Rovibronic energy transfer from N2(a 1π g ) to CO(A 1π) studied by laser REMPIspectroscopyG. Sha, D. Proch, and K. L. Kompa Citation: The Journal of Chemical Physics 87, 2742 (1987); doi: 10.1063/1.453061 View online: http://dx.doi.org/10.1063/1.453061 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/87/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A 2+1 Rempi study of the EX transition in CO AIP Conf. Proc. 312, 355 (1994); 10.1063/1.46619 Angular momentum reorientation in CO(A 1Π)–He rotational energy transfer studied by optical–opticaldouble resonance multiphoton ionization spectroscopy J. Chem. Phys. 98, 9487 (1993); 10.1063/1.464380 Theoretical potential energy function and rovibronic spectrum of CO+ 2(X 2Π g ) J. Chem. Phys. 94, 8070 (1991); 10.1063/1.460141 Double resonance studies of rotational energy transfer in the N2B3Πg state AIP Conf. Proc. 191, 664 (1989); 10.1063/1.38600 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 spectroscopy J. Chem. Phys. 87, 5251 (1987); 10.1063/1.453667

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.193.242.160 On: Sat, 22 Nov 2014 00:44:48

Rovibronic energy transfer from N2(a 11T g) to COCA 11T) studied by laser REMPI spectroscopy

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

(Received 30 December 1986; accepted 7 May 1987)

The collision-induced electronic energy transfer N 2 (a 11Tg ,V') + CO(X 11:+ ,v" = 0) .... N 2 (X 11:t ,v") + COCA 11Tg ,V') + AE is studied in a gas cell. N 2 (a 11Tg ,V', J') is prepared by two-photon (2hv l ) absorption from the ground state. CO(A 11Tg ,V', J') is probed by two­photon (hv I + hv2 ) ionization via CO (B 11: +) as the resonant intermediate state. Experiments show that the overall energy transfer cross sections exceed that of gas kinetic collisions by a factor of 3-4. The energy mismatch AB is the determining factor controlling the branching ratio from one N 2 e1Tg ,V') donor to different vibrational levels ofCO(A 11T,V'). For small values of AB, COCA 11Tg ,V', J') shows a Boltzmann-like rotational level population. Its rotational temperature scales with AB. About 28% of the excess energy funnels into the rotation of CO (A 11T). An explanation for the observed rotational distribution of CO· and the energy transfer mechanism is given. The rate constants are analyzed in terms of the surprisal.

I. INTRODUCTION

In 1972, Golde et al. I studied the E-E energy transfer process from N2 (a 11Tg) to CO: "Active nitrogen," pumped in a microwave discharge, transferred its energy to CO, giv­ing rise to the fourth positive emission of CO·. The rate constant of this energy transfer process was determined to be near the gas-kinetic N2-CO collision rate. Unfortunately, the active nitrogen was a mixture of many different vibra­tionallevels of a 11Tg and also other electronic states, which made the extraction of state-to-state rate constants some­what uncertain.

Later, Filseth et al. 2 utilized this same energy transfer to measure the N 2 (a 11TgV' = 5) +-N2 (X 11:g+ ,v" = 0) two­photon absorption spectrum by the technique of sensitized fluorescence. Since only the overall VUV emission from CO· (A 11T) was measured, no information on individual ro­vibrational levels was obtained.

The N 2 (a 11Tg )-CO(A 11T) E-E energy transfer process can be studied in greater detail by the two-color multipho­ton-ionization technique which combines high selectivity and sensitivity. As shown in Fig. 1, a single rovibronic state ofN2 (a 11Tg ,V', J') can be prepared by absorption of two UV photons from the ground state. The populations of CO· (A 11T,V', J') resulting from collisions between N! and CO may then be probed by a two-step (hv i + hv2 ) ioniza­tion proceeding via B 11: + as a resonant intermediate state.3,4 The rotationally resolved excitation spectra of the CO (B-A) transition reveal the nascent CO· (A) population provided the gas pressure is sufficiently low to preclude colli­sional relaxation during the pulse width of the exciting laser.

The experimental results presented in this paper will contribute to the understanding of the dynamics and mecha­nism of state-to-state E-E energy transfer.

aj Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Da­lian, P.R. China.

