ASTROPHYSICAL THE JOURNAL, 513 : 287293, 1999 March 1
( 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.
NEW H AND H REACTIONS WITH SMALL HYDROCARBON IONS AND THEIR ROLES IN BENZENE 2 SYNTHESIS IN DENSE INTERSTELLAR CLOUDS MURRAY J. MCEWAN AND GRAHAM B. I. SCOTT
Department of Chemistry, University of Canterbury, Christchurch, New Zealand ; m.mcewan=chem.canterbury.ac.nz
NIGEL G. ADAMS AND LUCIA M. BABCOCK
Department of Chemistry, University of Georgia, Athens, GA 30602-2556
R. TERZIEVA
Department of Chemistry and Chemical Physics Program, Ohio State University, Columbus, OH 43210-1106
AND ERIC HERBST
Departments of Physics and Astronomy, Ohio State University, Columbus, OH 43210-1106 ; herbst=mps.ohio-state.edu Received 1998 September 2 ; accepted 1998 October 8
ABSTRACT This paper summarizes the most recent knowledge concerning normal and three-body association ionmolecule reactions between small hydrocarbon ions (C H` ; m \ 16, n \ 09) and the neutral reactants m n H and H . Selected radiative association reaction rate coefficients have been calculated and estimated 2three-body laboratory results. Some of the normal and radiative association rate coefficients based on have been incorporated into our new standard model of dense cloud interstellar chemistry. We nd that atomic H provides an insufficiently appreciated mechanism to increase the level of saturation of C H` ions, with m [ 3 in dense interstellar clouds despite the fact that the H/H abundance ratio is m 2 only n10~4. New model results show in particular that a signicant abundance of the basic aromatic cyclic molecule benzene (c-C H ) can now be produced in dense clouds. 6 6 Subject headings : ISM : clouds molecular processes
1.
INTRODUCTION
Plausible mechanisms for converting molecular hydrogen and atomic carbon in interstellar clouds into hydrocarbon molecules via sequences of ion-neutral reactions have been proposed (Herbst, Adams, & Smith 1983, 1984 ; Smith 1992 ; Dalgarno & Fox 1994 ; Herbst 1995). These mechanisms have been incorporated into gas-phase chemical models (Lee, Bettens, & Herbst 1996 ; Millar, Farquhar, & Willacy 1997). The route to CH is initiated via equations (1) and 4 (2) : C` ] H ] CH` ] hl , (1) 2 2 H` ] C ] CH` ] H . (2) 3 2 Ensuing reactions of CH`, CH`, and CH` with H , fol2 3 2 lowed by dissociative recombination or proton transfer, result in the formation of CH (Herbst 1995). Once methane 4 is made, subsequent C` insertion reactions, condensation reactions, and association reactions take place, which generate larger hydrocarbons (Herbst et al. 1983, 1984 ; Hansel et al. 1989 ; Smith 1992 ; Dalgarno & Fox 1994), viz., C` ] CH ] C H` ] H (0.28) ; 4 2 2 2 ] C H` ] H (0.72) , 2 3 C H` ] H ] C H` ] hl , 2 2 2 2 4 CH` ] CH ] C H` ] H , 3 4 2 5 2 C` ] C H ] C H` ] H , 2 2 3 C` ] C H ] C H` ] H (0.50) ; 4 2 5 ] C H` ] C (0.45) . 4 2 (3a) (3b) (4) (5) (6) (7a) (7b) 287
A summary of some of the reaction sequences proposed by various workers for the production of hydrocarbons in dense interstellar clouds (including some to be proposed here) is shown in Figure 1. In addition to the ion-neutral reactions shown, there is also an accompanying neutral chemistry (Bettens, Lee, & Herbst 1995 ; Brownsword et al. 1997). Dense interstellar gas consists mainly of molecular hydrogen, and thus it might be anticipated that unsaturated (hydrogen poor) hydrocarbon ions would successively add H from H in a hydrogen-rich environment, either via 2 H-atom abstraction reactions (HAARs) or association reactions, leaving the bulk of interstellar hydrocarbon ions in a relatively saturated (hydrogen rich) form. Laboratory investigations of the reactions of several C H` (2 m 6) m n unsaturated hydrocarbon ions with H (Scott et al. 1997) 2 al. 1989 ; Giles, coupled with existing data (Hansel et Adams, & Smith 1989) show, however, that hydrogenation via H reactions proceeds efficiently only for those ions 2 having n 2 (see Table 1). The result is that models predict the gas to consist mainly of unsaturated hydrocarbons (Lee et al. 1996). When