Potential energy surfaces for the CN(X2Σ+,A2Π)Ar system and inelasticscattering within the A stateMillard H. Alexander, Xin Yang, Paul J. Dagdigian, Andreas Berning, and Hans-Joachim Werner Citation: J. Chem. Phys. 112, 781 (2000); doi: 10.1063/1.480720 View online: http://dx.doi.org/10.1063/1.480720 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v112/i2 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions

JOURNAL OF CHEMICAL PHYSICS VOLUME 112, NUMBER 2 8 JANUARY 2000

Potential energy surfaces for the CN „X 2S1,A 2P…Ar systemand inelastic scattering within the A state

Millard H. Alexandera)

Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742-2021

Xin Yangb) and Paul J. DagdigianDepartment of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218-2685

Andreas Berning and Hans-Joachim WernerInstitut fur Theoretische Chemie, Universita¨t Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany

~Received 10 August 1999; accepted 13 October 1999!

Adiabatic and diabatic potential energy surfaces~PES’s! for the interaction of Ar(1S0) with the CNmolecule in its ground (X 2S1) and first excited (A 2P) electronic states were determined usingmultireference configuration-interaction calculations. The three electronicallyadiabatic potentialenergy surfaces~PES’s 2A8 and 1A9! are transformed to threediabatic PES’s plus one additionalPES which describes the coupling between the two diabatic PES’s ofA8 symmetry which correlateasymptotically with theX 2S1 andA 2P states of CN. The appropriate diabatic PES’s are then usedin the study of rotationally inelastic scattering of CN(A 2P) in collisions with Ar. Experimentalstate-to-state rate constants were measured with an optical–optical double resonance technique. TheCN radical was prepared by 193 nm photolysis of BrCN diluted in slowly flowing argon at a totalpressure of;0.5 Torr. Specific fine-structureL-doublet levels of CN(A 2P,v53) were prepared byexcitation with a pulsed dye laser on various rotational lines in theA 2P –X 2S1(3,0) band, andcollisionally populated levels were probed after a short delay by laser fluorescence excitation in theB 2S1 –A 2P(3,3) band. State-to-state rate constants, both relative and absolute, were determinedfor several rotational levels withJ56.5 and 7.5. The final state distributions displayed an even–oddalternation as a function of the final angular momentumJ for scattering into certain fine-structureL-doublet manifolds. The measured state-to-state rate constants agreed quite well with rateconstants derived from quantum scattering calculations with theab initio CN(A 2P) – Ar PES’s. Theeven–odd oscillation in final state populations is ascribed to the near homonuclear character of thePES’s. © 2000 American Institute of Physics.@S0021-9606~00!00602-4#

uttice-

f t-thofaiti

esbl

a

rt

tial

s in

mol-c

rlynsithys-

so-

in

ngpa-

tedive.

I. INTRODUCTION

The application of modern experimental techniqueslizing lasers have allowed the study of rotationally inelascollisions between specific initial and final rotational/finstructure levels in open-shell electronic states.1 There havealso been parallel advances in the theoretical treatment oinelastic collision dynamics2 and in the computation of stateto-state cross sections. This synergistic experimental andoretical study of rotational energy transfer in open-shell mecules has led to a considerable detailed understanding ofactors governing the magnitudes of the cross sectionstheir dependence upon the quantum numbers of the inand final states.

Rotationally inelastic collisions of open-shell moleculin 2P electronic states have received consideraattention.1,3–6Because of the orbital degeneracy of aP state,the rotational levels of the isolated molecule appearclosely spaced levels~L-doublets! of opposite parity.7 Thisdegeneracy is lifted with the approach of the collision pa

a!Author to whom correspondences should be addressed.b!Present address: Department of Chemistry and Biochemistry, The Un

sity of California at Los Angeles, Los Angeles, California 90095-1569

7810021-9606/2000/112(2)/781/11/$17.00

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract.

i-

he

e-l-thendal

e

s

-

ner, and the interaction can be described by two potenenergy surfaces~PES’s! of A8 and A9 symmetry. For2Pstates which approach Hund’s case~a! coupling, the sam-pling of these PES’s affects the propensities for changethe fine-structure label and the identity of theL-doubletlevel. The collisional behavior is also subject to quantuinterference effects which can lead to differences in the clisional behavior of theL-doublets associated with a specifirotational level, particularly in the case~b! limit.8–11

Collisions of CN with rare gases represent a particulainteresting system, for which rotationally inelastic collisioin a 2P electronic state can occur simultaneously wcollision-induced electronic transitions. Indeed, these stems represent prototypes for the latter process.12–14 Elec-tronic quenching in CN is facilitated by a series of near renances between the vibrational levels of the ground (X 2S1)and first two excited (A 2P,B 2S1) electronic states.15–17

Quenching of electronically excited CN has been studiedNe matrices,18 in CNArn clusters,19 and in binary CNNecomplexes.20 State-to-state rotationally inelastic scatteriwithin the X 1S1 state has been investigated through preration of specific rotational levels in thev52 vibrationallevel by stimulated emission pumping.21,22In earlier collabo-rative experimental and theoretical studies, we investigar-

© 2000 American Institute of Physics

Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions

ini

wtivithl-

ic

b

.g

-HoeA

icre

nr tvreo

-e

e

ofins

re

lyolyttst-

thiclli-e

t

ordne intateota-

edw

aredixross

yti-nne

an

’’

con-ree-ofionn-

p-

d

ithe

a-

on,ndet-

le

p-

fs a

po-aticusly

782 J. Chem. Phys., Vol. 112, No. 2, 8 January 2000 Alexander et al.

collision-induced electronic transitions between specifictial vA53,7,8 and finalvX5vA14 rotational, fine-structurelevels. Optical–optical double resonance spectroscopyemployed for the experimental measurement of relastate-to-state rate constants for the collision of CN wAr.23–25 In the course of this work, rotationally inelastic colisions within theA 2P state were also investigated.

Alexander and Corey developed the general theoretformalism for transitions between2P and 2S states of adiatom in collisions with a closed-shell atom.26 In their for-mulation, electronically inelastic transitions are inducednonadiabatic coupling between the2S electronic state andthe component of theA 2P state ofA8 symmetry. Subse-quently, Werner and co-workers reported theab initiodetermination27 of diabatic PES’s for the CN–He systemThis work was followed later by quantum scatterincalculations28 based on theab initio PES’s. Werner and coworkers compared the theoretical predictions for CN–with the experiments on CN–Ar. At that time calculationsthe full CN–Ar PES’s were not performed, although Wernand co-workers did present several cuts in the CN–PES’s.28 In later experimental work, electronically inelastCN–He collisions were studied and the results compawith quantum calculations29 in which the isolated-moleculeA;X spectroscopic perturbations15 were included.

