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Differential and integral cross sections for the rotationallyinelastic scattering of methyl radicals with H2 and D2

Citation for published version:Tká, O, Ma, Q, Rusher, CA, Greaves, SJ, Orr-Ewing, AJ & Dagdigian, PJ 2014, 'Differential and integralcross sections for the rotationally inelastic scattering of methyl radicals with H

2 and D

2', Journal of

Chemical Physics, vol. 140, no. 20, 204318. https://doi.org/10.1063/1.4879618

Digital Object Identifier (DOI):10.1063/1.4879618

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Differential and integral cross sections for the rotationally inelastic scattering of methylradicals with H2 and D2Ondřej Tkáč, Qianli Ma, Cassandra A. Rusher, Stuart J. Greaves, Andrew J. Orr-Ewing, and Paul J. Dagdigian Citation: The Journal of Chemical Physics 140, 204318 (2014); doi: 10.1063/1.4879618 View online: http://dx.doi.org/10.1063/1.4879618 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/20?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Rotationally inelastic scattering of methyl radicals with Ar and N2 J. Chem. Phys. 142, 014306 (2015); 10.1063/1.4904901 Rotational excitation of HCN by para- and ortho-H2 J. Chem. Phys. 140, 224302 (2014); 10.1063/1.4880499 State-to-state differential and relative integral cross sections for rotationally inelastic scattering of H2O byhydrogen J. Chem. Phys. 134, 204308 (2011); 10.1063/1.3589360 Rotational relaxation of HF by collision with ortho- and para- H 2 molecules J. Chem. Phys. 129, 104308 (2008); 10.1063/1.2975194 Full-dimensional quantum wave packet study of rotationally inelastic transitions in H 2 + H 2 collision J. Chem. Phys. 117, 5183 (2002); 10.1063/1.1500731

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THE JOURNAL OF CHEMICAL PHYSICS 140, 204318 (2014)

Differential and integral cross sections for the rotationally inelasticscattering of methyl radicals with H2 and D2

Ondrej Tkác,1 Qianli Ma (���),2 Cassandra A. Rusher,3 Stuart J. Greaves,3

Andrew J. Orr-Ewing,1,a) and Paul J. Dagdigian2,b)

1School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom2Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218-2685, USA3School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom

(Received 11 April 2014; accepted 13 May 2014; published online 30 May 2014)

Comparisons are presented of experimental and theoretical studies of the rotationally inelastic scat-tering of CD3 radicals with H2 and D2 collision partners at respective collision energies of 680± 75 and 640 ± 60 cm−1. Close-coupling quantum-mechanical calculations performed using a newlyconstructed ab initio potential energy surface (PES) provide initial-to-final CD3 rotational level(n, k → n′, k′) integral and differential cross sections (ICSs and DCSs). The DCSs are comparedwith crossed molecular beam and velocity map imaging measurements of angular scattering distri-butions, which serve as a critical test of the accuracy of the new PES. In general, there is very goodagreement between the experimental measurements and the calculations. The DCSs for CD3 scatter-ing from both H2 and D2 peak in the forward hemisphere for n′ = 2–4 and shift more to sidewaysand backward scattering for n′ = 5. For n′ = 6–8, the DCSs are dominated by backward scattering.DCSs for a particular CD3 n → n′ transition have a similar angular dependence with either D2 or H2

as collision partner. Any differences between DCSs or ICSs can be attributed to mass effects becausethe PES is unchanged for CD3−H2 and CD3–D2 collisions. Further comparisons are drawn betweenthe CD3–D2 scattering and results for CD3–He presented in our recent paper [O. Tkác, A. G. Sage,S. J. Greaves, A. J. Orr-Ewing, P. J. Dagdigian, Q. Ma, and M. H. Alexander, Chem. Sci. 4, 4199(2013)]. These systems have the same reduced mass, but are governed by different PESs. © 2014AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4879618]

I. INTRODUCTION

The potential energy surface (PES) is a key theoreti-cal concept in the field of molecular reaction dynamics.1

Modern quantum chemistry provides methods to computeab initio PESs within the Born-Oppenheimer approximation,while measurement of state-to-state differential cross sections(DCSs) provide an excellent experimental test of the accuracyof the PES since the DCSs are sensitive to both attractive andrepulsive parts of the potential.2 The accuracy of a computedPES can hence be tested by comparing theoretical DCSs, cal-culated from quantum scattering theory, with experimentallymeasured DCSs. If theory and experiment are found to be ingood agreement, robust deductions can be drawn about thecollision dynamics, including the relationship between ex-perimental measurables (e.g., angular distributions and statepropensities) and features of the PES controlling the collisiondynamics.

We focus here on DCSs involving the inelastic scatter-ing of methyl radicals with molecular hydrogen. Studies ofcollisions of several important species (e.g., H2O, OH, NH3,and CH3) with molecular hydrogen are motivated by astro-physical applications, because of the high abundance of H2

in the universe. Collisions involving methyl radicals are of

a)Electronic mail: a.orr-ewing@bris.ac.ukb)Electronic mail: pjdagdigian@jhu.edu

particular interest for the hydrocarbon chemistry of the at-mospheres of the outer planets in the solar system,3–5 aswell as Titan.6 Methyl radical chemistry is important in thecombustion of hydrocarbons7, 8 and chemical vapour deposi-tion of diamond films.9, 10 In addition, methyl radicals maybe an integral part of a catalytic cycle for partial oxida-tion of methane to formaldehyde or methanol for chemicalfeedstocks.11

From a theoretical perspective, accurate close-couplingDCSs for methyl scattering are computationally tractable forcollisions involving the H2 or D2 molecule because theirlarge rotational constants [B(H2) = 60.853 cm−1 and B(D2)= 30.443 cm−1]12 mean that only a few rotational levels ofthe collision partner need to be included in quantum scat-tering calculations. Although D2 has the same mass as a Heatom, collisions involving the diatomic molecule can changethe internal state of both collision partners, along with therelative kinetic energy. Comparison of inelastic DCSs forcollisions of methyl radicals with He, H2, and D2 might there-fore distinguish the consequences of the additional molecu-lar rotational degrees of freedom from purely mass relatedeffects.