II. EXPERIMENT

Figure 2 shows the experimental setup. Two pulsed dye lasers (Lambda Physik FL-2002) are pumped by a single XeCI· excimerlaser (LambdaPhysikEMG-200). Dye laser 1 is frequency doubled (KDP) and emits between 270 and 290 nm. The second laser operates in the visible range (445-485 nm) and requires several dyes to cover the six bands of CO(B-A) that originate from v = Oto 5 of CO (A 11T). Both beams are merged by a dichroic mirror and focused into a gas cell equipped with two electrodes that collect an ion sig­nal. (The laser intensity within the focal volume was suffi­ciently low to preclude gas breakdown). This cell contains a mixture of N2 (p = 2 to 5 mb, purity>99.9999%) and CO(p=5 to 25 mb, purity >99.9996%). CO passes

CO" xZr" 11302gem-1

CO air" v:1, 88998em

71

~~ 0~1.~ { 64748 em-I

---- 2hV,

FIG. I. The processes involved in the N2 (a 'lTg, v' = 2) to COCA ''IT, v') en­ergy transfer.

2742 J. Chern. Phys. 87 (5),1 September 1987 0021-9606/87/172742-08$02.10 © 1987 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.193.242.160 On: Sat, 22 Nov 2014 00:44:48

Sha, Proch, and Kompa: Rovibronic energy transfer 2743

---I , , I

..--+-~ : I , ,

I , 1- _______ I

FIG. 2. Diagram of the experimental setup. DM = dichroic mirror.

through a liquid-N2 cooled trap before being admitted to the cell. The electric charge signal of the ions produced by the laser pulse and collected by the electrodes is preamplified, fed into a Boxcar averager (PAR 162), and displayed on an x-y recorder. This rather simple technique has a detection sensitivity of about 2 X 103 ions per laser pulse with a signal! noise ratio of 1.

The first step of the experiment is to measure the N2 Lyman-Birge-Hopfield (a I1Tg_X l1:t) two-photon spec­trum, excited by laser 1 alone. A representative (2 + 2) REMPI spectrum thus obtained at a gas temperature of77 K is shown in Fig. 3. The signal intensity is proportional to the N2 pressure up to 40 mb; its power dependence ranges between r at low laser intensities (four-photon ionization) and /2.5 at high intensities. The linewidth of the spectrum is limited by that of the laser. A few lines are abnormally in-

IS I

lp 10

I

-5

-5

U~IA ~ ~h ~ ..J4. I , , , I

276.7 276.8 276.9 217.0 277.1 X[nm]

FIG. 3. (2 + 2)-multiphoton ionization spectrum of the N (a '17" 2 g'

v' = 2 - X I ~g+ , v' = 0) transition. Pressure: 5 mb. Gas temperature: 77 K. Laser energy: 0.37 m1/pulse.

tense (e.g., P3' P4 + 0 3,06 ) which may be due to some acci­dental resonance in the 108360 cm- I range.

Then, in the second step, laser 1 is tuned to one rota­tionalline of the N2 (a l1Tg_X l1:t ) spectrum while laser 2 is scanned over the CO(B 11:+ -A 11T) transition. CO(B Il:+) is then subsequently ionized by absorption of additional UV photons from laser 1. Figures 4 (a) and 4 (b) show two of the spectra thus obtained. The abscissa gives the wavelength of laser 2, the ordinate marks the relative intensity of the CO+ ion signal. The background is due to N / formation resulting from the multi photon (2 + 2) ionization of this molecule. The spectra are rotationally resolved, except for some lines that overlap. The high intensity of laser 2 causes saturation broadening of the lines.

Several aspects of this experiment require particular at­tention:

( 1) Thorough elimination of impurities from the gas system by, e.g., LN2 trapping. Even trace amounts-in most cases polyatomic hydrocarbons-give rise to a substantial background signal since the ionization cross section of such species is very high.

(2) Careful alignment and adjustment of the spatial and temporal overlap of both laser beams. Early experiments that involved two separate pump lasers failed due to prob­lems with trigger jitter.

(3) The power density delivered by laser 1 must be suffi­cient to provide a large number of N 2 (a) molecules. How­ever, since raising the power will also enhance the (2 + 2) photon excitation yielding N 2+ (which contributes to the background signal) some compromise has to be found. Fair­ly soft focusing if = 500 mm) resulted in conditions where N/ amounted to no more than 0.5% of the N 2 (a) produc­tion.

(4) Laser 2 must saturate the CO(B -A) transition. Under such conditions the int~nsity of the spectral lines will be a measure of theA -state population and it will be unaffect­ed by intensity fluctuations of laser 2, nor by the magnitude of Franck-Condon factors for different vibrational levels as well as Honl-London factors for different rotational lines.

. (5) The gas pressure must be sufficiently low to provide smgle collision conditions on the time scale of the laser pulse ( - IOns). This eliminates the influence of secondary relaxa­tion processes. At pressures between 2 and 20 mb each CO molecule undergoes an average number of collisions between 0.1 and 1. Variation of pressure within these limits showed no effect on the observed rotational distribution.