In our earlier experimental work,23–25,29the CN radicalwas produced with a room-temperature Boltzmann rotatiostate distribution in a discharge-flow apparatus. In ordestudy collisions of a wider range of rotational levels, we harecently implemented the use of photolysis in order to ppare highly rotational excited CN. Employing 193 nm phtolysis of BrCN, we have recently reported30 the first resultson state-to-state inelastic collisions of CN(A 2P,v53) withrotational angular momentaJ'60.5, corresponding to;6000 cm21 of rotational energy. With this degree of rotational excitation, the CN(A 2P) state closely approaches thHund’s case~b! limit, and in rotationally inelastic collisionsdramatically different final state populations were observfor initial L-doublet levels ofA8 andA9 symmetry.30

In addition to exploring rotational energy transferhighly rotationally excited CN, we are also interested investigating collision-induced electronic transitions of theinitial levels. In particular, thevA53 and vX57 vibronicmanifolds cross in the range ofJ'62.5– 92.5.15 Our pho-tolytic method for generating CN thus allows us to explothe role of spectroscopically perturbed15 ‘‘gateway’’ levelsin enabling collision-induced electronic transitions of highrotationally excited CN. We have also found that this phtolytic production method is far superior to the previousemployed discharge-flow technique, and dramatically bedata have been obtained for the study of rotationally inelacollisions of CN(A 2P) of low rotational angular momentum.

In the present paper, we report the calculation ofcomplete CN–Ar PES’s which can be used in the theorettreatment of rotationally and/or electronically inelastic cosions of CN(X 2S1,A 2P). These calculations extend thearlier work of Werner and co-workers,28 in which a fewcuts in the CN–Ar PES’s were presented. It is interesting

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract.

-

ase

al

y

efrr

d

aloe-

-

d

-e

-

eric

eal

o

compare the CN–Ar PES’s with published PES’s fCN–He ~Ref. 27! and CN–Ne,31 as the greater range anstrength of the CN–Ar interaction may affect the collisiodynamics. The CN–Ar PES’s are subsequently used herquantum scattering calculations to compute state-to-scross sections and rate constants for collision-induced rtional transitions of low rotational levels of CN(A 2P,v53) whose collisional behavior is experimentally studiand reported here. It is of interest to study collisions of lorotational levels, whose energy spacings are small compwith kT and for which the strength of the coupling matrelements usually governs the magnitude of the inelastic csections.

In the present experiments, CN was prepared photolcally and allowed to relax to a room-temperature Boltzmadistribution. A specific rotational, fine-structure level in thA 2P state was prepared by ‘‘pump’’ laser excitation onisolated line in theA 2P –X 2S1 band system, while colli-sionally populated levels were monitored through ‘‘probelaser fluorescence excitation in theB 2S1 –A 2P band sys-tem. The computed and measured state-to-state ratestants are compared and found to be in quite good agment. We defer to future publications further studycollision-induced rotational transitions and the investigatof collision-induced electronic transitions of highly rotatioally excited CN(A 2P). A preliminary report on rotationallyinelastic collisions of high rotational levels has already apeared in print.30

II. AB INITIO POTENTIAL ENERGY SURFACES

Electronically adiabatic and diabaticab initio PES’swere determined for the interaction of Ar with the groun(X 2S1) and first excited (A 2P) electronic states of the CNmolecule. Although the present paper is concerned only winelastic scattering within theA state, we shall discuss herall the electronic PES’s since the calculation of the CN(A)Arand CN(X)Ar PES’s must be done together. The investigtion of electronically inelastic (A→X) scattering, based onthese PES’s, will be deferred to a later paper. In additimotivated by experimental work by Filseth, Carrington, aco-workers,22 Berning and Werner have completed a theorical study of rotational relaxation within theX state,32 whichmakes use of the CN(X)Ar PES described here.

The nominal electron configurations of the CN molecuin the X 2S1 and A 2P state are 1s2

¯5s11p4 and1s2

¯5s21p3, respectively. As a spherical partner aproaches, the cylindrical degeneracy of theA 2P state islifted to give rise to two electronic states ofA8 and A9 re-flection symmetry~in Cs geometry!,2,33–36while the X 2S1

state becomes a state ofA8 reflection symmetry. The PES oeach electronic state of the CNAr system is described afunction of the C–N distancer, the distanceR from the cen-ter of mass of CN to the Ar atom, and the angleu betweenRand r ~u50 corresponds to a linear CN–Ar geometry!. Thetechniques used to calculate the electronically adiabatictential energy surfaces and the transformation to a diabrepresentation are identical to those we have used previoin investigations of the interaction of CN(X,A) with He

Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions

foen

n

e,

nll

y

lef

he

is

iin

ro

o

m

v-

rnth

tee

e

in

-i-sth

est

wly

e

CNhr.

gles

i-ic

-ther

hes

sd

nal

er-

783J. Chem. Phys., Vol. 112, No. 2, 8 January 2000 PES for CN–Ar

~Ref. 27! and Ne~Ref. 31! and the isoelectronicN21(X,A)

ion with He.37 We refer the reader to these earlier papersfull particulars. Only those details pertinent to the presinvestigation will be given again.

We used the augmented correlation-consistent valetriple-zeta~avtz! basis set of Dunning and co-workers.38,39

Complete-active-space self-consistent-field~CASSCF!~Refs. 40–42! calculations were followed by multireferencinternally contracted configuration-interaction~MRCI! ~Refs.43,44! calculations. In the CI calculations, the contributioof higher-order excitations is estimated using the internacontracted multireference version45 of the Davidsoncorrection.46 Standard counterpoise47 and size-consistenccorrections are made, as described previously.27,31,37All cal-culations were carried out with theMOLPRO suite ofab initioprograms.48

In a coordinate system in which both the CN molecuand the Ar atom lie in thexz-plane, the degenerate pair oelectronic wavefunctions for the free CN molecule in tA 2P state are denoteduPx& and uPy&, and correspond todominant electron occupancies of ...5s21px1py

2 and...5s21px

21py , respectively. The former wavefunctionsymmetric (A8), and the latter antisymmetric (A9), with re-spect to reflection of the spatial coordinates in the triatomplane. The electronic wave function for the CN moleculethe X 2S1 state, which corresponds to a dominant electoccupancy of 1s2...5s1p4, is also of A8 symmetry. Wedenote this state asuS&.

The diabatic potential energy surfaces, which we denVS(R,r ,u), Vx(R,r ,u), andVy(R,r ,u), are the matrix ele-ments of the electronic Hamiltonian in the diabatic basis,uS&,uPx&, and uPy&. In nonlinear geometries, as the Ar atoapproaches, the twodiabaticwavefunctions ofA8 symmetry~uPx& and uS&! become mixed. The degree of mixing is goerned by a fourth diabatic PES, designatedV1(R,r ,u). In-stead ofVx andVy is more convenient2 to use the sum anddifference potentials,VP andV2 , defined by,

VP~R,r ,u!5 12~Vy1Vx! ~1!

and

V2~R,r ,u!5 12~Vy2Vx!. ~2!

The preceding development does not include the non-BoOppenheimer spin–orbit and spin-rotation coupling in2P and2S1 states,15 since these were not included in theabinitio calculation.

Because the extent of mixing of the two diabatic staof A8 symmetry is extremely small, we will also use thlabels CN~S!Ar and CN~P!Ar to refer, respectively, to theadiabatic electronic states in which the CN moiety is dscribed primarily by ...5s1p4 and ...5s21p3 electron occu-pancies.