The inelastic scattering of labile free radicals was ex-tensively reviewed in the mid 1990s,13–15 with a focus onstate-resolved integral cross sections (ICSs). Since then, ex-perimental studies using velocity map imaging (VMI)16, 17

and laser spectroscopic detection have revolutionized

0021-9606/2014/140(20)/204318/12/$30.00 © 2014 AIP Publishing LLC140, 204318-1

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measurement of state-resolved DCSs, for which the most ex-tensively studied molecules are the NO18–26 or OH27–35 di-atomic radicals. To date, the only reported measurement ofDCSs for inelastic scattering of polyatomic free radicals isour recent study of methyl radical scattering by He.36 Wefound excellent agreement between experimental measure-ments and DCSs calculated using the recent PES of Dagdi-gian and Alexander.37 The inelastic scattering of closed-shell polyatomic molecules is more extensively illustratedby determinations of DCSs for scattering of ammonia38–40

and deuterated ammonia41, 42 with rare gases and molecu-lar hydrogen, and for water with helium43 and hydrogen.44

The rotationally inelastic scattering of deuterated methylradicals and ammonia in collisions with helium were re-cently compared, using close-coupling quantum-mechanicalscattering calculations performed with accurate ab initioPESs.45

Dagdigian’s review of quantum scattering calculationsof collisional energy transfer in small hydrocarbon interme-diates provides a current perspective on polyatomic radi-cal scattering46 and highlights studies involving methylene(CH2)47, 48 and methyl.37, 48, 49 The energy transfer dynamicsfor a polyatomic species like the methyl radical are more com-plicated than for collisions of a diatomic molecule with anatom. In the latter case, the cylindrical symmetry limits theanisotropy to that associated with the polar angle away fromthe molecular axis. In contrast, for collisions of methyl radi-cals, anisotropies must be considered that are associated withthe polar angle (away from the C3 symmetry axis) and theazimuthal angle about this axis.

In the work reported here, DCSs for collisions of CH3

and CD3 with H2 and D2 were experimentally determined us-ing crossed molecular beam (CMB) and VMI methods. How-ever, we concentrate on the DCSs for collisions of CD3 sinceonly a few CH3 levels can be cleanly detected because ofpredissociation of the excited-state used for spectroscopic de-tection. We compare the measured DCSs with results fromquantum close-coupling scattering calculations performedusing a newly computed ab initio PES.

II. METHOD

A. Experimental apparatus

The compact crossed molecular beam apparatus used formeasurement of DCSs was described in detail previously,36

and we present only a brief summary of the experimentalmethod here. Schematic top and side views of the instru-ment were shown in Fig. 1 of Ref. 36. Molecular beams wereformed by supersonic expansion through a pair of pulsedvalves (General Valve Series 9) and were collimated byskimmers. The methyl radical primary molecular beam wasformed by 266 nm photolysis of CH3I or CD3I in 3% mix-tures in Ar, at a stagnation pressure of 4 bar, immediatelyafter the orifice of the pulsed valve. The secondary molecu-lar beam was formed by expansion of 4 bar of pure D2 or H2.The two skimmed beams propagated horizontally and crossedat a 90◦ intersection angle in a high vacuum scattering cham-ber. A typical base pressure for the scattering chamber was

<10−8 Torr with the pulsed valves turned off, and this rose to∼10−7 Torr when the valves were operating.

The intersection region of the two molecular beams waslocated within a vertically mounted stack of 20 electrodesforming an ion optics assembly for dc slice-imaging.50 Aprobe laser focused to the intersection of the beams ionizedthe scattered methyl radicals, and the electric field createdby the electrode stack accelerated the ions upwards towardsa position-sensitive detector. The ion detector (Photek) con-sisted of a pair of microchannel plates (MCPs), a phosphorscreen (P46 phosphor) and a CCD camera. The voltage ap-plied to the rear MCP was pulsed for 20 ns to time-gate thedetection of ions.

UV radiation in the wavelength range 285–288 nm re-quired for (2+1) resonance enhanced multiphoton ioniza-tion (REMPI) detection of the methyl radicals was generatedby frequency doubling the output of a tuneable pulsed dyelaser. The energy and linewidth of the probe laser beam were4.5 mJ/pulse and 0.0027 nm (0.32 cm−1), respectively. In ourexperiments, the maximum Doppler shift of inelastically scat-tered CD3 radicals was 0.12 cm−1, which is smaller than thelaser linewidth. Methyl radicals were therefore ionized usingfixed laser wavelengths chosen to probe particular rotationallevels.

The electrodes forming the homogeneous accelerationfield stretched the methyl ion packet along the flight axis ac-cording to the initial velocities of the neutral methyl radicals.The short voltage pulse applied to the rear MCP then allowedonly a thin central slice of the ion packet to be recorded,corresponding to methyl radicals scattered within, or closeto the plane of the crossed molecular beams. Direct analysisof this slice image gave the three-dimensional velocity dis-tribution of the inelastically scattered methyl radicals with-out the need for image reconstruction techniques. The nozzleproducing the secondary beam of pure hydrogen was oper-ated in a repeating mode of 50 shots on and 50 shots off. Thedesired scattering signal was than obtained by subtraction ofthe background (without H2/D2) image from the total signalimage.

Analysis of experimental images required a density-to-flux transformation because the detection efficiency ofthe scattered products depended on their laboratory framevelocity. To correct the images for this detection bias, we em-ployed the method of Monte Carlo simulation of the exper-iment as described previously,36 using a modification of thecomputer program of Eyles and Brouard.51 Further details ofthe density-to-flux transformation can be found in the sup-plementary material.52 Low signal levels prevented any studyof laboratory-frame angular momentum polarization of thescattered methyl radicals.

B. REMPI detection and state distributionin incident beams

The methyl radical is an oblate symmetric top, with ro-tations described by total rotational angular momentum n andits body-frame projection k. The fine-structure and hyperfinesplittings are very small53 and are ignored in our theoreticaltreatment. As discussed in detail previously,36 the CH3 and

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CD3 radicals exist in two and three nuclear spin modifica-tions, respectively, that do not interconvert in molecular colli-sions. The energies of low-lying rotational levels of CH3 andCD3 have been plotted in Fig. 3 of Ref. 36. The normal forms(statistical mixtures of ortho and para modifications) of theH2 and D2 collision partners were employed in the scatteringexperiments.

The rotational level populations in the incident radicalbeam and the inelastically scattered CD3 or CH3 final levelswere determined using (2+1) REMPI spectroscopy throughthe 00

0 band of the 4p2A′′2 ← X2A′′

2 transition.54, 55 The leveldistributions in the incident radical beams were determinedby comparison of experimental spectra with spectra simulatedusing the PGOPHER program.56 As was shown in our recentpaper,56 the methyl radicals cooled to a rotational temperatureof ∼15 K. The relative populations of the rotational levelswere presented in Table 1 of Ref. 36.

