Dynamics of OH Production in the Reaction of O(¹D₂) with Cyclopropane

Abstract

The OH($X^2{\Pi}$, ${\upsilon}^{\prime\prime}=0,1$) internal state distribution following the reaction of electronically excited oxygen atom ($O(^1D_2)$) with cyclo-$C_3H_6$ has been measured using laser-induced fluorescence, and compared with that following the reaction of $O(^1D_2)$ with $C_3H_8$. The overall characteristics of the OH internal energy distributions for both reactions were qualitatively similar. The population propensity of the ${\Pi}(A^{\prime})$ ${\Lambda}$-doublet sub-level suggested that both reactions proceeded via an insertion/elimination mechanism. Bimodal rotational population distributions supported the existence of two parallel mechanisms for OH production, i.e., statistical insertion and nonstatistical insertion. However, detailed analysis revealed that, despite the higher exoergicity of the reaction, the rotational distribution of the OH following the reaction of $O(^1D_2)$ with $C_3H_8$ was significantly cooler than that with cyclo-$C_3H_6$, especially in the vibrational ground state. This observation was interpreted as the effect of the flexibility of the insertion complex and faster intramolecular vibrational relaxation (IVR).

Introduction

The reactions of electronically excited atomic oxygen, O(1D2), with small hydrogen-containing molecules1 have attracted a significant amount of attention owing to their importance in establishing the chemical composition and physical structure of the atmosphere, and also their fund-amental interest in reaction dynamics. Thermal rate coeffici-ents for the reactions of O(1D2) with hydrocarbons are generally very large,2 approaching those of gas kinetic values. The channel producing electronic ground-state OH (reaction 1) has been studied comprehensively using laser-induced fluorescence (LIF),3 infrared chemiluminescence techniques,4 and crossed molecular beam studies.5 Reaction 1 is highly exothermic, releasing ~ 190 kJ mol−1 for CH4, and ~200-220 kJ mol−1 for higher saturated hydrocarbons,6 which is enough to produce vibrationally excited OH(X2П, 0 ≤ υ" ≤ 4).

Full characterization of the OH product distribution follow-ing the reaction of O(1D2) with various hydrocarbons, i.e., CH4, C2H6, C3H8, and C(CH3)4, has been reported using LIF on the transitions OH(A2Σ, υ′ = 0, 1 ← X2П, 0 ≤ υ" ≤ 4), and can be summarized as follows.7 The population of OH(X2Π, υ") products is broadly distributed over vibrational levels up to the energetic limit of υ" = 4, and extends over the avai-lable rotational levels within each υ". The rotational sur-prisals demonstrated bimodal characters and revealed signi-ficant nonlinearity in the lower vibrational levels of the heavier hydrocarbons. The product energy distributions were interpreted to reflect the roles played by two parallel mech-anisms leading to the formation of OH, in which both mechanisms involved the formation of vibrationally excited insertion complexes as typified in reaction 2.

One mechanism dominates the O(1D2)/CH4 reaction, as well as the higher vibrational levels of OH in heavier hydro-carbons. It favors the production of the rovibrationally excited product in a manner similar to analogous reactions of O(1D2) with substrates such as H2 and HCl, and probably involves the dissociation of short-lived ROH† prior to energy equipartition in the complex. The second mechanism leads, in the case of heavier hydrocarbons, to the production of rotationally and vibrationally cold OH. Deconvolution of the bimodal distribution based on information theoretic analysis and RRKM calculations have concluded that the production of OH(X2П, υ" = 0) following the reaction of O(1D2) with heavier hydrocarbons proceeds via an activated collision complex intermediate that is sufficiently long-lived to ensure the equilibration of the reaction exoergicity prior to dis-sociation.

For all hydrocarbons larger than CH4, there are generally more exothermic channels involved in the rupture of weaker C–C bonds. The relatively small yields of OH resulting from the reactions of O(1D2) with heavier hydrocarbons (< 5% relative to CH4)7 certainly support a mechanism in which the production of a chemically activated alcohol (reaction 2) is followed predominantly by C–C bond scission to yield products other than OH, because the C–C bond is much weaker than the C–O bond.