As discussed in the Introduction, in the accompanyexperiments the CN molecule is initially excited to thev53 level of theA 2P state. To account fully for the vibrational motion of the CN molecule would require a determnation of theab initio PES’s at several CN bond distanceTo avoid this additional computational expense, we usedFranck–Condon-type model introduced earlier.27,28 The av-

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract.

rt

ce

y

c

n

te

–e

s

-

g

.e

erage bond lengths in the two vibrational levels of interare ^r &A,v5352.396 bohr and r &X,v5752.344 bohr.27 Sincethese are quite similar, we assume that the PES’s are slovarying functions ofr, and make the approximation that

Vi~R,r ,u!>^v8~r !uv9~r !&Vi~R,r A ,u!, ~3!

wherer A is the average value ofr in thev53 level of theAstate~2.396 bohr!. Here the vibrational overlap is taken to b1 for the VS , VP , and V2 PES’s, which refer to a singleelectronic state, and 0.179 21~Ref. 27! for theV1 PES whichdescribes the coupling between theA andX states. Thus, inthe calculations of the potential energy surfaces, thebond distance was held to the single value of 2.396 boWith r so constrained, the PES’s were calculated at 7 an~u50°, 30°, 60°, 90°, 120°, 150°, and 180°! and 13 valuesof R ~ranging from 4 to 12 bohr!.

Figure 1 displays contour plots of the electronically dabatic VP and V2 PES’s. As expected from the electronconfiguration of theA 2P state, where the 5s orbital is dou-bly occupied, the states ofA8 andA9 symmetry which cor-respond to CN(A)Ar have minima in perpendicular geometry since the Pauli repulsion between the Ar atom and5s orbital is larger in the collinear geometry. Similarly, foperpendicular approach, in which the Ar atom approac

FIG. 1. Contour plots of the MRCI1Q diabatic potential energy surfacefor the CN(X 2S1,A 2P)Ar complex with the inclusion of counterpoise ansize-consistency corrections. The top panel displaysVP @corresponding tothe average of the PES’s for wave functions of nominal CN(A 2Px) andCN(A 2Py) electron occupancy# while the lower panel displaysV2 @corre-sponding to the half difference of the PES’s for wave functions of nomiCN(A 2Px) and CN(A 2Py) electron occupancy#. The linearC–N–Ar ge-ometry corresponds tou50°. The dashed contours indicate negative engies. The heavy solid contour indicates the zero of energy.

Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions

i-

sf

r

s

nar

wed

of

ini-

ear

e-d

s of

ients

CNt

drac-n-ly

fted

theter-

then-

sd

n

Th

784 J. Chem. Phys., Vol. 112, No. 2, 8 January 2000 Alexander et al.

along thex axis, the2Py(A9) state, in which thepx orbital isdoubly occupied, is more repulsive than the2Px(A8) state.Consequently the difference potential,V2 is positive, as canbe seen in the lower panel of Fig. 1.

Figure 2 displays contour plots of the electronically dabatic VS and V1 PES’s. Because the 5s orbital is singlyoccupied in theX 2S1 state, the Pauli repulsion is not apronounced for collinear CNAr geometries@as in the case othe CN(A)Ar PES#, so that the CN(X)Ar PES has a farbroader minimum. The off-diagonalV1 PES, responsible fothe coupling between the CN(X)Ar and CN(X)Ar states, hasa pronounced bimodal character, seen before in our invegations of the CNHe and CNNe systems27,31 and in the iso-electronic N2

1–He system.37 For all the PES’s displayed inFigs. 1 and 2, a near forward–backward symmetry as a fution of the angleu is observable and is indicative of the nehomonuclear nature of the CN–Ar interaction.

In the quantum treatment of the collision dynamicsexpand theVP and V2 diabatic PES’s in terms of reducerotation matrix elements49 in the angleu as follows:2,26

Vq~R,u!5 (l50

6

Vql~R!d00

l ~u!, ~4!

FIG. 2. Contour plots of the MRCI1Q diabatic potential energy surfacefor the CN(X 2S1,A 2P)Ar complex with the inclusion of counterpoise ansize-consistency corrections. The top panel displaysVS @corresponding tothe PES for a wave function of nominal CN(X 2S1) electron occupancy#while the lower panel displaysV1 @which represents the coupling betweethe CN(A 2Px)Ar and CN(X 2S1)Ar states#. The linearC–N–Ar geometrycorresponds tou50°. The dashed contours indicate negative energies.heavy solid contour indicates the zero of energy.

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract.

ti-

c-

where the subscriptq designates ‘‘S’’ or ‘‘ P.’’ We furtherexpand theV2 PES as

V2~R,u!5 (l52

6

V2l~R!d20

l ~u!. ~5!

The upper limit in the summations is set by the numberdistinct angles used in theab initio calculation. To determinethe expansion coefficientsVS

l (R) and VPl (R) for any value

of R andu, we first fit theab initio CNAr interaction energiesVS(Ri ,u i), Vx(Ri ,u i), andVy(Ri ,u i), for each value ofu i

separately, to the general functional form50

V~R,u i !5c1i exp~2b1iR!1~c2i1c3iR!exp~2b2iR!

1c4i$tanh@1.2~R2R0i !#21%/R6. ~6!

The linear and nonlinear parameters were adjusted to mmize the relative deviation of all points withV<7000 cm21. Then, for any value ofR, the expansion pa-rameters in Eq.~6! were used to determineV(R,u i) at the 7angles, for VS(R), VPx

(R), and VPy(R). The VP

l (R),

VSl (R), andV2

l(R) coefficients in Eqs.~5! and ~6! are sub-sequently obtained by solution of separate sets of linequations.

For theV1(R,u) PES, which represents the coupling btween theuS& anduPx& states, theu-dependence is expandeas

V1~R,u!5 (l51

5

V1l~R!d10

l ~u!, ~7!

and, for each value ofu i , theR-dependence expanded as

V1~R,u i !5~c1i1c2iR!exp~2biR!. ~8!

For the V1 and V2 PES’s, which vanish by symmetry incollinear geometry, there are only five independent valueu. Consequently, 1<l<5 for V1 and 2<l<6 for V2 .

Figures 3 and 4 display plots of theR-dependence of thelargest expansion coefficients for theVP andV2 PES’s andcompares these to the corresponding expansion coefficfor the CN(A)He ~Refs. 29, 32! and CN(A)Ne ~Ref. 31!systems. Due to the near homonuclear character of themolecule, differing from N2 by only one electron, the largesanisotropic term in bothVP andV2 hasl52. We observe aremarkable similarity in both the magnitude anR-dependence of the expansion coefficients for the intetion of CN(A) with the three noble gases. As might be aticipated, the expansion coefficients for Ar are qualitativesimilar to those for the smaller noble gases, except shi;0.5 bohr to largerR.

III. INELASTIC COLLISION DYNAMICS

A. Formalism

In this paper we will discuss only those aspects ofscattering calculations which are relevant to inelastic scating within the CN(A 2P) state. Although theVS and VP

interaction PES’s are degenerate asymptotically,asymptotic states of the CN molecule, in particular vibratiorotation-multiplet levels of either theA 2P andX 2S1 stateare separated by the internal energies~electronic, vibration,

e

Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions

in

rg

.rinly

id

ech-

-

-nite

-

se

eN

ththe

785J. Chem. Phys., Vol. 112, No. 2, 8 January 2000 PES for CN–Ar

rotation, spin–orbit!. In the experiments to be describedSec. IV below, the CN radical is excited to theJ56.5 and7.5 levels of thev53 manifold of theA 2P state. As can beseen in Fig. 2 of Ref. 28, the origins of thev53 manifold oftheA state is separated by;600 cm21 from the origin of thethe nearest vibrational level of theX 2S1 state (v57). Be-cause the coupling between theA andX states~theV1 PES ofSec. II! is small in the region accessed by thermal enecollisions, A→X electronically inelastic transitions will bevery improbable in the experiments to be described below28

Consequently, it is sufficient to assume that the scatteoccurs solely within theA state, so that we need retain onthe VP andV2 PES’s.