The lines in the REMPI spectrum of methyl are resolvedin the n rotational quantum number, but not in the k projectionquantum number. Depending upon the spectroscopic branch(hence �n of the transitions), the k projection levels of a givenn contribute differently. The levels associated with the DCSsreported below are denoted by nk1k2... to indicate that the un-resolved nk1 , nk2 , . . . levels have been detected on a giventransition. The relative contributions of the different k projec-tion levels to the measured REMPI intensity were determinedby calculating 2-photon line strength factors using the PGO-PHER program.

The levels of the excited 4p2A′′2 electronic state are pre-

dissociated, and the linewidths for the CH3 isotopologue arelarger than for CD3. Hence, the efficiency of detection of CH3

rotational levels is lower, and DCSs were determined for farfewer final levels than for CD3. For this reason, we concen-trate in this paper on the DCSs for CD3 collisions and experi-mental images and DCSs for CH3 radical can be found in thesupplementary material.52

C. Potential energy surface

The geometry of the CH3–H2 rigid-rotor complex can bedescribed by five coordinates, similar to those used in earlierwork by Rist et al. on the NH3–H2 system57 These includethe intermolecular separation R and four angles (θ1,φ1) and(θ2,φ2) describing the orientations of the CH3 and H2 colli-sion partners, respectively, relative to the Jacobian vector Rconnecting the two molecules. This body-frame coordinatesystem is illustrated in Fig. 1.

In order to determine the form of the angular dependenceof the potential, we follow the work by Rist et al.57 and con-sider the interaction of a symmetric top with a linear moleculeas the expectation value of the sum of electrostatic interac-tions between the two molecules:

V = 〈ψ1ψ2|V |ψ1ψ2〉 = 〈ψ1ψ2|∑ij

qiqj r−1ij |ψ1ψ2〉, (1)

where ψ1 and ψ2 are the electronic wave functions of thetwo molecules and qi is the charge of particle i. The inverseseparation between a pair ij of electrons can be expressed as

FIG. 1. Body-frame coordinate system to specify the geometry of the CH3–H2 complex. The Jacobian R vector lies along the z axis. The CH3 and H2molecule-frame axes are denoted by (x′, y′, z′) and (x′′, y′′, z′′), respectively.

a triple sum of modified spherical harmonics,58

r−1ij =

∑l1l2l

Al1l2l(ri, rj , R)

×∑

m1m2m

〈l1m1l2m2|lm〉Cl1m1 (ri)Cl2m2 (rj )C∗lm(�BS).

(2)

In Eq. (2), ri and rj are the space-fixed coordinates of the ithand jth particles of molecules 1 and 2, respectively, relative tothe center of mass of each molecule. The term 〈l1m1l2m2|lm〉is a Clebsch-Gordan coefficient, the Cλμ are modified spheri-cal harmonics,59 and �BS is the orientation of the body framewith respect to the space frame. For non-overlapping chargedistributions, we must have l = l1 + l2; however, l can have thefull range |l1 – l2| ≤ l ≤ l1 + l2 for overlapping distributions,60

as would be the case for an intermolecular potential.We transform the first two spherical harmonics to the

body frame59

Cl1m1 (ri) =∑μ1

Dl1∗m1μ1

(�1S)Cl1μ1 (ρi), (3)

and similarly for molecule 2. Substitution of Eqs. (2) and (3)into Eq. (1) and integration over the electronic coordinatesyields the following formal expression for the interaction po-tential:

V (R,�1S,�2S) =∑

l1l2lμ1μ2

Bl1l2lμ1μ2 (R)∑

m1m2m

〈l1m1l2m2|lm〉

×Dl1∗m1μ1

(�1S)Dl2∗m2μ2

(�2S)C∗lm(�BS). (4)

In Eq. (4), the B terms are radial expansion coefficients, andthe Dl

m′m are rotation matrix elements.59 Since V is indepen-dent of the choice of the space frame, we align the space framewith the body frame (i.e., we align R along the space frame zaxis). In this case, only m = 0 terms contribute to the poten-tial. Also, only μ2 = 0 terms contribute since the electronicwave function of H2 is cylindrically symmetric. From Fig. 1,we define the orientation between CH3 and H2 as follows:

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�B1 ≡ (φ1, θ1, 0) defines the Euler angles to rotate the CH3

molecule frame to the body frame, and �2B ≡ (φ2, θ2, 0) ro-tates the body frame to the H2 molecule frame. With theseconsiderations, we can rewrite Eq. (4) as

V (R, θ1, φ1, θ2, φ2)=∑

l1l2lμ1

Bl1l2lμ1 (R)∑m1

〈l1m1l2,−m1|l0〉

×Dl1∗m1μ1

(0,−θ1,−φ1)Dl2∗−m1,0

(φ2, θ2, 0).

(5)

Symmetry considerations restrict the allowed terms inEq. (5). The threefold symmetry of CH3 requires that μ1 bea multiple of 3. The potential is invariant to exchange of thehydrogen nuclei in H2, hence l2 must be even. Since V is real,it can be shown that

Bl1l2lμ1 (R) = (−1)l1+l2−l+μ1B∗l1l2l,−μ1

(R). (6)

Since V must be invariant to reflection of H2 through the xzplane of the CH3 molecule frame, we have

Bl1l2l,−μ1 (R) = (−1)l1+l2+l+μ1Bl1l2lμ1 (R). (7)

Equations (6) and (7) imply that the B coefficients in Eq. (5)are real. In addition, V is invariant to reflection of H2 throughthe xy plane of the CH3 molecule frame since CH3 is planar.It can be shown that this property restricts l2 + l + μ1 tobe even. The potential should also be invariant with respectto inversion of all coordinates; this parity invariance restrictsthe l1 + l2 + l to even values.57 However, this symmetry canbe broken for the interaction of a nonlinear molecule with adiatomic.61, 62

Substituting Eq. (7) into Eq. (5) and resolving the rota-tion matrix elements in Eq. (5) into products of complex ex-ponentials and reduced rotation matrix elements, dλ

μm,59 weobtain

V (R, θ1, φ1, θ2, φ2) =∑

l1l2l,μ1≥0

Bl1l2lμ1 (R)(1 + δμ10)−1∑m1

〈l1m1l2,−m1| l0〉

×[e−iμ1φ1dl1

μ1m1(θ1) + (−1)l1+l2+l+μ1eiμ1φ1d

l1−μ1,m1(θ1)

]e−im1φ2d

l2−m1,0

(θ2). (8)

The PES was fitted with a modified version of Eq. (8),

V (R, θ1, φ1, θ2, φ2)

=∑

l1l2l,μ1≥0

Cl1l2lμ1 (R)1

2π

([l1][l2]

2

)1/2

×∑m≥0

(1 + δm0)−1〈l1ml2,−m|l0〉dl2−m,0(θ2)

× [cos(μ1φ1 + mφ2)dl1

μ1m(θ1) + (−1)l1+l2+l+μ1

× cos(μ1φ1 − mφ2)dl1−μ1,m(θ1)

], (9)

where [x] = 2x + 1 and

Cl1l2lμ1 (R) = 4π

1 + δμ10

(2

[l1][l2]

)1/2

Bl1l2lμ1 (R). (10)

The angular expansion in Eq. (9) is normalized so that thesignificance of individual terms can be evaluated directly.