III. RESULTS AND DISCUSSION

A. Transfer from N;(a,v=2j at Tgas =220 K

Energy conservation allows the population of v = 0 to 5 of CO· from N~(a,v = 2), as Fig. 1 illustrates. In these ex­periments we have observed all six bands of CO (B-A ) origi­nating from v = 0 to 5. The strongest of these (vco = 2 and vco = 5 are displayed in Figs. 4(a) and 4(b). . T?e six bands differ from one another both in signal mtenslty and rotational population distribution. These dis­tributions are drawn as Figs. 5 (a) and 5 (b) for Vco (A) = 0, 2, 3, and 5, respectively. [For Vco (A) = 1 and 4, a similar

J. Chern. Phys., Vol. 87, No.5, 1 September 1987 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.193.242.160 On: Sat, 22 Nov 2014 00:44:48

2744 Sha, Proch, and Kompa: Rovibronic energy transfer

2,0 15 , __ ~ ____ ~ ____ ~ __ -z15 ____ ~ __ -L __ ~ __ -J __ ~1P __ ~~ __ ~-L~~~' w') Q

10 ,

, , 517 518

X (nm)

2!o 20 I , 20 l!o

I I I io l!o , I

X Inml

display is not possible because the signal is too weak to allow the extraction of reliable population distribution data.] Giv­en the accuracy attainable in the measurements it seems jus­tified to fit the data of Fig. 5 by a straight line, which suggests a Boltzmann-type distribution of rotational levels. The rota­tional temperature can be determined from the slope of this line. By summing up the population of all rotational levels in each band and normalizing them to the total population of six bands, we obtain the branching ratio data of energy trans­fer from vN ! = 2 to different v levels of CO"'. The results are

summarized and displayed in the bar diagram of Fig. 6. They seem plausible if we refer to the energy diagram of Fig. 7. This scheme shows the energy flow from the reagents of v

N!

= 2 and Vco = 0 through the various possible channels that lead to different combinations of products VN, and vco .... The energy mismatch AE involved in the corresponding transfer is also shown on the diagram (the rotational energy has been neglected in the calculation of AE). If we assume that the channels with smallest AE are most preferred, we may assign the branching ratio into different vco", to the corresponding channels, as shown in the rightmost column of Fig. 7. We may now interpret Fig. 6 by arguing that preferably those v

I

519

15 I I I

10 , , , !o I

R

,

,

I

520

Ip,,~}P ~ I ," Q

I R

582

FIG. 4, Two-step two-photon (hv1 + hv2 ) ionization spectra of the CO(B 11;+ .... A 117') transition. PN, = 4 mb, Peo = 16 mb, Trot

= 220 K. Ii = 276.928 nm [P(6) line of N 2 (a 117'g, v' = 2 .... X l1;g+,

v' = 0) transition]. (a) The spec­trum of CO(B 11;+, v = O .... A 117',

v' = 2). Laser 1:0.22 mJ/pulse. Laser 2: 16 /tJ/pulse. (b) The spectrum of CO(B 11;+, v = O .... A 117', v' = 5). Laser 1: 0.24

mJ/pu!se. Laser 2: 40 /tJ/pulse.

levels of CO'" (A) are popUlated that are characterized by a minimum energy gap to be compensated during the transfer.

A fraction of the excess energy is partitioned between the rotational levels of the CO'" product. For example, for vco", = 2, we find Trot = 206 ± 20 K, which is close to the gas temperature of 220 K. In this case, only a very small mismatch of - 51 cm -1 is involved. For vco ... = 5, we de­termine Trot = 370 ± 20 K, about 150 K above the cell tem­perature. Since AE = 447 cm -1 for this channel, a larger amount of excess energy is available for partitioning among the rotational degrees of freedom of CO"'.

B. Transfer from Nf(B, v=O, 1, and 2) at Tu •• = 77 K

The determining influence of AE on the rate constants suggested by our data is not just accidental. This is verified by additional measurements of the energy transfer rate con­stants from levels vN!(a) = 0, 1,2, performed at Tgas = 77 K.

The strongest bands which are observed in the cases of vN ! = 0 and 1 are VCO(A) = 1 and 4, respectively. They are shown in Figs. 8 and 9. Table I gives a synopsis of all transfer rate data. The final vibrational state of the relaxed N2 mole-

J. Chern. Phys" Vol. 87, No.5, 1 September 1987 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.193.242.160 On: Sat, 22 Nov 2014 00:44:48

Sha, Proch, and Kompa: Rovibronic energy transfer 2745

~f' ~I-~ -0.5

\ + v=O -1.0 008<>0

... 0 V = 2 10 O~\ -1.Sk 0\

. + 0 \\0 = '9 \ .. -2.0 '",+\ .., ... \ 0 ~ 0'i\. - ~ ~ -2.5 +\-.8'+.