More recently, based on the time-resolved ultrafast LIF measurements of the OH from the reaction of O(1D2) with CH4, Stephenson and co-workers proposed three distinguish-able mechanisms for reaction 1.8 The longest lifetime (5 ps) was associated with statistical insertion; that is, the inter-mediate ROH† was sufficiently long-lived for complete intramolecular vibrational relaxation (IVR). The intermediate lifetime (0.5 ps) was attributed to nonstatistical insertion, or an insufficient lifetime for complete IVR. The shortest lifetime (0.2 ps) was assigned to abstraction on the basis of its cold rovibrational distribution.

In the present study, using LIF, the OH(X2Π, υ" = 0,1) internal state distributions following the reactions of O(1D2) with C3H8 and cyclo-C3H6 were measured and compared (reactions 3 and 4).

As described above, the OH production channel for reac-tion 4 was studied up to the energetic limit using LIF.7 Since both substrate molecules, C3H8 and cyclo-C3H6, are saturated hydrocarbons with approximately the same molecular weights, it is expected that both reactions will follow kinematically the same reaction mechanism for the production of OH. Recently, a number of reaction pathways for the reaction of O(1D2) with cyclo-C3H6 have been observed using crossed molecular beam studies.9,10 Interestingly enough, in addition to the insertion into the C–H bond, it has been reported that O(1D2) inserts into the C–C bond of cyclo-C3H6, followed by the production of H2CO through long-lived complex formation, which is not generally observed for the reaction of O(1D2) with C3H8. Another main difference between reactions 3 and 4 lies in the molecular flexibilities of the substrates. Cyclo-C3H6 has a very rigid structure with a high ring strain energy (~114 kJ/mol), while C3H8 is very flexible because large-amplitude torsional motions around the C–C single bonds are possible. The different internal energy distributions of OH(X2Π, υ" = 0,1) products following reactions 3 and 4 are discussed in terms of the flexibility of the intermediate colli-sion complex in each reaction and the energy randomization rate of the initial local excitation of vibrations in the complex.

 

Experimental

Pulsed production of O(1D2) was accomplished using Nd:YAG laser (Spectra Physics, DCR-11) with photodis-sociation of O3 at 266 nm. The OH(X2П, υ", N", f ", λ") products were monitored by LIF using the (0,0) and (1,1) bands of the A2Σ-X2П transitions in the 306-324 nm region. The Nd:YAG (Spectra Physics GCR-150)-pumped dye laser (Lumonics HD500) used to excite the A2Σ-X2П transition was fired approximately 100 ns after the photolysis laser. Under typical experimental conditions (PRH = 50 mTorr, PO3, = 10 mTorr, PHe = 90 mTorr), an OH molecule undergoes an average of ~0.5 gas kinetic collisions in that time.

The fluorescence of A2Σ, υ′ = 0, 1 → X2П, υ" = 0, l near 310 nm was observed with a filtered (UG11) high-gain photomultiplier tube (PMT; Hamamatsu, R2059). The ex-citation laser power was kept as low as possible to prevent saturation. Variations in photolysis and probe laser signal intensities were monitored continuously, and the LIF signals were corrected accordingly. The electronic signal from the PMT was then sampled with a boxcar (EG&G 4161A, 4121B) and recorded by a laboratory computer system. All equip-ment was controlled and synchronized using the LabVIEW program.

No correction was made for the electronic quenching of the A2Σ state in collisions with RH in the absence of specific information about rotational level-dependent quenching rate constants. Under the present experimental conditions, these corrections were estimated to be relatively small and fall within the limit of experimental error.11,12 The photodis-sociation of O3 at 266 nm produces ~10% of the atomic oxygen in the ground electronic state, O(3PJ), which can have large translational energies. The rate coefficient of the O(3PJ) reaction with hydrocarbon is, however, at most 10−7 that of the O(1D2) reaction at room temperature.13 For this reason, the contribution of O(3PJ) as a source of the OH product was ignored.

All gas solutions were prepared and allowed to mix in a grease-free glass flow-cell through needle valve. The pre-paration and treatment of O3 and He have been previously described.7 Cyclo-C3H6 (Aldrich, 99.9%) and C3H8 (Aldrich, 99.9%) were used as received.