hydrocarbon ionH reactions become unfavor2 able on thermodynamic grounds or, alternatively, possess substantial activation barriers (Fairley et al. 1998), then H-atom reactions may circumvent the existing bottlenecks to hydrogenation via H chemistry. The atomic hydrogen 2 to molecular hydrogen abundance ratio in dense interstellar clouds is predicted to be 10~4. This fractional abundance is comparable to that of other abundant atoms, so that such reactions can be important if their rate coefficients are large. Consider, for example, a hydrocarbon ion that reacts with atomic hydrogen with a rate coefficient of 10~9 cm3 s~1 (the standard Langevin value) and combines with electrons with
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FIG. 1.Initial sequences of some ion-neutral reactions leading to the production of hydrocarbons in the interstellar medium. The species in boxes have been observed, and the species in circles are inferred. A new synthesis of benzene (c-C H ) proposed here is included. 6 6
a dissociative recombination rate coefficient of 10~6 cm3 s~1 (a typical value). If the fractional ionization is 10~7, the two reaction rates (reaction with H and recombination with electrons) are equal. Despite this analysis, the role of atomic hydrogen reactions in models of dense clouds has not been fully considered, possibly because hydrogenation can only occur via association, and association reactions typically occur at much lower rate coefficients than the Langevin value. Recently an extensive set of C H` /H atom reactions was m reported (Scott et al. 1997) ; this isn integrated with existing reaction information on C H` ions in Table 2 (the compam n rable data for molecular hydrogen are shown in Table 1).
2.
HYDROGENATION WITH H2 AND H
Reference to Table 1 conrms that it is not easy to hydrogenate ions even when H is in great excess, because the two 2 reaction mechanisms capable of increasing the level of saturation in an H atmosphereHAARs and associationdo 2 not occur for most hydrocarbon ions. Note that the association results reported here are from high-pressure selected ion ow tube (SIFT) measurements such that the stabilization mechanism is collisional rather than radiative. Determination of the rate coefficient for the radiative mechanism, which pertains to the interstellar medium, must be obtained by simple (and often inaccurate) conversion of the threebody results or by detailed theory, which can be partially
tested at high pressures (Bates & Herbst 1988). Of the known association reactions, those involving CH`, C H`, 3 2 2 and C H` have also been studied in the laboratory at low 3 densities, where the radiative stabilization mechanism dominates (Gerlich & Horning 1992), and at temperatures below 300 K, where the rate is sizeable. The other H 2 association reactions tabulated here involve the ions C` 6 and c-C H`, where c refers to a cyclic structure. Recent 6 5 measurements of still larger cyclic cations (c-C H`, 10 n n \ 69 ; Le Page et al. 1997) show that association with H 2 also occurs for c-C H`. 10 7 of atomic hydrogen inuence the How does the presence extent of hydrogenation ? Table 2 indicates that H atoms present a noticeably dierent behavior in their reactions with C H` ions than does molecular hydrogen. m n First, from Table 2 we note that C H` ions react with H m n atoms mainly by H-atom transfer or by association via a third body, M : C H` ] H ] C H` ] H (H-atom transfer) , (8) 2 3 2 2 2 C H` ] H ] M ] C H` ] M (association) . (9) 2 2 2 3 In an H-atom transfer reaction, n is reduced to n [ 1, whereas in an association reaction, n is increased to n ] 1. Second, from Table 2 we note that in contrast to the reactions with H summarized in Table 1, the C H` ion m n reactions with H2show quite dierent trends. Ions having low values of n (n \ 03) do not react efficiently with H by
TABLE 1 COMPILATION OF EXISTING DATA FOR C H` ] H REACTIONS AT 300 ^ 5 Ka m n 2 n\1 n\2 n\3 n\4 n\5 n\6 n\7 n\8 n\9
C H` . . . . m n m\1......
n\0
m\2......
m\3......
m\4......
m\5......
m\6......
