Rate coefficients for the relaxation of OH (v = 1) by O2 at temperatures from 204–371 K and by N2O from 243–372 K

Chemical Physics Letters 421 (2006) 111–117 www.elsevier.com/locate/cplett

Rate coefficients for the relaxation of OH (v = 1) by O2 at temperatures from 204–371 K and by N2O from 243–372 K D.C. McCabe a

a,1

, I.W.M. Smith

d,*,2

, B. Rajakumar

a,c,3

, A.R. Ravishankara

a,b,c,3

NOAA Earth Science Research Laboratory, 325 Broadway R/CSD 2, Boulder, CO 80305, USA Department of Chemistry and Biochemistry, University of Colorado, Boulder, CO 80309, USA c CIRES, University of Colorado, CO 80309, USA d The University Chemical Laboratory, Lensfield Road, Cambridge, CB2 1EW, UK

b

Received 5 January 2006 Available online 8 February 2006

Abstract We report rate coefficients for the relaxation of OH(v = 1) by O2 and N2O as a function of temperature. The rate coefficients for relaxation (in units of 1013 cm3 molecule1 s1) can be fit by the following expressions: for OHðv ¼ 1Þ þ O2 between 204 and 371 K:k ¼ ð0:50  0:06Þexpðð342  32Þ=T Þ; for OHðv ¼ 1Þ þ N2 O between 243 and 372 K:k ¼ ð1:08  0:08Þexpðð162  22Þ=T Þ.

The results are discussed in terms of the possible mechanisms for relaxation, especially the influence of the weak chemical interaction between OH radicals and O2.  2006 Elsevier B.V. All rights reserved.

1. Introduction The rates at which vibrationally excited OH radicals are relaxed in collisions with various collision partners is of interest both for fundamental reasons and because of the importance of OH radicals in the chemistry of the Earth’s atmosphere at all altitudes. In the lower troposphere, the lifetime of OH(v > 0) is undoubtedly very short as it is known to be relaxed efficiently by O2 and H2O [1–3]. Thus, under these conditions, the lifetime of OH(v = 1) is only about 1 ls and higher vibrational levels are removed even more rapidly. However, in the mesosphere, where concen*

Corresponding author. Fax: +1 1 44 122 333 6362. E-mail addresses: [email protected] (I.W.M. Smith), [email protected] (A.R. Ravishankara). 1 Present address: Division of Engineering and Applied Sciences, California Institute of Technology, Pasadena, CA 91125, USA. 2 Department of Chemistry, University of Cambridge. 3 NOAA and CIRES. 0009-2614/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.01.037

trations of O2 are less than 1016 molecule cm3 and there are negligible concentrations of H2O, the lifetimes with respect to vibrational quenching are significantly longer. Moreover, in the mesosphere, there is significant production of OH(v > 0) by the reaction H þ O3 ! OHðv 6 9Þ þ O2 ;

DH 0 ¼ 324:5

kJ mol1 ð1Þ

which is the source of the vibrationally excited OH that gives rise to emission from OH (v > 0) in the infrared [2], and in the high vibrational overtone bands of OH in the visible, usually referred to as the Meinel bands [4]. Since the main removal process for vibrationally excited OH is relaxation in collisions with O2 (relaxation by N2 is known to be much slower [2]), rate coefficients for the removal of OH(v > 0) by O2, and the temperature-dependence of these rate coefficients, are needed to obtain a full understanding of the observed emissions from vibrationally excited OH in the upper atmosphere. In addition, rate coefficients for

