be the best to evaluate the overall quality of the CW PES.

The CM flux for HCl(v0 ¼ 0) is then given by:

ICM(y,u) ¼ w3/2

Pj¼0,1,2,3,4 wjT3/2,j(y)P3/2,j(u)

þ w1/2

Pj ¼ 0,1,2,3,4 wjT1/2,j(y)P1/2,j(u) (4)

where w3/2 and w1/2 are the two spin–orbit state populations inthe beams, wj are the H2 rotational level populations in thebeams and the T3/2,1/2,j(y) functions are the calculated CMDCS for each initial j of H2 and Cl spin–orbit states. Theenergy dependence of the integral cross section as obtainedfrom calculations for each single initial j of H2 and spin–orbitstate of Cl (see Fig. 2) was explicitly considered in theconvolution routine.The comparison between the predicted and experimental

laboratory frame angular distributions is shown in Figs. 9–11.The QM calculations reproduce the general features of theexperimental results, such as the pronounced backward scat-tering observed at each Ec. However, at each energy thetheoretical simulations predict the peak to occur at somewhattoo large an angle. Also, for scattering at angles close to theposition of the CM (which corresponds to sideways scatteredproducts with low recoil speeds) the theoretically predictedintensities are too small, even when the experimental uncer-tainties are taken into account.In a comparison of the QM results with TOF distributions,

once again the general features are correctly predicted, but theQM calculations predict TOF distributions somewhat fasterthan the experimental ones for all angles and Ec’s considered(see Figs. 12–14).



Fig. 12 HCl product time-of-flight distributions at Ec ¼ 3.85 kcalmol�1. The solid lines represent the QM predictions. The separatecontributions from the reactions of Cl(2P3/2) (dashed lines) andCl(2P1/2) (dotted lines) are shown.



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The theoretical results obtained at the collision energy ofLiu’s experiment and for initial H2 j ¼ 0 and 1 are shown inFigs. 15 and 16. When comparing our QM predictions withLiu’s experimental CM functions,8 we must consider that theexperimental functions include the contributions of both j ¼ 0and 1, with an expected relative population of B25% for j ¼ 0and B75% for j ¼ 1. Interestingly, the predicted CM DCS forthe reaction of Cl(2P3/2) is very similar to that derived by Liu,when using a photolytic source of Cl atoms – a method which isknown to give almost exclusively atomic chlorine in the groundspin–orbit state (see Fig. 2a of ref. 8).

By contrast, some differences are noticeable when comparingthe theoretical DCS, see Fig. 16, for reaction of Cl(2P1/2) withthat inferred from the experiment performed using a dischargesource. In particular, the theoretical DCS is more sidewayspeaked than that derived by subtracting the signal arising fromreaction of ground-state atoms (photolysis source) from thesignal arising from reaction of both spin–orbit states (dischargesource). A more significant discrepancy occurs in the productrotational distributions: the QM distributions (Fig. 15) arepeaked at j0 ¼ 2–3 (for both initial H2 j0s) and j0 ¼ 5 (for thereaction of the dominant j ¼ 1 of H2) for reaction of Cl(2P3/2)and Cl(2P1/2), respectively. In contrast, Liu’s experimental dis-tributions (see Fig. 6 of ref. 8) are peaked at j0 ¼ 4 and j0 ¼ 8–10.

5. Discussion

The following factors are now considered as likely responsiblefor the disagreement between the simulated and experimentalangular and TOF distributions:

(I) The QM calculations on the CW coupled PESs predictvery little energy released in HCl(v0 ¼ 0) rotation, similarly tothe single-electronic state calculations on the BW PES.6 Con-sequently, the fraction of energy released as product transla-tional energy is very large and the product Pj(E

0t)’s are all

peaked at the maximum value of E0t allowed by energy con-servation. Thus, as implied by the Newton diagrams in Figs. 9–11, the transformation of the backward-peaked theoretical CMDCSs into the LAB frame coupled with very energetic Pj(E

0t)’s

generates angular distributions which are peaked at anglesquite displaced from the angle corresponding to the positionof the centre-of-mass, YCM. Also, the very large fraction ofenergy released as product translational energy produces veryfast product velocity distributions. In conclusion, one explana-tion of the observed discrepancies between experiment and thesimulations is that the calculations underestimate the fractionof energy released into rotation, thus overestimating the frac-tion released into translation. Notably, also, the energy parti-tioning derived in Liu’s experiment points to a higher degree ofrotational excitation than that derived by the QM calculations.We recall that in determining the translational energy dis-

tributions of the products, we have used the theoretical value ofthe enthalpy of reaction (þ1.43 kcal mol�1). Since the truevalue is smaller (þ1.03 kcal mol�1), the maximum energyattainable by the HCl products will, in fact, be larger. If theexperimental values were used in the forward simulation, thedegree of disagreement with experiment would be even greater.(II) The increase of reactivity with the increase of initial H2

rotation is very pronounced in the CW PES, as it was in theprevious BW PES,6,19 see Fig. 2. Once we account for therelative reactivity of each initial H2 rotational level and itsrelative population in the beam, reaction of j ¼ 3 dominates atall collision energies considered. The internal energy of thisstate is 2.03 kcal mol�1, which is a sizeable quantity, especiallyin the experiments at lower Ec. As a result of this extra energy,after transformation to the LAB frame, the products of thej ¼ 3 reaction are characterized by a backward peak signifi-cantly displaced from YCM. Because the j ¼ 3 reaction dom-inates, the overall angular distribution is shifted in the wrongdirection, in comparison with experiment. The same is true forthe QM TOF distributions which are somewhat too fastcompared with the experimental ones.The difference in the reactivity with increasing rotational

excitation is so large [s(j ¼ 3)/s(j ¼ 0) B 127 and 75 at Ec ¼3.85 and 4.25 kcal mol�1, respectively] that slight errors in ourestimate of the j ¼ 3 population in the beams would not alterthis conclusion.


