Scattering of Stark-decelerated OH radicals with rare-gas atoms

2 MB·English

by  Ludwig Scharfenberg

EPJ manuscript No.
(will be inserted by the editor)
Scattering of Stark-decelerated OH radicals with rare-gas atoms
Ludwig Scharfenberg1, Koos B. Gubbels12, Moritz Kirste1, Gerrit C. Groenenboom2, Ad van der Avoird2, Gerard
Meijer1, and Sebastiaan Y.T. van de Meerakker1
1 Fritz-Haber-Institutder Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
1 2 InstituteforMoleculesandMaterials, RadboudUniversiteitNijmegen,Heyendaalseweg135,6525AJNijmegen,TheNether-
1
lands
0
2
Received: date/ Revised version: date
n
a
J Abstract. We present a combined experimental and theoretical study on the rotationally inelastic scat-
5 tering of OH (X2Π3/2,J = 3/2,f) radicals with the collision partners He, Ne, Ar, Kr, Xe, and D2 as a
function of the collision energy between ∼ 70 cm−1 and 400 cm−1. The OH radicals are state selected

] and velocity tuned prior to the collision using a Stark decelerator, and field-free parity-resolved state-to-
s state inelastic relative scattering cross sections are measured in a crossed molecular beam configuration.
u
For all OH-rare gas atom systems excellent agreement is obtained with the cross sections predicted by
l
c close-coupling scattering calculations based on accurate ab initio potential energy surfaces. This series of
- experimentscomplementsrecentstudiesonthescatteringofOHradicalswithXe[Gilijamseetal.,Science
m
313,1617(2006)],Ar[Scharfenbergetal.,Phys.Chem.Chem.Phys.12,10660(2010)],He,andD2[Kirste
t et al.,Phys. Rev. A 82, 042717 (2010)]. A comparison of therelative scattering cross sections for this set
a
. of collision partnersreveals interesting trendsin thescattering behavior.
s
c
i PACS. PACS-key discribing text of that key – PACS-key discribing text of that key
s
y
h
p 1 Introduction withthespectroscopicdataoftheboundstatesofrelevant
[ complexes [16,17], offers stringent tests for ab initio po-

tentialenergysurfaces(PES’s)andforquantumscattering
1 The study of collisional energy transfer between simple
calculations.
v atomsandmoleculeshasbeenessentialforourpresentun-
8 derstandingofthedynamicsofmolecularinteractions,and Inrecentyears,newapproachestoperformhigh-precision
4 fortestingourabilitytoaccuratelycalculatepotentialen- inelastic scattering experiments involving radical species
9 ergy surfaces that governthese interactions [1]. Rotation- have become possible with the development of the Stark-
0 ally inelastic scattering is one of the simplest scattering decelerationtechnique[18].TheStarkdecelerationmethod
.
1 processes,and has been studied with everincreasing level exploitstheconceptsofcharged-particleacceleratorphysics
0 of detail during the last decades. Experimental studies at to produce molecular beams with a tunable velocity and
1 a full state-to-state level are nowadayspossible, revealing almost perfect state purity [19]. The method was first
1 detailed information on the potential energy surfaces and applied to molecular scattering studies in 2006, when a
v: the resulting motion on these surfaces [2,3]. Stark-deceleratedbeam of OH (X2Π3/2,J =3/2,f)rad-
i Rotationally inelastic scattering of free radicalspecies icalswasscatteredwith a conventionalbeamofXe atoms
X
[20]. By tuning the velocity of the OH radicals between
suchasOHorNOwithatomiccollisionpartnershasbeen
r 33 m/s and 700 m/s prior to the collision, the center-of-
a o5]f.sTpheceiasclainttteerriensgtoinftmheosleecouplaern-sschaetltlesrpinegcieesxpineraim2Πentesle[4c-, mass collision energy was varied between 60 cm−1 and
400 cm−1. This energy range encompasses the energetic
tronic state involves more than one Born-Oppenheimer
thresholds for inelastic scattering to the first excited ro-
potential surface, resulting in rich multi-surface dynam-
ics with various quantum interference effects [6]. At a tational levels of the OH radical, and the threshold be-
full state-to-state level, collision induced transitions be- haviorofthe inelasticstate-to-statecrosssectionswasac-
tween rotational, spin-orbit, and Λ-doublet levels have curatelydetermined. Excellentagreementwas foundwith
been studied [7,8,9]. Sophisticated beam production and cross sections derived from coupled channel calculations
product state detection methods have been developed to on ab initio computed potential energy surfaces.
measuredifferentialcrosssections[10,11],thestericasym- Since this first proof-of-principle experiment, a new
metry of the collision [12], and the alignment or orien- crossed beam scattering apparatus was developed that
tation of the collision products [13,14,15]. The wealth of employs an improved version of the Stark decelerator.
scatteringdatathatisavailableforthesesystems,together With this decelerator, packets of OH radicals can be pro-
2 Ludwig Scharfenberg et al.: Scattering of Stark-decelerated OH radicals with rare-gas atoms
duced with a superior number density, a narrower ve- only 0.05 cm−1. OH radicals that reside in the energeti-
locity spread, and a higher quantum state purity [21]. cally higher lying f-componentcan be focused and veloc-
This apparatus enables state-to-state scattering experi- itytunedusingtheStarkdecelerator,whereasOHradicals
ments as a function of the collision energy with a sen- inthee-componentaredeflectedfromthebeamaxis.After
sitivity that exceeds that of conventional crossed beam passing a skimmer, the packet of OH radicals enters the
scattering experiments. This was demonstrated first on 3×3 mm2 opening of the decelerator.A sequence of high
the benchmark OH (X2Π)-Ar system, for which parity- voltage pulses is applied to the decelerator electrodes to
resolvedintegralstate-to-statescatteringcrosssectionsfor generate time-dependent electric field configurations that
in total 13 inelastic scattering channels have been deter- eitherdecelerate,guideoracceleratetheOHradicals.The
mined as a function of the collision energy [22]. Recently, Stark decelerator that is used here employs the so-called
thesamemethodologywasappliedtothescatteringofOH s = 3 operation mode [24,25], and has been described in
radicals with He atoms and D2 molecules [23]. detail in Ref. [21].