CH` 1.2 ] 10~7 C H` 2 1.1 C H` 3 0.24 C H` 4 0.13 C H` 5 0.62 C H`, C H` 6 6 2 0.27i
CH` 2 1.2 C H` 2 2 1.1 C H`, C H` 3 2 3 3 2.6 ] 10~2 b C H` 4 2 0.165 ... ... C H` 6 2 1.3 ] 10~3 ... ... ... \4 ] 10~5 ... \5 ] 10~4 d ... \3 ] 10~3 g ... ... C H` 6 7 3.8 ] 10~2 k ... ... ... \1 ] 10~2 ... ... ... \4 ] 10~3 g ... ... ... \5 ] 10~3 l
CH` 3 1.2 C H` 2 3 1 ] 10~2 ... \5 ] 10~5 ... \4 ] 10~3 f ... ... ... ...
CH` 5 \5 ] 10~4 ... \5 ] 10~3 ... \5 ] 10~3 ... \2 ] 10~3 f ... ... ... ...
CH` 5 3.5 ] 10~2 ... \4 ] 10~5 ... \5 ] 10~3 c ... \3 ] 10~3 f ... ... ... \5 ] 10~4 j
... ... ... ... ... \5 ] 10~3 e ... ... ... ... ... ...
... ... ... ... ... ... ... \5 ] 10~4 h ... ... ... ...
... ... ... ... ... ... ... \5 ] 10~4 h ... ... ... ...
a Product ions and rate coefficients in units of 10~9 cm3 s~1 are shown. b Product distribution : c-C H` (4%), ac-C H` (16%), c-C H` (52%), and ac-C H` (28%). 3 2 3 2 3 3 3 3 c C H` from allene and propyne. 3 H4 from electron impact on C H . dC ` 3 5 2 4 e C H` from 1-bromopropane and 2-bromopropane. 7 f C 3H`, C H`, and C H` from electron impact on C H . 4 2 4 3 4 4 2 2 g C H`, C H` from 1, 3-butadiene. 4 H5 C4 H6 from 2-butene. h C `, ` 4 8 4 9 i C H` (20%), C H` (80%). 6 H`, \3 ] 10~3 for c-C H`. 6 2 j ac-C 6 4 6 4 k c-C H` ; \1 ] 10~3 for ac-C H`. 6 5 6 5 l C H` from benzene. 6 6
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TABLE 2 COMPILATION OF NEW AND EXISTING DATA FOR C H` ] H ATOM REACTIONS AT 300 ^ 5 Ka m n
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C H` . . . . . . m n m\1 ...... m\2...... m\3...... m\4...... m\5...... m\6......
n\0
n\1
n\2 ... ... C H` 2 3 7 ] 10~27 b C H`, C H` d 3 3 3 C H` 4 3 3 ] 10~26 h ... ... ...
n\3 ... \1 ] 10~2 C H` 2 2 6.8 ] 10~2 ... \3 ] 10~3 g C H` 4 4 5 ] 10~27 h ... ... ...
n\4
n\5
n\6 ... ... C H` 2 5 0.10 ... ... productsi 0.19 C H`, C H` k 6 5 6 7 0.21k
n\7 ... ... ... ... C H` 3 6 0.032 ... ... ... ... ...
n\8 ... ... ... ... ... ... C H` 4 7 0.11 ... ... ...
n\9 ... ... ... ... ... ... ... \0.02 ... ... ...
... C` ... 0.75 ... ... \0.1 \0.1 C H` C H` c 3 3 2 \7 ] 10~28 f 2 ] 10~26 c ... C H` 4 2 ... 6 ] 10~26 h ... ... ... ... ... ...