112

D.C. McCabe et al. / Chemical Physics Letters 421 (2006) 111–117

relaxation of vibrationally excited OH are needed for the quantitative interpretation of laboratory and field measurements on processes that generate OH. There is also a special fundamental reason for interest in the vibrational relaxation of OH(v > 0) by O2. It is now well known that the vibrational relaxation of OH, a free radical (i.e., a species with an open electronic shell), by other open shell species, such as NO and NO2, and by some unsaturated species, such as CO and SO2, is rather rapid [5]. This behaviour is attributed to the formation of strongly bound complexes involving the collision partners and facile intramolecular vibrational re-distribution (IVR) within these complexes prior to their re-dissociation. The question of whether a weak chemical bond forms between OH and O2 has long been debated and has remained controversial until very recently. Thus, it has been postulated [6] that the extraordinarily high yield of OH from reaction (1) in the highest accessible vibrational levels (v = 9 and 8) is due to the existence of a weak attractive interaction between the OH and O2 products. This makes the potential energy surface for the H + O3 reaction strongly attractive, without the potential well associated with this attraction being deep enough to ‘trap’ the products and ‘scramble’ the energy released. More recently, after some controversy [7–10], the formation of a weakly bound HO–OO complex has been definitively established in the microwave spectroscopic experiments of Endo and co-workers [11]. They estimate the bond dissociation energy of this species to be De = 16.3 kJ mol1. In this Letter, we report the determination of the rate coefficients for relaxation of OH(v = 1) by O2 and of OH(v = 1) by N2O, i.e., OHðv ¼ 1Þ þ O2 ! OHðv ¼ 0Þ þ O2 OHðv ¼ 1Þ þ N2 O ! OHðv ¼ 0Þ þ N2 O

ð2Þ ð3Þ

over the temperature ranges from 204 to 371 K for (2) and 243 to 371 K for (3). The experimental method is similar to that employed in recent investigations of the relaxation of OH(v = 1), OD(v = 1) by HNO3, DNO3 [12] and by H2O, D2O [13], where the results indicate a role for the hydrogen-bonded interactions in facilitating relaxation. Our main aim in the present work was to discover whether the weak chemical bond between OH and O2 plays a role in the collisional relaxation of vibrationally excited OH by O2. We note that chemical reaction between OH(v = 1) and O2 cannot contribute to the removal of OH(v = 1), reaction to HO2 + O being 179.5 kJ mol1 endothermic. The system OH(v = 1) + N2O, where there is no evidence for either a weak chemical or a strong hydrogen bond between the collision partners, has been investigated largely to compare its behaviour with that of OH(v = 1) + O2. 2. Experimental method Rate coefficients for the relaxation of OH(v > 0) by O2 and N2O were measured using a pulsed laser photolytic

method to produce vibrationally excited OH and pulsed laser-induced fluorescence (LIF) to observe how the concentrations of OH in specific vibrational levels varied with time. Gas mixtures containing the species required to create the vibrationally excited radicals (CH4 and, in experiments with O2, O3) and either O2 or N2O were diluted to between 10 and 35 Torr with helium and flowed slowly through the reaction cell. The excess of He ensured complete translational and rotational equilibration of species, on a time scale much shorter than that associated with the kinetic observations that we report, but did not cause significant quenching of the LIF signals. The flow rate was fast enough to ensure that a fresh sample of gas mixture was exposed to successive shots from the photolysis laser. The apparatus which was employed in the present study has been used in numerous previous kinetic studies in our laboratory, including that in which we measured rate coefficients for relaxation of OH(v = 1) or OD(v = 1) by HNO3 and DNO3 [12]. For all the kinetic measurements reported in this Letter, the reaction between O(1D) atoms, and CH4 was used to generate OH(v > 0). O(1D) atoms were produced either from the photolysis of O3 at 248 nm, in experiments with O2, or of N2O itself at 193 nm, in experiments with N2O, using the output of an excimer laser operating on KrF or ArF. The excimer laser beam (ca. 60 mJ per pulse at 248 nm, 2–4 mJ per pulse at 193 nm, and with a cross-sectional area of ca. 1.5 cm2) was directed perpendicular to the gas flow. The relative populations produced in different OH vibrational levels in the reaction of O(1D) with CH4 has been measured as (v = 1):(v = 2):(v = 3):(v = 4) = 0.315:0.40:0.205:0.08 [14– 16]. Given the appreciable production of OH in levels v > 1, it is necessary to consider carefully the effects of ‘cascading’ from these higher levels on the time-dependence of the population in v = 1 (see below). The second harmonic of a tuneable dye laser pumped by the second harmonic of a pulsed Nd:YAG laser (k = 532 nm) was passed through the reaction cell, perpendicular to both the gas flow and the photolysis laser. This probe laser excited the Q1(1) rotational line in the A2 Rþ ðv ¼ 0Þ X2 Pðv ¼ 1Þ band of OH, in order to detect  OH (v = 1), or, in a few experiments, the Q1(1) rotational 2 þ line in the A R ðv ¼ 1Þ X2 Pðv ¼ 2Þ band, to detect  OH (v = 2). 2 þ 2 OH A R ! X Pðv ¼ 0Þ fluorescence passed through a  band-pass filter (peak transmission at 307.5 nm, FWHM 10 nm) and was detected by a photomultiplier tube positioned orthogonally to the laser beams. When OH X2 Pðv ¼ 1Þ was excited to A2R+(v = 0), emission in the  A2 Rþ ðv ¼ 0Þ ! X2 Pðv ¼ 0Þ band (k  308 nm) was trans mitted by the band-pass filter and detected. When 2 OH X Pðv ¼ 2Þ was excited to A2R+(v = 1), emission  from two bands was detected: directly excited emission in the (1,1) band (k  313 nm), and, after vibrational quenching of OH A2R+(v = 1), emissions in the (0,0) band. Temporal profiles of the LIF signals were generated by varying the time delay between the pulses from the photolysis and probe lasers.