 

Results and Discussion

The LIF spectra observed following reactions 3 and 4 (Figure 1) display the characteristic OH(A2Σ+ ←X2П) transi-tions14 corresponding to the absorption by diatomic mole-cules formed in υ" = 0 and 1. A more extensive population of OH(X2П, υ" = 0) from reaction 3 is clearly seen from Figure 1; the R-band head of the (0,0) band begins at ca. 306 nm and that of the (1,1) band begins at ca. 312 nm. Conver-sion of the measured LIF signal S to the state-resolved OH(X2П) population requires correction for variation in the intensities of both the photolysis and probe lasers, Iphoto and Iprobe, as well as the accurate values of the Einstein coeffi-cients, , for the stimulated absorption. Tabulated values of provided by Crosley were used throughout.15 The linearity of the LIF measurements was confirmed by com-paring the relative intensities of the satellite and main branch transitions that probe the same level of OH(X2П, υ", N", f ", λ").

Figure 1.Merged LIF spectrum of the OH product arising from (upper) O(1D2) + cyclo-C3H6 → OH(X2П) + cyclo-C3H5, (lower) O(1D2) + C3H8 → OH(X2П) + C3H7 obtained under the experimental conditions described in the text.

Figure 2.Micropopulation distributions of the OH products derived from experimental spectrum for O(1D2) + cyclo-C3H6; P11(□ ), P22(■), Q11(○), Q22(●), R11(△), R22(▲).

Micropopulation distributions (population divided by the rotational degeneracy, 2J"+1) for the OH(X2П) product aris-ing from the O(1D2)/cyclo-C3H6 and O(1D2)/C3H8 reactions are displayed in Figure 2 and Figure 3, respectively. On the whole, the results reported previously7 for the internal energy distributions of the OH product following reaction 4 were satisfactorily reproduced. The micropopulation distributions for OH products indicated that the gross features of the OH distributions following reactions 3 and 4 closely resembled each other. Closer inspection of Figure 2 and Figure 3, how-ever, revealed that the rotational distribution of OH(X2П, υ" = 0) from reaction 4 was relatively more relaxed com-pared with that from reaction 3, especially in the low-J region. However, reaction 4 is more exothermic than reaction 3 by as much as ~34 kJ/mol, amounting to ca. 20% of the total exothermicity. This seemingly contradictory observation is reserved for the discussion.

Figure 3.Micropopulation distributions of the OH products derived from experimental spectrum for O(1D2) + C3H8; P11(□ ), P22(■), Q11(○), Q22(●), R11(△), R22(▲).

Spin-orbit coupling produces two fine structure states, f1 and f2, which correspond to X2П3/2 and X2П1/2, respectively. The f1 state is probed by the P11 and Q11 transitions, while the f2 is probed by the P22 and Q22. Analysis of the spectra revealed that the ratio of the fine structure state micro-populations summed over all the accessible rotational levels was about the same within experimental error for the two vibrational states, P(2П3/2)/P(2П1/2) = 1.1 ± 0.11 for OH(X2П, υ" = 1), and 1.3 ± 0.13 for OH(X2П, υ" = 0) (Table 1). Thus, for the reactions examined here, there was no significant difference between the populations of the fine structure levels in υ" = 1, and there was a slight difference favoring the production of the lower level (2П3/2) in υ" = 0. This observation is in contrast to the previously reported pro-nounced preferential population of the lower-lying f1state (about two times larger population) of the OH product produced in the reaction of ground state atomic oxygen (O(3PJ)) with hydrocarbons,16 a reaction that is known to proceed via a direct abstraction mechanism.

Two Λ-doublet fine structure states arise from orbital and rotational angular momenta coupling, namely П(A′) and П(A"). The former corresponds to the orientation of the half-filled π orbital in the plane of the OH rotation in the limit of high rotational states, while the latter corresponds to the orientation perpendicular to that plane. Preferential produc-tion of П(A′) in the O(lD2)/H2 reaction, for example, has been ascribed to the establishment of oriented product rotation during the dissociation of the planar HOH intermediate complex.17 Direct abstractions, on the other hand, do not result in the preferential formation of either Λ-doublet state.

Figure 4.Dependence of Λ-doublet population ratios P(A′)/P(A") upon rotational state in (upper) OH(X2П, υ" = 0) from O(1D2) + cyclo-C3H6, and (lower) OH(X2П, υ" = 0) from O(1D2) + C3H8; P11/Q11 (□ ), R11/Q11 (△), P22/Q22 (■), R22/Q22 (▲).