... CH` 4 \1 ] 10~2 0.15 C H` C H` 2 3 2 4 0.3 D1 ] 10~2 C H` e C H` 3 3 3 6 0.3e [2 ] 10~26 h ... ... ... \0.04 ... ... C H` j ... 6 5 3 ] 10~27 \1 ] 10~2 l
a Product ions and rate coefficients in units of 10~9 cm3 s~1 are shown unless specied otherwise. b k [ 7 ] 10~27 cm6 s~1. This is the termolecular rate coefficient for a helium bath gas. c Linear and cyclic product ions are formed from l-C H`. The linear C H` ion is the major product. The termolecular rate coefficient is k \ 2 ] 10~26 3 3 2 cm6 s~1 for a helium bath gas. d There are two product ions in this reaction ; see, e.g., Scott et al. 1997, Hansel et al. 1989. l-C H` reacts via a bimolecular process to give l-C H` (60%, 3 2 k \ 6 ] 10~11 cm3 s~1), and 40% of the products are formed in a termolecular process, giving both l-C H` and c-C H`. The termolecular rate3coefficient 3 3 3 3 (M \ He) is k \ 4 ] 10~27 cm6 s~1. e Isomeric structure of C H` product was not determined. The rate coefficients are k \ 3.0 ] 10~10 cm3 s~1 for C H` from HCCCH (propyne) and 3 3 3 4 3 k \ 1.7 ] 10~10 for C H` from H CCCH (allene). 3 4 2 2 f k \ 7 ] 10~28 cm6 s~1. This is the termolecular rate coefficient for a helium bath gas ; linear and cyclic C H` product ions are formed. 3 g No reaction observed from either c-C H` or ac-C H`. 3 3 3 3 h The rate coefficient shown is the termolecular association rate coefficient for a helium bath gas. i The reaction is dissociative. The product distribution is C H` ] C H (D15%) ; C H` ] C H (D65%) ; C H` ] H (D20%). 2 3 4 2 2 2 j The rate coefficient shown is the termolecular association rate2 coefficient (M 2 He) for the reaction 4 5 \5 of c-C H`. The ac-C H` does not react 6 4 6 4 (k \ 5 ] 10~12 cm3 s~1). k The C H` ion is the benzene c-C H` ion. The branching ratios are C H` ] H (D35%) and C H` (D65%) at a helium pressure of 0.3 Torr. The rate 6 6 6 6 5 2 6 7 for termolecular association is estimated as k D 1 ] 10~26 cm6 s~1 for a6helium bath gas. l No reaction observed for either ac-C H` (k \ 5 ] 10~12 cm3 s~1) or c-C H` (k \ 1 ] 10~11 cm3 s~1). 6 5 6 5
H-atom transfer (the exception is CH`), but they may react by association. The consequence of these reactions is that many C H` ions that are unreactive in a molecular hydrom n gen environment become reactive in an H-atom environment. However, unless they undergo association, the extent of saturation is not increased.
3.
sonable to assume it will also occur under conditions where radiative stabilization dominates. Once c-C H` is formed, 6 5 equation (12) leads to c-C H`, which in turn can react with 6 7dissociative recombination : electrons to form benzene via c-C H` ] e ] c-C H ] H . (14) 6 7 6 6 Benzene has not previously been included in models of interstellar clouds. We have used two methods to estimate the radiative association rate coefficients for reactions (10)(12). The simpler (but less accurate) of the two methods consists of comparing two approximate formulae for association reactions (Bates & Herbst 1988) : k \ (k /k )k , (15a) 3b 1 ~1 c k \ (k /k )k . (15b) ra 1 ~1 r The rate coefficient for ternary association, k , contains k , 3b 1 the rate coefficient for the formation of a collision complex ; k , the rate coefficient for the dissociation of the collision ~1 complex into reactants ; and k , the rate coefficient for collisional stabilization of the ccomplex by the bath gas (typically helium in laboratory measurements). The radiative association rate coefficient, k , shown in equation ra (15b), contains the radiative stabilization rate coefficient k r rather than the collisional stabilization rate coefficient. Starting from the measured ternary rate, one can then estimate the radiative association rate coefficient at the same temperature by estimating both k and k , typically approxc r imately 10~10 cm3 s~1 and 102 s~1, respectively (Bates & Herbst 1988). The temperature dependence can be approximated from theoretical values for the k /k ratio based on 1 ~1 the modied thermal model of Bates (Bates & Herbst 1988), in which the temperature dependence is T ~R@2, where
RADIATIVE ASSOCIATION CALCULATIONS
Three radiative reactions association not currently included in our dense cloud models and which have the possibility of strongly aecting calculated abundances for selected species are C H` ] H ] C H` ] hl , (10) 4 2 4 3 C H` ] H ] C H` ] hl , (11) 4 3 4 4 c-C H` ] H ] c-C H` ] hl . (12) 6 5 2 6 7 These association reactions have been studied under threebody conditions and are listed in Tables 1 and 2. Reactions (10) and (11) may produce larger abundances of C H` and 4 3 C H` than currently obtained. These species can then be 4 4 converted into cyclic species such as c-C H` by Diels6 5 Aldertype association and normal reactions (Anicich, Huntress, & McEwan 1986 ; Scott et al. 1997) with acetylene (C H ), viz., 2 2 C H` ] C H ] c-C H` ] hl , (13) 4 3 2 2 6 5 and possibly other neutrals such as C H (see Fig. 1). Such 2 3 reactions are already included in our model networks based on experiments at low gas densities (Anicich et al. 1986), although we have not heretofore explicitly considered the possible cyclic nature of the products. Ring closure has occasionally been measured to occur in association reactions under three-body associative conditions, and it is rea-
