Gomathi Ramachandran and Gregory S. Ezra- Vibrational deactivation in planar ion-neutral collisions....

8/3/2019 Gomathi Ramachandran and Gregory S. Ezra- Vibrational deactivation in planar ion-neutral collisions. A classical traj

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Volume 199,number 3,4 CHEMICALPHYSICSLETTERS 6 November 1992

Vibrational deactivation in planar ion-neutral collisions.A classical trajectory studyof the fixed orientation angle approximationGomathi Ramachandran and Gregory S. Ezra Baker aboratory,epartm ent of Chemistry, Cornell Un iversity, thaca, NY 14853, USAReceived 4 May 1992; n final form 17 August 1992

Vibrational deactivation of 0; (v= 1) in lowenergy collisions with K r is studied within the framew ork of planar classicalmechanics. An approximation in w hich the relative orientation of the diatom is fixed fails o describehe extent f vibrationaldeactivationound n exact lan ar ynam ics. e lso onsider lanar i+/N2 (u=1) collisions.or hissystem,n contrastoKr/O: , he vibrationalnergyransfers describeduite ccuratelyn he ixed-anglepproximation.

1. IntrodlKtionThere has been much recent interest in the deac-

tivation of vibrationally excited ions in low-energycollisions with neutrals [ 11. For several such sys-tems, the vibrational qu enching rate show s pro-nounced deviations from standard Landau-Tellerbehavior [2] at collision energies smaller than 1.0eV or so [ 11. In some case s, notably K r/OZ+ [ 3 1,aminimum is observed in the quenching rate versuscollision energy (see fig. 3 of ref. [ 3 ] ).

The origin of the upturn in quenching rate at verylow collision energies has been the subject of somediscussion [ 1,4,5]. According to the mechanismproposed by Ferguson [ 11, vibrational deactivationat very low collision energies proceedsvia transientorbiting complexes, formed by transfer of energyfrom translation into rotational deg rees of freedom.Vibrational quenching then occurs upon v ibrationalpredissociation of the orbiting complexes [ I]. Athigher collision energies, deactivation by direct, im-pulsive collisions presumably takes over. Classicaltrajectory studies have shown that deactivation by

Correspondence to : G.S. Ezra, Baker Laboratory, Departmentof Chemistry, Cornell University, Ithaca, NY 148 53,USA. Camille and Hemy Dreyfus Foundation Teacher-Scholar.

both direct and complex forming collisions occurs atlow collision energies [ 5,151.On the basis of an approximate quantum-me-chanical study of vibrational quenching in Li+/N2[4], Tanner and Maricq have however concludedthat complex formation and rotational degrees offreedom play no role in the deactivation process [41 ,and that deviations from standard LT behavior aredue solely to the influence of the attractive compo-nent of the potential upo n a n effectively one-dimen-sional vibrational deactivation probability. They havealso proposed a modified Landau-Teller expressionto fit the energy dependence of the quenching ratecoefficient for Kr/O$ in the energy range of interest.The utility of such expressions s discussed elsewhere[61-Quan tum close-coupling (CC) calculations of vi-brational quenching in Kr/O: including all rota-tional channels are impractical at present. Rota-tional decoupling schemes such as the centrifugalsudden approximation (CSA ) or infinite-order sud-den approximation (IOSA) have long been used toreduce the com putational effort required by C C cal-culations of rotational and v ibration-rotation en-ergy transfer in atom -diatom collisions (for reviews,see refs. [ 7-9 ] ). Tanner an d M aricq have applied acombination of the IO SA and the distorted wave ap-proximation to treat vibrational deactivation in Li+/

0009 -261 4/92/ $ 05.0 0 0 199 2 Elsevier Science Publishers B.V. A ll rights reserved. 397


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Volume 199,number 3,4 CHEMICALPHYSICS LETTERS 6 November 199 2mined from spectroscopic data [ 151. The secondterm I / s o o t r o p i c consists of a long-range ionlinduced-dipole attraction plus a short-range exponential re-pulsion term. The third term Va,,,ic mode ls thestrong chemical interaction between Kr and 0:.The potential function eq. (2) is described in detailin ref. [6]; contours are shown in fig. la.2.3. Li+/N2 potential

