Download Rapid neutral–neutral reactions at low temperatures

Mon. Not. R. Astron. Soc. 350, 323–330 (2004)
doi:10.1111/j.1365-2966.2004.07656.x
Rapid neutral–neutral reactions at low temperatures: a new network
and first results for TMC-1
Ian W. M. Smith,1 Eric Herbst2 and Qiang Chang3
1 School
of Chemistry, The University of Birmingham, Edgbaston, Birmingham B15 2TT
of Physics, Astronomy, and Chemistry, The Ohio State University, Columbus, OH 43210, USA
3 Department of Physics, The Ohio State University, Columbus, OH 43210, USA
2 Departments
Accepted 2004 January 19. Received 2003 December 30; in original form 2003 October 14
ABSTRACT
There is now ample evidence from an assortment of experiments, especially those involving
the CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme) technique, that
a variety of neutral–neutral reactions possess no activation energy barrier and are quite rapid
at very low temperatures. These reactions include both radical–radical systems and, more
surprisingly, systems involving an atom or a radical and one ‘stable’ species. Generalizing
from the small but growing number of systems studied in the laboratory, we estimate reaction
rate coefficients for a larger number of such reactions and include these estimates in a new
network of gas-phase reactions for use in low-temperature interstellar chemistry. Designated
osu.2003, the new network is available on the World Wide Web and will be continually updated.
A table of new results for molecular abundances in the dark cloud TMC-1 (CP) is provided
and compared with results from an older (new standard model; nsm) network.
Key words: molecular processes – ISM: molecules.
1 INTRODUCTION
Many gas-phase reactions involving two neutral species possess
activation energy barriers, and their rate coefficients k are typically
given by the Arrhenius expression (Smith 1980; Herbst 1996):
k(T ) = A(T ) exp(−E a /T )
(1)
where T is the temperature, E a is the activation energy in K, and
A(T ) (cm3 s−1 ) is a weakly temperature-dependent term known as
the pre-exponential factor. Reactions that possess barriers greater
than 1000 K can for the most part be excluded from gas-phase reaction networks that represent the low-temperature chemistry in
both dense and diffuse interstellar clouds (Herbst & Klemperer
1973). Unlike the case for neutral reactions, most studied exothermic ion–molecule reactions do not possess activation energy barriers
(Anicich & Huntress 1986; Rowe 1988), and these reactions have
dominated chemical networks for low-temperature regions (Le
Bourlot et al. 1995; Terzieva & Herbst 1998; Le Teuff, Millar &
Markwick 1999; Tiné et al. 2000; Viti et al. 2001). Not all neutral
reactions, however, have non-zero barriers. It has been known for
many years (Smith 1980) that atom–radical and radical–radical processes, where a radical is defined as a species with an odd number of
electrons, occur rapidly with E a = 0 and a pre-exponential factor approaching the so-called collision limit. Such neutral reactions have
been included in interstellar reaction networks (Terzieva & Herbst
E-mail: [email protected]
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2004 RAS
1998; Le Teuff et al. 1999). In the absence of experimental evidence
at low temperatures, however, it has often been assumed for these
reactions that the reaction rate coefficient k can be approximated by
the hard-sphere relation (Smith 1980)
k(T ) = A(T ) = k(300 K)(T /300)0.5
(2)
where the temperature dependence stems from the average thermal
velocity of the reactants, and a typical value for the rate coefficient at
room temperature, which is related to the size of the reactants, is 1.0–
3.0 × 10−11 cm3 s−1 . With such an assumption, the rate coefficients
are considerably smaller for a 10-K cloud.
This picture of low-temperature interstellar chemistry has been
changing over the last decade, as experimental and theoretical
probes of neutral–neutral chemistry have radically altered our understanding in several ways. First, experiments at and around room
temperature have shown that some atoms, especially atomic carbon, and radicals such as CH, CN and CCH can react rapidly
(E a = 0) with a wide variety of unsaturated (hydrogen-poor) hydrocarbons and other supposedly ‘stable’ species (Husain 1993),
and therefore might be rapid at very low temperatures. Second,
crossed-beam experiments at both variable low collision energies
(Naulin & Costes 1999; Chastaing et al. 2000a; Geppert et al. 2000;
Geppert, Naulin & Costes 2001; Cartechini et al. 2002) and fixed
collision energies (Kaiser et al. 1998, 2000; Cartechini et al. 2002),
often in conjunction with ab initio quantum chemical calculations,
have confirmed that the neutral–neutral reactions have zero threshold energy and proceed via strongly bound energized complexes.