No. 1, 1999
H AND H REACTIONS 2
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R is the number of rotational modes of the two reactants. Using this method, we obtain the following expressions for the radiative association rate coefficients (cm3 s~1) of reactions (10)(12) : 3 ] 10~14(T /300)~1.0, 5 ] 10~15(T /300)~1.5, and 4 ] 10~15(T /300)~2.0, respectively. At 300 K, these deduced rate coefficients represent (possibly severe) lower limits since the three-body rate coefficients determined in the SIFT apparatus used are themselves lower limits obtained near the so-called saturated regime. Other possible problems with this simple conversion method are (1) the partial rate coefficients in equation (15) are really functions of energy and angular momentum, and an expression involving their ratio, as well as k and k , r c has to be averaged over distributions of these parameters relevant to the collisions being considered (Herbst 1985) ; and (2) the temperature-dependence assumed may be too large since it only pertains to reactions in which the collisional frequency is determined by the Langevin value. From many studies of ion-atom reactions, it is known that these systems seem to have weaker long-range forces than assumed in the Langevin potential [see Table 2, in which the rate coefficients are uniformly somewhat smaller than the Langevin value of (12) ] 10~9 cm3 s~1]. To obtain more accurate values for the radiative association reaction rate coefficients of reactions (10)(12), we have used the detailed phase-space approach (Herbst 1985 ; Bates & Herbst 1988) with molecular data from a variety of sources including the so-called standard hydrocarbon model of Dunbar (see Herbst & Dunbar 1991). We have modeled the relatively weak long-range forces (Klippenstein 1997) with articially small values of the polarizability a (0.04 A3 for H, and 0.001 A3 for H ). An alternative 2 approach, which achieves similar results, is to use a longrange van der Waals potential, as in neutral-neutral systems. Both approaches have the eect of removing relatively high angular momentum partial waves. An even more detailed possibility for handling the dynamics is represented by the exible transition state theory (Holbrook, Pilling, & Robertson 1996), which, however, requires details about the potential surfaces that are not currently available for these systems. Using the phase-space approach, we have been able to reproduce to a reasonable extent the SIFT results for reactions (10)(12). The comparison is best made by utilizing an eective two-body rate coefficient, which consists of the product of the ternary rate coefficients and the gas density (1016 cm~3). We obtain the eective rate coefficients (cm3 s~1) at 300 K for reactions (10)(12) of 5 ] 10~10, 3 ] 10~10, and 6 ] 10~11, respectively, which can be compared with the experimental values of 3 ] 10~10, 5 ] 10~10, and 3.8 ] 10~11. (The experimental values correspond to three-body rate coefficients shown in Tables 1 and 2.) Use of the actual values of the polarizability for H and H leads to Langevin values for the eective rate 2 coefficients, which are too large by factors of 1050. For the case of equation (12), the particularly low yet apparently saturated (or near saturated) experimental value for the eective binary rate coefficient suggests a very weak longrange potential. Whatever strength of the long-range potential we use, however, the calculated two-body association rate coefficient is predicted to lie near the collisional limit at all densities studied for temperatures in the range of 10300 K, whether the stabilization mechanism is collisional or radiative. Indirect corroboration of this theoretical prediction is shown by the experimental results on the association
of the analogous system c-C H` with H , which is found 10 7 2 to have a rate coefficient nearly independent of density at 300 K even though it is considerably below the Langevin limit (LePage et al. 1997). The phase-space calculations show that the calculated radiative association rate coefficients at 300 K are considerably larger than their estimated lower limits found from equations (15a) and (15b), but that the weak long-range forces lead, in general, to much weaker inverse temperature dependencies than those estimated above. These two eects are expected to cancel each other at low temperatures, although the theoretical results are signicantly larger for equations (10) and (12). Our calculated phase-space results for the radiative association rate coefficients (cm3 s~1) are k \ 7 ] 10~11(T /300)~0.1, k \ 6 ] 10~14(T /300)~0.7, 10 11 and k \ 6 ] 10~11 over a temperature range of 10300 12 K. At a temperature of 10 K, as pertains to dark interstellar clouds such as TMC-1, the rate coefficients for all three associations are expected to be large, although they are not at the Langevin level. It is therefore unclear whether they will make a signicant dierence to the chemistry of C H`, 4 2 C H`, and c-C H` ions in dense cloud models. 4 3 6 5
4.