~\ '). o '0 ,_

\ '--3.0

, -, \ + '" 0\ -3.5

-4.0

o

-1.Sk i 100

6 ,.6

200 J (J.1)

-2'0~'" "61··~. .,. -2.5 • "~

=. ~,

\ 0 \ 0\

300

• v =3

A v=S

.!; -3.0. • "" N I .... ,

o

- -15 '. ~ _. :.,~ ·.t .... c • • • •• • .",

400

• • •• .. ~ •

-4.0

-4.5

-5.0

o 100

•

L ___ .~~L--L __ ~~

200 300 400 J (J + 1)

FIG. 5. Population distributions of rotational levels ofCO(A '17, v') states produced by the energy transfer process Nt(a 'l7g, v' = 2) + CO(X '1;+,

v" = 0) ..... N 2(X'1;g+ ,v") +CO*(A '17, v'). T ... =220 K. S=relative signal intensity. J = rotational quantum number.

0:: W IL

~> « . 0:: I:!

:;:~ .2 00 OU

:i f 0::-

N

0" Z > Z a..1 u~ z" «-0:: N mz

o

602 1393 -

~ o

liE (em-'I 52 837 1790 541 447 -

Te= 220K

> I:!-

SOO-«

0 U

IL 0

~

0

~ ~

0 4 5

FIG. 6. The vibrational branching ratio and rotational temperature of COCA '17) acceptor states. T ... = 220 K.

7.3

7.2

';

E ~ ~

0 -w 7.1

7.0

REAGENTS

I I

, POSSIBLE PRODUCTS

YN2: 3, Yeo·:l

I YN2: 1, Yeo·:4 /..-,;...--- -508

-51

YIBRATIONAL BRANCHING

RATIO

<0.05

0.28 Y "-2" -0 I YN2:2,Yeo*:2

N2- ,-eo- ~--:---- - --- -- - - ---

, \ , , YN2 : 1, Yeo":3 , \ , \ YN2 = 2, Yeo*: 1 \ I \ I YN2:0. Veo":4 \ \ \ .YN2 :1,Yeo"'=2

838 0.11

1395 0.05

1790 <0.05

2257

FIG. 7. Energy level diagram showing the energy mismatch (M) of differ­ent transfer channels starting from the reactants Nt (v = 2) + CO( v = 0) to the products N 2(v) + CO*(v). The corresponding vibrational branch­ing ratio is also shown.

cule is not measured in this experiment. The figures given are determined assuming that the transfer will proceed along the route characterized by the smallest energy mismatch.

The rate constants for the electronic energy transfer (B-V) can be expressed in terms of a generalized exponential energy gap law K = Ko exp( - A, IL\E l/kT).

The validity of this model is checked by subjecting the results to a surprisal analysis.5

•6 Surprisal describes the devi­

ation of the actual rate K (i -+ j)--equivalent to r in Table 1-from a calculated reference Ko(i-+j). The apparent asym­metry of K on the sign of L\E (cf. Table I) is a result of the energy dependence of the prior rate: Ko statistically favors exothermal reactions because of increased translational state densities.

The surprisal is found to be linear in the absolute magni­tude of the B-V energy change (Fig. 10). This suggests that the assumptions concerning the vibrational state ofN2 after the collision are reasonable.

Gordon and Chiu,7 in an attempt to explain the remark­able efficiency of electronic energy transfer between isotopic NO molecules,8 postulate a first-order transition dipole mo­ment interaction. The result oftheir first-order Born approx­imation calculations leads them to predict cross sections for the collision-induced transfer of electronic excitation from 14NO to lsNO that scale inversely with L\E, which agrees with our data.

Callear and Wood9 and Taylor and SetserlO report an experimental study of the intermolecular electronic energy transfer between the triplet state N 2 (A) and CO(X). Their data show that the rate constants of transfer to different vi­brationallevels decrease with increasing L\E.