Moreover, the experiments can, in favourable cases, identify the
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I. W. M. Smith, E. Herbst and Q. Chang
reaction products. Finally, and of most direct relevance to the matters considered in the present paper, experimental studies down to
low ( 220 K) and very low ( 77 K) temperatures, the latter
undertaken mainly with the CRESU apparatus (a French acronym
for Cinétique de Réaction en Ecoulement Supersonique Uniforme),
have indicated that the temperature dependence of the rate coefficients for many neutral–neutral systems is definitely not given by
equation (2) (Rowe, Canosa & Sims 1993; Sims & Smith 1995;
Smith 1997; Chastaing et al. 1998; Rowe, Rebrion-Rowe & Canosa
2000; Chastaing et al. 2001). Instead, the reactions have been found
to have little temperature dependence or become slightly more rapid
as the temperature is decreased, and their rate coefficients can often
be fit to a weak inverse power law in temperature. Reaction rate
coefficients at temperatures below 50 K can approach a size (
10−10 cm3 s−1 ) comparable with those for reactions between ions
and non-polar neutral species. Taken together, the evidence from
these studies suggests that bimolecular reactions involving atoms or
radicals that have rate coefficients within a factor of about 10 of the
collisional value at room temperature are likely to remain equally
fast, or increase at low temperatures.
In applying and generalizing these results to astrochemical networks, some caution is in order. It is certainly true that large networks of exothermic ion–molecule reactions were built up based on
much smaller amounts of laboratory data, yet ion–molecule reactions tend to be rather regular. Their rates are normally governed
by so-called capture theories involving long-range potentials only
(Smith 1980; Clary, Stoecklin & Wickham 1993; Herbst 1996). For
ion–molecule reactions with non-polar neutral reactants, the capture
result leads to a very simple temperature-independent form first derived by Langevin (Smith 1980; Herbst 1996):
k(T ) = A(T ) = 2πe
α/µ,
(3)
where (in c.g.s.-e.s.u. units) e is the electronic charge, µ is the reduced mass, and α is the polarizability of the neutral species. Typical values for the parameters yield a rate coefficient on the order
of 10−9 cm3 s−1 , which is almost always in reasonable agreement
with experiment. Although capture theories for reactions involving polar neutral reactants are more complex, they tend to correctly reproduce an inverse temperature dependence for the rate
coefficient which, for example, goes as T −1/2 for a charge-dipole
potential (Adams, Smith & Clary 1985; Clary 1988). Moreover,
the exothermic pathways lead to sets of products which can often be guessed at successfully based on analogous systems studied
experimentally.
The favourable conditions for the construction of large networks
of ion–molecule reactions do not exist to the same extent for neutral–
neutral reactions. The number of systems measured down to low
temperatures is still quite small. Only those neutral reactions with
E a = 0 have rates conceivably governed by the long-range part of
the intermolecular potential, and this potential is both less strong
and more dependent on the physical and chemical nature of the
reagents than for ion–molecule systems. For these systems, capture
theories are generally less reliable than for ion–molecule processes
(Clary et al. 1993, 1994; Herbst & Woon 1997; Dashevsakaya et al.
2003). Transition state theories have also been applied to neutral–
neutral systems without activation energy (Georgievskii & Klippenstein 2003), but not to our knowledge at very low temperatures. A
more detailed quantum mechanical treatment has shown success for
the reaction between C and C 2 H 2 (Clary et al. 2002) over a wide
range of temperature, but it is not feasible to attempt such a treatment
for large numbers of reactions. Moreover, trying to make analogies
between studied and unstudied systems is not always facile. Anal-
ogous but unstudied neutral reactions, which might appear similar
to systems with E a = 0, can be governed by short-range potential
barriers. For example, both neutral C and O atoms lie in the same
ground electronic state: 3 P. Yet, while C is quite reactive, experimental studies show that O is relatively unreactive with non-radicals
even at room temperature (Baulch et al. 1992). As another example,
although the radical C 2 H is reactive with unsaturated hydrocarbons
down to low temperatures (Chastaing et al. 1998), it definitely does
not react with HCN because of a barrier (Fukuzawa & Osamura
1997). Even in the absence of activation energy, the inverse temperature dependence detected for rapid neutral–neutral reactions is not
exactly the same from one system to another, and may not hold over
the whole 10–300 K range (Canosa et al. 1997). Finally, the product
channels can be tricky to elucidate unless only one is exothermic in
nature (Cartechini et al. 2002; Clary et al. 2002) since the CRESU
technique does not yield information about the products of reaction.