The OH formed in reaction 3 displayed a characteristic propensity for the production of the П(A′) Λ-doublet sub-level, as observed in the OH product of reaction 4 (Figure 2 and Figure 3). The values of П(A′)/П(A") in Table 1 were estimated by averaging over all the observed J levels. This ratio is known to increase as J increases.18 Dependence of the Λ-doublet population ratios P(A′)/P(A") on the rotational state in OH(X2П, υ" = 0) are plotted in Figure 4. Preferential population of the П(A′) state observed in reaction 3 demon-strates that the half-filled π orbital of the OH radical lies preferentially oriented in its rotational plane.3 This, in turn, implies that OH production results from the dissociation of a cyclo-C3H5OH† complex, with the nascent π orbital remain-ing in the plane containing the C–O bond.

It has been reported that in the reaction of O(lD2) with CH4, C2H6, C3H8, and C(CH3)4, the degree of preferential orientation of OH in the plane of product rotation depends on the size of the substrate.7 The population ratio of P[П(A′)]/P[П(A")] revealed that the OH produced from the O(lD2)/CH4 reaction displayed the greatest preference, while that from O(lD2)/C(CH3)4 showed the least. That seems reason-able in view of the increasing complexity of the ROH† inter-mediate arising from the O(lD2) insertion into larger substrates and hence, the more poorly defined plane of dissociation. Increased Λ-doublet selectivity of the OH from reaction 3 compared with that from reaction 4 (Table 1) may reflect the strengthening of this planarity constraint in the cyclo-C3H5OH complex due to the planar geometry of the cyclopropane moiety. The evidence presented here certainly suggests that the reaction, O(lD2)/cyclo-C3H6 or O(lD2)/C3H8, is dominated by a mechanism in which O(lD2) inserts into a C–H bond to yield a chemically activated alcohol as typified in reaction 2, which then dissociates to yield either OH or a pair of frag-ments that could not be detected in the present experiments. The reaction of C–C rupture is heavily favored because the C–C bond is weaker than the C-O bond by ~25 kJ/mol.

Vibrational populations are estimated by summing over the observed rotational distributions in each vibrational level. Due to the predissociation at higher rotational levels (J′ > 22.5 and 13.5 at υ′ = 0 and 1, respectively) of the OH A2Σ+ caused by the crossing of the 4Σ− state, populations of the highest rotational levels were estimated by extrapolating the linear rotational surprisals up to the thermochemical limit of the reaction. To calculate the rotational surprisals, I( fr|fυ) = –ln[P( fr|fυ)/P0(fr| fυ)], statistical prior distributions of the OH products, P0(fr| fυ), were obtained using the method presented elsewhere.7 Table 1 reveals that, despite the higher reaction exothermicity, reaction 4 exhibits a cooler vibrational distribution (P(υ" = l)/P(υ" = 0) = 0.22) compared to reaction 3 (P(υ" = l)/P(υ" = 0) = 0.30) (vide infra).

The rotational surprisals presented in Figure 5 and Figure 6 vividly demonstrate the bimodal character in the rotational distributions characterizing the OH(X2П) product of the O(lD2) reaction with C3H8 and cyclo-C3H6, especially in the ground vibrational state. It has been reported7 that rotational surprisals for the reaction of O(lD2) with heavier hydro-carbons, i.e., C2H6, C3H8, and C(CH3)4, exhibit significant nonlinearities in the lower vibrational levels, which agrees with our results. The bimodal rotational surprisals, which can be deconvoluted into two apparently linear unimodal components, i.e., high-J and low-J components, strongly imply that both reactions produce the OH product in its lower vibrational levels via two distinct channels.7

Table 1.Observed OH population distributions following the reaction of O(1D2) with cyclo-C3H6 and C3H8

The higher-lying rotational levels with positive slopes, dI(fr|fυ)/dgR where gR =fr/(1 − fυ), indicate a much higher production of the rotational levels in the high-J component of the distribution than statistically expected. Such values are often associated with products formed in the dissociation of highly energized intermediates like HOH† in the reaction of O(lD2) with H2, and reflect the effective conversion of R–O–H bending of the highly energized collision complex into OH rotation. That, in turn, suggests that the high-J compo-nent may arise from the dissociation of an ROH† intermediate prior to the equilibration of available reaction exoergicity in that complex through intramolecular energy transfer among available modes. On the other hand, the low-J component, which nearly vanishes in the rotational distribution of OH above υ" = l as reported in previous work,7 appears to be nearly thermal in nature. In the case of a relatively large substrate, the resulting collision complex, ROH†, would be expected to be long-lived and the available reaction exoergi-city would be randomized as to preclude the vibrational excitation of the OH product following dissociation. This intuitive view supports the lack of significant vibrational excitation of OH following the reaction of O(lD2) with large alkanes, as well as the much cooler rotational distribution of OH in its ground vibrational level.