Energy conservation requires L\E to appear as kinetic

J. Chern. Phys., Vol. 87, No.5, 1 September 1987 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.193.242.160 On: Sat, 22 Nov 2014 00:44:48

2746 Sha, Proch, and Kompa: Rovibronic energy transfer

1

20 ........... 1

'0 \ P , , , , II ) ',I

1,5 1,0 a R 10 , 15 ,

X (nm)

FIG, 8. Two-step two-photon (hv, +hv2 ) ionization spectrum ofCO(B '1.+, v=O-A 'tT, v' = 1),PN, = 5mb,Peo = 10mb, Taa, = 77K,A, =290.209 nm [P(6) ofN2 (a 'tTg, v' = O-X '1.t, v· = 0) transition]. Laser 1: 0.6 mJ/pulse. Laser 2: 30 IlJ/pulse.

and/or internal energy of the product molecules. We may thus correlate the rotational temperature increase to the en­ergy mismatch. This is illustrated in Fig. 11. The dependence is linear with a slope of 40 K/l00 cm -1 up to !1E = 700 cm -1. For diatomic molecules which have two rotational degrees offreedom, the rotational energy increment is kTR •

Thus, 28% of the excess energy appear as rotational motion of CO·, and the remainder must be partitioned among rota­tion of N 2 and translation of both molecules.

CO (A) exhibits a Boltzmann distribution for small !1E, but a pronounced deviation from it as the energy mismatch gets large. How can we rationalize this observation, since we study a single-collision energy transfer?

We believe that CO· in the observed distribution does not originate from a single J level of the ground-state mole­cule. Ground-state CO is characterized by a rotational dis­tribution corresponding to the gas temperature. Small values of the energy mismatch result in small angular momentum changes during the transfer: CO· will largely show the same Boltzmann distribution as its parent, CO. High values of !1E, on the other hand, will give rise to large W, thus destroying the initial rotational distribution.

The experiment as it has been performed did not allow to extract information about the rotational branching ratio, which precludes any statements on angular momentum se­lection. A supersonic beam arrangement could provide

1

2,0 11 10 ••• ~}p __ ~ __ ~~ __ ~'.~5~ __ ~~~~10~~~~~, 1 a

536 537 538 539 540 ~ (nm)

FIG. 9. Two-step two-photon (hv, + hv2 ) ionization spectrum of CO(B '1.+, v = I-A 'tT, v' = 4),PN, = 5 mb,Peo = 10 mb, TaBS = 77 K, A, = 283.360 nm [P(6) ofN2 (a 'tTg, v' = I-X '1.t, v· = 0) transition].

Laser 1: 0.3 mJ/pulse. Laser 2: 50 IlJ/pulse.

CO(X) almost exclusively in its lowest rotational level and would thus be rewarding.

Katayama studied inelastic A-X transitions in N2+ 11,12

and rotational energy transfer in the B state of nitrogen, 13

induced by collisions with a rare gas. His data reveal a pro­pensity towards W = 0, rather than !l.E = O. This is not in contradiction with our findings since we defined "energy mismatch" as the difference between the sums of electronic and vibrational energies of both molecules before and after the collision. By this definition, Katayama's measurements were performed at a fixed value of !l.E.

Two recent papers of Dagdigian and co-workers, 14.15

reporting on collisional A-X energy transfer in CN also dem­onstrate a propensity towards small W for a fixed value of the energy mismatch, as it has been defined above.

c. Measurement of the overall energy transfer rate constants

To determine the overall energy transfer rate constant we measured the number of CO+ product ions as a function

TABLE I. The branching ratio r for the energy transfer from N 2 (a 'tTg,

v = 0, 1,2) to different vibrational levels ofCO(A 'tT) and their rotational temperature. The uncertainty of TR is ± 20 K. The vibrational state of N2 after the collision is not measured. The figures given designate the transfer channel characterized by the smallest energy mismatch. flE values are cal­culated neglecting rotational energy contributions. Gas temperature is 77 K.

Veo./VN, flE (em-I)

0/1 1873 1/1 391 2/0 1276 3/0 -137 0/2 1238 1/2 -244 2/1 612 3/0 1529 4/0 151 0/3 604

1/2 1395 2/2 - 51 3/1 838 4/0 1790 5/0 447

r (%)

9.4 63.1 20.3 7.2 7.0

18.6 27.6 3.4

43.4 27.0 4.5

11.8 25.4

2.7 28.1

236

297

168 300

110 475

280

J. Chem. Phys., Vol. 87, No.5, 1 September 1987 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.193.242.160 On: Sat, 22 Nov 2014 00:44:48

Sha, Proch, and Kompa: Rovibronic energy transfer 2747

8~--~---.----.----,---.----,---~

T:77K; + VNt:O o 1 • 2 6

T: 220K; .. 2

.5 2

o

_2L---~--~L-~~--~----~--~----~

o 10 20 30 IflE 1/ kT

FIG. 10. SurprisaJ plot displaying the energy transfer rate data that have been obtained for T ... = 77 and 220 K, respectively. The abscissa is in units of the absolute magnitude of the (dimensionless) energy defect.