Following Tanner and M aricq [4], we use theLi+Nz potential of Billing [ 161, which is a 19 pa-

0.0 1.9 3.8 5.7 7.7X (au>

3om6)_

9

0d- 0.0 1.9 3.8 5.7 7.7X (au)

Fig. 1. (a) C ontour plot of the k/O: potential [6]. The 0:molecule ies along he x axis, with the midpoint of the O-O bondat the origin. The O-O bond length is fwed at s=s,=2.10 9 au.Contours are at multiples of 0.046 eV. (b) Contour plot for theLi+/N, potential [la]. The N2 molecule lies along the x axis,with the midpoint of the N-N bond a t the origin. The N-N bondlength is fued at s=s,=2 .067 au. Contours are at multiples of0.046 eV.

rameter fit to an ab initio potential energy surface.The form of this potential is given in ref. [ 161. Acontour plot is show n in fig. lb, where contours areat 0.046 eV intervals as in fig. la. Note that the in-teraction w ell depth of this potential is much deeper(about 0.6 eV) than that for the Kr/O$ potential.2.4. Classical fixed-angle approximation

The FAA considered here is an essential part ofthe classical IOSA as discussed by Mulloney andSchatz [ 121 (see also ref. [ 13 ), and our treatmentclosely follows ref. [ 121. In the plan ar F AA , the ro-tor d egree of freedom is frozen, thereby redu cing thenum ber of degrees of freedom by one. Operationally,both orbital angu lar mom entum pf and rotor angularmomentum py are held fixed along a trajectory, a ndare taken to have their initial values 1 and j, respec-tively [ 121. The Ha miltonian for planar motion inthis approximation is then

(3)As the Ham iltonian is independent of the dynam icalvariable pr the angle y remains fixed at its initialvalue, yit and V depends only parametrically on yCVibrational energy transfer probabilities are calcu-lated by ensem ble averaging over the rotor orienta-tion yi.2.5. Eelection of initial conditions

Two different trajectory en sembles are u sed in thispaper. The first is that used in our p revious study ofthe Kr/O; system [6 1.At each collision energy 3000trajectories were run, with a two-dimensiona l Boltz-mann w eighteddistribution of integral pt values usedfor the 0: rotor, corresponding to a rotor temper-ature of 300 K. For each value of the rotor a ngularmom entum, so andp,0 values were chosen uniformlyin vibrational angle at fixed vibrational actionJvib= 1.5% The angle y was randomly chosen be-tween 0 and 7~. he impact parameter b was chosenrandomly in the interval -b,,,, to b,,,,, where b,,is a value of impact parameter beyond which vibra-tional inelasticity is negligible in the exact classicaldynam ics. Trajectories w ith final vibrational action

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Volume 199,number 3,4 CHEMICALPHYSICS LETTERS 6 November 199 2JYia etween 0 and 1 Ofiwere considered to b e deac-tivated. This set of initial conditions was used to cal-culate the vibrational quenc hing cross length for IQ/0: (t= 1) using both exact planar classical dynam -ics and the plana r fmed-angle approximation.In the second ensemble, the initial rotor angularmomentum p: was not thermally averaged, but hadthe same initial value for all trajectories in theensemble.Vibrational deactivation is classicallydynamicallyforbidden for Li+/N2, so that as a measure of thedeactivation efficiency we compute the sum of theabsolute values of the differences between the initialand final vibrational actions of each trajectory di-vided by the total number of trajectories in theensemble:

3. Results3.1. IWO:

Ou r classical trajectory results for the vibration aldeactivation cross length uPI, (appropriate forplanar dyna mics) as a function of the collisional en-ergyE, are sho wn in fig. 2. The exact planar classical

A A

A *AA A

1 0 - t 1 0Co l l i s ion Ensrpy (eV)

Fig. 2. Vibrational deactivation cross length for 0: (u= 1 /K ras a function of collision energy I$, (A ) xactlanar classical,(l classical planar fixed-angle approximation.

