Rotational transitions of N2(a 1Π g ) induced by collisions with Ar/He and N2(a 1Π g)–N2(X 1Σ+ g ) rovibronic energy transfer studied by laser REMPI spectroscopyG. Sha, D. Proch, and K. L. Kompa Citation: The Journal of Chemical Physics 87, 5251 (1987); doi: 10.1063/1.453667 View online: http://dx.doi.org/10.1063/1.453667 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/87/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Energy transfer models in nitrogen plasmas: Analysis of N 2 ( X Σ g + 1 ) – N ( 4 S u ) – e − interaction J. Chem. Phys. 141, 184302 (2014); 10.1063/1.4900508 Quantum scattering studies of the Λ doublet resolved rotational energy transfer of OH(X 2Π) in collisions withHe and Ar J. Chem. Phys. 103, 2067 (1995); 10.1063/1.469682 Electronic fine structure transitions and rotational energy transfer of NO(X 2Π) in collisions with He: Acounterpropagating beam study J. Chem. Phys. 102, 3151 (1995); 10.1063/1.468626 Rovibronic energy transfer from N2(a 1π g ) to CO(A 1π) studied by laser REMPI spectroscopy J. Chem. Phys. 87, 2742 (1987); 10.1063/1.453061 Collision energy dependence of the cross sections for the electronic excitation transfer reactions: Rg(3 P0,2)+N2(X 1Σ g )→Rg(1 S 0) +N2(C 3Π u ) (Rg=Ar, Kr) J. Chem. Phys. 84, 4919 (1986); 10.1063/1.450822

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Rotational transitions of N2(a 1 fig} induced by collisions with Ar/He and N2(a 1fig }-N2(X 1.It} rovibronic energy transfer studied by laser REMPI spectroscopy

G. Sha,a) D. Proch, and K. L. Kampa Max-Planck-Institutfur Quantenoptik, D-8046 Garching, West Germany

(Received 8 June 1987; accepted 30 July 1987)

This paper reports the results of two related experiments: (A) The state-to-state rotational transition probabilities ofN2(a Ing) in collisions with rare gas atoms (Ar or He) were measured by the technique of two-step multiphoton ionization. Results show that the selection rule antisymmetric ~ symmetric is obeyed. The transition probability drops rapidly with increasing IAT I. A propensity rule related to the n+ or n- symmetry conservation of the electronic wave function during the collision induced rotational transition holds. (B) The cross section for the rovibronic energy transfer between N 2 ( I ng ) and N2 (X I ~t ) is found to be -28 A.z. N 2 (a Ing) product populations show a Boltzmann-like distribution with a rotational temperature suggesting an equipartition of the available energy among the rotational and translational degrees of freedom of the products. A mechanism invoking an intermediate collision complex along with intermolecular electron exchange may explain the results.

I. INTRODUCTION

The rotational transitions of N2 induced by collisions with rare gas atoms

N 2 (J) + Ar, He-N2 (J') + Ar, He (1)

have been investigated both theoretically and experimental­ly by many authors as a classic example of the R-T energy transfer process.

Information on the energy gap dependence of state-to­state cross sections UJI' as well as differential cross sections du JI' / dw for the rotational energy transfer have been ob­tained from classical trajectory calculations for a variety of diatom-atom systems. 1,2

Kistemaker et al. have measured the ultrasonic absorp­tion in N2-rare gas mixtures and obtained information on the overall R-T relaxation rate.3 Individual state-to-state cross sections could, however, not be extracted from these data due to the simultaneous involvement of many rota­tionallevels. Toennies et al.4 used a crossed molecular beam arrangement to study inelastic N2-He scattering. They achieved an energy resolution of 0.8 meV and observed the rotational transitions 0-2, 1-3, and 2-4, but did not de­termine absolute values for the cross sections.

All of the above publications referred to the electronic ground state of N2. The present contribution is the first to report inelastic rotational transition cross sections of elec­tronically excited N 2 (a Ing) colliding with rare gas atoms. The detection scheme is based on resonantly enhanced mul­tiphoton ionization (REMPI) spectroscopy.