of concentration of the reactant, Pco' All other parameters remained constant. A typical result is shown in Fig. 12. The signal rises rapidly with increasing CO pressure, as N2(a)­CO(X) encounters become more probable. Later, the signal levels off, indicating exhaustion ofthe N 2 (a) supply, as ex­pected for a pseudo-first-order reaction. The signal decrease at high partial pressures can be reasonably explained by col­lision-induced relaxation/quenching processes. We propose a model (Fig. 13) taking into account a variety of processes involved. From it we have derived a relationship connecting the signal intensity to the energy transfer rate constant and the relaxation parameters. Given our experimental condi­tions, we may write (For the derivation, please refer to the Appendix)

[CO+] =g*[(1 + Ca)(1 +a2 )]-I*{a2 + 0.676[1

+ exp( - 717'a/12) - exp( - 517'a/12)

- exp( - 17'a) n. (3)

C and g are constant factors under fixed experimental condi­tions. Parameters a (thus also k) and C can be found by calculating values for [CO+] and fitting to the experimental data. In Fig. 12, the solid line has been calculated for k = 6X 10- 10 cm3 molecule-I S-I and C = 0.16. The error of k thus evaluated is estimated to be about ± 20%.

We measured the overall rate constant k in the cases of

300 /

200 ! /~/I

/I/( VN~ Tc(K) :.: ;Y 0 77 / x: ~ 100 )/

/ .. ' 1 77 .: 2 77

0[/

./ 0' 2 220

0 SOD 1000 liE (em-1)

FIG. 11. Rotational temperature increase ~T = Trot - T ... as a function of l1E for different energy transfer channels.

1.0 f""'-~-2---f--E ( ~

0

I VNi ,,1 c::

...J Te " 220K

"" z 0.5 f : expo C!)

III -: calc z Q

o 10 20

Peo (mbarl

FIG. 12. Plot of the relative CO+ ion signal as a function of CO pressure. 0: experimental values. -: result of model calculation, using C = 0.16 and k = 6.0X 10- 10 cm3 molecule-I S-I.

VN1

= 0, 1, and 2 at gas temperatures of 220 and 77 K, re­

spectively. Thhe results are listed in Table II. The corre­sponding energy transfer cross sections q are given in paren­theses (k is related to q by the definition q = k /vr' where Vr is the mean relative velocity of the colliding molecules). [Since VN, ;:::;Vco , Vr = (2}1/2*ii, where ii is the arithmetic mean velocity of the CO (or N 2 ) molecules.] The data seem to indicate that k decreases slightly with increasing VN, • Re­garding the error bars of the present measurement, however, this observation has to await confirmation from a future in­vestigation. Presently we may say that neither the gas tem­perature nor the vibrational excitation of Nr has a marked influence on the k (or q) values within the uncertainty of our data.

It is interesting to note that these energy transfer cross sections are a factor of 3-4 larger than gas kinetic (31.2 A 2

for N2-CO collisions). Two arguments may be invoked to , +

+ (0 I N2

I I

f R2

R]

~ CO( A) I I I I

I N2 (a)

t kN; I

R-l t k CO* kC

Rl

(0 (X ) N2 ( X)

FIG. 13. Energy flow model assumed for the derivation ofEq. (A7).

J. Chern. Phys., Vol. 87, No.5, 1 September 1987 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.193.242.160 On: Sat, 22 Nov 2014 00:44:48

2748 Sha, Proch, and Kompa: Rovibronic energy transfer

TABLE II. Overall energy transfer rate constants k and cross sections 0'

from v = 0, I, and 2 ofdonorN2(a l1Tg) at Tg .. = 220 and 77 K, respective­ly. The uncertainty of the data is estimated to be about ± 20%.

o 1 2

Tc=220K k (cm3/molecule s)

6.2XlO- 1O (104A2) 6.0X 10- 10 (100A2) 5.4XlO- 1O (86A2)

Tc =77 K k (cm3 Imolecule s)

6.3X 10- 10 (183 A2) 4.2X 10- 10 (120 A2) 3.6X 10- 10 (104 A2)

explain this fact: one is the larger extension of the 1T g (2p ) orbitals of N 2 {a 11Tg) which results in a larger interaction distance between Nt and CO. The second argument claims that the two-electron jump involved in the energy transfer is an inter- rather than an intramolecular process, as will be explained in the following paragraph.