We performed the explicitly correlated restrictedcoupled-cluster calculations with full inclusion of singleand double excitations and perturbative inclusion of tripleexcitations [RCCSD(T)-F12a]63, 64 of the CH3–H2 PES.We employed the aug-cc-pVTZ correlation-consistent basissets,65, 66 with aug-cc-pVTZ/MP2FIT and cc-pVTZ/JKFIT asthe density fitting basis and the resolution of identity basis,respectively.67, 68 A counterpoise correction was appliedto correct for basis-set superposition error.69 All calcula-tions were carried out with the MOLPRO 2010.1 suite ofprograms.70

The CH3–H2 interaction energies were determined on afive-dimensional grid of 33 values of the intermolecular sep-aration R [R (in bohr) = 3–8 in steps of 0.25; 8.5, 9, 9.5, 10,11, 12, 13, 14, 15, 16, 18, 20]. The interaction energy wascomputed over a random angular grid71 of 1600 orientations,consisting of uniform distributions of both cosθ1 and cosθ2

over [–1,1] and both φ1 and φ2 over [0,2π ]. The total numberof nuclear geometries for which the interaction potential wascomputed was 52 800. The interaction energies for an addi-tional 1400 orientations at R = 5 bohr were also computed tochoose statistically important terms in Eq. (9) to be used inthe final fit.

These (l1, l2, l, μ1) terms were chosen in the followingway. We first performed a least-squares fit of the 3000 ge-ometries at R = 5 bohr to a large 418-term angular basisconsisting of all symmetry-allowed terms with l1 ≤ 12 andl2 ≤ 6 to obtain estimated expansion coefficients for all theseterms. We started from a minimal angular basis with only theisotropic term, fit the ab initio points, and computed the esti-mated fitting error ei with a Monte Carlo error estimator.71 Wethen iteratively added terms whose estimated expansion coef-ficients have an absolute value greater than 8ei, and recom-puted ei with this new angular basis until no extra terms couldbe included with this criterion. The total number of terms in-cluded was 55. Unlike several other PESs describing the in-teraction of a symmetric or an asymmetric top with a linearmolecule,62, 72 all terms in our PES have even l1 + l2 + l, andnone of the odd l1 + l2 + l terms is statistically important.

The ab initio points were fitted using this 55-term angularbasis and the least-squares method. The root mean squares(RMS) of the fit62 increases with decreasing R but is <0.1%

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204318-5 Tkác et al. J. Chem. Phys. 140, 204318 (2014)

5 6 7 8 9 10−600

−400

−200

0

200

400

600

R / bohr

ener

gy /

cm−

1

l1=0, l2=2, l=2, μ1=0

l1=3, l2=2, l=5, μ1=3

l1=2, l2=2, l=4, μ1=0

l1=5, μ1=3

l1=4, μ1=0

l1=2, μ1=0

l1=3, μ1=3

l1=0, μ1=0

l1=5, l2=2, l=7, μ1=3

−600

−400

−200

0

200

400

600

ener

gy /

cm−

1

FIG. 2. Dependence of the larger expansion coefficients Cl1l2lμ1 (R) [definedin Eq. (9)] upon the CH3–H2 separation R. Upper panel: coefficients with l2= 0 (and hence l = l1); lower panel: coefficients with l2 = 2. The expansioncoefficients are the same for the interaction of CH3 or CD3 with D2 since thecenters of mass of the hydrogen molecule and methyl radical do not changeunder isotopic substitution.

of the average of the absolute value |V| of the potential forR ≥ 4.75 bohr [|V| = 2500 cm−1]. Using the Monte Carloerror estimator,71 we found the norm ‖S−1‖ for our randomlygenerated orientations and angular basis is 1.52. A value of‖S−1‖ close to 1 indicates sufficient angular sampling.

Figure 2 presents a plot of the larger expansion coeffi-cients Cl1l2lμ1 (R) as a function of the intermolecular separa-tion R in the region of the van der Waals well. For the termsinvolving the interaction with spherically averaged H2 (i.e., l2= 0), shown in the upper panel of Fig. 2, the largest coeffi-cients are the same as for CH3–He,37 namely (l1, μ1) = (3,3) and (2, 0). These reflect the leading anisotropies involv-ing approach of the collision partner within and perpendicu-lar to the plane of the methyl radical, as discussed previouslyfor CH3–He.37 The lower panel of Fig. 2 displays the largerCl1l2lμ1 (R) coefficients with l2 = 2, which reflect the molecu-lar nature of the collision partner. The plotted coefficients aredirect analogs of the l2 = 0 coefficients plotted in the upperpanel, namely (l1, μ1) = (0, 0), (3, 3), (2, 0), and (5, 3), withl = l1 + l2.

The global minimum of the PES has De = 99.0 cm−1, ata geometry of R = 6.57 bohr, θ1 = 0◦, θ2 = 0◦ (the φ anglesare meaningless here). The H2 molecule thus lies along the C3

axis of the methyl radical above (or below, by symmetry) themolecular plane. The well depth De is thus significantly largerthan that for CH3–He [27.0 cm−1 (Ref. 37)]. The equilibrium

θ1 / degrees

φ 1 / de

gree

s

θ2 = 0o

0 30 60 90 120 150 180 0 30 60 90 120 150 180θ

1 / degrees

θ2 = 90o, φ2 = 0o

00

0 0

0

00

0

00

50

50

50

5050

50

5050

100

100

100

100

100

100

175

175

175

175

−95

−95

−95

−95

−95−95

−90

−90

−90

−90−90

−90

−75

−75

−75

−75

−75

−75

−75

−75

−50−50

−50 −50

−50 −50

−50

−50

−50 −50

−50

−50

0

60

120

180

240

300

360

0 0

0

00

0

0 0

0

00

0

0 0

0

00

0

44

4

4

4

44

4

44

44

−70

−70

−70

−50−50−50

−50

−50−50

−50

−50−50

−25 −25

−25−25

−25 −25

−25−25

−25 −25

−25−25

−10 −10

−10−10

−10

−10 −10

−10−10

−10

−10 −10

−10−10

−10

FIG. 3. Dependence of the potential energy (in cm−1) on the orientation (θ1,φ1) of the methyl radical for two orientations (θ2, φ2) of the H2 collisionpartner for an intermolecular separation R = 6.5 bohr. The φ2 angle is mean-ingless in the left-hand panel, with θ2 = 0◦.

geometry differs from that of the global minimum for CH3–He,37 for which the He atom lies in the molecular plane andbisects two C–H bonds.