Theseexperimentschallengethe mostaccuratepoten- The packet of OH (X2Π3/2,J = 3/2,f) radicals that
tial energy surfaces and quantum scattering calculations emerges from the decelerator has a quantum state purity
presentlyavailable.ForthescatteringofOHradicalswith of >99% and intersects the central axis of the secondary
ArandHe atoms,excellentagreementwasfoundbetween beam under 90◦ at a distance of 16.5 mm from the de-
experimentandtheory,althoughathighcollisionenergies celerator exit. Collisions take place in a field free region
and for specific inelastic channels deviations were found. andtheinitiallyunevendistributionoverM -components
J
For the OH-He system, the almost perfect quantum state which is present inside the decelerator is assumed to be
purity offeredby the Stark deceleratorenabled the obser- scrambled completely while the molecules move towards
vation of the strong propensities for preferred excitation the collision region.
into final states of certain parity that had been predicted A temperature controlled solenoid valve produces the
for this system [7]. secondary beam of rare-gas atoms or D2 molecules. The
Here we report new measurements on the rotationally meanforwardvelocityofthisbeamisinferredfromatime-
inelastic scattering of OH (X2Π ,J = 3/2,f) radicals of-flight measurement using two microphone-based beam
3/2
with Ne, Kr, and Xe atoms at collision energies between detectorsthatareplaced300mmapart.Toensuresingle-
60 cm−1 and 400 cm−1. The measured cross sections for collision conditions, the intensity of the secondary beam
the OH-Xe system confirm the cross sections that were is kept sufficiently low so that the decrease of the initial
determined for this system in our earlier work [20]. For population in the J = 3/2,f level remains below 4 per-
all three systems, excellent agreement is obtained with cent.
cross sections that are derived from quantum scattering The collision products are state-selectively detected
calculations based on available potential energy surfaces. via saturated laser-induced fluorescence when the most
These studies complement our previous investigations intense part of the OH packet is in the center of the col-
onthescatteringofOHradicalswithHeatoms,Aratoms lision region. A pulsed dye laser is used to induce various
and D2 molecules, and together form a complete data set rotational transitions of the A2Σ+,v = 1 ← X2Π,v = 0
on the scattering of OH radicals with rare-gas atoms. A band.Thelaserbeamintersectsbothmolecularbeamsun-
comparisonoftherelativescatteringcrosssectionsforthe der 90◦ and the off-resonantfluorescence is collected by a
various collision partners is presented that reveals inter- lensandimagedontoaphotomultipliertube(seetheinset
esting trends in the scattering behavior. of Figure 1).
2 Experiment 2.2 Measurement procedure and data analysis
The collision energy range between 60 and 400 cm−1 is
2.1 Experimental setup
covered using two measurement intervals with overlap-
ping energy, as described in Ref. [22]. For these intervals,
The experiments are performed in a crossed molecular molecular beams of OH radicals are produced using Kr
beam apparatus that is schematically shown in Figure 1. and Ar as seed gases,resulting in OH radical beams with
A detailed description of this machine, as well as of the mean initial velocities of 430 m/s and 615 m/s, respec-
production, Stark deceleration, and detection of OH rad- tively. Within each interval, the collision energy is varied
icals can be found in Ref. [21,22]; only the most essential by tuning the velocity ofthe OHradicalspriorto the col-
aspects of the experiment are described here. lision using the Stark decelerator. For collisions with Ne,
ApulsedsupersonicbeamofOHradicalsiscreatedby Ar, Kr and Xe atoms, the mean velocity of the rare-gas
photolysisofnitricacidseededineitherkryptonorargon. atom beam is kept constant for all measurements. The
After the supersonic expansion nearly all OH radicals re- meanspeedandcorrespondingvalvetemperaturesforthe
side in the lowest rotational (J = 3/2) and vibrational differentrare-gasbeamsare:445m/s(Ne,93K),400m/s
level of the X2Π electronic ground state. The two Λ- (Ar,110K),330m/s(Kr,163K)and300m/s(Xe,220K).
3/2
doubletcomponentsofthislevel,labeledeandf,arepop- For collisions with He atoms and D2 molecules, the small
ulatedequally in the beamsince their energydifference is reduced mass makes it inconvenient to vary the collision
Ludwig Scharfenberg et al.: Scattering of Stark-decelerated OH radicals with rare-gas atoms 3
to probe the individual levels, as well as the excitation
rates that are used to convert measured fluorescence in-
tensities to populations, are specified in [22].
The experimental scattering signals are most easily
compared with theoretical calculations when relative in-
elasticscatteringcrosssectionsarederivedfromtheobser-
vations.The relativescattering crosssectionfor a specific
channel is proportional to the total number of molecules
thatisdetectedinthecorrespondingquantumstate.How-
ever, the detection volume is necessarily limited and in
general not all molecules can be detected. A density-to-
fluxtransformationisrequiredto relatethe measuredrel-
ativepopulationsinfinalstatestorelativescatteringcross
sections.Underourexperimentalconditions,theresulting
correctionis small[22]. Forthe scatteringofOHwithNe,
Ar,KrandXe atoms,we haveperformedthe transforma-
Fig. 1. Scheme of theexperimental setup. A pulsed beam of tion using the differential cross sections determined from
OHradicalsisproducedbylaserphotolysisofHNO3seededin theory. For He and D2, the density-to-flux correction can
eitherKrorAr.Theradicalspassa2.6mlongStarkdecelera- be safely omitted due to the small mass of the collision
torandarescatteredbyapulsedbeamofrare-gas(Rg)atoms partner compared to the mass of the OH radical.
orD2molecules.TheOHradicalsarestate-selectivelydetected
using a laser-induced fluorescence scheme. The fluorescence is
imagedontoaphotomultipliertubebyalens.Theupperright 3 Theory
insetshowsaphotographofthebeamcrossingregionwithlens
holder, light baffle, and the exit of the Stark decelerator. The The theory for the scattering of 2Π-state molecules with
secondary beam source is protruding from thetop. 1S-stateatomsiswellestablished[26].Inparticular,colli-
sionstudies betweenOH molecules and rare-gasatoms at
low collision energies have received a lot of attention over
energybysolelytuningthespeedoftheOHpacket.There-
the last years [20,27,28,29]. In this section we only give
fore, the speed of the secondary beam is varied in com-
a brief summary of the relevant theory. A more extensive
parativelylarge steps by changing the temperature of the
account can be found in Ref. [30].