In our experiment a single level ofN! (v,J) [throughout this article N! will denote N 2 (a Ing)] is populated by two photon laser excitation of an Ar or He buffered N2 sample. An additional laser monitors any change in the popUlation of N! by ionization spectroscopy via a higher resonant inter-

0) Da!ian Institute of Chemical Physics, Chinese Academy of Sciences, Da­!ian, P.R. China.

mediate state. From the ionization spectra both the individ­ual rotational levels ofN! and their symmetry properties can be deduced. For the I ng state of a homonuclear diatomic the two components of the A doublets correspond to the sym­metric ortho and the antisymmetric para modification, re­spectively. Our results indicate that collision induced rota­tional transitions occur only between states of like symmetry, obeying a quantum mechanical selection rule5 ' which rigorously prohibits intercombinations between the symmetric and antisymmetric states. This nuclear statistics restriction has previously been observed by Steinfeld,6 Dem­troder,7 and Ottinger8

,9 in their early experiments on 12, Na2, and Li2 molecules, respectively. Furthermore, our results indicate that an additional propensity rule relevant to sym­metry changes of the electronic wave function favors rota­tional transitions between n + and n + or n - and n - sub­levels of the A doublets over n + ++ n - transitions. A similar propensity has been found in a study of the rotational energy transfer behavior of the CO(A In) state by Sha and co­workers. lo

Collisions between N! and N2 not only induce rota­tional transitions, as in the previous set of measurements, but also electronic energy transfer from excited to ground state molecules

N!(vi = 2,Ji) + ~dv; = O,J;)

-N2 (vi'=0,Ji') +~Hv; =2,J;). (2)

We determined the cross section for this process to be - 28 A 2 for J i = 15 by measuring the overall E-E energy transfer probability (cf. Sec. III B).

Another example of E-E energy transfer between like diatomics that has been reported refers to NO (A 2~ + ,

v') ..... NO (X 2n, v"). II The cross sections range from 1.4 to 20 A 2, depending on the vibrational levels involved. A dis­tinction between a vibronic and a pure V-V transfer was achieved by using 15NO and 14NO isotopes.

J. Chern. Phys. 87 (9), 1 November 1987 0021-9606/87/215251-05$02.10 © 1987 American Institute of Physics 5251

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5252 Sha. Proch. and Kompa: Rovibronic energy transfer

Gordon et al. 12 treated the NO*-NO (E-E) energy transfer on the basis of electronic dipole-dipole interaction between the two molecules. Their calculation reproduced the experimental data very satisfactorily. This procedure is, however, not applicable to the case ofE-E transfer between N* and N2 since the dipole transition N 2(a Ing_X ll:g) is fo~bidden. We therefore suggest a mechanism which in­volves an intermediate collision complex.

II. EXPERIMENT

The experimental setup has been described previously. \3

Two dye lasers (Lambda Physik FL 2002) ar~ pumped by a common Xeel excimer laser (Lambda Physik EMG 200). Both dye lasers are frequency doubled and emit betw.een.270 and 290 nm. Their beams, which are synchronous In time, are merged by a dichroic beam splitter and then fo~used into a liquid nitrogen cooled gas cell. The curre~t slgna~ pro­duced by photoionization is collected by a paIr of staInI~ss steel electrodes biased at 22.5 V and then processed and dIS­played by a preamplifier, Boxcar integrator and x-~ record­er. The preamp delivers approximately 1 m V of SIgnal per 1000 ions.

The scheme of the two-step resonance enhanced ioniza­tion is shown in Fig. 1. Laser (1) pumps a single rovibronic level [a In (v' = 2,J')] ofN2 via two-photon absorption. The seconllaser is tuned to excite a transition from a I ng to anyone of the higherintermediate states b " C3, c;, or 03' The final ionization step is accomplished either by VI or V2 pho­tons. All experiments presented in this paper involve b 'Il:u+ (Vi = 7) as the higher intermediate state.

18

16

14

12

> ..! 10 >-(!) a:: w 8 z w

6

4

2

0

_-N2+ A 2n u1/2 134721cm-1 ---4------- 2 1 ---+---- ----Ni A nuJ12 134644crri

--+------Ni X 2Eg 125667cm-1

hV2

--r--v=2 ___ +-_______ 0' ng

-~------x 'Eg

105683cm1

104438cm-1

104138cm-1

103701cm-1

68951cm'

o

FIG. I. Schematic diagram showing the two-step resonant multiphoton ionization of nitrogen.

III. RESULTS A. N;-Ar(He) collisions

Figure 2(a) shows the ionization spectrum of the N2 [a Ing (v" = 2) .... b IILu+ (Vi = 7)] band, laser (1) being tuned to the P(6) line of the N2 [X ll:t (v" = O) .... a IIIg (Vi = 2)] transition. This signal was ob­tained with 1 mbar of N2. As the Herzberg diagram of

2hv(1) hv(2)

IL.ot -+ lng .... ILu+ sequential transitions (Fig. 3) sug-

gests, only the Q( 5) line is observed. When N2 is diluted by 10 mbar of Ar, additional weak

lines appear. They can be identified as members of the P, Q, and R branches as shown in Fig. 2(b). Obviously, the initial population of Nt (v = 2, J = 5) has to a small extent been redistributed among other rotational states Nt (v = 2, J ') as a result of the collision with Ar atoms. Noticeably, all Q lines belong to odd J quantum numbers as does the parent Q( 5), whereas P and R lines are even in J. This indicates (cf. Fig. 3) that all involved N 2 (a lng) molecules must be of "s" symmetry.