To describe the rotational levels of the CN(A) moleculein its 2P electronic state we use a Hund’s case~a! basis,51

uLSJMV«&5221/2@ uJMV&uLS&1«uJM2V&u2L2S&].~9!

HereJ denotes the total angular momentum of the diatommolecule, with projectionsM and V along the space- anmolecule-fixedz-axes, respectively. The ketuLS& designatesthe electronic component of the wave function, for whichLand S denote the molecule-frame projections of the eltronic orbital and spin angular momenta, respectively. TL-~or ‘‘parity’’ ! doublet levels are distinguished by the symmetry indexe which can take the value11 ~e-labeled levels!or 21 ~f-labeled levels!.52 The total parity of the wave func

FIG. 3. Plots of theR-dependence of the largestVl(R) terms in the expan-sion in reduced matrix elements of the diabaticVP PES’s for CNHe~upperpanel, see Refs. 29 and 32!; CNNe ~middle panel, see Ref. 31!, and CNAr~lower panel, present work!. The abscissas all span a range of 4 bohr, butorigin is shifted outward 0.5 bohr in the CNAr plot.

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract.

y

g

c

-e

tions is given by«(21)J21/2.52 For simplicity in what fol-lows, we will suppress the electronic wavefunctionuLS& andthe L andS quantum numbers, except when needed.

The J–S term in the molecular Hamiltonian51 mixes theV51/2 andV53/2 case~a! basis functions. The eigenfunctions can be expressed as linear combinations of the defiV functions of Eq.~13!, namely,

uJMFi«&5(V

DFiV«J uJMV«&. ~10!

The expansion coefficientsDFiV«J are obtained by diagonal

ization of the Hamiltonian of the isolated CNmolecule.15,51,53 The eigenfunctions are denotedF1 and F2

in terms of increasing energy.7 Figure 5 displays the energieof the lower rotational, fine-structure levels in thCN(A 2P,v53) vibronic manifold. For this range ofJ, thewave functions are fairly well described by Hund’s case~a!coupling.

The complete wave function for the CN(A)Ar system isexpanded as

CJ M5~1/R! (JlFi«

CJlFi«J ~R!uJFi« l J M&, ~11!

where J is the total angular momentum. Here, thuJFi« l J M& functions are composed of products of the Celectronic-rotation functionsuJMFi«& @Eq. ~10!# and angularmomentum functions which describe the orbital~end-over-end! rotation of the CNAr complex (l5J 2J), namely,

e

FIG. 4. Plots of theR-dependence of the largestVl(R) terms in the expan-sion in reduced matrix elements of the diabaticV2 PES’s for CNHe~upperpanel, see Refs. 29 and 32!; CNNe ~middle panel, see Ref. 31!, and CNAr~lower panel, present work!. The abscissas all span a range of 4 bohr, butorigin is shifted outward 0.5 bohr in the CNAr plot.

Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions

-

ed

v

o

dr-

x

te

w

beN

eom

as-i-

ofter-nal

ns-lly.

on

pe-ed

the

-

the

al-the

00

nts,

xedateCS

ob-andnsi-tecon-red

ntsI.

ion-em-

ants

bed

ot

e

786 J. Chem. Phys., Vol. 112, No. 2, 8 January 2000 Alexander et al.

uJFi« l J M&5 (MJml

~JMJlml uJ M!Ylml~R!uJMJFi«&,

~12!

where Ylml(R) is a spherical harmonic and~¯u¯! is a

Clebsch–Gordan coefficient.49 Each state included in the expansion of Eq.~11! defines a ‘‘channel.’’

The expansion coefficients,CJlFi«J (R), in Eq. ~11! are

independent ofM and satisfy the standard close-coupl~CC! equations. In matrix notation these are

F d2

dR2 1W~R!GCJ~R!50, ~13!

where

W~R![k22l 2

R222m

\2 V~R!. ~14!

wherek2 designates the diagonal matrix containing the wavectors of the individual coupled channels, andl 2 andV(R)are the full matrices of the square of the orbital angular mmentuml and the interaction potential~s!, respectively. Thematrix elements of the interaction potential for a2P systemin the intermediate coupling basis of Eq.~10! have beengiven previously.2,54

Close-coupled2,36,54 scattering calculations were carrieout for the CN(A)Ar system at a large number of total enegies. The size of the state expansion in Eq.~11! ~number ofchannels!, as well as the integration parameters and mamum value of the total angular momentumJ , were chosento ensure an accuracy of better than 1% in the calculaprobabilities for all transitions out ofJ57.5 levels of CN.All scattering calculations were based on the formalismhave developed2,36,54 and performed with our Hibridoncode.55

The asymptotic dependence of theCJlFi«J (R) coefficients

in Eq. ~11! defines the fundamental scatteringS matrix. In-tegral cross sections for a collision-induced transitiontween initial and final electronic-rotational terms of the C

FIG. 5. Energies of the lower rotational levels of the CN(A 2P,v53) vi-bronic manifold. The levels are labeled with the rotational quantum numJ and separated into theF1 andF2 fine-structure manifolds. Each displayelevel is further split intoe and fL-doublets, but the splitting is too small tbe resolvable here. The left-hand ordinate gives the energies relative toof the CN(A 2P,v53,J51/2F1e) level. The right hand ordinate gives thenergies relative to the CN(X 2S1,v50,N50) level.

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract.

e

-

i-

d

e

-

molecule (JFi«→J8Fi8«8), averaged over all values of throtational projection quantum numbers can be obtained frthe correspondingS-matrix elements.2,36,54 Thermal rate co-efficients can then be obtained by integration over ansumed Maxwellian distribution of relative collision velocties. In terms of relative collision energies, we have56

k~JFi«→J8Fi8«8;T!

5@8/pm~kT!3#1/2E0

`

s~JFi«→J8Fi8«8;E!E

3exp~2E/kT!dE. ~15!

Scattering calculations were carried out on a fixed gridtotal energies. For each initial state, subtraction of the innal energy transforms this to a grid in relative translatioenergies, which is the integration parameter in Eq.~15!. Thecross sections are then interpolated over a finer grid of tralational energies, and the integration performed numerica

B. Calculations

The present set of scattering calculations focusedstate-to-state collisions of CN(A) in low rotational levels, tocompare with the experimental results presented below. Scifically, we determined cross sections for collision-inductransitions out of the J56.5F1e, J56.5F2e, and J57.5F1f levels. Exact close-coupled~CC! scattering calcu-lations were done for 16 collision energies which spanrange 5 cm21,Ecol,450 cm21. The most probable collisionenergy in thermal experiments atT5295 K is Emp

5205 cm21, and the full-width at half-maximum of the distribution is DEfwhm.500 cm21. Thus the CC calculationsspan a large fraction of the collision energies which makemajor contribution to the integrand in Eq.~15!. To samplethe tail of the distribution at higher energies where CC cculations become computationally onerous, we usedfaster coupled-states~CS! approximation.57 These were car-ried out at an additional 18 energies ranging from 5,Ecol,4000 cm21.