N2 and CO have identical electron configurations, both in their ground and the N 2 {a 11Tg) or COCA 11T ) states l6

,17:

Ground states: KK{O'g 2<;) 2 {O'u 2s)2{ 1Tu 2p )4{O'g2p )2,

N 2 {a l1Tg ),} 2 2 4 I :KK{O'g2s) (O'u2s) (1Tu2p) (O'g2p)(1Tg2p),

COCA 1T)

The E-E energy transfer from Nt -+ CO must be a two-elec­tron transition process which may proceed along two differ­ent pathways, as indicated by separate sets of arrows:

O'g2p 1Tg2p

N2 (a 11Tg) ~t ~ ~ )2 CO{X 11;+) 2' ( t ~ I --. II' Arrows 1 and l' represent intramolecular electron transi­tions, whereas arrows 2 and 2' symbolize an electron ex­change between Nt and CO. The latter mechanism seems more plausible if we consider the much smaller energy dis­crepancy involved [4225 cm- I between 1Tg2p{N2 ) and 1Tg2p(CO), compared to 69290 cm- I between 1Tg2p(N2 )

and 0' g 2p (N 2) orbitals]. Symmetry considerations, plus the fact that 0' and 1T orbitals hardly overlap also favor the inter­molecular route.

The intermolecular electron exchange mechanism that we propose may be imagined as a "harpoon" typel8 change:

Nt + CO-+N2+ + CO-,

followed by a charge neutralization process l9:

Nt + co- -+N2 + CO·,

We note that there are six additional electronic states of CO in the neighborhood of A, namely (cf. Fig. 14) a 31T, a,31;+,

d 3a, e 31:-,1 11;-, andD la.20 An investigation oftheprob­ability of energy transfer from N2 (a 11Tg) to these states may provide important information on the selection (or propen­sity) rules controlling the collisional E-E energy transfer process. We also note that Callear et al.9 and Taylor et al. lo

have observed the triplet-triplet process N 2(A 31;u+ )

+ CO(X 11:+) -+N2 (X l1;t) + COCa 31T ). However, to our knowledge, an energy transfer process which violates spin conservation has not yet been observed. This fact may imply that this law is obeyed in collision-induced processes just as in optical transitions.

30000

a L-~~L-____ L-____ L-__ ~

O.B 1.3 l.B 2.3 2.B

r (A)

FIG. 14. Potential energy curves of CO, adopted from Ref. 20.

IV. CONCLUSIONS

The main results can be summarized as follows: (1) The N 2 (a l 1Tg );CO{A 11T ) E-E energy transfer pro­

cesses are highly efficient with cross sections a factor of 3-4 larger than the gas kinetic cross section ofN2-CO collisions.

(2) The energy mismatch t:..E of the energy transfer channel largely determines the branching ratio from one vi­brationallevel of the N 2 {a 11Tg) donor to different vibration­al states of the acceptor CO (A 11T ). The surprisal is linear in the absolute magnitude of t:..E.

(3) The rotational population ofCO{A 11T,V) shows a Boltzmann-like distribution as long as t:..E is less than 600-700 cm- I

• Under such conditions the corresponding rota­tional temperature increases linearly with t:..E as well as with the gas temperature. Approximately, aT / t:..E = 40 K/100 cm -I, i.e., about 28% of the excess energy appear as rotation of CO (A). The remainder must be partitioned among rota­tion of N2 and translation of CO· and N2. The present ex­periments are not sensitive to this product energy distribu­tion.

J. Chern. Phys., Vol. 87, No.5, 1 September 1987 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.193.242.160 On: Sat, 22 Nov 2014 00:44:48

Sha, Proch, and Kompa: Rovibronic energy transfer 2749

As a follow-up experiment we plan to measure the Doppler width of different rotational lines of the CO (B-A ) spectra. This requires a narrow band dye laser at intensities far below the transition saturation value. We thus hope to obtain data on the translational motion ofCO(A 11T).

ACKNOWLEDGMENTS

We wish to thank Professor R. Levine for a stimulating discussion on the merits of surprisal analysis. When it came to running the calculations, we enjoyed the support of Dr. F. Rebentrost. We would also like to express our gratitude to Dr. T. Trickl, Mr. S. Opitz, and Mr. H. Bauer for their ex­pert and valuable help with the experiments.

APPENDIX

The proposed model of energy flow is illustrated in Fig. 13. Under the present experimental conditions, the number of excited N!(a 11T) molecules amounts to only 10-5 ofthe population of one J level of the ground state N2 (X Il:g+ , VU

= 0, J " ). Therefore we may ignore the reverse stimulated process R -I' The N; ion formation by absorption of two more photons from the same source, R2, is also negligible because the ratio [Nt ]/[N!] is less than 1%, as verified by measurement. Furthermore, the spontaneous emission rate ofN2(a 11T) is very small because its lifetime (10-4 s) is much longer than the laser pulse width ( IOns). Considering all the above simplifications we may write:

d [N!] 2 [ k [ ] [ *] ---==-----=-=u2*1 (t)* N2]0- * CO 0* N2 , dt

(Al)

where

u 2: two-photon absorption cross section of the N 2 (a-X) transition.

[N2]0,[CO]0: Concentration of ground state N2 and CO which are assumed to be constant because of the very small degree of excitation (10 - 5

) •

k: Overall energy transfer rate constant. l(t): Intensity oflaser I as a function of time, which we

empirically approximate by a half-wave of the cosine func­tion:

l(t) =/oCOS(1Tt!r-1T12)

= 10 cos(x)

for x = 1Tt!r - 1T 12

where

( - 1T12<.x<. + 1T12),

r: full pulse width of the laser.

(A2)

To integrate Eq. (Al) we use the following approximate expressions:

cos2(x) = 1.035 cos(x + 1T/I2) for O<.x<. 51T/I 2, (A3)

cos2(x) = 1.035 cos(x - 1T/I2) for - 51T/I2<.x<.0.

Combining Eqs. (Al), (A2), and (A3) one obtains as an approximate solution for the range r/12<.t< 11r/12:

[N!J = [A(1 +a2)]-I*{exp[ - (x ± 1T/12 + 1T12)a)

+ sin(x ± 1T/12) + a*cos(x ± 1T/12}, (A4)

where

A = 1TI(1.035*U2*/~*[N2]0*r),

a = (r/1T)*k*[CO]o'

The total amount of CO*(A 11T) produced by the energy transfer from N! during a laser pulse is [CO*]o:

i11l121"

[CO*]O = k [CO]o[N!]dt. 11121"

(A5)

Several routes are open starting from CO*: Ionization by two-photon absorption (hv1 + hv2 ),

forming CO+: R 3•

Spontaneous emission: kco* . Collisional relaxation or quenching to other states: k c •

For the CO formation we thus obtain

[CO+] = (R3*[CO*])/(R3 + kco + k)CO]o) (A6)

or, using Eq. (A5):

[CO+] =gl[ (1 + Ca) (1 + a2) ]*{a2

+ [2(1-sin1T/I2)]-I[1 +exp( -71TaI12)

- exp( - 51TaI12) - exp( -1Ta) n, (A7)

where

C = 1Tkc/[ k *r*(R3 + kco ],

g= [2(1-sin1T/I2)A(1 +kcoIR3)]-I.

1M. F. Golde and B. A. Thrush, Proc. R. Soc. London Ser. A 330, 109 ( 1972).

2S. V. Filseth, R. Wallenstein, and H. Zacharias, Opt. Cornrnun. 23, 231 (1977).

3G. Sha, X. Zhong, S. Zhao, and C. Zhang, Chern. Phys. Lett. 110, 405 (1984).

4G. Sha, X. Zhong, S. Zhao, and C. Zhang, Chern. Phys. Lett. 110,410 (1984).

51. Procaccia and R. D. Levine, J. Chern. Phys. 63, 4262 (1975). 6R. D. Levine and J. Manz, J. Chern. Phys. 63, 4280 (1975). 7R. G. Gordon and Y. N. Chiu, J. Chern. Phys. 55, 1469 (1971). 8L. A. Melton and W. A. Klernperer, J. Chern. Phys. 55,1468 (1971). 9A. B. Callear and P. M. Wood, Trans. Faraday Soc. 67, 272 (1971). lOG. W. Taylor and D. W. Setser, J. Chern. Phys. 58,4840 (1973). liD. H. Katayama, J. Chern. Phys. 81, 3495 (1981). 12D. H. Katayama, Phys. Rev. Lett. 54, 657 (1985). 13D. H. Katayama, J. Chern. Phys. 84, 1477 (1986). 14N. Furio, A. Ali, and P. J. Dagdigian, J. Chern. Phys. 85, 3860 (1986). ISG. Jihua, A. Ali, and P. J. Dagdigian, J. Chern. Phys. 85, 7098 (1986). 16G. Herzberg, Molecular Spectra and Molecular Structure. I, Spectra of

Diatomic Molecules (Van Nostrand, New York, 1950), p. 343. 17A. Lofthus and P. H. Krupenie, J. Phys. Chern. Ref. Data 6, 113 (1977). 18R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics (Oxford

University, New York, 1974), p. 86. 19Reference 18, p. 175. 20S. G. Tilford and J. D. Simmons, J. Phys. Chern. Ref. Data 1, 147 (1972).

J. Chem. Phys., Vol. 87, No.5, 1 September 1987 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.193.242.160 On: Sat, 22 Nov 2014 00:44:48