Figure 2 (c) displays the ionization spectrum obtained with laser (2) scanning over the same band as before, but laser (1) tuned to the P( 7) line. The most intense feature now is Q(6), and all Q branch satellite lines are now even while P and R lines are odd in J. Again referring to Fig. 3 we now find that all N 2 (a Ing) molecules show "a" symmetry.

The spectra thus evidence the rigorous observation of a selection rule "s"~"s", "a"~"a", and "s"~"a" not only for optical transitions, but also for collision induced events.

The rotational transition probability PJJ ' can be evaluat­ed from the spectra in the limit of single collision conditions. We write

Nt(J') = NteJ)*Z*'Tetf*PJJ' , (3)

where NTeJ) and NteJ ' ) designate the number densities of the parent and daughter molecules, respectively. Z is the Nt-Ar(He) collision frequency, 'Tetf represents an effective collision time determined both by the lifetime of Nt and the laser pulse duration. Approximately

llretf = 1/TR + lire + 1/TL , (4)

where TR is the radiative lifetime of N!( -1.4x 10-4 s) 14

and'TL the laser pulse width (FWHM~ 10 ns). Te denotes the collisional quenching lifetime of Nt, which increases with decreasing pressure. At zero pressure the term 1/Te'

may be ignored. Using Eq. (4) rather than the rigorous treatmeneo which takes into account the time profile of the laser pulse introduces a maximum error of ± 10% which seems acceptable in view of the accuracy of the experiment.

Given sufficient intensity oflaser (2) the transition Nt (a -+ b ') is saturated. The cross section for the ionization from Nt (b ') should not change appreciably over the small wavelength variation (.;;;;5 A), since this transition termin­ates in the continuum. We thus write

N!(J')/N~(J) = S(J')IS(J) , (5)

whereS(J) andS(J') are the relative signal intensities of the parent and the satellite line. Combining Eqs. (3) through (5) yields

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Sha, Proch, and Kompa: Rovibronic energy transfer 5253

o C 01

1.5

.;;; 0.5 c 2

o

1.5

c:: 1.0 ::;)

.ci ~

0

'0 c 01

'iii 0.5 c: 0

h:6.S5

5 1 R ~1 a 5

p 1

~-.,. .....

272.5

h :7.25

5 1

RL 5

a,

Pi , ,

10 15

5 10

.A.

272.7 nm 272.9

10 15 0

lp

o '----'----"2-='7'o-2.=-5 --'----'--.L..--2-:!-72-. 7=--~n-m--J.--'--2:-::-'72.9

c: ::;)

.ci ~

o c: .~ III

c:

h:7.2

2 0.5

O'--~-::-~~--~~~~~--L-~~ 272.5 272.7 nm 272.9

FIG. 2, Spectra of N 2 [a °ng(u· =2)~b' 11:: (u' = 7)] transition ob­tained by (2 + 1 + 1) mu1tiphonon ionization, Pulse energies of lasers (1) and (2): 0,18 and 0.03 mJ, respectively. (a) Pump line: P(6) of the N 2 [X I 1:.+ (u" =O)~a Ill.(u' = 2)] transition. Pressure ofN2: 1 mbar, (b) Pump line: P(6) of the N 2 (X ~a) transition.p(N2 ): 0,8 mbar;p(Ar): 10 mbar. (c) Pump line: P(7) of the N2(X~a) transition. p(N2 ): 0.8 mbar;p(He): 1Ombar.

2 hv -- --PIG)

a s a 5 a

J 3 4 5 G 7

FIG. 3. Herzberg diagram illustrating the selection rules for the sequential 11:.+ ~ In. ~ Il:"+ transitions. The dashed lines show the collision induced rotational energy transfer pathways permitted by the nuclear symmetry li­mitation.

(6)

As long as the single collision condition is not met (p > 0), Eq, (6) yields an approximate probability value, P' JJ"

However, PJJ ' may be extracted from our data by extrapolat­ing P JJ' to zero pressure as shown in Fig. 4.