Figures 6–8 present calculated relative rate constanormalized to theDJ522 fine-structure andL-doublet con-serving transition. As an additional assessment of our miCC/CS calculations, we also compare with calculated rconstants based on cross sections determined within themethod over the entire range of collision energies. Weserve in general excellent agreement between the CC/CSCS rate constants. The largest discrepancies occur for trations withDJ561, where, in a number of cases, the CS raconstants are overestimates. The calculated relative ratestants will be discussed in Sec. VI when they are compawith the experimental results presented in Sec. V.

Absolute magnitudes of the total removal rate constafor the initial levels under study are presented in TableThese rate constants represent the sum over all collisinduced rotational transitions out of the initial level. Thcomputed rate constants presented in Table I will be copared with experimentally determined absolute rate constin Sec. V.

r

hat

Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions

en

ft o

1eo

isTheumsof

pa-d

ith

ofy

ti-ay,

eredis-thla-elayom

d

le

sed

d

le

sed

d

les,

sed to

787J. Chem. Phys., Vol. 112, No. 2, 8 January 2000 PES for CN–Ar

IV. EXPERIMENTAL APPARATUS

The apparatus in which the experimental measuremwere carried out has been briefly described previously.30 Thereagents were slowly flowed through a cell consisting ocentral chamber with opposing sidearms for entry and exithe laser beams. Cyanogen bromide~Aldrich, 97%! was bledinto the central chamber, while argon~99.999%! was intro-duced through the ends of the sidearms. A mixture ofmTorr BrCN in typically 0.5 Torr Ar was employed. Thabsolute pressure was monitored with a capacitance maneter ~MKS!.

FIG. 6. Thermal (T5295 K) rate constants for transfer out of theJ56.5F2e level of CN(A) in collisions with Ar. The four panels corresponto each of the four possible spin–orbit andL-doublet combinations of eachfinal rotational level. The dashed and solid lines, marked with open circdenote the results of CS and CC/CS calculations~CC up to a collisionenergy of 600 cm21!, respectively, while the filled circles with error bardenote the experimental results. All rate constants have been normalizthat for theJ56.5F2e→4.5F2e transition.

FIG. 7. Thermal (T5295 K) rate constants for transfer out of theJ57.5F1f level of CN(A) in collisions with Ar. The four panels corresponto each of the four possible spin–orbit andL-doublet combinations of eachfinal rotational level. The dashed and solid lines, marked with open circdenote the results of CS and CC/CS calculations~CC up to a collisionenergy of 600 cm21!, respectively, while the filled circles with error bardenote the experimental results. All rate constants have been normalizthat for theJ57.5F1f→5.5F1f transition.

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract.

ts

af

0

m-

The central 6 mm diam portion of a 193 nm photolyslaser beam entered the cell through one of the sidearms.effective pulse energy of the excimer laser in the vacuchamber was 2–3 mJ. The pump and probe laser beam@6and 4 mm diam, respectively, both with temporal FWHM,3 ns ~detector limited! and spectral FWHM of 0.2 cm21#were generated with Nd:YAG laser pumped dye lasers, stially overlapped with a dichroic mirror, and were introduceinto the cell through the opposite sidearm.

The delays between the three lasers were controlled wa digital pulse generator. A delay of 200ms between thephotolysis and pump lasers was employed for the studycollisions of the low-J initial levels studied here. This delais much longer than that employed30 for the study of colli-sions of highly rotationally excited levels~10 ms!. In the 200ms time interval, not only does the emission from photolycally generated electronically excited fragments decay awbut the concentration of low-J CN(X 2S1) rotational levelsincreases due to rotational relaxation.58,59

At these photolysis-probe delays, the CN radicals wequilibrated to a room-temperature translational energytribution, as shown previously through Doppler widmeasurements.59 The delay between the pump and probesers was 10 ns for most recorded OODR spectra. This dwas monitored by detecting reflections of laser beams frthe entrance window with a fast photodiode~Hamamatsu

s,

to

s,

to

FIG. 8. Thermal (T5295 K) rate constants for transfer out of theJ56.5F1e level of CN(A) in collisions with Ar. The four panels corresponto each of the four possible spin–orbit andL-doublet combinations of eachfinal rotational level. The dashed and solid lines, marked with open circdenote the results of CS and CC/CS calculations~CC up to a collisionenergy of 500 cm21!, respectively, while the filled circles with error bardenote the experimental results. All rate constants have been normalizthat for theJ56.5F1e→4.5F1e transition.

TABLE I. Measured and computed total removal rate constants~in10211 cm3 molecule21 s21! for the relaxation of CN(A) in low rotationallevels.

Initial state Expt. Theory

J56.5F1e 37.462.0 39.3J56.5F2e 33.062.0 36.4J57.5F1f 34.262.0 37.5

Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions

sela

u

-r

nmn

etivthovfm

to

th

-at

d

ssab

Tllo

nay,lo

thta

tio

rgas

o

toi-

he

the

n-n--

vels

ev-an--ionthe

bu-

er

ta-

n.

fordns

ra-nts.rateibu-

al

e

788 J. Chem. Phys., Vol. 112, No. 2, 8 January 2000 Alexander et al.

S4751! and a digital oscilloscope~LeCroy model 9360!.Real-time display of the pump–probe pulse delay was estial in measuring absolute rate constants, for which the dewas varied in an iterative fashion.

Fluorescence was detected with two separate photomtiplier detectors. One~Thorn EMI 9816! was employed tomonitor A 2P→X 2S1 fluorescence from the initially excited level in theA 2P state. This allowed us to check fochanges in the initial state CN(A 2P) concentration due tovariation of the BrCN partial pressure and/or the 193laser energy. Wavelength drift of the pump laser was fouto be negligible. The second detector~Thorn EMI 9813!monitoredB 2S1→X 2S1 fluorescence excited by the problaser, and this signal was employed to compute the relapopulations of the collisionally populated levels. For bodetectors, the fluorescence was imaged through a telescand optical filters were inserted to isolate the desired walength detection range. To register the probe laser energypower normalization of the OODR spectra, a reflection froa glass flat was monitored with a pyroelectric detec~Molectron J4-05!.

The transient signals from the photomultipliers andpower meter were directed to gated integrators~Stanford Re-search Systems SR250!, and their outputs were collected under computer control and stored on magnetic media for lanalysis. Since the probe laser alone excited fluorescenceto the presence of vibrationally excited CN(X 2S1) and elec-tronically excited CN(A 2P) fragments from the photolysiand subsequent partial collisional relaxation, the pump lawas fired every other shot, and the laser on and off signwere separately summed over a preset number of shotsfore the probe laser was stepped to the next wavelength.OODR spectrum, used to determine the populations of cosionally populated levels, was obtained by subtractionthese two signals. In contrast to the study of high rotatiolevels, which employed a shorter photolysis-pump dela30

there was little fluorescence excited by the probe laser ain the spectral range scanned.