D.C. McCabe et al. / Chemical Physics Letters 421 (2006) 111–117 3 2

1000

Signal (arb. units)

Ozone was prepared by passing ultra-high purity (UHP) O2 through an electrical discharge and then trapping the O3 that was formed on silica gel at ca. 197 K. Dilute (ca. 200 ppmv) mixtures of O3 in He were then prepared manometrically and stored in a darkened 12 l glass bulb. O2, N2O and CH4 (all UHP grade) were used without further purification. Helium (UHP grade) was also used directly out of its cylinder. The concentrations of the gases in the reaction cell were calculated from the measured flow rates of the gases and the measured temperature and pressure in the cell, the pressure being determined using a capacitance manometer. The electronic mass flow meters were calibrated by measuring the rate of pressure rise as gas was flowed through the meter into a known volume. We estimate the uncertainty in the concentrations of O2 and N2O to be ±8% (2r).

6 5 4 3 2

100 6 5 4 3 2

3. Analysis of experimental signals The level of the LIF signals directly reflects the populations in specific vibrational states of OH. Moreover, the concentrations of OH in all of the vibrational levels are very much smaller than those of the gases (O2, N2O and CH4) causing vibrational relaxation. Consequently, the kinetics of OH(v) are in a pseudo-first-order regime. However, account must be taken of the fact that, in the reaction of O(1D) with CH4, OH is created in several vibrational levels (v 6 4) and therefore the variation of population in vibrational levels lower than v = 4 is affected by relaxation both into and out of the specified vibrational state. In practice, the temporal profiles for OH(v = 1) were fitted to an expression of the form

k 01st;1 ½OHðv ¼ 2Þ0 ½expðk 01st tÞ  expðk 001st tÞ k 001st  k 01st

10 0

50

100

150

200

250

300

Reaction time (microseconds) Fig. 1. Temporal profiles of LIF signals from OH (v = 1) following the reaction of O(1D) atoms with CH4 at two different concentrations of CH4: s, [CH4] = 2.7 · 1016 molecule cm3, and d, [CH4] = 1.37 · 1017 molecule cm3. The lines represent fits to Eq. (4).

of OH (v > 2) is shorter than that for the decay of OH (v = 1), so that the formation and relaxation of OH (v > 2) has little impact on the measured rate coefficient for removal of OH (v = 1). 4. Results