Figure 3 presents contour plots of the dependence of thepotential upon the orientation of the methyl radical for twoorientations of H2 for R = 6.5 bohr. For θ2 = 0◦ (left-handpanel of Fig. 3) the CH3 orientation for the most attractiveinteraction is the same as that of the global minimum. In thiscase the maximum repulsion occurs for θ1 = 90◦ and φ1 = 0◦,120◦, 240◦; this corresponds to approach of one end of the H2

molecule in the CH3 plane toward one of the C–H bonds. Theright-hand panel of Fig. 3 displays a contour plot of the po-tential for θ2 = 90◦, φ2 = 0◦. In this case, the most attractiveCH3 orientation (θ1 = 90◦ and φ1 = 60◦, 180◦, 300◦) corre-sponds to approach of the center of the H2 molecule in themolecular plane and bisecting two C–H bonds, with the H2

internuclear axis lying perpendicular to the CH3 plane. Thenew PES can be used without modification in scattering cal-culations on CD3–H2 and CD3–D2 collisions since the cen-ters of mass are unaffected for both molecules upon isotopicsubstitution.

D. Quantum scattering calculations

State-to-state DCSs and ICSs for collisions of CD3 withH2 and D2 were calculated using the HIBRIDON suite ofprograms73 and the PES described in Sec. II C. Rotationalenergies for CD3 were computed with a rigid rotor symmet-ric top Hamiltonian using rotational constants from a spec-troscopic study by Sears et al.74 Separate calculations werecarried out for each nuclear spin modification of both CD3

and H2/D2 since they are not interconverted in molecular col-lisions. The close-coupling channel basis consisted of CD3

rotational levels whose energies were less than 960 cm−1 andH2/D2 rotational levels with j2 ≤ 2, and the calculations in-cluded total angular momenta J ≤ 100 ¯. Convergence ofthe DCSs to within ∼5% was checked with respect to thesize of the rotational basis and the number of partial wavesin the calculation. The scattering calculations used up to5366 channels.

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Since the CD3 incident beam contained several rotationallevels, DCSs for formation of a specific final rotational levelnk were determined by weighting the computed state-to-stateDCSs at the experimental collision energy by the experimen-tally determined incident beam rotational level populationspresented in Table 1 of Ref. 36. Since the k projection num-ber is not resolved in the REMPI spectra, computed DCSsfor comparison with the experimental measurements wereweighted according to the 2-photon line strengths factors forthe given detection line. We assume the H2/D2 incident beamcontains a statistical mixture of j2 = 0 and 1 rotational lev-els and did not consider initial levels with j2 ≥ 2. The onlyj2-changing transition included in our DCS calculations wasj2 = 0 → 2. Including both the j2 = 0 → 0 and j2 = 0 →2 transitions changes the averaged DCSs by < 10% (exceptfor θ < 20◦, an angular range obscured by the incident beam)compared to including j2 = 0 → 0 transitions alone. We ex-pect the DCSs of other j2-changing transitions to be even lesssignificant due to larger energy gaps.

In previous work,37, 37, 46 we examined propensitiescaused by the leading angular expansion coefficients of thePES in the ICSs for CH3 and CD3 transitions induced by col-lision with He. We briefly explore here these propensities forcollisions of CD3 with D2. Figure 4 presents computed state-resolved ICSs for collision of the CD3 10 level, the lowestlevel of A1 nuclear spin modification, with the D2 j2 = 0 and1 rotational levels for which j2 is the same after the collision.These cross sections were calculated for a collision energy of

k

n

k

n

j2 = 0

j2 = 1 0 3 6 9

01

23

45

67

89

10

0

2

4

6

cros

s se

ctio

n / Å

2

0 3 6 9

01

23

45

67

89

10

0

2

4

6

cros

s se

ctio

n / Å

2

FIG. 4. ICSs for transitions out of the CD3 10 level (the lowest level of theA1 nuclear spin modification) in collisions with D2 at a relative translationalenergy of 640 cm−1. The rotational level of the collision partner is j2 = 0(upper panel) and j2 = 1 (lower panel). The initial level is indicated with anopen square. Since the cross sections for transitions to CD3 high n levels aresmall, the plots show cross sections for final levels with n′ ≤ 10.

640 cm−1. ICSs for transitions out of the lowest rotational lev-els of the A2 and E nuclear spin modifications can be found inthe supplementary material.52

We see in Fig. 4 that for most CD3 transitions the ICSs forj2 = 1 are only slightly larger than for j2 = 0. The major ex-ception is for the 10 → 30 transition, for which the cross sec-tion for j2 = 1 is ∼70% larger than for j2 = 0, and this increaseis seen in the DCS for θ ≤ 45◦. In some other molecule–H2 systems, e.g., OH–H2,75 H2O–H2,76 NH3– H2,77 the crosssections for the j2 = 1 initial level are much larger than forj2 = 0. In these systems, the collision partners of H2 havenonzero dipole moments so that the leading electrostatic termis the dipole-quadrupole interaction. This interaction corre-sponds to the l1 = 1, l2 = 2, l = 3, terms and could contributeto the cross sections for the j2 = 1 but not j2 = 0 initial level.Since methyl has no dipole moment, this interaction is miss-ing for CD3–H2/D2. For both these systems, the transitionswith the largest cross sections are to the 33 and 30 levels; thesame propensities were found for collisions with He.45 Thesefinal levels are directly coupled by the (l1, μ1) = (3,3) and(2,0) terms, respectively, of the PES.

III. RESULTS

Newton diagrams for inelastic scattering of CD3 with D2

and H2 are shown in Fig. 5 and illustrate the laboratory framevelocities of CD3 [v(CD3) = 550 ± 30 m s−1], D2 and H2

[v(D2) = 2090 ± 210 m s−1 and v(H2) = 2950 ± 320 m s−1],and the pre- and post-collision center-of-mass (CM) framevelocities of the methyl radical u(CD3) and u′(CD3), respec-tively. The CM-frame scattering angle θ is defined as the an-gle between the CM-frame velocities of CD3 before and aftera collision. The displayed Newton spheres correspond to aCD3 transition from initial level nk = 00 into final level n′

k ′

= 20, with an associated energy transfer of �E = 29 cm−1,and to �j2 = 0 and j2 = 0 → j2′ = 2 transitions betweenrotational levels of D2 and H2.