Figure 5.Rotational surprisals of OH(X2П, υ") produced from the O(1D2)/cyclo-C3H6 reaction that have been derived from the statistical prior [P0(fr|fυ)] and the experimental distributions displayed in Figure 2, with the abscissa defined as gR = fr/(1 − fυ); P11(□), P22 (■), Q11(○), Q22(●), R11(△), R22(▲).

Figure 6.Rotational surprisals of OH(X2П, υ") produced from the O(1D2)/C3H8 reaction that have been derived from the statistical prior [P0(fr|fυ)] and the experimental distributions displayed in Figure 3, with the abscissa defined as gR = fr/(1 − fυ); P11(□), P22 (■), Q11(○), Q22(●), R11(△), R22(▲).

The evidence presented thus far certainly suggests that the O(lD2)/cyclo-C3H6 or O(lD2)/C3H8 reaction is dominated by a mechanism in which O(lD2) inserts into a C–H bond to yield a chemically activated alcohol, which then dissociates to yield OH. The bimodal rotational product population distribution provides significant support for the existence of two parallel mechanisms for the OH product, which is in accord with Stephenson’s mechanisms mentioned in the previous section; i.e., statistical insertion and nonstatistical insertion.8

As pointed out previously, the micropopulations in Figure 2 and Figure 3 show that the rotational distribution of OH(X2П, υ" = 0) following reaction 4 is cooler than that following reaction 3, especially at lower-lying rotational levels. The difference in the rotational distributions of OH between the two reactions can be seen more vividly in Figure 7, where relative rotational populations of OH(X2П, υ" = 0) following both reactions are plotted as a function of rotational quantum number, N", and spin-orbit states, f1 and f2. The rotational degeneracy, 2J" + 1, is counted to estimate the population, and the total population of OH(X2П, υ" = 0) for each reac-tion is normalized for comparison. Despite the higher exo-thermicity of reaction 4 (~34 kJ/mol), the rotational di-stribution of OH(X2П, υ" = 0) following reaction 4 shows a more pronounced rotational relaxation compared with that following reaction 3. The reaction exothermicity and maxi-mum collision energy available for each reaction are pre-sented in Table 2. Collision energies for both reactions are estimated to be similar, since the mass difference between C3H8 and cyclo-C3H6 is only two amu.

According to previous discussions, the low-J component of OH, especially in its lowest vibrational level, is produced from the collision complex ROH† that is sufficiently long-lived to ensure the equilibration of the reaction exoergicity prior to dissociation, or intramolecular vibrational relaxation (IVR). Then, this argument strongly implies that the rate of intramolecular vibrational relaxation of cyclo-C3H5OH† is slower than that of n-C3H7OH† or i-C3H7OH†, which, in turn, indicates that cyclo-C3H5OH† has a longer lifetime, at least in the context of IVR.

Table 2.Reaction exothermicity and maximum collision energy available for the reaction: O(1D2) + RH → OH(X2П) +R

Figure 7.Relative rotational populations of the OH(X2П, υ" = 0) products as a function of rotational quantum number, N", and spin-orbit state, f1 (solid) and f2 (shaded); (upper) O(1D2) + cyclo-C3H6; (lower) O(1D2) + C3H8. The total population of OH(X2П, υ" = 0) for each reaction is normalized for comparison.

Even though IVR is conceptually very simple, experimental and theoretical efforts are still in progress to understand and predict IVR phenomena. However, empirical evidence has shown that molecular flexibility plays an important role in accelerating IVR through large-amplitude vibrational modes.19,20 Large-amplitude methyl rotor motion and other large-amplitude torsional modes, such as around single C–O and C–C bonds, are known to enhance IVR. Furthermore, it has been pointed out that molecular flexibility can give rise to substantial low- and high-order couplings that may enhance the rate of intramolecular relaxation.