½OHðv ¼ 1Þt ¼ ½OHðv ¼ 1Þ0 expðk 01st tÞ þ

113

ð4Þ

[OH(v = 1)] and [OH(v = 2)]0 are the concentrations of those species immediately after photolysis and the rapid reaction of O(1D) atoms with CH4. k 001st and k 01st are the pseudo-first-order rate coefficients for the removal of OH(v = 2) and OH(v = 1), respectively, while k 01st;1 is the pseudo-first-order rate coefficient for the relaxation of OH (v = 2) to OH (v = 1). This equation would correctly describe the temporal behaviour of OH (v = 1) if only one higher vibrational state of OH (i.e., OH (v = 2)) was present. This is not the case when vibrationally excited OH is produced in the O(1D) + CH4 reaction. Nevertheless, we found that this simplified two-state treatment of the temporal profiles led to good fits of the temporal profiles of LIF signals and it was used to determine rate coefficients for removal of OH(v = 1). Fig. 1 shows the excellent quality of fit to Eq. (6) for two traces from experiments containing different concentrations of CH4. Generally, removal of vibrationally excited OH becomes faster for higher vibrational states. Thus, the time scale for loss

The rate coefficients (k2 and k3) for processes (2) to (3), that is for relaxation of OH(v = 1) by O2 and N2O, which we have measured at different temperatures, are listed in Table 1. These second-order rate coefficients are derived from plots of the first-order rate constants ðk 01st Þ, derived from the analysis of the variation of LIF signals versus delay times via Eq. (4), versus the concentrations of O2 or N2O included in the gas mixtures. Examples of such plots are shown in Fig. 2. The uncertainties in the slopes of the lines, i.e., the second-order rate coefficients k2 or k3, obtained by weighted fits of k 01st versus [O2] or [N2O] were typically 2–10% (at the 2r level). As indicated earlier, we estimate the uncertainties in the concentrations of O2 or N2O in the reaction cell to be ±8% at the 95% confidence level. The uncertainties listed for the rate coefficients in Table 1 are the sum (not in quadrature) of this uncertainty and the statistical error. Some uncertainty in the derived rate coefficients also arises because OH is formed in vibrational states v > 2 and relaxation from these levels means that Eq. (4) does not provide an entirely accurate description of the variation in [OH(v = 1)] with time. To estimate the magnitude

114

D.C. McCabe et al. / Chemical Physics Letters 421 (2006) 111–117

Table 1 Measured rate coefficients for the relaxation of OH(v = 1) by O2 and N2O with some of the experimental parameters used in the measurements OH(v = 1) + N2O

OH(v = 1) + O2 16

T/K

[CH4]/10 cm3

[O2]/10 cm3

204 221 247 274 295 330 371

4.0 3.2 3.0 2.4 2.3 1.9 1.9

0–3.8 0–3.3 0–2.8 0–2.5 0–2.1 0–2.0 0–1.9

17

13

Number of k 01st

k2/10 cm 3 molecule1 s1

T/K

[CH4]/1015 cm3

[N2O]/1016 cm3

Number of k 01st

k3/1013 cm3 molecule1 s1

9 7 9 9 8 8 9

2.64 ± 0.34 2.25 ± 0.28 1.91 ± 0.24 1.80 ± 0.27 1.57 ± 0.31 1.37 ± 0.13 1.19 ± 0.20

243 271 297 331 372

7.1 7.3 6.3 5.8 5.3

0.64–5.77 0.82–4.90 1.1–4.9 0.97–4.4 0.60–4.33

9 6 7 7 7

2.09 ± 0.24 2.00 ± 0.20 1.88 ± 0.22 1.77 ± 0.22 1.66 ± 0.16

Table 2 Comparison of rate coefficients for the relaxation of OH(v = 1) and HF(v = 1) by O2 and N2O at ca. 298 K

10

Process

k/1013 cm3 molecule 1 s1

Reference

OH(v = 1) + O2

1.57 ± 0.31 1.3 ± 0.4 1.3 ± 0.4 0.75 ± 0.22 1.88 ± 0.18 (1.38 ± 0.09) · 102 10.4 ± 0.9

This work Dodd et al. [1] Dodd et al. [2] D’Ottone et al. [3] This work Bott and Cohen [18] Bott and Cohen [19]