200 m s–1

ΔE = 29 cm–1

CD3: 00 20

(b) CD3–H2

(a) CD3–D2

u(H2)v(CD3) vrel

v(H2)

180o

vcm

H2(Δj2 = 0)

u(CD3) θ0o

u (CD3)

H2(0 2), ΔE=354 cm–1

v(CD3)

0o

u(CD3)

v(D2)

vcm

θ

u (CD3)

D2(Δj2 = 0)

vrelu(D2)

D2(0 2), ΔE=183 cm–1

FIG. 5. Newton diagrams for inelastic scattering of CD3 with (a) D2 and(b) H2. The Newton spheres are drawn for inelastic scattering of CD3 fromthe initial state nk = 00 to the final state n′

k ′ = 20, which corresponds to anenergy transfer of �E = 29.0 cm−1 and for �j2 = 0 and j2 = 0 to j′2 = 2transitions between rotational levels of D2 and H2.

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FIG. 6. Raw images for inelastic scattering of CD3 radicals by D2 at a col-lision energy of 640 ± 60 cm−1. The images are labelled by the symbolY(n′k′

1−k′N

) for final rotational levels with n′ = 2–7 for the CD3 radical, with

unresolved final k′ projection levels as discussed in Sec. II B. Y denotes thespectroscopic branch. The orientation of the relative velocity vector vrel isindicated in one panel.

Collision energies for inelastic scattering of CD3 with D2

and H2 were 640 ± 60 and 680 ± 75 cm−1, respectively.Figure 6 presents the raw images recorded for detection ofCD3 after collision with D2. Raw images for detection ofCD3 after collision with H2 can be found in the supplemen-tary material.52 It should be noted that conservation of mo-mentum during a collision implies that images for CD3–H2

scattering obtained from detection of the methyl radicals aresmaller than for D2 (and He) as a collision partner. The scat-tered products cannot be observed in the parts of the imagesclosest to the forward direction because of imperfect subtrac-tion of background signals arising from unscattered and in-completely cooled CD3 radicals in the parent molecular beam.Asymmetry in the images about the relative velocity vectoris a consequence of speed-dependent detection bias, as men-tioned in Sec. II A, but is corrected for by density-to-fluxtransformation of the data.

In most cases, more than one spectroscopic branch wasprobed for a given final n′, giving different contributions ofthe unresolved k′ projections with weighting according to the2-photon line strength factors, as discussed in Sec. II B. Fromexamination of the images, we see that the scattering is con-fined relatively close to the incident beam direction for de-tection of low n′ final levels of CD3. This suggests that thescattering is largely in the forward direction for these levels.By contrast, the intensity shifts to larger scattering angles forhigh n′ final levels of CD3.

The Newton diagrams shown in Fig. 5 demonstrate thatthe Newton spheres for the rotational transition of D2 fromj2 = 0 to j2′ = 0 and 2 would not be distinguishable in themeasured images. Comparison of measured images for H2

as a collision partner with the Newton diagram indicates thattransitions involving rotational excitation of H2 in a collisiondo not contribute significantly to the scattering, as also foundin the scattering calculations (see Sec. II D). DCSs are differ-ent for a given final level n′ of CD3 but various changes of theH2 and D2 rotational angular momentum; however, it is notpossible to separate these types of Newton spheres from themeasured images. The reason is that the experimental imagesresult from superposition of many Newton spheres differingslightly in the magnitude and direction of the initial veloci-ties of the collision partners and these Newton spheres are notperfectly concentric.

The recorded images were corrected with the density-to-flux transformation in order to derive the DCSs. Figure 7 dis-plays the determined DCSs for CD3–D2 for final levels n′ = 2– 4, while Fig. 8 presents the DCSs for n′ = 5–7. Also plottedin Figs. 7 and 8 are the theoretical DCSs. The experimentaland calculated DCSs for the CD3–H2 system are shown in

FIG. 7. Experimental (red) and theoretical (black) DCSs for inelastic scat-tering of CD3 radicals by D2 at a collision energy of 640 ± 60 cm−1 intofinal rotational levels n′ = 2–4. The REMPI line employed for detection isindicated, along with the range of k′ projection levels contributing to the scat-tering. The method of normalization of the experimental DCSs is describedin the main text.

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FIG. 8. Experimental (red) and theoretical (black) DCSs for inelastic scat-tering of CD3 radicals by D2 at a collision energy of 640 ± 60 cm−1 intofinal rotational levels n′ = 5–7. The REMPI line employed for detection isindicated, along with the range of k′ projection levels contributing to the scat-tering. The method of normalization of the experimental DCSs is describedin the main text.

Fig. 9 for final levels n′ = 2–4 and in Fig. 10 for n′ = 5–8.For quantitative comparison with the theoretical calculations,the experimental DCSs were normalized by scaling the ex-perimental value at 60◦ scattering angle to match the theoret-ical value at that angle. Since the scattering is mainly into thebackward hemisphere for large �n transitions, the DCSs forthe R(7) and P(8) lines for collision with H2 were normalizedat 90◦.

The experimental DCSs are not shown for θ < 30◦ forfinal levels with n′ = 2 and 3 and for θ < 20◦ for final levelswith higher n′ because of contributions to these angles fromunscattered radicals in the parent beam. The calculated DCSsshow pronounced diffraction oscillations in this strongly for-ward scattered region, but the angular resolution of the ex-periments would be insufficient to resolve these structuresclearly, even with greater initial state purity. The angular reso-lution is limited by the velocity and angular spreads of the twomolecular beams, and for the current experiments on the CD3

+ D2/H2 systems, varies from 3◦ to 18◦ depending on the scat-tering angle.36

The error bars associated with the experimental DCSswere determined by combining the standard deviation deter-mined from comparison of several measured images for a sin-gle final state with the uncertainty introduced by applicationof the density-to-flux transformation. The latter factor wasquantified by comparing DCSs extracted from the two halvesof the image separated by the relative velocity vector (whichshould be symmetric after perfect transformation).