Fig. 15 Quantum reactive integral cross sections (ICS) plotted as afunction of final HCl rotational quantum number for reaction ofH2(v ¼ 0,j ¼ 0,1) at Ec ¼ 5.2 kcal mol�1 (the collision energy in theCMB experiment of Liu and co-workers, ref. 8). The filled squares andopen diamonds designate, respectively, cross sections for reaction ofCl(2P3/2) and Cl(2P1/2).

Fig. 16 Quantum CM differential cross sections (DCS), summedover all HCl product rotational and vibrational levels for reaction ofH2(v ¼ 0,j ¼ 0,1) at Ec ¼ 5.2 kcal mol�1 (the collision energy in theCMB experiment of Liu and co-workers, ref. 8). The filled squares andopen diamonds designate, respectively, cross sections for reaction ofCl(2P3/2) and Cl(2P1/2).


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(III) The calculated DCSs show a pronounced anisotropy,being strongly backward peaked. The use of CM DCSs whichare less anisotropic than those derived on the CW PESs reducesthe discrepancies observed in the LAB angular distributions bycompensating for the missing intensity at angles close to theCM position. However, even if the CM DCSs were less back-ward peaked than those predicted by the QM calculations thecomparison with the TOF distributions would not be signifi-cantly improved.

(IV) Since the present QM calculations on the CW coupledPESs predict that the BO forbidden reaction of the 2P1/2 statemakes only a small contribution at all energies, we mightwonder whether the discrepancy between theory and experi-ment is due to an underestimation of the 2P1/2 contribution.However, we observe in Figs. 9–11 that the peaks of theangular distributions predicted for reaction of Cl(2P1/2) alwaysoccur at laboratory angles larger than those for the groundspin–orbit state. This is because, for an initial collision energy,the products of the Cl(2P1/2) reaction will always have a greatertranslational energy, due to the internal spin–orbit energy ofCl(2P1/2). The argument is similar to that, presented above, forthe products of reaction of H2(j ¼ 3). Consequently, were we toincrease the weight of the Cl(2P1/2) contribution, the peak ofthe predicted LAB angular distributions would be shifted evenmore in the wrong direction and TOF distributions wouldbecome faster, and hence in poorer agreement with experiment.

An increase in the Cl(2P1/2) contribution would help resolvethe observed discrepancy only if the DCSs and energy releaseassociated with reaction of Cl(2P1/2) were dramatically differentthan those associated with reaction of Cl(2P3/2). This is un-likely, since the coupling of the reactive and repulsive PESsoccurs in the entrance channel,28 and since only a single PEScorrelates with the products (Fig. 1). Consequently, regardlessof the initial spin–orbit state of the reactants, the same PES willgovern the separation of the products, and hence the form ofthe DCSs and the degree of HCl rotational excitation. Thisconclusion is further supported by Liu’s observation,8 that theDCSs for reaction of the two spin–orbit states are quite similar,both strongly backward peaked.

6. Conclusion

In summary, the calculations presented here are based on acomplete description of the open-shell character of the reac-tion, with DCSs calculated on coupled electronic PESs. Thesecalculations were undertaken to assess the contribution of theexcited spin–orbit state of Cl to the observed laboratorydistributions for the title reaction, and to understand whetherinclusion of this adiabatically-forbidden channel was the originof the discrepancy between simulations based on the BW PESand the results of crossed-molecular-beam experiments.6 Tofocus on the contribution of the excited spin–orbit state, newCMB experiments were carried out at lower collision energy.

The multi-electronic-state QM scattering calculations pre-dict angular and TOF distributions which still differ somewhatfrom both prior and our new CMB results. This disagreementis likely due to an underestimation of the degree of rotationalexcitation of the HCl product, possibly due to residual im-perfections in the exit channel of the ab initio PESs. An earlierstudy67 showed that for the H þ HCl exchange reaction quasi-classical trajectory calculations indicated that the Bian–WernerPESs gave worse agreement with experiment than calculationson other PESs. Since the exit channels of the CW and BW PESsare identical, this result would seem to support our conclusionhere that more work may need to be done in describing theClH2 PESs.

The calculations described here indicate that the magnitudeof both integral and differential cross sections for the spin–orbit excited state reaction are much smaller than those of theground state reaction. Further, an increase in the reactivity of

the excited spin–orbit state would result in a shift of theangular distributions toward larger angles, in poorer agree-ment with experiment. Consequently, the present comparisondoes not support the conclusion, by Liu and co-workers,8,9 thatthe title reaction is dominated by reaction of the excitedspin–orbit state of the Cl atom.Even for this simple, and important, elementary reaction,

crucial features of the reaction dynamics remain as yet not fullyunderstood, in particular the details of the product internalenergy release and the relative reactivity of the excited spin–orbit state. The need for more work, both experimental andtheoretical, is clear. It is likely that the remaining differencesbetween theoretical simulations and the present experimentalresults may reflect some residual inaccuracies in the underlyingpotential energy surfaces.

Acknowledgements

The research described herein has been supported by MIUR(COFIN 2003) of Italy, the EC within the Research TrainingNetwork Reaction Dynamics including post-doctoral fellow-ships for D. S. and G. C. (Contract No. HPRN-CT-1999-00007), the Deutsche Forschungsgemeinschaft and Fonds derChemischen Industrie of Germany, and the U. S. NationalScience Foundation (grants CHE99-71810 and CHE-0413743).

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