valve. For a given valve temperature, the OH velocity is
TheHamiltonianthatdescribesthescatteringofground
then tuned from 168 to 741 m/s. The D2 molecules are state OH (X2Π) with rare-gas atoms is given by
assumed to be distributed between ortho and para rota-
tional levels according to the statistical weights, i.e., 67% −¯h2 ∂2 Lˆ2
ofthemoleculesareexpectedtopopulaterotationallevels Hˆ = 2µR∂R2R+2µR2 +X|Λ′iVΛ′,Λ(R,θ)hΛ|+HˆOH,
with J even and 33% levels with J odd. Λ′,Λ
The Stark deceleratorprovidespackets ofOH radicals (1)
atarateof10Hz.Thesecondarybeamisoperatedat5Hz where R is the length of the vector R that connects the
and collision signals are inferred from the fluorescence in- center-of-massoftheOHmoleculeandthe rare-gasatom,
tensity difference between alternating shots of the exper- µ is the reduced mass of the atom-OH complex, Lˆ is the
iment. The collision energy dependence of the scattering angular momentum operator corresponding to end-over-
channels is measured via a quasi-continuous cycle, as ex- endrotationoftheOH-raregasatomcomplex,andHˆOHis
plainedinRef.[22].Thecollisionsignalsareobtainedfrom theHamiltonianoftheOHmoleculeinthe(X2Π)ground
typically 1000 runs of the experiment, and quoted error state.TheX2Π electronicgroundstateoftheOHradical
bars represent the statistical fluctuation of the measured has two degenerate components with projections Λ= ±1
mean values. Both photon counting and analog detection of the orbital electronic angular momentum on the inter-
are used in the data acquisition [22]. nuclearrˆ-axis.The OH-raregasinteractionisrepresented
Our experiment is not sensitive to elastic scattering; by the operators |Λ′iVΛ′,Λ(R,θ)hΛ| that couple different
only scattering events that change the internal quantum electronic states Λ and Λ′. The angle θ defines the an-
state of the OH radicalcanbe detected. Within the stud- gle between the unit vector Rˆ and the OH bond direc-
iedcollisionenergyrange,collisionalexcitationtoatmost tion rˆ, with θ = 0 corresponding to collinear atom-HO.
13 rotational levels can occur. These levels are labeled as The Hamiltonian of OH includes rotation,spin-orbitcou-
Fi(Je/f), where i=1 denotes the X2Π3/2 and i=2 the plingandΛ-doubling,whereweusetheOHrotationalcon-
X2Π spin-orbit manifolds, and the parity labels e and stantB =18.5487cm−1,the spin-orbitcouplingconstant
1/2
f correspond to the two Λ-doublet components of each A=−139.21cm−1,andΛ-doublingparametersp=0.235
rotationallevel.Anenergyleveldiagramwithallrelevant cm−1 and q =−0.0391cm−1 [31]. FromEq. (1) it follows
rotational levels is shown in Figure 3. Note that the Λ- thatdifferences in the collisionsbetween OHand the var-
doublet splitting is largely exaggerated in this figure for ious rare gas atoms originate from the differences in the
reasonsofclarity.Therotationaltransitionsthatareused interaction potential and the reduced mass.
4 Ludwig Scharfenberg et al.: Scattering of Stark-decelerated OH radicals with rare-gas atoms
When the rare-gasatomapproachesthe OHmolecule, motion of the OH molecule was performed [22]. For the
the electronic degeneracy of the Π state is lifted. The re- other systems, the OH molecular geometry was assumed
sultingmatrixelementsVΛ,Λ′ ofthepotentialarenonzero frozen at its equilibrium bond length (OH-He, Ne, Kr) or
for Λ′−Λ=0,±2, and two potential energy surfaces are at its vibrationally averageddistance (OH-Xe).
involved in the scattering process. The potential energy In order to calculate the OH monomer eigenfunctions
surfaces can be expanded in Racah normalized spherical it is convenient to use a parity adapted Hund’s case (a)
harmonics basisset,labeledby|Ω,J,M ,piwithJ thetotalangular
J
momentumoftheOHmolecule,ΩandM theprojections
V1,1 =V−1,−1 = VA′ +VA′′ =Xvl,0(R)Cl,0(θ,0), on the molecular and space-fixed quantiJzation axes, and
2 p the parityunder inversion.For the exactOHeigenfunc-
l
tions,|Ω|isnearlyagoodquantumnumber.Thetotalan-
VA′′ −VA′
V1,−1 =V−1,1 = =Xvl,2(R)Cl,2(θ,0),(2) gular momentum of the OH-atom complex is represented
2
l by the operator Fˆ = Jˆ+Lˆ, whose eigenfunctions are ob-
tained by coupling the monomer basis with the spherical
where A′ and A′′ refer to the reflection symmetry of the
harmonics |L,M i=Y (ϑ,ϕ), where ϑ and ϕ are the
electronic states. The surfaces V1,1 and V1,−1 are often space-fixedspherLicalcoLo,rMdLinates ofthe vectorR. Assum-
referred to as the sum Vsum and difference Vdiff potential ing that the OH bond length is fixed, we write the scat-
energy surface, respectively.
tering wave functions as products of radial and angular
Ab initio calculationsfor the OH-atominteractionen-
functions,
ergycanbeperformedusingtheMOLPROprogrampack-
a[3g3e],[3O2H],-Nwhei[c3h3,h3a4s],rOesHul-tAedr [i2n2]p,oOteHn-tKiarls[3f5o]ratnhde OOHH--XHee ΨβF,,LMF,P = R1 X χβF′,,MLF′←,Pβ,L(R)ψβF′,,ML′F,P(Rˆ,rˆ), (3)
[20]complexes.Themostrelevantpropertiesofthevarious β′,L′
interacting systems, such as the reduced mass of the OH-
rare gas atom complex, the polarizability of the rare gas where β is a shorthand notation for the monomer quan-
atom, the minima of the potential energy surfaces in the tum numbers (Fi,J) with i to distinguish betweenthe F1
two different linear configurations of the complex (θ =0◦ and F2 spin-orbit manifolds of the OH eigenstates. Note
and θ = 180◦), as well as the position and energy of the that the total angular momentum F, its space-fixed pro-
minimum of the A′ potentialata nonlinear geometry,are jection MF and the parity of the complex P = p(−1)L
listed in Table 3. areconservedin the collisionprocess.The experimentally
The potential energy surfaces vary in the quality of relevant scattering properties, i.e. the cross sections, are
the basis set used, and the quality of the method. All conveniently expressed in terms of the scattering matrix,
potentials used the counterpoise procedure to correct for which can be obtained using standardasymptotic match-
the basis setsuperpositionerror[36].The OH-He andthe ingprocedures[37].TheobtainedS-matrixisthenrelated
OH-Ne potentials of Lee et al. were both calculated with to the scatteringamplitudes,which inturndetermine the
a spin-restricted coupled-cluster method with single and differential cross sections [38].
double excitations and perturbative triples [RCCSD(T)]. Inordertoachieveconvergenceofthecalculatedcross-
Theaugmentedtriple-zetacorrelation-consistentbasisset sections, we used a basis set that included all OH rota-
(aug-cc-pVTZ) was used with an additional (3s, 3p, 2d, tional states up to an angular momentum of J = 21/2,
2f, 1g) set of bond functions centered in the midpoint andtookintoaccountallpartialwavecontributionsupto
of the vector R [33]. The Ne-OH potential was also cal- a total angular momentum of F = 241/2. For the prop-
culatedmorerecentlybySumiyoshietal.,whousedanex- agation of the wavefunction, the renormalized Numerov
plicitlycorrelated,spin-unrestrictedapproach[UCCSD(T)- method was used, starting at 4a0 and continuing to 35a0
F12b]withalargerquintuple-zetabasisset(aug-cc-pV5Z) with a0 the Bohr radius. The cross sections were evalu-
[34]. Although we calculated the cross sections for both ated on an energy grid with a 5 cm−1 interval spacing,
Ne-OHpotentials,weonlyshowtheresultswiththemost wellbelowtheexperimentalenergyresolutioninallcases.
recent potential, which gave a clearly better agreement It is noted that this energy grid is too sparse, however,
with experiment. This is probably due to the larger basis to identify individual scattering resonances that occur at
set and the improved calculation method, which includes collision energies around the energetic thresholds.
explicitelectroncorrelationsthatparticularlyenhancethe In Fig.2 the totalintegralinelastic crosssections (the
accuracy of the short-ranged behavior of the potential. sum of the integral cross sections over all inelastic chan-
For the Xe-OH potential, RCCSD(T) was used with a nels)areshownfor collisionsofOH (X2Π ,J =3/2,f)
3/2
qaudruple-zeta basis set (aug-cc-pVQZ) and with a set radicals with the five different rare-gas atoms. In this fig-
of (3s, 3p, 2d, 1f, 1g) mid-bond orbitals with geometry- ure,thecontributiontothetotalcrosssectionofcollisions
dependent exponents [20]. For the Kr-OH potential, the thatpopulate levelswithinthe F1 manifoldareindicated.
UCCSD(T)-F12bapproachwasusedwiththeaug-cc-pVQZ The total inelastic cross section is seen to rise with in-
basisset[35].Finally,theAr-OHpotentialsurfacewascal- creasingreducedmass,increasingatompolarizabilityand
culated with a spin-unrestricted approach [UCCSD(T)], increasing well depth of the potential. The total inelas-
where the basis set was extrapolated to the complete ba- tic cross sections as presented in Figure 2 can be used to
sis set limit, and where also an averaging over the v = 0 deduceabsolutestate-to-stateinelasticcrosssectionsfrom
Ludwig Scharfenberg et al.: Scattering of Stark-decelerated OH radicals with rare-gas atoms 5
atom µ α E R θ PES
60
He 3.24 0.21 -27.1 6.54 0 A′, A′′
-21.8 6.09 180 A′, A′′
50 Xe
′
-30.0 5.69 68.6 A
Ne 9.22 0.40 -59.34 6.53 0 A′, A′′ Kr
2 40
Å
-45.18 6.14 180 A′, A′′ n / Ar
-59.60 5.82 67.6 A′ ctio 30
e
Ar 11.9 1.64 -141.7 7.01 0 A′, A′′ s s
s
-92.4 6.70 180 A′, A′′ cro 20
′
-137.1 6.18 74.8 A
Ne
Kr 14.14 2.48 -172.5 7.2 0 A′, A′′ 10 He
′ ′′
-110.3 6.8 180 A, A
′
-177.0 6.25 78 A 0
50 100 150 200 250 300 350 400
Xe 15.05 4.04 -202.3 7.6 0 A′, A′′
-117.9 7.3 180 A′, A′′ collision energy / cm-1
′ Fig.2.Thecalculatedtotalintegralcrosssectionsforinelastic
-224.4 6.45 84 A
scattering of OH (X2Π3/2,J = 3/2,f) radicals with He, Ne,
Table 1. Properties of the Rg-OH interaction. Values for Ar,Krand Xeatoms (solid lines). The contribution of transi-
thepotentialminimaadaptedfrom [20,22,33,34,35].Reduced tionsintotheF1 spin-orbit manifold are shown bythedashed
mass µ in u, polarizability α in 10−24cm3, potential energy E lines.
in cm−1, coordinate R in a0, coordinate θ in degree.
cm−1 the scatteringisdominatedbyrotationalexcitation
theexperimentallydeterminedrelativestate-to-statecross to the F1(5/2e) state. For spin-orbit manifold conserving
sections. These are presented in the next section. transitions, there is a strong propensity for final states
of e parity. For spin-orbit manifold changing collisions, a
strongΛ-doubletpropensityisonlyobservedforexcitation
4 Results and discussion into the F2(1/2) states.Note the little bump that is mea-
suredin the crosssection for scattering into the F1(5/2f)
channel at a collision energy just below 200 cm−1. This
4.1 Scattering of OH radicals with Ne, Kr, and Xe
bump is also measured for the OH-He system, and possi-
atoms
bly resultsfromscatteringresonancesassociatedwiththe
In this section, we first describe our new results on the opening of the F1(7/2) channels at a collision energy of
200 cm−1. Pronounced scattering resonances are indeed
scattering of OH radicals with Ne, Kr, and Xe atoms. A
predictedfromthetheoreticalcalculationsforOH-Heand
detailedcomparisonofthescatteringbehaviorforthevar-
OH-Ne at these collision energies, although their specific
ious systems is given in section 4.2.
structureissmearedoutintheexperimentduetothe col-
The measured relative state-to-state cross sections for
lision energy spread.
the scattering of OH radicals with Ne, Kr, and Xe are
shown in Figures 3 and 4. The theoretically computed The scattering behavior of OH with Kr is observed to
cross sections, convoluted with the experimental energy be very similar to the scattering of OH with Xe atoms,
resolution,are includedas solidcurves.For completeness, and dominated by the Λ-doublet changing F1(3/2f) →
the experimental and theoretical cross sections from our F1(3/2e)channelatallprobedcollisionenergies.Forrota-
previousworkfortheOH-He,OH-D2,andOH-Arsystems tional excitation, the cross sections generally rise sharply
[23,22] are also shown in these figures. The fine structure from the energetic threshold, reach a maximum, and be-
conserving(transitionswithinthe F1 spin-orbitmanifold) come rather insensitive to a variation of the collision en-
andfinestructurechangingcollisions(transitionsfromthe ergyathigherenergies.Forspin-orbitmanifoldconserving
F1 into the F2 manifold) are summarized in Figure 3 and collisions, there is a small propensity for excitation into
Figure 4, respectively. In both figures, the state resolved final states of e parity. For spin-orbit changing collisions,
scattering channels are labeled following the color codes noclearpreferenceforexcitationintooneoftheΛ-doublet
as indicated in the rotational energy level diagrams. components of a final rotational state is observed.
For the scattering of OH(F1(3/2f)) with Ne, the Λ- For all three scattering systems, the measured cross
doublet changing F1(3/2f) → F1(3/2e) channel domi- sectionsarecomparedtothecrosssectionsdeterminedby
nates at low collision energies; at energies above ∼ 150 quantumclose-coupledcalculations basedon highquality
6 Ludwig Scharfenberg et al.: Scattering of Stark-decelerated OH radicals with rare-gas atoms
100 200 300 400 100 200 300 400
15
100
%
/n 80 5/2f
o
He secti 60 10
ss 5/2e
o
cr 40 5 7/2e
e
v
relati 20 5/2f 3/2e 97//22ef
0
0 9/2f
15
100
%
/n 80 7/2e
Ne ctio 5/2e 10
e 60
s 5/2f
s
s
cro 40 5
relative 20 5/2f 3/2e 0 7/2f
0
100 15
%
/n 80 5/2f
o
Ar secti 60 3/2e 10
s
s
cro 40 5/2e 5 7/2e
e
ativ 20 5/2f 7/2f 9/2e
rel 0 0 9/2f
15
% 100 5/2f
/n 80
o 3/2e
Kr secti 60 10
s
s
o
cr 40 5 7/2e
ve 5/2e
elati 20 5/2f 7/2f
r 0
0
15
100 5/2f
%
/n 80
Xe ectio 60 3/2e 10
s
s
e cros 40 5/2e 5 77//22ef
ativ 20 5/2f 9/2e
rel 0 0 9/2f
100 15
% 5/2f
/n 80
D ectio 60 3/2e 10
2 s s 7/2e
os 40 5
e cr 5/2e 7/2f
ativ 20 9/2e
el 5/2f 0 9/2f
r 0
100 200 300 400 100 200 300 400
mean collision energy / cm-1
Fig. 3. Relative state-to-state inelastic scattering cross sections for spin-orbit conserving (F1 → F1) collisions of OH
(X2Π3/2,J = 3/2,f) radicals with He, Ne, Ar, Kr, and Xe atoms and D2 molecules as a function of the collision energy.
The theoretically calculated cross sections are included as solid curves. In the energy-level scheme, the splitting between both
parity components of each rotational level is largely exaggerated for reasons of clarity.
Ludwig Scharfenberg et al.: Scattering of Stark-decelerated OH radicals with rare-gas atoms 7
100 200 300 400 100 200 300 400 100 200 300 400
8 2 30
3/2f
% 1/2e
He /ection 6 1/2e 20
s s 4 1
s 5/2f
o 10
cr
e 5/2e 3/2f
relativ 2 1/2f 0 3/2e 0
0 100 200 300 400
8 2
3/2f
% 1/2e
/n 6
o 3/2e
Ne cti
ss se 4 1 5/2f
o
cr
ve 2 5/2e
relati 1/2f 0
0
8 2
3/2f
%
/n 6
Ar ctio 1/2e 3/2e
e
s s 4 1 5/2f
s
o
cr
e 2
ativ 1/2f 5/2e
el 0
r 0
8 2
3/2f
%
/n 6
o 3/2e
Kr cti
e
s 1
s 4 5/2f
s
o
cr 1/2e
ve 2
relati 1/2f 0 5/2e
0
8 2
%
/n 6 3/2f
Xe ctio 3/2e
e 1
s s 4 5/2f
s
o
cr 1/2e
e 2 5/2e
v
elati 1/2f 0
r
0
8 1/2e 2
3/2f 3/2e 3/2f
/n % 6 5/2e 4
D ctio 3/2e
2 ss se 4 1/2f 1 2 5/2e
o 5/2f
cr
e 2
v
elati 0 0 5/2f
r 0
100 200 300 400 100 200 300 400 100 200 300 400
mean collision energy / cm-1
Fig.4.Relativestate-to-stateinelasticscatteringcrosssectionsforspin-orbitchanging(F1 →F2)collisionsofOH(X2Π3/2,J =
3/2,f) radicals with He, Ne, Ar, Kr, and Xe atoms and D2 molecules as a function of the collision energy. The theoretically
calculated cross sections are included as solid curves.