trajectory results are compared with those obtainedin the FA A.The ftxed angle results show negligiblevibrationaldeactivation for energies below 1 eV, in m arked con-trast to the exact planar case. We conclude that theFAA s unable to describe vibrational energy transferin p lanar Kr/O,+ collisions at low collision energies.The fixed orientation angle approximation is an es-sential part of the IOSA as applied to vibrationaldeactivation [41. The fact that the FA A is so poorat low collision energies is consistent with the sug-gestion that active involvement of rotational deg reesof freedom is essential for vibrational deactivationin the Kr/O: system [ 11 .3.2. Li+/N,

The v ibrational deactivation of Nz by collisionwithLi+ is at a given energy much less probable thanquenching in the Kr/O: system. In fact, just as forHe/N: [ 171, vibrational deactivation in Li+/Nz isclassically dynamically forbidden at thermal colli-sion energies [ 141 (it is classically dynamically al-lowed for Kr/O: ). In fig. 3 we therefore p lot the av-erage absolute change in vibrational action as afunction of collision energy E, obtained for planardynam ics with and w ithout the FA A for an initialrotor action of 2fi. This plot show s that the plan arFAA results follow the trend of exact planar me

A.

A . : aA A I1 -1 lo - 10

Collision EnergyFig. 3. Averagemagnitude of vibrational action change for Li+/N2( U= 1) as a function of collision energy E,. (A ) E xact planarclassical; (A ) lassical planar fixed-angle approximation.

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Volume 99, umber ,4 CHEMICALHYSICSETTERS 6November1992chanics as a function of E, quite closely, although thevibrational inelasticity is smaller in the FM . At verylow energies there is a slight upturn in the inelasticityfor both exact planar an d FA A trajectories. The clas-sical FAA therefore qualitatively reproduces the ex-tent of vibrational energy transfer in planar Li+/N*.Our results show that the c lassical FAA is a usefulapproximation for Li+/N,, and we may conclude thatrotational degrees of freedom are not as importantas they are for Kr/OZ+3.3. Comparison of Kr/O f and Li +/N,

There are as yet no experimental data on the col-lision energy dependence of the quenching rate at lowcollision energies for Li +/Nz (although d eactivationrates have been me asured at high energies [ 18]), sothat the extent of anomalous quenching is unkno wn.Vibrational deactivation is moreover dynamicallyforbidden in classical mecha nics [ 141. We cannevertheless compare our planar classical trajectoryresults for the two systems Kr/O: and Li+/N,.The classical planar dyn amics of these two sys-tems show s striking differences. C lassical trajectorycalculations for Kr/OZ + are able to reproduce thenonmonotonic experimental behaviour of thequenching rate coefficient as a function of collisionenergy [ 5,6]. Within the approximation of planardynam ics, the classical FAA fails completely for K r/0:. For Li+ /N2, on the other hand, classical planarFAA calculations are in quite reason able, though n otquantitative, ag reement with exact plana r trajectoryresults.In our previous work on the Kr/O: system [6],we have show n that the anisotropy of the interactionpotential has a strong influence on the probability ofvibrational d eactivation at low collision energies (cf.also ref. [ 51). Furthermore, we indicated that thiseffect could be due to the im portance in vibrationaldeactivation of transient resonances between bend-ing (libration/hindered rotation) and diatomstretching [61. Reduction of potential anisotropyleads to a softening of the libration mode and lowerbending frequencies, which are not as effective incoupling to vibration [ 61. Comparing the potentialcontours for Kr/O: and Li+/N2 (figs. la and lb)we see that, although the interaction well depth inLi+/N2 is greater than in Kr/O$ , the Li+/N* well

is much broader. It is then reasonable hat the sm alleranisotropy of the Li+ /N, potential reduces the im-portance of the type of rotation-vibration interac-tion that occurs in Kr/O:

4. ConclusionsWe have investigated the accuracy of a classicalfixed orientation angle approximation for describingvibrational deactivation in planar ion-neutral col-lisions. We emphasize again that use of planar dy-

namics is a drastic approximation.The following results and conclusions wereobtained:( 1) We recdl that both 3D [ 51 and planar [6]classical rajectory treatments of vibrational quenc h-

ing in Kr/O$ collisions are able to reproduce the ex-perimentally observed [ 3 ] non-monotonic depen-dence of the deactivation rate on collision energy.The planar classical fixed angle approximation how-ever fails completely to describe vibrational energytransfer at low collision energies in K r / O $ . Activeinvolvement of the rotational degree of freedom isessential for classicalvibrational deactivation at lowcollision energies in planar Kr/O$ ,