There is generally quantitative agreement between the(normalized) experimental and computed DCSs, although

FIG. 9. Experimental (red) and theoretical (black) DCSs for inelastic scat-tering of CD3 radicals by H2 at a collision energy of 680 ± 75 cm−1 intofinal rotational levels n′ = 2–4. The REMPI line employed for detection isindicated, along with the range of k′ projection levels contributing to the scat-tering. The method of normalization of the experimental DCSs is describedin the main text.

some small discrepancies are evident for scattering angles<45◦ for some probe transitions with n′ ≤ 4. Here, the ex-perimental DCSs are slightly larger than the computed DCSs,which could be a consequence of our limited experimental an-gular resolution or imperfect background subtraction. Theremay also be contributions to the scattering signals from ini-tial levels with higher initial n present at low density in our∼15 K beam, because elastic scattering events will give strongforward scattering with high integral cross sections. The onlysignificant differences between the experimental and com-puted DCSs are for detection of some high-n′ final rotationallevels, in particular via the S(5) and S(6) lines in collisionswith D2 and the R(5) and S(5) lines in collisions with H2.Even for these cases, there is satisfactory qualitative agree-ment between the shapes of the experimental and computedDCSs.

IV. DISCUSSION

Although the focus of our study is on inelastic scat-tering, the collision of a methyl radical with molecularhydrogen can also follow a reactive pathway. However, the

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FIG. 10. Experimental (red) and theoretical (black) DCSs for inelastic scat-tering of CD3 radicals by H2 at a collision energy of 680 ± 75 cm−1 intofinal rotational levels n′ = 5–8. The REMPI line employed for detection isindicated, along with the range of k′ projection levels contributing to the scat-tering. The method of normalization of the experimental DCSs is describedin the main text.

vibrationally adiabatic barrier height on the potential energysurface for reactive formation of methane and atomic hy-drogen has been computed to be 3847 cm−1.78 This energybarrier is much higher than the collision energy in our exper-iments and calculations so the reactive path is closed. More-over, the PES was computed with the assumption of rigidmolecular geometries. Our comparisons of experimental andcomputed DCSs therefore test the quality of the ab initio PESand the accuracy of the scattering calculation methods in re-gions of the global PES below the transition state for reaction.

For both D2 and H2 as collision partners, the measuredimages and the corresponding DCSs directly reveal the de-pendence of the scattering upon CD3 final rotational angularmomentum n′. The DCSs peak in the forward hemisphere forn′ = 2–4 and shift more to sideways and backward scatteringfor n′ = 5. For n′ = 6–8, the DCSs are dominated by back-ward scattering. A similar trend was observed for scatteringof methyl radicals with He, and we discussed the origins ofthis behavior in terms of partial cross sections (or impact-parameter dependence of the scattering) in a recent paper.36

DCSs were measured for different spectroscopic branches toprobe a given methyl rotational level n′, but a different subsetof the k′-projection quantum numbers. These DCSs differ, es-pecially for n′ = 5, demonstrating the sensitivity of scatteringto the k ′value, even if it is not fully resolved in the currentexperiments.

With inspection of Figs. 7–10, we see that there are a fewclear differences between DCSs measured for H2 and D2 ascollision partners with CD3, the most apparent being that theDCSs for the CD3–D2 system decrease more sharply from a

maximum at small scattering angles towards larger angles. Inview of good agreement between the experimental and com-puted DCSs, we can compare in detail the computed state-resolved DCSs for the two systems. It should be noted thatwe have no clear experimental information on the rotationalinelasticity of the D2/H2 collision partner.

Figure 11 compares the DCSs for transitions from theCD3 10 rotational level, the lowest level of A1 nuclear spinmodification, into selected final levels in collisions with D2

and H2 at relative translational energies of 640 and 680 cm−1,respectively. State-to-state ICSs corresponding to the DCSsplotted in Fig. 11 are displayed in Fig. 4 for D2 as a collisionpartner. DCSs for transitions involving other final levels andfor collisions out of the 00 and 11 rotational levels, the lowestlevels of the A2 and E nuclear spin modifications, respectively,can be found in the supplementary material.52 We see inFig. 11 that DCSs for the same transitions have a similar angu-lar dependence for the D2 and H2 collision partners. For finallevels n′ ≤ 4, the DCSs for the D2 collision partner are largerfor small angles, while the DCSs for H2 extend to larger scat-tering angles than do the DCSs for D2. For intermediate states(n′ = 5 and 6), the DCSs for D2 are dominated by sidewaysscattering with peaks around θ ∼ 90◦, whereas the DCSs for

FIG. 11. Computed state-to-state DCSs for inelastic scattering of CD3, ini-tially in the 10 rotational level, with D2 (red) and H2 (blue) into selectedfinal rotational levels at collision energies of 640 and 680 cm−1, respectively.The left and right panels are DCSs for which the initial rotational level j2 ofthe collision partner equals 0 and 1, respectively, and is the same after thecollision.

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H2 are shifted more to backward hemisphere. The DCSs forhigher final levels are dominated by backward scattering forboth collision partners as demonstrated in Fig. 11 by DCSsfor the 70 final level. We notice that the CD3–D2 DCSs arevery similar for the D2 j2 = 0 and 1 initial rotational levels.The DCSs for the j2 = 0 → 2 transition (not plotted) are ingeneral more backward scattered for H2 than for D2 for small�n changes (n′ ≤ 5) and have the same angular dependencefor larger �n changes. In addition, for a given CD3 transition,the ratio of the ICSs for the j2 = 0 → 2 to the j2 = 0 → 0transition is much smaller for the H2 collision partner thanfor D2; this is presumably due to the larger energy gap for�j2 = 2 transition in H2. The PESs for CD3–D2 and CD3–H2

scattering are identical, so observed differences in DCSs mustbe attributed to the effects of different masses of the collider,and any associated changes to the quantized rotational energylevels of H2 and D2.

Conversely, collisions of CD3 with D2 and He have thesame reduced mass, but are governed by different PESs. Afurther difference between He and D2 collision partners isthat D2 has a rotational degree of freedom, so can be rota-tionally excited or de-excited in a collision, and collisions canalso occur with an initially rotationally excited molecule. Inour experiments (present work and Ref. 36), the D2 molec-ular beam has a larger mean speed than does the He beam(because of the larger heat capacity ratio for a monatomic gas(γ = 5/3) than for a diatomic gas (γ = 7/5)). To make a clearcomparison of these two systems, we have calculated CD3–He DCSs at the same collision energy (and hence relativevelocity) as the present experiments on CD3–D2. Figure 12presents computed DCSs for selected transitions from the 11

rotational level, the lowest level of the E nuclear spin modifi-cation, for CD3 in collisions with D2 and He at a collision en-ergy of 640 cm−1. Each DCS depicted represents an exampleof a transition directly coupled by one of the largest expansioncoefficients of the PES for the CD3–He system (see Fig. 3 inRef. 45). For the D2 collision partner, DCSs are presented forinitial rotational levels j2 = 0 and 1, with no collision-inducedchange in j2. DCSs for a wider range of CD3 initial and finalrotational levels can be found in the supplementary material.45

The DCSs for initial j2 = 1 of D2 are often larger, in particularin the forward direction (note the scaling of the j2 = 1 → 1DCS in Fig. 12(a)).