The intensity of OODR signals usually depends onlaser polarizations, as well as geometric arrangement ofexperiment. The pump and probe laser beams had the spolarizations, namely parallel to the fluorescence detecdirection. The initially prepared level in theA 2P stateshould have an isotropicMJ distribution since theA 2P←X 2S1 transition was saturated at the 10 mJ pulse eneat which the pump laser was usually operated. By contrthe probe laser pulse energy was adjusted low enough~typi-cally 30 mJ! so that theB 2S1←A 2P probe transition wasin the linear regime. It was verified that the probe laser flurescence signals scaled linearly with energy up to 100mJ.For comparison, it should be noted that the oscillastrength of theB–A(3,3) band is about 3 orders of magntude smaller than that of theB 2S1 –X 2S1(0,0) band,60 forwhich pulse energies of the order of 1mJ are required foroperation in the linear regime~see, for example, Ref. 59!.The line strength factors relating fluorescence signalspopulations in the linear regime are readily calculable.61

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract.

n-y

l-

d

e

pe,e-or

r

e

erue

erlse-

hei-fl

ne

ehemen

yt,

-

r

to

V. EXPERIMENTAL RESULTS

A. OODR spectra

Figure 9 presents an OODR spectrum in tB 2S1 –A 2P ~3,3! band for the initial J57.5F1f level,which was prepared by pump laser excitation onA 2P –X 2S1 ~3,0! Q1(7) line.62 Two lines in the OODRspectrum, i.e.,Q1(7) andR21(7), are offscale and involvedetection of the initially prepared level. The spectrum cotains many lines, indicative of the large number of collisioally populated levels from the initial level. This, in part, reflects the fact that the spacings between the rotational leare small compared withkT ~see Fig. 5!. We also see in Fig.9 an even–odd alternation in the intensities of lines in seral of the rotational branches as a function of the finalgular momentumJ8. As we discuss further below, this implies that the final-state populations exhibit an alternatwhich arises from the near homonuclear nature ofCN–Ar PES’s, noted above.

To investigate the dependence of the final state distritions on the fine-structure label and thee/ f symmetry of theinitial level, we recorded OODR spectra for several othlow-J rotational levels, specifically theJ56.5F1e and J56.5F2e levels, which were prepared by pump laser excition on theP1(7) andR21(5) lines, respectively.62 We choseinitial levels in different fine-structureL-doublet manifoldswith rotational angular momentumJ near the most probablevalue for a room-temperature Boltzmann state distributio

B. Relative state-to-state rate constants

Two types of measurements of rate constantsCN(A 2P) – Ar rotationally inelastic collisions were carrieout, namely the measurement of final state distributio~relative state-to-state rate constants! and of total removalrate constants. The determination of the latter allows calibtion of the absolute size of the experimental rate constaSince the experimental uncertainties of the total removalconstants were greater than those of the final state distr

FIG. 9. OODR fluorescence excitation spectrum of the CNB 2S1 –A 2P~3,3! band with the pump laser tuned to theQ1(7) line of theA 2P –X 2S1

~3,0! band in the presence of 500 mTorr Ar and 10 mTorr BrCN. Individulines are identified by the lower state quantum numberN. The spectra weretaken 200ms after the production of CN by ArF photolysis of BrCN, and thpump–probe delay was 10 ns.

Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions

dilut

inho

nthy

itiangthth

ihiovoanonotrnrg

de

ya

-ao

lsfo

is

th

in

hestb

tra.of

ven

Thisly

rateoluteants,

thetra-hets10

d.hep–rageon-s forsesuch

d intheleThethetly

omeden-theis

.

ure-

789J. Chem. Phys., Vol. 112, No. 2, 8 January 2000 PES for CN–Ar

tions, we present the latter in this subsection and defercussion of the experimental determination of their absomagnitudes until Sec. C.

The relative state-to-state rate constants were determfrom OODR spectra such as those shown in Fig. 9. The spump–probe delay employed~10 ns! ensures that multiplecollision effects on the distribution are negligible. As showin the next subsection, for this delay the population ofinitially prepared level is reduced from its initial value b,5%. Under these conditions, transfer between the inlevel and a final level through secondary collisions involviintermediate levels is negligible since the populations ofcollisionally populated levels are considerably less thanof the initially prepared level.

Figures 6–8 present the derived relative state-to-stateelastic rate constants for the initial levels investigated in tstudy. These relative rate constants, and the total remrate constants presented in Sec. C, pertain to inelastic csions with Ar as the collision partner, as this is the domincollisional process changing the populations of the rotatifine-structure levels. The concentration of the BrCN phtolytic precursor and the photolysis products are presendensities>2 orders of magnitudes smaller than that of Aand the cross sections for rotationally inelastic collisiowith trace species are not expected to be dramatically lathan those with Ar.

The state-to-state rate constants graphically displayeFigs. 6–8 generally drop in magnitude with increasing valuof the absolute value ofDJ. We observe that in almost evercase the largest cross sections are associated with the trtions with smallestDJ, not ~as can be seen in Fig. 5! with thesmallest energy gap (DE). For transitions into certain finestructureL-doublet manifolds, the rate constants displayobvious even–odd alternation in magnitude as a functionthe final angular momentumJ8. This alternation arises fromthe near homonuclear nature of the CN–Ar PES’s. We asee from Figs. 6–8 that there is a considerable probabilitya collision-induced change of theL-doublete/ f symmetrylabel. For collisions within theF1 fine-structure manifoldthis probability nearly the same as that fore/ f conservingtransitions, while the probability fore/ f changing transitionswithin the F2 manifold is somewhat less than those fore/ fconserving transitions.

The probability for fine-structure changing transitionssomewhat different forF1 andF2 initial levels. We see fromFig. 6 that the rate constants forF2→F1 transitions are ap-proximately 80% of those forF2→F2 transitions. By con-trast, the ratios of the rates ofF1→F2 to those ofF1→F1

transitions~see Figs. 7 and 8! are significantly lower,;30%.These differences can be explained, in part, by the factF2 manifold lies slightly higher in energy than theF1 mani-fold ~see Fig. 5!, so that F1→F2 transitions with smallchanges inJ are endothermic.

Rotationally inelastic collisions were also investigatedour previous OODR study24 of CN(A 2P,v53) for one ofthe initial levels studied here (J56.5F1e). The final statedistributions from these two studies are fairly similar. In tpresent study, we have been able to determine state-to-relative rate constants to a larger number of final states,

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract.

s-e

edrt

e

l

eat

n-sal

lli-t,

-at,ser

ins

nsi-

nf

or

e

atee-

cause of a greater signal to noise ratio in the OODR specIn these new results, we clearly observe that the ratioupward fine-structure-changingF1→F2 to F1→F1 rates issmaller than the ratio of downwardF2→F1 to F2→F2 rates,discussed above. The final state distributions into a gifine-structureL-doublet manifold as a function ofJ8 werebroader in the previous study than those reported here.is an indication that multiple-collision effects altered slightthe final state distributions in the earlier study.

C. Total removal rate constants

In order to put the measured relative state-to-stateconstants presented in the previous subsection on an absscale, we measured absolute total removal rate constwhose determination is described in this subsection.

In separate runs, the intensities of the parent lines inOODR spectra, which provide a measure of the concentions of the initial levels, were recorded as a function of tpump–probe delay~20 ns increment between measuremen!and then were fitted to a single exponential decay. Figurepresents a typical plot for one of the initial levels studieWithin the experimental uncertainties, the intensity of tparent line drops exponentially as a function of the pumprobe delay. Rate constants were computed from the aveof the results from several runs. The total removal rate cstants can be equated with the sum of the rate constantcollision-induced rotational transitions since other processuch as electronic quenching and diffusion occur on a mlonger time scale.