8 Ludwig Scharfenberg et al.: Scattering of Stark-decelerated OH radicals with rare-gas atoms
ab initio PES’s. For the scattering of OH with Ne and be estimated from the rotational energy level structure
Kr atoms, excellent agreement is found between the ex- of the OH radical and the different expansion coefficients
perimentallydeterminedandtheoreticallycomputedscat- vl,0(R) and vl,2(R) of the sum and difference potential
tering cross sections. The cross sections for all scatter- energy surfaces, respectively.
ingchannels,bothforspin-orbitconservingandspin-orbit A close inspection of the nature of the interaction po-
changing collisions, and for all collision energies are per- tential and the relevant coefficients that determine the
fectly reproduced by the calculations. state-to-state cross sections can yield a satisfying under-
For the scattering of OH radicals with Xe atoms, the standing of the physical origin of general scattering fea-
measured cross sections confirm the cross sections that tures [40]. As outlined in Ref. [23], for instance, the pro-
weredeterminedinourpreviousworkonthis system[20]. founddifferenceinthescatteringbehaviorthatisobserved
It is noted that both experiments were performed in dif- for the inelastic scattering of OH with He atoms or D2
ferent apparatuses and with different levels of sensitiv- moleculescanbe explainedbythemuchlargeranisotropy
ity. For the present experiment, in which state-to-state of the OH-D2 PES’s compared to the OH-He PES’s. In
cross sections for a larger number of final states are mea- general,asmallF1(3/2f)→F1(3/2e)Λ-doubletchanging
sured,excellentagreementisobtainedbetweenexperimen- crosssection,astrongpropensityforrotationalexcitation
tal and theoretical cross sections. The relative scattering into the e parity component of the F1(5/2) state, and a
cross sections, as well as the threshold behavior of indi- strong cross section for scattering into the F2(1/2e) level
vidual channels, are reproduced well. Also the increase in indicates that the scattering is dominated by the sym-
the relative scattering cross section for the F1(3/2f) → metric l = even terms, whereas the opposite scattering
F1(5/2e) channel at collision energies just above the en- behavioris expectedfor systemsinwhichthe asymmetric
ergetic threshold is perfectly reproduced. The only pro- l = odd terms play a large role. The former is the case
nounced difference between experiment and theory is ob- forthe weaklyinteractingOH-He systemthatresults ina
served for the F2(1/2f) channel at energies just above potential energy surface with small anisotropy; the latter
threshold. This discrepancy could possibly be explained applies to the strongly interacting OH-D2 system.
bysmallimperfectionsinthedifferencepotential.Wehave
Thesequalitativeargumentscanalsobe usedtoratio-
observed in the calculations that the cross sections for
nalizethetrendsthatareobservedforthescatteringofOH
scattering into the F2(1/2) channels are particularly sen- with the series of rare-gasatoms He, Ne, Ar, Kr, and Xe.
sitivetosmallvariationsofVdiff.Atlowcollisionenergies, Indeed,withincreasingpolarizabilityofthecollisionpart-
there appears to be a small shift of a few cm−1 between
ner,thescatteringisgovernedbypotentialenergysurfaces
the experimental and the theoretical values for the col-
with increasing well depth and larger anisotropy.This re-
lision energy. The origin of this shift is not known, but
sults in more dominant l = odd expansion coefficients,
could well be the result of an uncertainty in our Xe beam
and hence in a larger F1(3/2f) → F1(3/2e) Λ-doublet
velocity measurements.
cross section, smaller e over f propensities for excitation
into the F1(5/2) state, and reduced cross sections for the
F1(3/2f)→F2(1/2e) spin-orbit changing channel.
4.2 Comparison between the various collision partners
The trends that are observed are thus consistent with
what may be expected from the nature of the OH-rare
Interesting trends are observed when the general scatter-
gas atom interaction potential. However, for the series of
ing behavior for the various OH-rare gas atom systems
collision partners also dynamic effects that are related to
arequalitativelycomparedwitheachother.Forthe series
the increasing mass of the collision partner may play a
OH-He, Ne, Ar, Kr, Xe it is observed that the role of the
role.Itisnotapriori clearwhichfeaturesinthescattering
F1(3/2f)→F1(3/2e) channel gradually increases. At the
behavior are due to the nature of the PES’s, and which
same time, propensities for preferredscatteringinto the e
features result from the atomic and molecular motion on
parity state of the other rotational states of the F1 man-
these PES’s.
ifold tend to get weaker. Finally, the contribution of the
spin-orbit changing F1(3/2f) → F2(1/2e) channel to the Tostudytheinfluenceofbothparametersonthescat-
scatteringisgraduallyreducedfrom∼20%forOH-Heto tering, we have performed calculations for two hypothet-
∼ 2 %for OH-Xe.We note that these qualitative changes ical OH-rare gas atom systems. In the first system, we
are strongest when the collision partner He is replaced have used the OH-He PES’s, but performed the scatter-
by Ne, and when Ne is replaced by Ar. When Ar is re- ing calculations with the He atom mass replaced by the
placed by Kr, smaller changes are observed, while hardly Xe atom mass. In the second system, we have used the
anychangesoccuringoingfromKrto Xe.The scattering OH-Xe PES’s, but performed the scattering calculations
of OH radicals with D2 molecules does not fit entirely in with the Xe atom mass replaced by the He atom mass.
this trend; the overall scattering behavior for this system These model systems thus yield information on the scat-
resemblesthatoftheOH-Ar,OH-KrandOH-Xesystems. teringofOHradicalswithaweaklyinteractingbutheavy
A qualitative understanding of the inelastic scattering collisionpartner,andwithastronglyinteractingbutlight
of OH radicals with rare-gas atoms can be obtained from collision partner. The resulting inelastic scattering cross
a general analysis given by Dagdigian et al. [39]. Accord- sections for both systems are shown in Figure 5.