Significant evidence has been accumulated regarding the accelerating effect of a single methyl rotor substituent on IVR, and one example includes a study of the IVR rate of C–H stretching by comparing p-fluorotoluene and p-difluoro-benzene.21 The results indicated a remarkable increase in IVR rates upon methyl group substitution. The coupling between methyl rotation and low-frequency ring modes is known to be important for the promotion of the vibrational state mixing.22,23 Moreover, aliphatic methyl internal rotation in combination with another large-amplitude modes, may play a role in enhancing IVR even if, by itself, it is generally less effective than other types of molecular flexibility. For skeletal torsion as an IVR accelerator, the effects of centers of flexibility (COF) on IVR state mixing have been reported. A particularly relevant example of this effect was published using comparative studies of 1-butene and trans-2-butene.24 Both species are isomeric and have the same vibrational degrees of freedom. The structural difference between these two molecules is that the carbon chain in 1-butene is floppy with a low barrier to C–C–C torsional isomerization, whereas trans-2-butene is essentially rigid due to the central double bond. This modification resulted in a dramatic change in their high-resolution jet-cooled spectra. The presence of a low-barrier C–C–C torsional mode in floppy 1-butene was interpreted to bring about rotationally induced IVR state mixing not present in rigid trans-2-butene. In other words, the proximity of a prepared C–H vibration to a center of flexibility is associated with accelerated IVR.

Even though the experimental evidence regarding IVR rates discussed above were obtained primarily from CH- or OH-stretch IVR dynamics, this simple picture can potentially be applied to collision complexes presented in this work. Initial local vibrational excitation of the collision complex caused by the insertion of O(lD2) into a C–H bond may comprise the R–O–H bending and OH-stretching motions, which, in turn, are converted to the rotational and vibrational excitation of OH diatomic products following dissociation. The structural difference between the insertion complexes studied in this work is essentially the same as the case of 1-butene and trans-2-butene mentioned above. The insertion of O(lD2) into a C–H bond in reaction 4 can produce two isomers, namely n-C3H7OH and i-C3H7OH. The carbon chain in n-C3H7OH is floppy with a low barrier to C–C–C torsional isomerization, whereas the framework of cyclo-C3H5OH produced from reaction 3 is essentially rigid due to the strictly planar character of the cyclopropyl ring. On the other hand, the main structural difference between i-C3H7OH (reaction 4) and cyclo-C3H5OH (reaction 3) is two additional methyl rotors in i-C3H7OH, which may also play an additional role in enhancing IVR. Less vibrational excitation of OH following reaction 4 (P(υ" = l)/P(υ" = 0) = 0.22) than that following reaction 3 (P(υ" = l)/P(υ" = 0) = 0.30) despite the higher exothermicity could also be interpreted as faster IVR in intermediate insertion complexes in reaction 4.

 

Conclusion

The present work reports the OH(X2Π, υ" = 0, 1) internal state distributions following the reaction of O(1D2) with cyclo-C3H6 and C3H8 using LIF. Both reactions showed qualitatively similar internal energy distributions for the OH products as expected. The propensity for the population of the П(A′) Λ-doublet sublevel suggests that the O(lD2)/cyclo-C3H6 or C3H8 reaction is dominated by a mechanism in which O(lD2) inserts into a C–H bond to yield a chemically activated alcohol, which then dissociates to yield OH. Bi-modal rotational distributions support the existence of two parallel mechanisms for OH production. One mechanism is statistical insertion, i.e., sufficiently long lifetime of the intermediate ROH† for complete IVR, and the other is nonstatistical insertion, i.e., insufficient lifetime for complete IVR. As pointed out in the introduction, the present work was designed to elucidate the effect of the flexibility of the substrate on the internal energy distributions of the diatomic OH product. Despite the higher exothermicity of the reac-tion, the rotational and vibrational distributions of OH follow-ing the reaction of O(1D2) with C3H8 were significantly cooler than those with cyclo-C3H6. This experimental observation was interpreted as the acceleration of IVR due to the pre-sence of large-amplitude modes in the complexes, i.e., the C–C–C skeletal and methyl torsions in the insertion complexes intermediating the O(1D2)/C3H8 reaction.