Previous attempts to incorporate a significant number of rapid
neutral–neutral reactions into interstellar networks by changing earlier estimated rates and adding new reactions were made by Herbst
et al. (1994) and Bettens, Lee & Herbst (1995), the latter referring to their network as the ‘new neutral–neutral model (nnnm)’.
In these networks, the small number of low-temperature studies
then extant was generalized based on the chemical intuition of
the authors. In general, the models failed to produce sufficiently
large abundances of organic molecules to explain observations in
the well-studied source TMC-1. Although it was later shown that
some of the discrepancies with observation could be removed by
altering the carbon and oxygen elemental abundances (Terzieva &
Herbst 1998), the nnnm has not been used extensively either by
its originators or by the community at large, nor have less extensive modifications proven popular. Indeed, most astrochemists use
the assorted UMIST (University of Manchester Institute of Science
and Technology) files (Millar, Farquhar & Willacy 1997; Le Teuff
et al. 1999), while a smaller number use the so-called ‘new standard
model (nsm)’ (Terzieva & Herbst 1998); in neither case are many
rapid neutral–neutral reactions presumed to occur unless specifically
studied.
In this paper, we introduce a new network of gas-phase reactions
for use in interstellar chemistry. The network is based on the most
recent version of the new standard model (nsm), but differs from
it in several ways. First, as part of a general updating of rate coefficients, we have removed the hard-sphere approximation from
unstudied reactions already in the network (equation 2) and replaced it with more modern estimates. Secondly, we have added
new rapid neutral reactions based on those in the nnnm (Bettens
et al. 1995), but with the advantage of more experimental data
and chemical expertise. In general, we have limited new rapid reactions to those studied at room temperature or below and their
analogues. Many of the room-temperature rates with experimental references are for radical–radical reactions and come from the
National Institute of Standards and Technology (NIST) Chemical
Kinetics Database (http://kinetics.nist.gov/index.php), an uncritical
compilation, from which choices among different measurements
often had to be made. A smaller number come from the critical compilation of Baulch et al. (1992) and later evaluations (see,
e.g. http://www.iupac-kinetic.ch.cam.ac.uk). In addition to our own
views, we have been given assistance in this project by physical
chemists from a former European network on astrophysical chemistry, including Michel Costes (Bordeaux), Ian Sims and Bertrand
Rowe (Rennes), and Juergen Troe (Goettingen). Finally, we have
added some endothermic processes needed for high-temperature
chemistry. These come mainly from the NIST Chemical Kinetics
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A new interstellar network
325
Table 1. Rate coefficients for neutral–neutral reactions in the osu.2003 network.
Reactanta
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
Reactant
Product
Product
alpha (cm3 s−1 )
CH
HS
NH
NO
NO
NS
O2
OH
PH
S2
SIH
SO
SO
CH2
HCO
HCO
C2N
C2H
CCO
NH2
C2
CS
CN
CN
CO
CN
CO
CO
CP
S
SIC
CO
CS
C2H
CH
CCO
C2
C3
C2
HNC
H
H
H
O
N
S
O
H
H
CS
H
S
O
H
CO
H
CN
H
CO
H
6.59E−11
1.00E−10
1.20E−10
6.00E−11
9.00E−11
1.50E−10
4.70E−11
1.00E−10
7.50E−11
7.00E−11
6.59E−11
3.50E−11
3.50E−11
1.00E−10
1.00E−10
1.00E−10
1.00E−10
1.00E−10
2.00E−10
3.40E−11
beta
0.00E+00
0.00E+00
0.00E+00
−1.60E−01
−1.60E−01
−1.60E−01
−3.40E−01
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
−0.36E+00
gamma
No.
Ref.
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
O+CH
1,2,3**
1,2,3**
C+NO
3,4**
C+CH
5
a First
20 lines of the table only; the full table is available at http://www.blackwellpublishing.com/products/journals/
suppmat/MNR/MNR7656/MNR7656sm.htm.
Database (http://kinetics.nist.gov/index.php) and the UMIST compilation (Le Teuff et al. 1999).
The new reaction network, to be labelled osu.2003, will be
updated continually and remain available on the Web page
http://www.physics.ohio-state.edu/∼eric/research.html as the file
CDDATA. There is, of course, no guarantee that the results obtained
using osu.2003 will be any better than those of the now defunct
new neutral–neutral model network; the only guarantee is that
the adopted parameters for unstudied or partially studied neutral–
neutral reactions represent our best estimates with help from other
experts.
The remainder of this paper is organized as follows. In Section 2,
we discuss the osu.2003 network. Section 3 contains results obtained
by utilizing the network in pseudo-time-dependent gas-phase models to study the dark cloud source TMC-1 (CP), for which much
molecular information is available. The principal aim in performing
these calculations has been to examine how the calculated abundances are modified by the new estimates of the rate coefficients
for neutral–neutral reactions. In Section 4, we consider what reactions are most important in causing differences between the new
results and those obtained with the nsm. A discussion is included in
Section 5.
2 THE NEW NETWORK
The neutral–neutral reactions in osu.2003 are given in Table 1. In
addition to the reactions and their rate coefficients, there is a number
for each reaction and, if applicable, a reference to a paper, Web site,
or a closely analogous reaction. The references to papers and Web
sites are defined at the end of the table. In general, experimental references are made to databases unless conclusive low-temperature
experiments have been performed. Such experiments have been undertaken on fewer than 20 reactions in the list. A few references
are to theoretical or mainly theoretical work. The total number of
neutral–neutral reactions (317) is greater than the number in the
new standard model (194) and the new neutral–neutral model (260),
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2004 RAS, MNRAS 350, 323–330
although some of the additions (≈60) represent endothermic processes, and are useful mainly for high-temperature chemistry. The
rate coefficients in Table 1 are expressed in the standard form:
k(T ) = α(T /300)β exp(−γ /T ).
(4)
In presenting the rate coefficients in terms of this simple formula, we
have been forced to represent the temperature dependence of those
reactions with a slight peak in the rate coefficient versus temperature
plot at 50–100 K followed by a slight dip at lower temperatures in
terms of a very small activation energy barrier (≈20 K). This barrier
need not be real.
It should be emphasized that the network is written mainly for an
oxygen-rich source, especially for temperatures at or below 300 K.
Although a selection of endothermic processes is now included for
the first time, the most recent UMIST network (Le Teuff et al.
1999) contains a more extensive set of reactions important at higher
temperatures. Readers interested in our updated rate coefficients
for other classes of reactions (ion–molecule, dissociative recombination, etc.) can find them in the file CDDATA on the Web site
http://www.physics.ohio-state.edu/∼eric/research.html.
As already indicated, the present model differs from the previous models (nnnm and nsm) mainly in respect of the numbers of
neutral–neutral reactions and values of their rate coefficients that are
included in the model. Because there are only direct experimental
data at low temperatures for fewer than 20 of the neutral–neutral
reactions included in Table 1, rate coefficients for the other 240
exothermic reactions had to be estimated. For some of these reactions, experimental results at room temperature and above are
available, and the estimates involve a choice of temperature dependence only. For these systems, the T 1/2 dependence, arising from
the hard-sphere approximation, has been dropped.
For about 50 reactions, rate coefficients were estimated on the
basis of chemical similarity with the one or more of the relatively
small number of reactions for which rate coefficients have been measured at low temperatures. Here, we can identify several categories
of comparison. The first is exemplified by the reactions of C(3 P)
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I. W. M. Smith, E. Herbst and Q. Chang
atoms with unsaturated hydrocarbon molecules; that is, alkenes and
alkynes. The reactions of C(3 P) with C 2 H 4 and with C 2 H 2 are known
to occur, even at low temperatures, with rate coefficients close to the
collision limit. We assume that this is also so for reactions of C(3 P)
with larger alkenes and alkynes, which have lower ionization energies than the simplest members of these families. A similar analysis
pertains for reactions involving the radicals CN and C 2 H. Secondly,
we assume that reactions involving species involving elements in
the same column of the periodic table have similar rate coefficients.
One such example involves the reaction between O + OH, for which
some measurements and theoretical estimates are available, and the
analogues S + OH, O + SH and S + SH. These assumptions have
allowed us to estimate the rate coefficients for a further 50 reactions
in Table 1, for which the better-studied reactions are listed in the
reference column.