The rotational transition probabilities thus obtained are displayed as Fig. 5(a) for Ar and Fig. 5(b) for He as colli­sion partner. PJJ ' drops rapidly with increasing laJ I , which agrees with the energy gap law. IS Interestingly, the data in Figs. 5 (a) and 5 (b) show a different behavior for II - ..... II­and II - ..... II + transitions. This indicates the validity of a propensity rule which favors rotational transitions with " + " or " - " symmetry conservation over those involving a " + " to " - " conversion.

B. N;-N2 collisions

In surprising contrast to the above experiments with rare gas buffered N2, the spectrum obtained with 10 mbar of

1 Pjj'

,0 /'

,/

,/

/'

01 /' /' 0

/'

50 q/

/'

/ /" :l /'0 --.... 0 0 3 .--........... +

---' -O· --0 +.--- --0-+ ___ --- 7

_0--0

00 50 100

PAr (mbar)

FIG. 4. Plot of the inverse of the rotational transition probability P J}' as a function of the Ar partial pressure. Parent line: Q( 5),

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5254 Sha, Proch, and Kompa: Rovibronic energy transfer

0.1r----r----~---,-----r--~

-

Ar

0 0.1 1, Pjj' ,

, n-=-n \

~ , ... 2 ...... n:-n+

, , ,,~\ ...... ...... ...... 9 ......

He 0

0 5

FIG. 5. Rotational transition probability ofN2 [a(v = 2, J = 5) 1 colliding with rare gas atoms as function of the absolute magnitude of the quantum number change. Gas temperature: 77 K. Upper trace: n - - n -. Lower trace: n - - n +. (a) Rare gas: Ar; (b) rare gas: He.

pure nitrogen [Fig. 6 (a) ) shows the appearance of both even and odd numbered P, Q, and R branch lines. This shows that both "s" and "a" symmetry N~ daughter molecules are produced by the collisional energy transfer processes. Con­sidering the rigorous selection rule "s" -<++"a, " which is evi­denced by our and many other authors' experiments as de­scribed in the previous section, the "a" symmetry N~ can only be produced as the result of collisional E-E energy transfer between the parent Nt ("s") and the "a" species of ground state Nz. That is,

N! (v' = 2,J; ,"s") + ~z(v" = O,J~,"a")

Nz(v" = O,J;', "s") + ~!(v' = 2,J ~,"a") , (7)

where "s" symmetry NT daughter molecules exist as a conse­quence of the rotational relaxation of NT ("s") parent mole­cules and also of an Nt ("s")-N z ("s") E-E energy transfer.

The spectrum of Fig. 6(b) presents further evidence for the above NT-Nz (E-E) energy transfer hypothesis. It was obtained with laser (1) populatingahighJ level (J = 16) of NT. Under such conditions satellite lines of low J (e.g., J< 10) should appear mainly due to an E-E transfer process, since rotational relaxation becomes less and less likely for large values of II1J I . In agreement with the assumed transfer

..c 10 t; .

-0 c

.!?l III

gO.5

C ::J

-e ~ 1.0

o C 01

III

c .:= 0.5

h=5.7

10

272.5 272.7 272.9nm

h=7

10

OL-~--~~~~~--L-~--~~--L-~

272.5 272.5 272.9 nm

FIG. 6. Spectraofthe N2[ a In. (v" = 2) -b' 'l:u+ (v' = 7)] transitionob­tained by (2 + 1 + 1) multiphoton ionization. Pressure of N2 : 10 mbar. Pulse energies of lasers (1) and (2): 0.25 and 0.02 mJ, respectively. (a) Pump line: P(6); (b) pump line: P(17).

scheme, the spectrum of Fig. 6 (b) indicates a ratio of popu­lations NT ("s") INT ("a") of approximately 2, as shown in Fig. 7(a). This is obviously due to the fact that Nz("s")1 Nz("a") = 2 for the ground state [cf. Fig. 7(b)), making collisions between NT and Nz("s") twice as likely as those with Nz("a").

The overall E-E energy transfer probability of reaction (7) with J; = 15 is measured to be 0.9, which corresponds to a cross section of -28 Az.