6

k / 10 4 s

-1

8

OH(v = 1) + N2O HF(v = 1) + O2 HF(v = 1) + N2O 4

2

0 0

1

[O2] / 10

2 17

molecule cm

3 -3

Fig. 2. Examples of the plots used to determine second-order rate coefficients for relaxation of OH(v = 1). Here, the pseudo-first-order rate constants derived from experiments on mixtures containing O2 are plotted against the concentration of O2 present in the mixtures. The filled circles (–d–) represent results obtained at 247 K and the plot yields the secondorder rate constant k = (1.91 ± 0.24) · 1013 cm3 molecule1 s1; the open circles (- - s - -) represent results obtained at 371 K and the plot yields the second-order rate constant k = (1.19 ± 0.20) · 1013 cm3 molecule1 s1.

ferent sources of vibrationally excited OH: O(1D) + CH4, O(1D) + H2O and O(1D) + H2. They reported a similar discrepancy between their rate coefficient for OH(v = 2) + O2 and earlier values [1,2,17], but good agreement for higher vibrational levels, i.e., for OH(v = 3, 4 and 5) + O2. The values of the rate coefficients listed in Table 1 for relaxation of OH(v = 1) by O2 and N2O become larger as the temperature is lowered, this negative dependence on temperature being stronger for OH(v = 1) + O2 than for OH(v = 1) + N2O. We have matched the temperaturedependence of the rate coefficients to two analytical expressions: (i) the Arrhenius equation kðT Þ ¼ A expðEact =RT Þ;

ð5Þ

yielding negative activation energies, and (ii) the form n

kðT Þ ¼ kð298ÞðT =298Þ . of error that results from the two-state approximation inherent in the derivation of Eq. (4) we performed modelling calculations. These calculations indicate that the use of Eq. (4) may lead to an underestimate of the rate coefficient for relaxation of OH(v = 1) of no more than 10%. In Table 2, we compare the value of k2 that we have determined at ca. 298 K with the rate coefficients for this process reported in the literature [1–3]. The agreement with the values reported by Dodd et al. [1,2] is very satisfactory but their value and ours are about twice the rate coefficient reported by D’Ottone et al. [3]. The reason for this discrepancy is not clear. D’Ottone et al. used very much the same method as employed in our experiments and used three dif-

ð6Þ

The derived fitting parameters are given in Table 3. Fig. 3, in which logarithmic values of the rate coefficients are plotted against the reciprocal of temperature, displays the quality of the fits to the Arrhenius expression. The error bars Table 3 Parameters describing temperature-dependence of the rate coefficients Process

OH(v = 1) + O2 OH(v = 1) + N2O a b c

kðT Þ ¼ AeEa =RT

k(T) = k(298)(T/298)n

Ab

(Ea/R)/K

k(298)c

n

0.50 ± 0.06 1.08 ± 0.08

342 ± 32 162 ± 22

1.57 ± 0.31 1.88 ± 0.18

1.32 ± 0.14 0.56 ± 0.63

Error bars are 2r representations of the uncertainties of the fits. Units are 1013 cm3 molecule1 s1. Units are 1013 cm 3 molecule1 s1.

10 (a)

k / 10

-13

cm 3 molecule-1 s-1

D.C. McCabe et al. / Chemical Physics Letters 421 (2006) 111–117

1 3

4

5

6

10 (b)

k / 10

-13

cm 3 molecule-1 s-1

2

1 2

3

4

5

1000 K / T Fig. 3. Arrhenius plots of the rate coefficients for vibrational relaxation of OH: (a) in collisions with O2, d for OH(v = 1), and s for OH(v = 10) with the rate coefficients [25] reduced by a factor of 25; (b) in collisions with N2O, j for OH(v = 1), and h for OH(v = 10) with the rate coefficients [25] reduced by a factor of 100.