There are very few experimental data available concerning the
kinetics of reactions between radical species (atomic or molecular)
at low temperatures. In general, the approach of two such species
with open electronic shells will give rise to a number of potential
energy surfaces; for example, two radicals each with one unpaired
electron but no electronic orbital angular momentum will give rise
to a singlet and a triplet potential energy surface. We have typically
assumed that reaction can occur rapidly but only on the surface of
lowest electronic spin (assuming this is not forbidden by the spin
correlation rules). This assumption lowers the rate coefficient below
the value expected on a simple collision basis. In considering these
and other reactions, we have also been guided by any measurements
of the rate coefficient made at or around room temperature. For
example, estimates have been made for exothermic reactions of
N(4 S) and O(3 P) with other radicals. However, there is clear evidence
that N(4 S) atoms do not react with unsaturated hydrocarbons, in
agreement with the lack of spin correlation. Such reactions have
been given low rate coefficients. The reactions of O(3 P) atoms with
unsaturated hydrocarbons are even more problematical. There is
evidence that such reactions for the smaller alkenes and alkynes have
small but significant barriers but these may decrease or disappear
for larger species. Nevertheless, we have not included any such
reactions in our calculations.
As two detailed examples, consider the reactions
H(2 S) + HCO(2 A) −→ H2 (1 g+ ) + CO(1 + ),
(5)
C(3 P) + C2 H(2 ) −→ C3 (1 g+ ) + H(2 S).
(6)
The rate of reaction (5) has been measured around 15 times at
room temperature and above (http://kinetics.nist.gov) with rate coefficients found between 1 × 10−10 and 5 × 10−10 cm3 s−1 . The
value preferred in the critical compilation of Baulch et al. (1992)
at 300 K is 1.5 × 10−10 cm3 s−1 . Reaction is likely to occur, by a
spin-allowed route, over the 1 A 1 potential energy surface describing the ground surface of the H 2 CO molecule. Measurements at and
around room temperature suggest no T-dependence and we assume
the rate coefficient to be 1.5 × 10−10 cm3 s−1 at 10 K.
In contrast there is no experimental or theoretical information
about the rate of reaction (6). The reaction as written is 38 kcal
mol−1 exothermic (1 kcal mol−1 = 503 K) and is spin-allowed.
The production of C 2 + CH is quite strongly endothermic (36 kcal
mol−1 ). The rate coefficient has been chosen to be approximately
one-third of that for C(3 P) + C 2 H 2 to allow for the lack of reaction
on the excited quartet surface. Moreover, rather than assume the
minimal temperature dependence found for C(3 P) + C 2 H 2 , we have
adopted a temperature-independent value.
Table 2. Chosen fractional abundances relative to
hydrogen and their initial forms.
Element
(initial form)
Fractional
abundance
H2
He
N
O
C+
S+
Si+
Fe+
Na+
Mg+
P+
Cl+
0.5
1.4(−1)
2.14(−5)
1.76(−4)
7.3(−5)
8.0(−8)
8.0(−9)
3.0(−9)
2.0(−9)
7.0(−9)
3.0(−9)
4.0(−9)
3 R E S U LT S
With the new network, we have studied the gas-phase chemistry of a
dense cloud condensation with a fixed density of n H = 2 ×104 cm−3
and a fixed temperature of 10 K. The best-known source in this class
is TMC-1 (CP), for which the observed fractional abundances of 50
molecules with respect to H 2 have been measured with varying
degrees of accuracy (Ohishi, Irvine & Kaifu 1992; Pratap et al.
1997; Ohishi & Kaifu 1998; Markwick, Millar & Charnley 2000;
Turner, Herbst & Terzieva 2000). It is useful to compare calculated
abundances from our new network and an older network with those
detected in TMC-1 (CP).