The derived total removal rate constants are presenteTable I and compared with computed rate constants forsum of all rotationally inelastic collisions out of the initialevel ~described in Sec. III B!. The agreement between thexperimental and theoretical rate constants is very good.experimental rate constants are only slightly smaller thancomputed ones, in most cases with differences only slighgreater than the estimated experimental uncertainties. Sdependence of the total removal rate constant upon the itity of the initial level can be seen. The dependence uponinitial level in the computed total removal rate constantsreproduced quite well in the experimental rate constants

FIG. 10. Semilogarithmic plot of the population of the initially preparedJ56.5F1e level, as monitored by the laser fluorescence intensity of theB–A~3,3! P1(6) line, as a function of the pump–probe delay. For these measments, the Ar pressure was 0.51 Torr.

Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions

anof-edone

eo

raina

on

s

to

m

bi

-

(

ttho

-eior

ut–Da

evtaan

i-eodve

e of

ible

ow

s

cesns.

fory

andperi-antsests

m.rllyly

heE-by

der

i-

d S.

s.

g,

m.

of

ns.

790 J. Chem. Phys., Vol. 112, No. 2, 8 January 2000 Alexander et al.

VI. DISCUSSION AND CONCLUSION

We have presented here a collaborative theoreticalexperimental study of rotationally inelastic collisionsCN(A 2P) with Ar. The theoretical portion of this work consisted of theab initio calculation of the PES’s describing thinteraction of CN(X 2S1,A 2P) – Ar. These were then useto compute cross sections and rate constants for collisitransitions between specified initial and final rotational, finstructure levels within theA 2P state. For comparison withthe computed rate constants, an OODR method wasployed to determine experimental state-to-state rate cstants. In these experiments, the CN molecule was genephotochemically through the 193 nm photolysis of BrCN,contrast to our use of the discharge-flow method in our elier studies23–25 of collisional energy transfer in CN.

The rotational levels investigated here involve low-J lev-els populated in a room-temperature Boltzmann distributiThese levels fairly closely approach Hund’s case~a! cou-pling. In contrast to the well studied case of NO(X 2P) – Arrotationally inelastic scattering,3–6 there is a high probabilityin the CN(A 2P) – Ar system for collision-induced changein the fine-structure label. This reflects the fact that theV2

term in the interaction potential is significant comparedthe VP term, unlike the situation for NO(X 2P) – Ar.63,64

Within a Hund’s case~a! limit, which is valid for CN atlow J, the coupling between rotational levels in the saspin–orbit manifold is governed by theVP PES, while thecoupling between rotational levels in different spin–ormanifolds is governed by theV2 PES.36 At a collision energyof 295 K (Emp5205 cm21! the classical turning point determined from thel50 term of theVP PES is 6.64 bohr. Atthis CN–Ar separation the magnitudes of the largestl52) anisotropic terms in the expansion of theVP and V2

PES’s are 663 and 125 cm21, respectively. Since in a firsBorn approximation the cross sections are proportional tosquare of the coupling, we anticipate that the largest crsections forFi changing~spin–orbit changing! cross sectionswill be roughly (125/663)250.04 of those forFi conserving~spin–orbit conserving! cross sections. While this is an underestimate of our observed ratio of rates and is indicativthe inadequacies of such a simple model of the collisdynamics, this ratio ofV2

l52 to VPl52 terms is much greate

than for NO(X 2P) – Ar.The agreement between the experimental and comp

relative state-to-state rate constants, displayed in Figs. 5is quite good. Because of spectral congestion in the OOspectra, it was not possible to determine experimentallyof the relative rate constants of significant magnitude. Nertheless, both the computed and measured rate consdisplay even–odd alternations as a function of the finalgular momentumJ8 for collisional transitions into somefine-structureL-doublet manifolds. In general, the magntude of the oscillations are somewhat greater in the expmental than computed rate constants. A similar even–alternation in the final state distributions have been obserin NO(X 2P) – Ar rotationally inelastic collisions.3–6 Forboth the CN(A 2P) – Ar and NO(X 2P) – Ar systems, these

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract.

d

al-

m-n-ted

r-

.

e

t

ess

ofn

ed7,Rll-nts-

ri-dd

oscillations arise because of the near homonuclear naturthe atom–molecule interaction.

For one of the initial levels studied (J56.5F2e), even–odd alternations of the final state populations are discernand are opposite in phase for transitions toF2f ~L-doubletchanging! and F2e ~L-doublet conserving! final levels ~seeFig. 6!. In the quantum scattering dynamics, one can shthat theeven-l terms in the angular expansion of both theVP

and V2 PES’s will coupleL-doublet conserving transitionof even DJ and L-doublet changing transitions ofoddDJ.2,36 The opposite propensity holds for theodd-l terms.With the near homonuclear character of the CN(A 2P)ArPES’s, these consideration explain the observed differenin the phases of oscillations in the final state distributioThe amplitudes of the oscillations in the CN(A 2P) finalstate populations are significantly less thanNO(X 2P) – Ar ~Refs. 63, 64! since the head–tail asymmetrof the PES’s is greater for CN(A 2P)Ar.

Despite the slight differences between the measuredcomputed relative state-to-state rate constants, the exmental and theoretical absolute total removal rate constare in quite reasonable agreement. This comparison suggthat the computedab initio CN(A)Ar PES’s provide a verygood description of the interaction energies for this systeIn future work, this collaborative study of inelastic CN–Acollisions will be extended to a detailed study of rotationaand electronically inelastic collisions of highly rotationalexcited levels of CN.

ACKNOWLEDGMENTS

M. H. A. and P. J. D. acknowledge the support of tNational Science Foundation, under Grant No. CH9971810. The work of H. J. W. and A. B. was supportedthe Deutsche Forschungsgemeinschaft and the FondsChemischen Industrie, Germany.

1P. J. Dagdigian, inThe Chemical Dynamics and Kinetics of Small Radcals, Part I, edited by K. Liu and A. F. Wagner~World Scientific, Sin-gapore, 1995!, p. 315.

2M. H. Alexander, Chem. Phys.92, 337 ~1985!.3J. J. van Leuken, F. H. W. van Ameron, J. Bulthuis, J. G. Snijders, anStolte, J. Phys. Chem.99, 15573~1995!.

4M. Drabbels, A. M. Wodtke, M. Yang, and M. H. Alexander, J. PhyChem. A101, 6463~1997!.

5P. L. James, I. R. Sims, I. W. M. Smith, M. H. Alexander, and M. YanJ. Chem. Phys.109, 3882~1998!.

6A. Lin, S. Antonova, A. P. Tsakotellis, and G. C. McBane, J. Phys. CheA 103, 1198~1999!.

7G. Herzberg,Molecular Spectra and Molecular Structure. I. SpectraDiatomic Molecules, 2nd ed.~Van Nostrand, Princeton, 1950!.

8P. J. Dagdigian, M. H. Alexander, and K. Liu, J. Chem. Phys.91, 839~1989!.

9S. M. Ball, G. Hancock, and M. R. Heal, J. Chem. Soc., Faraday Tra90, 1467~1994!.

10M. H. Alexander and P. J. Dagdigian, J. Chem. Phys.101, 7468~1994!.11P. Heinrich and F. Stuhl, J. Chem. Phys.102, 618 ~1995!.12P. J. Dagdigian, Annu. Rev. Phys. Chem.48, 95 ~1997!.13J. B. Halpern and Y. Wang, inResearch in Chemical Kinetics, edited by

R. G. Compton and G. Hancock~Elsevier, Amsterdam, 1993!, Vol. 1, p.347.

14M. C. Heaven, Y. Chen, and W. G. Lawrence, inAdvances in MolecularVibrations and Collision Dynamics, edited by J. M. Bowman and Z. Bacic~JAI, Greenwich, 1998! Vol. III, p. 91.

Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions

c-

c-

d

ki

th

m

H

.

ne.

ic

H., J.

l.

tumH.n-r-

g-om

ns

-

em.

m

791J. Chem. Phys., Vol. 112, No. 2, 8 January 2000 PES for CN–Ar

15A. J. Kotlar, R. W. Field, J. I. Steinfeld, and J. A. Coxon, J. Mol. Spetrosc.80, 86 ~1980!.

16H. Ito, Y. Ozaki, K. Suzuki, T. Kondow, and K. Kuchitsu, J. Mol. Spetrosc.127, 283 ~1988!, and references therein.

17N. H. Keiss and H. P. Broida, J. Mol. Spectrosc.7, 194 ~1961!.18V. E. Bondybey, J. Chem. Phys.66, 995 ~1977!.19H.-S. Lin, M. G. Erickson, Y. Lin, W. H. Basinger, W. G. Lawrence, an

M. C. Heaven, Chem. Phys.189, 235 ~1994!.20W. G. Lawrence, Y. Chen, and M. C. Heaven, J. Chem. Phys.107, 7163

~1997!.21R. Fei, H. M. Lambert, T. Carrington, S. V. Filseth, and C. M. Sadows

J. Chem. Phys.100, 1190~1994!.22R. Fei, D. E. Adelman, T. Carrington, C. H. Dugan, and S. V. Filse

Chem. Phys. Lett.232, 547 ~1995!.23N. Furio, A. Ali, and P. J. Dagdigian, J. Chem. Phys.85, 3860~1986!.24G. Jihua, A. Ali, and P. J. Dagdigian, J. Chem. Phys.85, 7098~1986!.25A. Ali, G. Jihua, and P. J. Dagdigian, J. Chem. Phys.87, 2045~1987!.26M. H. Alexander and G. C. Corey, J. Chem. Phys.84, 100 ~1986!.27H.-J. Werner, B. Follmeg, and M. H. Alexander, J. Chem. Phys.89, 3139

~1988!.28H.-J. Werner, B. Follmeg, M. H. Alexander, and D. Lemoine, J. Che

Phys.91, 5425~1989!.29P. J. Dagdigian, D. Patel-Misra, A. Berning, H.-J. Werner, and M.

Alexander, J. Chem. Phys.98, 8580~1993!.30X. Yang and P. J. Dagdigian, Chem. Phys. Lett.297, 506 ~1998!.31M. Yang and M. H. Alexander, J. Chem. Phys.107, 7148~1997!.32A. Berning, Ph.D. thesis, Universita¨t Stuttgart, 1995.33K. Bergmann and W. Demtro¨der, Z. Phys.243, 1 ~1971!.34H. Klar, J. Phys. B6, 2139~1973!.35S. Green and R. N. Zare, Chem. Phys.7, 62 ~1975!.36M. H. Alexander, J. Chem. Phys.76, 5974~1982!.37A. Berning and H.-J. Werner, J. Chem. Phys.100, 1953~1994!.38R. A. Kendall, T. H. Dunning, Jr., and R. J. Harrison, J. Chem. Phys.96,

6796 ~1992!.39T. H. Dunning, Jr., J. Chem. Phys.90, 1007~1989!.40H.-J. Werner and P. J. Knowles, J. Chem. Phys.82, 5053~1985!.41P. J. Knowles and H.-J. Werner, Chem. Phys. Lett.115, 259 ~1985!.42H.-J. Werner, Adv. Chem. Phys.49, 1 ~1987!, and references therein.43H.-J. Werner and P. J. Knowles, J. Chem. Phys.89, 5803~1988!.44P. J. Knowles and H.-J. Werner, Chem. Phys. Lett.145, 514 ~1988!.45H.-J. Werner and P. J. Knowles, Theor. Chim. Acta78, 175 ~1990!.46E. R. Davidson and D. W. Silver, Chem. Phys. Lett.53, 403 ~1977!.47S. F. Boys and F. Benardi, Mol. Phys.19, 553 ~1970!.48MOLPRO is a package ofab initio programs written by H.-J. Werner and P

Downloaded 14 Apr 2013 to 137.99.31.134. This article is copyrighted as indicated in the abstract.

,

,

.

.

J. Knowles, with contributions from J. Almlo¨f, R. Amos, S. Elbert, K.Hampel, W. Meyer, K. Peterson, E. A. Reinsch, R. Pitzer, and A. Sto

49R. N. Zare,Angular Momentum~Wiley, New York, 1988!.50A FORTRAN program to determine the radial expansion coefficientsVl(R)

in the expansion of the CN(X,A)Ar PES’s as a function ofR are availableon request from the corresponding author by electronic mail~address:millard–h–alexander@umail.umd.edu!. Please supply a return electronmail address.

51H. Lefebvre-Brion and R. W. Field,Perturbations in the Spectra of Di-atomic Molecules~Academic, Orlando, 1986!.

52J. M. Brown, J. T. Hougen, K.-P. Huber, J. W. C. Johns, I. Kopp,Lefebvre-Brion, A. J. Merer, D. A. Ramsay, J. Rostas, and R. N. ZareMol. Spectrosc.55, 500 ~1975!.

53R. N. Zare, A. L. Schmeltekopf, W. J. Harrop, and D. L. Albritton, J. MoSpectrosc.46, 37 ~1973!.

54G. C. Corey and M. H. Alexander, J. Chem. Phys.85, 5652~1986!.55HIBRIDON is a package of programs for the time-independent quan

treatment of inelastic collisions and photodissociation written by M.Alexander, D. E. Manolopoulos, H.-J. Werner, and B. Follmeg, with cotributions by P. F. Vohralik, D. Lemoine, G. Corey, B. Johnson, T. Olikowski, W. Kearney, A. Berning, A. Degli-Esposti, C. Rist, and P. Dadigian. More information and/or a copy of the code can be obtained frthe website http://www-mha.umd.edu/;mha/hibridon.

56I. W. M. Smith, Kinetics and Dynamics of Elementary Gas Reactio~Butterworths, London, 1980!, p. 18.

57D. J. Kouri, inAtom–Molecule Collision Theory: A Guide for the Experimentalist, edited by R. B. Bernstein~Plenum, New York, 1979!, p. 301.

58S. Hay, F. Shokoohi, S. Callister, and C. Wittig, Chem. Phys. Lett.118, 6~1985!.

59S. A. Wright and P. J. Dagdigian, J. Chem. Phys.103, 6479~1995!.60P. J. Knowles, H.-J. Werner, P. J. Hay, and D. C. Cartwright, J. Ch

Phys.89, 7334~1988!.61P. J. Dagdigian, inAtomic and Molecular Beam Methods, edited by G.

Scoles, U. Buck, and D. Laine´ ~Oxford University Press, New York,1988!, Vol. 1, p. 596.

62S. P. Davis and J. G. Phillips,The Red System(A 2P –X 2S) of the CNMolecule~University of California Press, Berkeley, 1963!. Following thenotation in this atlas, we designate lines in theA–X and B–A bandsystems byP, Q, andR according to the change in the angular momentuJ and indicate the value of the quantum numberN, whereN5J2S, forthe lower level.

63M. H. Alexander, J. Chem. Phys.99, 7725~1993!.64M. H. Alexander, J. Chem. Phys.111, 7426~1999!.

Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions