Volume 127, number 5 CHEMICAL PHYSICS LETTERS 27 June 1986

THE NASCENT PRODUCT VIBRATIONAL ENERGY DISTRIBUTION OF THE REACTION 0( ’ D) + Hz BY THE GRATING SELECTION CHEMICAL LASER TECHNIQUE

Yulin HUANG, Yukun GU, Chengshan LIU, Xuefeng YANG and Yusheng TAO

Daban Institute of Chemrcal Physrcs, Dalian, People’s Republic of China

Received 23 January 1986; in final form 2 April 1986

The nascent product vibrational energy distribution of the reaction O(‘D)+ H, has been determined by using the grating

selection chemical laser technique. The main experimental results are: N, /Nc = 0.69, N,/N, = 0.92, Ns/N, = 0.80, N.,/Ns <

0.71. A computer modeling is carried out which shows that the combined effects of vibrational relaxation and secondary

reaction 0, + H + OH + 0, in all vibrational energy levels are less than 20% under our experimental conditions. The results

are discussed in terms of surprisal analysis, resulting in the relative contribution of insertion and abstraction reaction channels

being about 2 to 1. A comparison with laser-induced fluorescence and infrared chemiluminescence and with theoretical

calculations is presented.

1. Introduction

There has been interest in the reaction O(lD) t H2(lZg) + 0H(211j) t H(2S) not only because of its importance in atmospheric chemistry [ 11, chemical lasers [2] and combustion processes, but also because of its importance in molecular reaction dynamics. A great deal of macroscopic and microscopic reaction kinetics information on this reaction is available. It

has been shown that the reaction is characterized by very large rate constants, nearly gas kinetic, and the absence of any barrier [3]. Most microscopic data from the experimental studies of flash-photolysis spectroscopy [4], infrared chemiluminescence (IRCh) [5], molecular beam reactive scattering [6], laser- induced fluorescence (LIF) [7,8] and chemical lasers

[2] concern product energy partitioning which are comparable with the various kinds of theoretical com- putations [9,10].

In this paper, we report the chemical laser determi- nation of the product vibrational state populations of the reaction

O(lD) + H, + 0H(211,; u,K) + H , (1)

with the grating selection method. A comparison with the experimental results of LIF and IRCh and the re-

sults of theoretical calculations and statistical theory is presented.

2. Experimental

Fig. 1 shows the experimental device. A suprasil quartz laser tube (18 mm inner diameter, 240 cm long) was closed at one end by a 5 m radius of curva- ture, gold-coated spherical mirror. The other end of

Fig. 1. Experimental device. (1) Flash lamp, (2) power system,

(3) grating, (4) monochromator, (5) InSb detector, (6) gas mixing system, (7) vacuum system, (8) tailgas system, (9) CaF2 window, (10) oscilloscope.

432 0 009-2614/86/s 03.50 0 Elsevier Science publishers B.V. (North-Holland Physics publishing Division)

Volume 127, number 5 CHEMICAL PHYSICS LETTERS 27June1986

the laser tube was closed by a CaF, window which was mounted turning aside 3’ from the Brewster angle. The optical cavity was completed by position- ing a grating (blazed at 3 pm, 300 lines/mm) 3 m away from the spherical mirror. The suprasil quartz tube was concentrically covered by a fused quartz tube (40 mm outer diameter, 200 cm long). The con-

centric space bounded by the two tubes is filled with 2-5 Torr of Xe, forming the flash lamp for the sys- tem. The capacitor bank was 8.47 I.~F (Maxwell Lab. Inc.) and typical discharge voltages were in the range

16- 18 kV. Detection of the amplified vibration- rotation OH emissions was accomplished by direct- ing the radiation through a Jobin-Yvon HR-1500 monochromator to a liquid-nitrogen-cooled InSb de- tector. The laser signals were monitored and recorded by a Tektronix model 7633 storage oscilloscope. The ratio of premixed reactants O,/H,/He were from l/2/4 to l/5/40. After triggering the flash lamp, ozone molecules were photodissociated by absorbing 2000- 3000 A ultraviolet rays, forming O(lD) atoms and oxygen molecules

0, + O(lD) + O,(a lA,&.

O(lD) reacted with H2 rapidly

O(lD) + H, + 0H(21-Ii;u,K) + H ,

AH = -43.5 kcal/mol, k= 2.3 X lo-lo cm3/mo1ecule s) [ 111. The vibrationally excited OH (up to u = 4) re- sulted from the above reaction.

3. Results

Table 1 lists the observed transitions and their rela- tive threshold times in reaction (1) using the grating cavity. OH u = 4 to 3 transitions could only be ob- served by using a free running laser cavity. OH F,P,, transitions were observed in the experiment. It is clear that FIP21(4) has the shortest threshold time;

therefore it has the highest optical gain coefficient under all experimental conditions.

Information about the vibrational distribution of the reaction products can be obtained via comparison of the optical gain coefficients of the observed transi- tions [12]:

Table 1 Observed laser transitions and their relative threshold times by the grating selection method. Note: Threshold times in ps are relative to threshold time of F1 Pzl(4) which is defined as zero

Transition Experimental conditions (OS/Hz/He)

1/3/8(30Torr 1/3/12(40Torr l/3/16 (SOTorr total pressure) total pressure) total pressure)

FlP10(4)

F1P10(5)

FlPlO(6)

hPz1(3)

FlP21(4)

bP21(5)

FI P2 l(6)

FlP2lU)

FI p32 (4)

hP32(5)

FlP32(6)

bP21(5)

FzP21(6)

1.30 0.95 -

0.45 0 0.05 0.75 2.15 1.50 1.40 1.95 1.80 2.30

1.00 1.10 -

0.55 0 0.05 0.90 1.90 1.30 - _

1.90 3.40

1.00 1.40 _

0.70 0 0.30 1.25 3.00 1.90 1.15 2.05 2.10 _

o,,&) = (In 2)li2hgK,A

8,3/2v2kgTAvD exp(x2)erf (x)N”_r

X W$,/Nv__~ )B, exp [-~,(K’)W~B Tl

-B “-1 exp [-~,_~UWdk~Tl~~ (2) where v and AvD are the transition frequency and its Doppler width; B, and F,(K) are the rotational con- stant and rotational term, respectively. gK is the rota- tional degeneracy. T is the translation-rotation tem- perature for the OH system,

x = (In 2)lj2AvL/AvD , (3)

Av, = 2v,(ln 2)1/2(2k,T/Mc2)1/2, (4)

erfc (x) = 1 - 27r-‘j2 fexp(x2) dx . (5) 0

For F, + FI transitions [ 131:

F,(K) = B,{(K+ 1)2 - 1 -f [4(K+l)2+a(a-4)]1’2}

-D&2(K+1)2. (6)

For F2 -+ F2 transition:

F,(K) = B, (K2 -1 + + [4K2 t a(a - 4)] 112)

- D,K2(K+ 1)2 , (7)

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Table 2

CHEMICAL PHYSICS LETTERS 27June1986

Experimental and calculated resulst of reaction (1). Note: The experimental result of N41Ns is derived from the free-running method The calculated data are recalculated from experimental data by taking account of the relaxation and secondary reactions

NI INQ NzINI NdN2 NdN3

experimental calculated

0.69r0.05 0.92kO.06 0.80*0.08 0.71to.07 0.79 0.97 0.90 0.45

where a is the so-called coupling constant. In eq. (2), we have introduced the a~umption of rotational therm~~ation of the samples,

iv u~=N,g~~exp[-F,(K’)lzclkBT]. w Because there is a difference in energy-transfer cross sections between molecular vibration and rotation, we can find a condition under which the rotational Boltzmann distribution has been reached but only a minimal relaxation of vibrational distribution has oc- curred. In order to validate the above assumption, reactant pressures were kept constant (03,2.5 Torr; H,, 7.5 Torr) while helium pressure was varied widely. A comparison of the behavior of relative thre~oId times in i/3/8, l/3/12,1/3/16 03/HZ/He (table 1) reveals no drastic changes apart from likely pressure- broadening effects.

The relative laser gain coefficients of allvibration- rotation transitions (Au = 1) of 0H(211j state) have been calculated according to eq. (2), in which we sup- pose that no difference of rotational distribution be- tween the F1 rotational energy levels and the F2 and the populations of all occupied rotational energy levels are distributed according to Boltzmann’s distri- bution. The analytical results of the population ratios between two vibrational m~~olds are shown in table 2 for reaction (1). The ~4~~~ in table 2 is the upper limit obtained by using a free-running laser technique. There is no population difference between the F1 and i;, energy level within the error limit. This indicates there there is no energy distribution difference be- tween F, and F2 states in reaction (I), or the specifi- city of the energy distribution has been wiped out be- cause of molecular collisions.

4. Discussion

4.1. General

The main problems for obtaining reliable data are

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vibrational relaxation of product OH by ozone and the secondary reaction process

H+03-+OH(u~9)C02. (9)

This reaction preferentially populates the OH u = 4-9 energy levels [ 141. Although it is much slower than reaction (1) (about l/9) [ 151 and we did not get any laser signal radiated from u > 4 levels, it might have some effect on the experimental results because of vibrational energy relaxation. The computer modelling showed [ 121 that under the experimental conditions, reaction (9) may increase the distribution of reaction (1) about 30% for u = 4,2% for u = 3, O,l%foru=2,a~dnoeffectonu=O~du=l. These results may suggest that the ~4/~~ value of the product of reaction (1) is simply the upper limit of the actual population ratio because of a radiative cas- cade effect and secondary reaction.

The relaxation of product OH of reaction (1) in the 0, t H2 t He system is very complicated and we are unable to calculate complete relaxation process

Fig. 2. The effects of relaxation processes by 03, Hz, H, and the effects of secondary reaction. l : Neither the relaxation ef- fect nor secondary reaction effect is considered. X : AR effects are included. o: Only H relaxation effect is considered. +: 0s and Ha relaxation effects are considered.

Volume 127, number 5 CHEMICAL PHYSICS LETTERS 27 June 1986

via modelling computations. The only processes that

can be considered here are corresponding relaxations of product OH by O,, HZ, H, 0, OH, He. Fig. 2 shows the corresponding relaxation processes by 03, H2, H, respectively, and combined relaxation by 03, H2 and H. The effects of 0, OH, He are smaller than that of the above species so that they might not be considered at all [ 121.

The nascent vibrational distribution of reaction (1) obtained by computation are shown in table 2. It could be considered to be accurate except for errors introduced by (a) experimental precision; (b) input data required for the calculation of the optical gain coefficients which were obtained from spectroscopic data;(c) the inaccuracy of available rate constants; (d) and what is more, the approximate extent of the

rotational equilibrium hypothesis which is not quanti- tatively explicit.

4.2. The mechanism of reaction (1)

It has been found that reaction (1) occurs by two possible mechanisms. The oxygen atom can insert

into the hydrogen bond and, therefore, form a relati- vely long-lived complex which subsequently breaks

apart. Alternatively, the oxygen atom can abstract a hydrogen atom from one end of the H2 molecule and never sample the deep H20(X 1 A') potential well. Whitlock et al. [9] suggested theoretically that the partitioning of the vibrational energy of the product OH be more in favour of statistical, which implied

that the ratio of the probability for the insertion to the abstraction reaction was larger than one. This re- sult was consistent with the classical trajectory calcu- lation on fitted ab initio potential surfaces [lo]. According to Whitlock [9], the insertion reaction dis- tribution is almost the same as the statistical distribu- tion. The abstraction reaction hardly populated the ground vibrational energy level. In this way, we can estimate the microscopic branching ratio for insertion and abstraction with our CLG experimental results. The results showed that theN,-,/&,Nv = 0.28 while h$/Zt=qNt = 0.42. So the probability of the insertion reaction is about 0.67. Now let us check this result with the u = 2 distribution. Nz/&,NV = 0.22, @2/Ctz& = 0.18, the probability of the abstrac- tion reaction should be (N2 - 0.67f12)/ [( 1 - 0.67) X &h’,j = 0.29. A ccording to the actual distribution,

Table 3 The probabilities of the insertion and abstraction branch of the product of reaction (1). Note: e is derived from a priori distribution, (Nv/~&Nv)expt is derived from table 2. (Nv/C&,Nv),bst is the relative population of the abstraction branch of reaction (l), (~v/.&,lvv)~aSe is the relative popu- lation of the imaginary distribution of reaction (1)

u=o u=l u=2 u=3 v=4

Wv/$=oNv)expt 0.28 0.22 0.22 0.19 0.09

gX&@ 0.42 0.29 0.18 0.09 0.03

W,.&=eNv)image 0.14 0.16 0.25 0.30 0.15

@‘v~&o~v)abst 0.00 0.09 0.29 0.41 0.21

the probability of imaginary distribution (opposite to the statistical distribution, the real distribution (experi- mental) is an average distribution of the statistical and

imaginary distribution) should be about 0.25, this value is close to the above 0.29. We can therefore infer that the probability 0.67 is suitable for the insertion reac- tion. The experimental and calculated results are shown

in table 3. The insertion probability 0.67 confirms that the reaction mechanism is really more due to the O(lD) atom inserting into the H-H bond to form a

long-lived collision complex than due to the O(lD) atom end-on attack. The theoretical calculations [9,10] of quasiclassical trajectory are obvious judged by the

results of our experiment. The difference between the distribution of imaginary

and abstraction reaction resulted from (a) the error of

both experiment and modelling calculation, (b) popu- lation distribution of insertion reaction being not ex- actly statistical, (c) the error of estimated abstraction distribution which assumes no population in the lowest vibrational level (u = 0) and this point will be discussed later.

4.3. CoYnparison of reaction (1) with the F + Hz react&

It is now appropriate to compare reaction (1) with

FtH2+HF(u)+H, (10)

which is the best studied elementary reaction both experimentally and theoretically. Both reactions are benchmark reactions of fundamental importance in molecular reaction dynamics.

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Volume 127, number 5 CHEMICAL PHYSICS LETTERS 27 June 1986

In both cases, the reactions are highly exothermic and the reaction rates are very fast, almost gas kinetic [ 10,161. Both are of H t LL type atom-diatomic molecule exchange reactions. The ab initio calcula- tions show that reaction can occur with no entrance- channel potential barrier for reaction (1) [lo] or with very small potential barrier for reaction (10) [ 171. However, the vibrational energy distributions of the product are quite different for both reactions. A highly inverted vibrational distribution is found in reaction (10) which compared with a more statistical

vibrational distribution of reaction (1). These results convinced us that there are notable-intrinsic differ- ences in the two reactive systems in spite of their seeming similarities.

Theoretically, it has been shown by quasiclassical trajectory calculations on either an ab initio or valence bond diatomics-in-molecules potential energy surface that no barrier exists when an O(lD) atom attacks H2

along the vertical direction of the H-H bond while as the attacking direction approaches collinear, the height of the energy barrier increases for reaction (1). This implies that the 0( 1 D) atom prefers side-on at- tack to end-on attack. A collision complex is formed for most of the reaction processes. This reaction usually occurs with a microscopic branching, and the branching ratio depends upon the magnitude of the relative translational energy of the reactants. These have been confirmed by both theoretical calculations. On the other hand, there is a barrier separating FH + H from F + H2, and the barrier is the smallest for col- linear geometries. The reactants preferentially ap- proach via collinear or near-collinear geometries, no long-lived complex would occur and the reaction pro- ceeds by a direct mechanism resulting in a non-statisti- cal vibrational distribution. No microscopic branching has been discovered with this reaction. A collision complex formed for a brief period of time only with non-reactive inelastic collisions in the trajectory caI- culations. This conclusion is consistent with experi- mental results of Berry [ 181.