involving HF are usually stronger than those involving OH. The comparisons of rate coefficients made in Table 2 are quite striking. It is noticeable that, whereas the rate coefficient for relaxation of OH(v = 1) by O2 is ca. two ordersof-magnitude larger than that for the relaxation of HF(v = 1) by O2, N2O relaxes HF(v = 1) ca. 6.6 times faster than it relaxes OH(v = 1). This difference suggests that some different mechanisms are at work in the relaxation of OH(v = 1) and HF(v = 1) by O2 and N2O. In the case of OH + N2O, there is no experimental evidence for the formation of a complex held together, for example, by a hydrogen bond. Ab initio calculations [21] suggest that there is a very high barrier to the exothermic reaction to produce N2 + HO2, and that the bound HONNO complex on the potential energy surface leading to the endothermic products NO + HNO lies at substantially higher energies than separated OH + N2O. Our tentative conclusion is that the relaxation of OH(v = 1) by N2O probably does not involve the temporary formation of a complex. Rather vibrational relaxation both in this case and in HF(v = 1) + N2O probably involves near-resonant vibrational–vibrational (V–V) energy exchange. N2O might undergo transitions to a number of combination levels: for OH(v = 1), the most likely of these V–V processes is OHðv ¼ 1Þ þ N2 Oð000Þ ! OHðv ¼ 0Þ þ N2 Oð101Þ; DE=hc ¼ 89 cm1

shown on the points in Fig. 3 represent only the statistical uncertainties. In addition to measurements of rate coefficients for the relaxation of OH(v = 1), we measured the value of the rate coefficient for relaxation of OH(v = 2) by N2O at 297 K by monitoring the temporal profiles of LIF signals from OH(v = 2). For this process, we found k = (4.5 ± 0.7) · 1013 cm3 molecule 1 s1, in excellent agreement with the one previously reported result [17] for this rate coefficient of (4.6 ± 0.6) · 1013 cm3 molecule1 s1. 5. Discussion In this section, we discuss the possible mechanisms for the relaxation processes for which rate coefficients have been measured in this work. This discussion is based, not just on the magnitude and temperature-dependence of the rate coefficients for relaxation of OH(v = 1) by O2 and N2O, but also on a comparison with the rate coefficients for the relaxation of HF(v = 1) by O2 and N2O. The latter rate coefficients were measured at room temperature by Bott and Cohen [18,19] some years ago and are given in Table 2. This comparison is interesting because of the similarities between OH and HF. Thus, the v = 1 ! v = 0 vibrational transition energy in HF is equivalent to 3961.6 cm1 (in OH it is 3569.6 cm1) and HF has a dipole moment of 1.826 D (OH 1.668 D) [20]. Both species can, in general, form strong hydrogen bonds, although those

115

ð7Þ

which may occur under the influence of long-range dipole– dipole coupling as first proposed by Sharma and Brau [22]. In such processes, the collisional probability is related, inter alia, to the squares of the electric dipole moments for the radiative transitions in the two molecules. With this in mind, we note that the transition dipole moment for the (000 ! 101) radiative transition in N2O is unusually large for a combination band [23]. The mild negative dependence of the rate coefficient for relaxation of OH(v = 1) by N2O on temperature, shown in Fig. 3a, is consistent with this proposal. The energy discrepancy for the corresponding process involving HF(v = 1) is much larger but this may be compensated by the transition dipole for the fundamental (1,0) band in HF being much larger than that for OH. We know of no previous measurements of the rate of relaxation of OH(v = 1) by N2O, but Copeland and co-workers [17,24,25] have made a series of measurements on the relaxation from higher vibrational levels of OH. In Fig. 3a, we also show the rate coefficients for relaxation of OH(v = 10) by N2O measured by Lacousie`re et al. [25]. These are much larger than those for OH(v = 1) + N2O but show a similar dependence on temperature. As already pointed out, the relative values of the rate coefficients for relaxation of OH(v = 1) and HF(v = 1) are reversed when the collision partner is O2. Now the rate coefficient for OH(v = 1) is much larger than for HF(v = 1). In contrast to the situation with N2O, there is

116

D.C. McCabe et al. / Chemical Physics Letters 421 (2006) 111–117

only one remotely resonant V–V energy exchange channel. These processes

k diss ƒ ðHOðv ¼ 1Þ  O2 Þ OHðv ¼ 1Þ þ O2 ƒ! k ass

k IVR

OHðv ¼ 1Þ þ O2 ðv ¼ 0Þ ! OHðv ¼ 0Þ þ O2 ðv ¼ 2Þ; DE=hc ¼ 481:5 cm1 HFðv ¼ 1Þ þ O2 ðv ¼ 0Þ ! HFðv ¼ 0Þ þ O2 ðv ¼ 2Þ; DE=hc ¼ 873:5 cm1