(2) Planar trajectory studies of vibrational deac-tivation in Li+/N* show that, in contrast to Kr/0:) this process is classicallydynamically forbiddenin the energy range of interest.( 3) The classicalplanar FAA for Li+ /N2 gives re-sults in qualitative agreem ent with exact planar tra-jectory results for the average magnitude of thechange in vibrational action, although the FAA con-

sistently underestimates the vibrational inelasticity.(4) The above points lead us to conclude that, inthe plana r approximation at least, the m echanism ofvibrational energy transfer in LiC/N2 is differentfrom that in Kr/O: otation-vibration and rota-tion-translation interaction appe ars to be much lessimportant in LiC/Nz, and the classical FAA is ofsome utility in treating the d eactivation.It rem ains for future w ork to study the validity ofrotational decoupling approximations for vibra-tional deactivation in the 3D case. The results obtained here for planar co llisions however suggest hatthe use of mass-scaled quantum DW A/IOSA results

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Volume 199,number 3,4 CHEMICALPHYSICS LETTERS 6 November 199 2for Li+/N2 to describe vibrational deactivation inKr/O$ should be viewed with some caution [4].

Acknowledgement

This work was supported by NSF Grant CHE-9 1013 57. Com putations reported here were per-formed in part on the Cornell National Supercom-puter F acility, which is supported in p art by NSF andIBM Corporation.

References[1) E.E. Ferguson, J. Phys. Chem. 90 (1986) 731.[2] R.D. Levine and R.B. Bernstein, Molec ular reaction

dynamics and chemical reactivity (Oxford Univ. Press.,Oxford, 1987).[3] M. Kricgl, R. Richter, P. Tosi, W. Federcr, W. Lindingerand E.E. Ferguson, Chem. Phys. Letters 124 (1987) 583.[4] J.J. Tanner and M.M. M aricq, Chem. Phys. Letters 138(1987) 495.

[ 51P. To si, M. Ronchetti an d A. Lag ana, Chem. P hys. Letters136 (1987) 398 ; J. Chem. Phys. 88 (1988) 4814.[61 G. Ramachandranand G .S. Ezra, I. Chem. Phys., submittedfor publication.[7]A.S. Dickinson, Computer Phys. Commun. 17 (1979) 51.[81 D.J. Ko uri, in: Atom-molecule collision theory, ed R.B.Bernstein (Plenum Press, New York, 19 79).[9]V.Sidis,Advan.At.Mol.Phys.26 (1990) 161.[ 1 0 M.F. Jarrold, L. Misev and M.T. Bowers,J. Chem . Phys. 81(1984) 4369.

[11 1S. Augustin and H. Rab itz, J. Chem Phys. 64 (1976) 4821;SM. Tarr, H. Rabitz, D.E. Fitz and R.A. Marcus, J. Chem.Phys. 66 (1977) 2854.

[12 1T. Mulloney and G .C. Schatz, Chem. Phys. 45 (198 0) 2 13.[ 13 1H.R. M ayne, Chem. Phys. Letters 1 30 (1986) 2 49;J.A. Harrison and H.R. Mayne, Chem. Phys. Letters 158

(1989) 356.[ 14 1W.H. Miller, Advan. Chem. Phys. 25 (1974) 69.[ 15 1A.A. Radzig and B .M. Smimov, Reference data on atoms,molecules and ions (Springer, Berlin, 1985).[ 16 1G.D. Billing,Chem. Phys. 36 (1979) 127.[ 17lV.A. Zenevich, W. Freysinger, S.K. Pogrcdyna, W.Lindinger, I.K. Dmitrieva, P.I. Porshnev and P. Tosi, J.

Chem. Phys. 94 ( 1991) 7972.[IS] R. Bottner, U. Ross and J.P. Toennies, J. Chem. Phys. 65(1976) 733.

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Gomathi Ramachandran and Gregory S. Ezra- Vibrational deactivation in planar ion-neutral collisions....

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