It is well known that direct abstraction reaction re- sults in linear surprisals of vibration energy popula- tion of products such as F t H2 reaction [ 181. This results in a finite negative temperature corresponding to population inversion. Fig. 3 shows the vibrational surprisal analysis of reaction (1). It is not surprising to have a non-linear surprisal because of the mixed

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Fig. 3. Vibrational surprisal analysis of reaction (1). X : Real surprisal analysis based on experimentalresults. o: Abstraction branch. A: Insertion branch.

mechanism of reaction (1). It may be expected ac- cording to Whitlock [9] that the insertion reaction would essentially have a prior distribution and hence no surprisal while the abstraction reaction would have a linear surprisal with a negative slope. If we divide the actual distribution into insertion and abstraction branch in proportion as 0.67 :0.33 (table 3), we can obtain two straight lines. One for the insertion branch with a horizontal line, which represents the statistical distribution. Another for an abstraction branch with a negative slope, which represents an inverted vibra- tional energy distribution with h, = -5.32 (or Tvib = -4.3 X lo3 K). It should be noticed that Zu # 00 (Zu = 2.2) means (NU=O)abstr = 0.02. As a consequence, this implies that the population contribution of the abstraction reaction to the lowest level (u = 0) is not quite equal to zero (fig. 3). Note also that as expected from information theory, the insertion branch which is less constrained has the higher branching fraction.

4.4. Comparison of the results of CLG method with other methods

So far, the only experimental results of product vibrational energy distribution of reaction (1) have been obtained using LIF [7,8] and IRCh [5] as well as CLG. As far as we know, this is the first elemen- tary gas reaction which has been studied by all three methods to probe the nascent product vibrational energy distribution. Comparing these results with theoretical calculations is instructive. Because of pre-

Volume 127, number 5 CHEMICAL PHYSICS LETTERS 27 June 1986

dissociation of the OH 2E excited state, only N1/NO = 0.9 can be obtained using LIF. Alternatively, IRCh can be used to probe all the vibrational energy distri- bution except u = 0. Butler et al. [5] obtained the complete vibrational distribution of reaction (1) by combining LIF and IRCh results. Analysis of their re- sults with the abovementioned method (see section 4.2), the insertion probability is about 0.52 which is

different from our experimental result, 0.67. It is un- expected to discover that both Butler’s and our results

fit very well into the pattern of Whitlock’s [9] calculation in which Butter’s results correspond to the reaction condition of high temperature and

ours to low temperature, except a lower abstrac- tion probability for the theoretical calculation comparing with both of the experimental results. These are consistent with both of our experimental

conditions. Our experiment was conducted under ap- proximate room temperature because a lot of buffer gas (03/H2/He = i/3/8-16) was used while Butler used much less buffer gas (03/H2/He = l/2/0-2). These results show that both theoretical calculations and experiments are successful for this elementary reaction. We suggest that theoreticians should modify their calculations somewhat. We point out another difference between our results, Butler’s, Whitlock’s, and Schinke’s [lo] and the results of Ransome and Wright [ 191. It is qualitatively consistent that for most available experimental results and theoretical calculations, the maximum population ratio between upper and lower vibrational energy levels of the prod- uct OH of reaction (1) is in NU=2/Nvz1, except for a quantitative difference in Butler’s results where NUz2/ Nu=l > 1 [5]. But Ransome’s calculation showed that the maximum is in N&NV=,.

5. Conclusion

Our work provides the most complete data of the nascent product vibrational energy distribution for reaction (1) by a single experimental technique. The

experimental results are: N1/No = 0.69, N2/N1 = 0.92, Ns/N2 = 0.80, Nq/N3 < 0.7 1. Our results are similar to the other results obtained by LIF and IRCh methods, except that the Nvz2/N,, values are not very close. According to our data, the relative contri- bution of insertion and abstraction channels for reac-

tion (1) is about 2 to 1. This is in agreement with

various theoretical calculations [9,10]. Reaction (1) has been studied thoroughly by vari-

ous theoretical methods. But experimental studies are relatively scant. Our research results not only reveal some of the microscopic reaction mechanisms but aso supply experimental evidence for theoreticians.

Acknowledgement

We thank Mr. Ke Wang, Mr. Shaoping Lu, and Mr. Zheng Li for stimulating discussions and help in the

experiment.

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