NEW MODEL RESULTS
We have used our new standard model (Bettens et al. 1995) to calculate chemical abundances as a function of time for a cold dense cloud core resembling TMC-1, with a xed gas density n of 2 ] 104 cm~3, a temperature of 10 K, H and low metal elemental abundances (Terzieva & Herbst 1998). The new standard model network consists of approximately 3800 chemical and photochemical reactions involving 400 gas-phase species through 14 atoms in size. The elements included are H, He, C, N, O, Si, S, Fe, Na, Mg, P, and Cl. A complete list of reactions and corresponding rate coefficients can be obtained from the authors. A compendium of calculated chemical abundances as a function of time for assorted physical conditions is contained in Lee et al. (1996). For TMC-1, the calculated abundances are in order-of-magnitude agreement with observed values for up to 80% of the 50 species detected (Terzieva & Herbst 1998). The new standard model reaction network has been augmented for this work by the inclusion of reactions (10)(12) and (14), and a variety of other reactions involving three
FIG. 2.Calculated fractional abundance of benzene (c-C H ) with 6 6 respect to H as a function of time for a dark cloud resembling TMC-1. 2
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TABLE 3 REACTIONS INVOLVING THE NEW SPECIES C H , C H , AND C H` 4 3 6 6 6 7 Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A (cm3 s~1) B Reference
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C` ] C H ] C H` ] H . . . . . . . . . . . . . . . . . 3.10 ] 10~10 [0.5 1 4 3 5 2 C` ] C H ] C H` ] H . . . . . . . . . . . . . . . . 3.10 ] 10~10 [0.5 1 4 3 5 2 C` ] C H ] C H` ] C . . . . . . . . . . . . . . . . . 3.10 ] 10~10 [0.5 1 4 3 4 3 C` ] C H ] C H` ] C H . . . . . . . . . . . . . . 3.10 ] 10~10 [0.5 1 4 3 3 2 2 H` ] C H ] C H` ] H . . . . . . . . . . . . . . . . . 2.00 ] 10~9 [0.5 1 4 3 4 3 H` ] C H ] C H` ] H . . . . . . . . . . . . . . . 2.00 ] 10~9 [0.5 1 4 3 4 2 2 He` ] C H ] C H` ] He ] H . . . . . . . . . 6.70 ] 10~10 [0.5 1 4 3 4 2 He` ] C H ] C H` ] He ] C . . . . . . . . . 6.70 ] 10~10 [0.5 1 4 3 3 3 He` ] C H ] C H` ] CH ] He . . . . . . . 6.70 ] 10~10 [0.5 1 4 3 3 2 He` ] C H ] C H` ] H ] He . . . . . . . . . 7.00 ] 10~10 0.0 1 6 6 6 5 He` ] C H ] C H` ] CH ] He . . . . . . . 7.00 ] 10~10 0.0 1 6 6 5 5 H` ] C H ] C H` ] H . . . . . . . . . . . . . . . . 2.30 ] 10~9 [0.5 1 3 4 3 4 4 2 H` ] C H ] C H` ] H . . . . . . . . . . . . . . . . 3.90 ] 10~9 0.0 2 3 6 6 6 7 2 HCO` ] C H ] C H` ] CO . . . ...