!ðHOðv ¼ 0Þ  O2 Þ ! OHðv ¼ 0Þ þ O2 ð8aÞ ð8bÞ

involve O2 being excited from v = 0 to v = 2, and they cannot occur under the influence of dipole–dipole forces. The mechanism represented by (8a) therefore seems inconsistent with the rapidity of the observed relaxation of OH(v = 1) by O2. Moreover, if the dominant mechanisms for relaxation were via hydrogen-bonded complexes, we would expect HF to form a stronger hydrogen-bond with O2 than OH and therefore for HF(v = 1) to be relaxed faster by O2 than OH(v = 1). We believe that our results for OH(v = 1) + O2, that is the magnitude of the rate coefficient for relaxation and its temperature dependence, as well as the comparison with HF(v = 1) + O2 system, strongly suggest that the weak chemical bond formed between OH and O2 plays an important role in facilitating relaxation in collisions between OH(v = 1) and O2. In other words, the difference between the rate coefficients for relaxation of OH(v = 1) and HF(v = 1) by the di-radical O2 is due to OH being a free radical. The presence of a shallow potential well on the potential surface governing the dynamics of bimolecular collisions between OH(v = 1) and O2 could help induce vibrational energy transfer in two (related) ways, depending on whether or not something that can be called a ‘collision complex’ is formed. Using quasiclassical trajectories, Osborn and Smith [26] investigated how the presence of a shallow minimum on the potential energy surface might facilitate energy transfer in collisions between a vibrationally excited diatomic molecule, AB(v) and an atomic collision partner (M). They found that, even when the potential well was as deep as 50 kJ mol1, a high proportion of the collisions might proceed directly. Moreover, the propensity for energy transfer depended not only on the depth of the well but also on (i) its ‘location’, in particular whether the internuclear separation of A and B was very different at the minimum of the potential well from the equilibrium value in the AB molecule, and (ii) the angular anisotropy of the potential energy surface in the vicinity of the well. The second way to view the influence of intermolecular attraction of intermediate strength on vibrational relaxation is to assume, just as when a strong chemical bond is formed, that a collision complex forms and that IVR within that complex can occur at a rate competitive to redissociation without loss of the original vibrational excitation [4]. If such an analysis is appropriate in the case of OH(v = 1) + O2, the mechanism can be written as [5,12]

ð9Þ

where (HO(v = 1)–O2)* is a complex in which energy is retained in the O–H vibration and (HO(v = 0)–O2)** is a complex in which that energy has been transferred into other modes by IVR and which will almost instantly dissociate to OH(v = 0) + O2. The relatively small value of the rate coefficient for relaxation, as well as other considerations, strongly suggest that kdiss, the rate coefficient for re-dissociation of the initially formed complex, is much greater than kIVR, the rate coefficient for IVR, so that the rate coefficient for relaxation can be written as k relax ¼ k IVR ðk ass =k diss Þ

ð10Þ

Within the context of this mechanism, the moderately large negative dependence of krelax on temperature is associated with the positive temperature dependence of kdiss; the more internal energy within the (HO(v = 1)–O2)* the shorter its lifetime will be with respect to re-dissociation. We have discussed earlier the level of agreement between the rate coefficient that we find for relaxation of OH(v = 1) by O2 at ca. 298 K and those values measured previously. Copeland and co-workers [17,24,25] have also determined rate coefficients for the relaxation of OH(v > 1) by O2. The temperature-dependent results [25] for OH(v = 10) + O2 are displayed in Fig. 3b. These rate coefficients are approximately two orders-of-magnitude larger than those for OH(v = 1) + O2 and show less dependence on temperature: (Ea/R) = (115 ± 30 K) compared with – (342 ± 32 K) for OH(v = 1) + O2. If the complex-forming mechanism is indeed operative the increase in krelax on going from (v = 1) to (v = 10) presumably reflects a corresponding increase in kIVR, as a result of the increasing anharmonicity in the O–H vibration and the decrease in the energy for a v ! v  1 vibrational transition. Moreover, the increase in kIVR, making IVR competitive with re-dissociation, would reduce the temperature dependence of the rate coefficient for overall vibrational relaxation, as is observed. In summary, we have measured rate coefficients for the relaxation of OH(v = 1) by O2 and N2O over a range of temperatures. In the case of OH(v = 1) + N2O, we suggest that relaxation probably occurs by V–V energy exchange under the influence of long-range dipole–dipole forces. For OH(v = 1) + O2, where there are no near-resonant, single quantum, V–V channels, relaxation is nevertheless rather facile reflecting, we believe, the role of the weak chemical bond between OH radicals and O2, for which definitive spectroscopic evidence has recently been obtained [11]. Acknowledgments This work was funded in part by the NASA Upper Atmosphere Program. D.C.M. acknowledges an NSF graduate research fellowship.