ing to this analysis, the relative strength of the various FortheOH-Heinteractionpotential,significantchanges
scattering channels (in particular for low values of J) can in the cross sections are observed upon replacement of
Ludwig Scharfenberg et al.: Scattering of Stark-decelerated OH radicals with rare-gas atoms 9
100 10 2
80 F1 15 F1 8 F2 F2
1/2e
5/2e 3/2f
60 6
10
% 1
/on 40 5 5/2f 4 3/2e
ecti 20 5/2f 3/2e 7/2e 2 1/2f 5/2f
s 7/2f 5/2e
s 0 0 9/2e 0 0
s 9/2f
ve cro 10800 3/2e F1 15 F1 108 F2 6 F2
ati 1/2e
el 5/2f 4 3/2f
r 60 6
10
40 4
2
5/2e 5
20 7/2e 9/2e 2 1/2f 3/2e 5/2f
0 5/2f 0 7/2f 9/2f 0 0 5/2e
100 200 300 400 100 200 300 400 100 200 300 400 100 200 300 400
collision energy / cm-1
Fig. 5. Calculated relative state-to-state inelastic scattering cross sections for twohypotheticalOH (X2Π3/2,J =3/2,f)-rare
gas atom systems. Top row: calculations are based on the OH-He PES’s from Ref. [33], but the scattering calculations are
performed with the He atom mass replaced by the Xe atom mass. Bottom row: calculations are based on the OH-Xe PES’s
from Ref. [20], but thescattering calculations are performed with theXeatom mass replaced by theHe atom mass.
the He atom mass with the Xe atom mass. In particular, an independent variation of the relevant parameters [41,
the relative cross section for scattering into the F1(3/2e) 42].
state increases, while the contributions of the F1(5/2e)
and F2(1/2e) channels to the scattering decrease. Note
thatalsothethresholdbehaviorofvariouschannelschanges
5 Conclusions
significantly;thecrosssectionsriselesssharplyatcollision
energies above threshold. The resulting state-to-state rel-
We have presented new measurements on the state-to-
ativeinelasticcrosssectionscloselyresemblethoseforthe
state rotational inelastic scattering of Stark-decelerated
OH-Ne system,i.e., ofa weaklyinteracting systemwith a
OH (X2Π ,J = 3/2,f) radicals with Ne, Kr, and Xe
larger reduced mass compared to OH-He. 3/2
atoms. For each collision system, a total of 13 inelastic
Forthe OH-Xeinteractionpotential,oppositechanges
scattering channels is studied at collision energies in the
inthescatteringcrosssectionsareobserveduponreplace- 70−400 cm−1 range. The collision energy dependence of
mentoftheXemasswiththeHeatommass.TheF1(3/2f)→the relative inelastic scattering cross sections, the thresh-
F1(3/2e)channelbecomeslessdominant,andtheF1(5/2e) old behavior of inelastic channels, and the energy depen-
andF2(1/2e)channelsgainimportance.Theresultingrel- denceofthe state-resolvedpropensitiesareaccuratelyde-
ative state-to-state cross sections resemble those that are
termined. Excellent agreement is found with the inelastic
measured for the OH-D2 system, i.e., of a strongly inter- scattering cross sections determined from quantum close-
acting system with a smaller reduced mass compared to coupled scattering calculations based on ab initio poten-
OH-Xe.
tial energy surfaces.
These model calculations indicate that the nature of Thesemeasurementscomplementourrecentstudieson
the potential energy surface and the reduced mass of the thescatteringoftheOHradicalswithHeatoms,Aratoms,
system can both have a profound and qualitatively simi- andD2molecules,andconfirmthemeasuredcrosssections
larinfluenceonthescatteringcrosssections.Thissuggests ofouroriginalworkonthe scattering ofOHradicalswith
that the interesting trends that are observedfor the scat- Xeatoms.Together,thesestudiesrepresentthemostcom-
tering of OHwith He, Ne, Ar,Kr,and Xe are in partdue plete combined experimental and theoretical study of the
to the increasing interaction strength of the OH radical inelastic scattering of an open shell radical in a 2Π elec-
with the collision partner, and in part due to the increas- tronicstatewithrare-gasatoms.The excellentagreement
ing mass of the rare-gas atom. It is not straightforward that is obtained with the cross sections that are derived
to disentangle the influence of both effects using ab ini- from ab initio potential energy surfaces for all OH-rare
tio potential energy surfaces and close-coupled scattering gas atom systems clearly indicates that the scattering of
calculationsasemployedhere.Theindividualinfluenceon these systems is well understood.
thescatteringofpropertiessuchaswelldepth,anisotropy Significant differences are found in the scattering be-
and reduced mass can be studied best using models for havior of OH radicals with the various collision partners,
the potential and the scattering dynamics that allow for andinterestingtrendsareobservedintherelativeinelastic
10 Ludwig Scharfenberg et al.: Scattering of Stark-decelerated OH radicals with rare-gas atoms
scatteringcrosssectionsforthe seriesOH-He,Ne,Ar,Kr, 14. G. Paterson, S. Marinakis, M.L. Costen, K.G. McK-
and Xe. Replacement of the He atom by heavier rare-gas endrick, J. K los, R. Tobo la, J. Chem. Phys. 129, 074304
atoms results in a more dominant F1(3/2f) → F1(3/2e) (2008),Erratum:G.Paterson,S.Marinakis,M.L.Costen,
Λ-doublet changing cross section, smaller propensities for K.G.McKendrick,J.K losandR.Tobo la,J.Chem.Phys.
preferredexcitationintooneoftheΛ-doubletcomponents 131, 159901 (2009)
of excited rotationallevels,and reduced crosssections for 15. G. Paterson, S. Marinakis, J. K los, M.L. Costen, K.G.
the F1(3/2f) → F2(1/2e) transition. These trends result McKendrick, Phys.Chem. Chem. Phys.11, 8804 (2009)
16. M.C. Heaven,Ann.Rev.Phys. Chem. 43, 283 (1992)
in part from the increasing strength of the OH-rare gas
17. M.C. Heaven,Int.Rev. Phys.Chem. 24, 375 (2005)
atom interaction,and in part from the increasing mass of
18. S.Y.T.vandeMeerakker,H.L.Bethlem,G.Meijer,Nature
the rare-gasatom.
Physics 4, 595 (2008)
The resonances in the scattering of OH with He and
19. H.L.Bethlem,G.Berden,G.Meijer, Phys.Rev.Lett.83,
Ne atoms at energies close to threshold – hinted at in the
1558 (1999)
present measurements – will be subject of future experi-
20. J.J.Gilijamse,S.Hoekstra,S.Y.T.vandeMeerakker,G.C.
ments with increased collision energy resolution [43].
Groenenboom, G. Meijer, Science 313, 1617 (2006)
21. L.Scharfenberg,H.Haak,G.Meijer, S.Y.T.vandeMeer-
akker, Phys.Rev.A 79, 023410 (2009)
6 Acknowledgements 22. L.Scharfenberg,J.K los,P.J.Dagdigian,M.H.Alexander,
G. Meijer, S.Y.T. van de Meerakker, Phys. Chem. Chem.
ThisworkissupportedbytheESFEuroQUAMprogramme, Phys. 12, 10660 (2010)
andispartoftheCoPoMol(CollisionsofColdPolarMolecule2s)3. M.Kirste,L.Scharfenberg,J.K los,F.Lique,M.H.Alexan-
project. The expert technical assistance of Georg Ham- der,G.Meijer,S.Y.T.vandeMeerakker,Phys.Rev.A82,
mer, Henrik Haak, Uwe Hoppe and the FHI mechanical 042717 (2010)
24. S.Y.T. van de Meerakker, N. Vanhaecke, H.L. Bethlem,
and electronics workshops are gratefully acknowledged.
G. Meijer, Phys.Rev. A 71, 053409 (2005)
We thank Anne McCoy and Yoshihiro Sumiyoshi for pro-
25. S.Y.T. van de Meerakker, N. Vanhaecke, H.L. Bethlem,
vidingustherequiredinformationtoevaluatethefittothe
G. Meijer, Phys.Rev. A 73(2), 023401 (2006)
OH-NeandOH-Krpotentials,andthankLiesbethJanssen
26. M.H. Alexander, J. Chem. Phys. 76, 5974 (1982)
and Jacek Kl os for help and discussions. AvdA thanks
27. M. Lara, J.L. Bohn, D. Potter, P. Sold´an, J.M. Hutson,
the Alexander von Humboldt Foundation for a Research
Phys. Rev.Lett. 97(18), 183201 (2006)
Award.
28. L.Gonz´alez-Sa´nchez,E.Bodo,F.A.Gianturco,Phys.Rev.
A 73(2), 022703 (2006)
29. Z.Pavlovic,T.V.Tscherbul,H.R.Sadeghpour,G.C.Groe-
References nenboom, A. Dalgarno, J. Phys. Chem. A 113, 14670
(2009)
1. R.Levine,R.Bernstein,Molecular reaction dynamics and 30. T.V.Tscherbul,G.C.Groenenboom,R.V.Krems,A.Dal-
chemical reactivity (Oxford University Press, New York, garno, Faraday Discussions 142, 127 (2010)
1987) 31. J.P.Maillard,J.Chauville,A.W.Mantz,J.Mol.Spec.63,
2. A. Schiffman, D.W. Chandler, Int. Rev. Phys. Chem. 14, 120 (1976)
371 (1995) 32. MOLPRO,version2008.1,apackageofabinitioprograms,
3. K. Liu, R.G. MacDonald, A.F. Wagner, Int. Rev. Phys. H.-J. Werner, P. J. Knowles, R. Lindh, F. R. Manby, M.
Chem. 9, 187 (1990) Schu¨tz, and others, see http://www.molpro.net.
4. D.W. Chandler, S. Stolte, Gas Phase Molecular Reaction 33. H.S. Lee, A.B. McCoy, R.R. Toczy lowski, S.M. Cybulski,
and Photodissociation Dynamics (Transworld Research J. Chem. Phys.113, 5736 (2000)
Network, 2007), chap. Inelastic energy transfer: The NO- 34. Y.Sumiyoshi,I.Funahara,K.Sato,Y.Ohshima,Y.Endo,
rare gas system, pp.1–63 Phys. Chem. Chem. Phys. 12, 8340 (2010)
5. J.C. Whitehead, Rep.Prog. Phys.59, 993 (1996) 35. Y.Sumiyoshi,I.Funahara,K.Sato,Y.Ohshima,Y.Endo,
6. H.Kohguchi,T.Suzuki,Annu.Rep.Prog.Chem.,Sect.C Mol. Phys. 108, 2207 (2010)
98, 421 (2002) 36. S.F. Boys, F. Bernardi, Mol. Phys. 19, 553 (1970)
7. K. Schreel, J. Schleipen, A. Eppink, J.J. ter Meulen, J. 37. B.R. Johnson, J. Comp. Phys.13, 445 (1973)
Chem. Phys.99, 8713 (1993) 38. M.S. Child, Molecular Collision Theory (Academic Press,
8. M.C.vanBeek,J.J.terMeulen,M.H.Alexander,J.Chem. London, 1974)
Phys.113, 628 (2000) 39. P.J. Dagdigian, M.H. Alexander, K. Liu, J. Chem. Phys.
9. J.J. van Leuken, F.H.W. van Amerom, J. Bulthuis, J.G. 91, 839 (1989)
Snijders, S.Stolte, J. Phys. Chem. 99, 15573 (1995) 40. A.DegliEsposti,A.Berning,H.J.Werner,J.Chem.Phys.
10. H.Kohguchi,T.Suzuki,M.H.Alexander,Science294,832 103, 2067 (1995)
(2001) 41. A.Gijsbertsen,H.Linnartz,C.A.Taatjes,S.Stolte,J.Am.
11. A. Gijsbertsen, H. Linnartz, G. Rus, A.E. Wiskerke, Chem. Soc. 128, 8777 (2006)
S. Stolte, D.W. Chandler, J. K los, J. Chem. Phys. 123, 42. M. Lemeshko, B. Friedrich, J. Chem. Phys. 129, 024301
224305 (2005) (2008)
12. S.Stolte, Nature 353, 391 (1991) 43. L.Scharfenberg,S.Y.T.vandeMeerakker,G.Meijer,sub-
13. M.C.vanBeek,G.Berden,H.L.Bethlem,J.J.terMeulen, mitted (2010)
Phys.Rev.Lett. 86, 4001 (2001)