The CD3–D2 DCSs show similar propensities forchanges in the CD3 rotational quantum numbers n and k asfor CD3–He collisions.36 For small changes �n in the rota-tional angular momentum, the DCSs for �k = 0 transitionshave fairly sharp forward peaks and broad, lower intensitypeaks in the backward hemisphere (Fig. 12(a)). These tran-sitions are enabled mainly by the (l1, μ1) = (2, 0) terms, in asimilar fashion to the role of the v20 term for CD3–He.37 The�k �= 0 transitions for small �n changes display broad DCSsextending over the entire angular range, with oscillations forangles θ ≤ 45◦ (Fig. 12(b)). Such transitions involve directcoupling through the (l1, μ1) = (3, 3) terms, in analogy to therole of the v33 term for CD3–He.37 The �k = 1 transitionsfor the E nuclear spin modification, e.g., the 11 → 32 transi-tion in panel (b), have DCSs very similar in shape to those for�k = 3 transitions for A1 and A2 levels, e.g., the 00 → 33

FIG. 12. (a)–(f) Computed state-to-state DCSs for inelastic scattering ofCD3 from the 11 rotational level into various final rotational levels in col-lisions with D2 (red) and He (blue) at a collision energy of 640 cm−1. Thesolid and dashed red curves are CD3–D2 DCSs for which the initial rota-tional level j2 of the D2 collision partner equals 0 and 1, respectively, andis the same after the collision. In panel (a), the j2 = 1 → 1 DCS has beenmultiplied by a factor of 1/3.

transition. As discussed in detail previously for CD3–He,36, 37, 45 these �k �= 0 transitions for E levels are also en-abled by the (l1, μ1) = (3,3) terms. For transitions with largerchanges in the rotational quantum number n, the DCSs shifttoward the backward hemisphere, as can be seen in the com-parison of experimental and computed DCSs displayed inFigs. 8 and 10 for D2 and H2 collision partners, respectively.

V. CONCLUSIONS

The experimental measurements reported here of inelas-tic scattering of CD3 radicals with H2 and D2 molecules repre-sent the first DCSs obtained for collisions of a polyatomic rad-ical with a diatomic molecule. We have compared these exper-imental DCSs with the outcomes of close coupling quantum-mechanical calculations performed using a newly determinedab initio PES computed at the RCCSD(T)-F12a level of the-ory. We find good agreement between the experimental andcalculated DCSs, with the exception of scattering into then′ = 5 and 6 levels of CD3, as probed by the S(5) and S(6)REMPI lines in collisions with D2 and the R(5) and S(5) linesin collisions with H2. This agreement suggests that the PESand the scattering calculations provide an accurate descrip-tion of the interaction of CD3 with these diatomic molecules,at least at energies around 600–700 cm−1 corresponding toour experimental conditions.

The DCSs for inelastic scattering of CD3 with H2 and D2

peak in the forward hemisphere for n′ = 2–4 and shift more tosideways and backward scattering for n′ = 5. As the energy

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transfer in a collision increases, the DCSs are increasinglydominated by backward scattering (n′ = 6–8). This same be-havior is recognized for inelastic scattering of diatomic andpolyatomic molecules and it is also consistent with our priorreport36 of inelastic scattering of CD3 with He. DCSs for agiven n, k → n′, k′ transition show similar angular depen-dences for D2 and H2 as collision partners. Since CD3–D2 andCD3–H2 interactions are described by the same PES, smalldifferences between DCSs or ICSs for D2 and H2 collisionpartners can be attributed to mass effects, or, in the case oftransitions involving a change in the rotational angular mo-mentum of the diatomic collider, to mass-related changes inthe quantized energy level structure.

We also computed rotational-level resolved integral crosssections for collision of CD3 with D2 and H2. The ICSs forinelastic scattering of CD3 with D2 and H2 j2 = 1 are largerthan for j2 = 0, indicating that an initially rotating D2 or H2

molecule increases the probability of a given CD3 transition.The ratio of ICSs for j2 = 0 → 2 to j2 = 0 → 0 transitionsin the diatomic, for a particular change in the CD3 angularmomentum, is much smaller for H2 than for D2 because ofthe larger energy gap between rotational levels of the lighterisotopologue. CD3–D2 DCSs are very similar for collisionswith D2 initially in j2 = 0 and 1 rotational levels.

We also compare the DCSs for CD3–D2 with CD3–Hemeasured previously.36 Comparison of these systems is inter-esting because they have the same reduced mass, but the scat-tering dynamics of CD3 with D2 and He are governed by dif-ferent PESs, and thus the forces acting between the collisionpartners. For example, the global minimum of the CD3–D2

PES has De = 99.0 cm−1, which is significantly larger than forCD3–He [27.0 cm−1 (Ref. 37)]. The equilibrium geometry forCD3–D2 is R = 6.57 bohr, θ1 = 0◦, θ2 = 0◦. The D2 moleculethus lies along the C3 axis of the methyl radical as opposedto the equilibrium geometry of the global minimum for CD3–He, for which the He atom lies in the molecular plane andbisects two C–H bonds at R = 6.52 bohr.

When comparisons are made between computed DCSsfor CD3–D2 and CD3–He scattering at the same collision en-ergy, we find a similar dependence on scattering angle. Thisobservation is particularly the case for transitions directlycoupled by terms representing the threefold anisotropy asso-ciated with the azimuthal angle about the C3 symmetry axis ofthe radical. ICSs for CD3-He and CD3–D2, in which the D2 isin an initial level with j2 = 0, are of comparable magnitudes.

ACKNOWLEDGMENTS

The Bristol group acknowledges financial support fromthe EPSRC under Programme Grant No. EP/G00224X andfrom the EU Marie Curie Initial Training Network ICONIC(for an Early Career Researcher position for OT). TheHeriot-Watt group thanks EPSRC for support via Grant No.EP/J002534/2. The theoretical portion of this work was sup-ported by the Chemical, Geosciences and Biosciences Divi-sion, Office of Basic Energy Sciences, Office of Science, U.S.Department of Energy, under Grant No. DESC0002323. Theauthors gratefully acknowledge the encouragement and ad-vice of Millard Alexander.

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