D.C. McCabe et al. / Chemical Physics Letters 421 (2006) 111–117

References [1] J.A. Dodd, S.J. Lipson, W.A.M. Blumberg, J. Chem. Phys. 92 (1990) 3387. [2] J.A. Dodd, S.J. Lipson, W.A.M. Blumberg, J. Chem. Phys. 95 (1991) 5752. [3] L. D’Ottone, D. Bauer, P. Campuzano-Jost, M. Fardy, A.J. Hynes, Phys. Chem. Chem. Phys. 6 (2004) 4276. [4] R.P. Wayne, Chemistry of Atmospheres, third ed., Oxford University Press, Oxford, 2000, p. 547. [5] I.W.M. Smith, J. Chem. Soc., Faraday Trans. 93 (1997) 3741. [6] D. Klenerman, I.W.M. Smith, J. Chem. Soc., Faraday Trans. 2 (83) (1987) 229. [7] M. Speranza, Inorg. Chem. 35 (1996) 6140. [8] F. Carace, G. de Petris, F. Pepi, A. Troiani, Science 285 (1999) 81. [9] B. Nelander, A. Engdahl, T. Svensson, Chem. Phys. Lett. 332 (2000) 403. [10] P.A. Denis, M. Kieninger, O.N. Ventura, R.E. Cachau, G.H.F. Dierckson, Chem. Phys. Lett. 365 (2002) 440. [11] K. Suma, Y. Sumiyoshi, Y. Endo, Science 308 (2005) 1885. [12] D.C. McCabe, S.S. Brown, M.K. Gilles, R.K. Talukdar, I.W.M. Smith, A.R. Ravishankara, J. Phys. Chem. A 107 (2003) 107.

117

[13] D.C. McCabe, I.W.M. Smith, B. Rajakumar, A.R. Ravishankara, Phys. Chem. Chem. Phys., to be submitted. [14] A.C. Luntz, J. Chem. Phys. 73 (1980) 1143. [15] C.R. Park, J.R. Wiesenfeld, J. Chem. Phys. 95 (1991) 8166. [16] P.M. Aker, J.J.A. O’Brien, J.J. Sloan, J. Chem. Phys. 84 (1986) 745. [17] K.J. Rensberger, J.B. Jeffries, D.R. Crosley, J. Chem. Phys. 90 (1989) 2174. [18] J.F. Bott, N. Cohen, J. Chem. Phys. 58 (1973) 4539. [19] J.F. Bott, N. Cohen, J. Chem. Phys. 61 (1974) 681. [20] CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 1989. [21] A.M. Mebel, M.C. Lin, K. Morokuma, C.F. Melius, Int. J. Chem. Kinet. 28 (1996) 693. [22] ‘R.D. Sharma, C.A. Brau, J. Chem. Phys. 50 (1969) 924. [23] M.A.H. Smith, C.P. Rinsland, B. Fridovich, K.N. Rao, in: K.N. Rao (Ed.), Molecular Spectroscopy: Modern Research, vol. 3, Academic Press, New York, 1985, chap. 3. [24] K. Knutsen, M.J. Dyer, R.A. Copeland, J. Chem. Phys. 104 (1996) 5798. [25] J. Lacoursiere, M.J. Dyer, R.A. Copeland, J. Chem. Phys. 118 (2003) 1661. [26] M.K. Osborn, I.W.M. Smith, Chem. Phys. 91 (1984) 13.