The rotational population distribution of NT ("a") is characterized by a rotational temperature TR = 168 ± 15 K, as displayed in Fig. 8. This graph may be rationalized if we assume the formation of a NT-Nz collision complex which is sufficiently long lived to permit the equipartitioning of the total available energy E among the rotational and translational degrees of freedom of the products. 16 In the evaluation of the rotational temperature of NT ("a") pro­duced by reaction (7) we need to consider only the rota­tional and translational energy of NT and ~2' since equal

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Sha, Proch, and Kompa: Rovibronic energy transfer 5255

J = 5

2 3 4 5 6 7 8 9 10 11 12 asasasasasa

(a)

J = 0 2 3 4 5 6 7 8 9 10 11 sa sasa sa sa sa

(b)

FIG. 7. Population distribution of the rotational levels of nitrogen. (a) Measured average population distribution of N 2 (a lfig) daughter mole­cules. The parent levels ofN2(a I fig ) were J = IS and J = 16. (b) Calcu­lated data for N 2 (X), assuming T = 77 K.

amounts of electronic and vibrational contributions appear on both sides of the equation. Thus

E = ER (N!) + ER (~2) + ErCN!) + ET(~2)' (8)

where

ER (N!) = Bv·*Ji *(Ji + 1) = 377 cm- I

(Bv' = 1.5718 cm- I, Ji = 15) ,

ER (~2) = 2*1I2*kTc = 53.5 cm- I

(Tc = 77 K, k = 0.695 cm-I/K) ,

ET(N!) = ETC~2) = 3*1I2*kTc = 80.3 cm- I•

According to the equipartition assumption the rotational temperature of N! should be

TR(N!) = [fR(N!)/FRT ]*E*lIk, (9)

wherefR (N!) = 2: Rotational degrees offreedom ofa di­atomic; F RT = 10: The summed rotational and translational degrees of freedom of two diatomics.

Combining Eqs. (8) and (9) yields TR (N2 ) = 170 K, which is in very satisfactory agreement with the measured value.

As noted in the Introduction, unlike the NO*-NO elec­tronic energy transfer, the behavior of the Nt-N2 system seems inexplicable by the Forster type of electronic dipole interaction. 12 In fact, the intensity of an electronic dipole transition N2 (a lIIg_X I~t ) is a factor of 103 below that of an NO (A 2~ + -X 2II) transition, while the energy transfer cross sections are comparable. Since N! has an open shell electronic structure we may assume that Nt and N2 form a rather long-lived collision complex, as we have discussed in the previous section. This intermediate complex permits an intermolecular electron exchange between both constitu­ents. An intramolecular mechanism, though basically con­ceivable, seems very unlikely, following the same (energet-

2.0

1.0

o

-1.0 '---------"--------"----'----' o 100 200 300

J (J .. 1)

FIG. 8. Rotational population of NT ("a") daughter molecules correspond­

ing to a rotational temperature T = 168 ± 15 K. Parent molecule: N~ ("s")

in level J = IS.

ic) arguments as those invoked to rationalize the Nt-CO (E-E) energy transfer measurements.13 The transfer pro­cess would thus proceed as the arrows indicate

N!(a lIIg)

a,lr'l) N2(XI~/)

N*· 2 •

+ + a'l n,j --+

N2 :

N 2 (X I~g+) Nt(a IIIg)

ACKNOWLEDGMENT

G. Sha wishes to thank Professor Y. S. Tao for helpful discussions.

I A Metropoulos, J. Phys. Chern. 88, 1 (1984). 2Ph. Brechignac and B. J. Whitaker, Chern. Phys. 88, 425 (1984). 3p. G. Kisternaker and A. E. de Vries, Chern. Phys. 7,371 (1975). 4M. Faubel, K. H. Kohl, and J. P. Toennies, J. Chern. Phys. 73, 2506 (1980).

sG. Herzberg, Molecular Spectra and Molecular Structure. 1. Spectra of Diatomic Molecules (van Nostrand, New York, 1950), p. 131.

6R. B. Kurzel and J. I. Steinfeld, J. Chern. Phys. 53, 3293 (1970). 7K. Bergmann and W. Demtroder, Z. Phys. 243, I (1971). ·Ch. Ottinger, R. Velasco, and R. N. Zare,J. Chern. Phys. 52,1636 (1970). 9Ch. Ottinger and D. Poppe, Chern. Phys. Lett. 8, 513 (1971). lOG. Sha, X. Zhong, S. Zhao, and C. Zhang, Chern. Phys. Lett. 110,410

(1984 ). IlL. A. Melton and W. Klernperer, 1. Chern. Phys. 55,1468 (1971). 12R. G. Gordon and Y. N. Chiu, J. Chern. Phys. 55, 1469 (1971). 13G. Sha, D. Proch, and K. L. Kornpa, J. Chern. Phys. 87, 2742 (1987). 14D. E. Shernansky, J. Chern. Phys. 51, 5487 (1969). ISJ. C. Polanyi and N. Sathyamurthy, Chern. Phys. 29, 9 (1978). 16R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics (Oxford

University, New York, 1974), p. 217.

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