The so-called ‘low metal’ elemental abundances, known to be
superior for the production of large molecules compared with abundances used in diffuse cloud studies, are chosen here (Ruffle &
Herbst 2000), while the cosmic ray ionization rate is set at the ‘standard’ value of 1.3 × 10−17 s−1 , which is appropriate for dense objects
through which low-energy cosmic rays cannot penetrate. Listed in
Table 2, our chosen abundances represent an attempt to take into
account the fact that heavy elements are more likely to be depleted
on to dust particles than they are in diffuse clouds. A more detailed
approach would be to start with elemental abundances measured in
diffuse clouds, consider both the chemistry occurring in the gas and
on the surface of dust particles, allow for both adsorption on to and
desorption from grains, and include the collapse of the cloud from
diffuse to dense conditions (assuming that collapse is the correct
direction to follow). Although such a treatment is desirable, it is
our purpose here only to compare the use of the new network with
comparable gas-phase treatments undertaken by astrochemists in
the past (Millar et al. 1997; Terzieva & Herbst 1998; Turner et al.
2000).
Each element starts out in its neutral or ionized atomic form depending on the ionization potential and dominant form in diffuse
clouds, except for hydrogen, which begins as H 2 . The idea in choosing these initial abundances is to mimic to some extent what is actually observed in more diffuse clouds where, except for hydrogen,
the molecular abundances are low and carbon is mainly in ionic
form. Other choices of initial abundances can also be defended.
A common one is to start with hydrogen equally divided between
atomic and molecular forms. Less common for the ‘simple’ objects
discussed here is to start with the steady-state results of a calculation representing an era in between the diffuse and dense stages (see
Section 5 below). Again, our intent here is only to compare the new
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A new interstellar network
network with results obtained in rather standard calculations with
current networks.
With oxygen-rich (C<O) elemental abundances, the results of
models with static physical conditions starting from mainly atomic
abundances typically show best agreement at a so-called ‘early
time’, which for the density chosen here is ≈ 105 yr, well before the
onset of steady-state abundances. The use of early-time abundances,
first discussed in Herbst & Leung (1989), has always been controversial since the abundances do depend to some extent on the initial
conditions. With those chosen here and in many previous papers,
there is little difference between early-time and steady-state concentrations for most small molecules, but for larger species, calculated
abundances at steady-state tend to be many orders of magnitude too
small. So, it is useful to compare the results of networks at early
time, mainly because it is only at this time that a high degree of
agreement with observed abundances can be achieved for classic
dense clouds.
Table 3 shows both observed and calculated early-time (1 × 105
yr) fractional abundances with respect to H 2 for TMC-1. The observed values are often the result of several measurements, of varying degrees of uncertainty. When faced with differing fractional
abundances for the same species, we have taken arithmetic or geometric means, depending on the disparity. Given these differences,
we have only kept one significant figure. The results of four calculations are shown in columns 2–5, to the right of the observed
abundances. Theoretical abundances too high and too low by more
than an order of magnitude are highlighted by italics and boldface,
respectively. The results in columns 2 and 3 are for the osu.2003 and
nsm networks with the ‘low metal’ abundances, for which C/H =7.3
× 10−5 and C/O = 0.42, while the third and fourth columns show
the results of calculations with the osu.2003 network in which C
and O elemental abundances have been changed. Let us first discuss
the results with the abundances in Table 2. Although the order-ofmagnitude criterion indicated by the bold and italic fonts in Table
3 is somewhat arbitrary, its use does show that the nsm results are
clearly superior with respect to this criterion. In addition, it can be
seen that most of the problem with osu.2003 lies in its inability to
produce sufficiently large abundances of organic molecules such as
the cyanopolyynes (HC 2n+1 N). Indeed, for the 22 molecules with
abundances more than an order of magnitude different from those
calculated with the osu.2003 network, all but one (C 3 O) are underproduced by the network. With the nsm network, on the other
hand, four are overproduced and eight underproduced. If, instead of
focusing on all abundances equally, we had weighted our concerns
towards the more abundant, smaller species, the differences between
the two models would be smaller.
To determine if this disappointing result for osu.2003 can be improved by changing the C and O elemental abundances, we performed several sets of variations (Terzieva & Herbst 1998). The
fractional abundances calculated at a time of 1.0 × 105 yr are listed
in the two rightmost columns of Table 3 for two representative sets
of revised C and O elemental abundances: one in which the C/O
elemental abundance ratio is increased to 1.2 by a decrease in the
O abundance, and the second in which the C/O ratio is increased to
0.8 by suitable decreases in both the C and O abundances. For the
calculation with C/O = 1.2 especially, fewer large molecules are
underproduced by more than an order of magnitude; of the eight
molecules underproduced by more than this amount, most (five)
contain oxygen. Of course, it should be noted that our networks are
not really designed for carbon-rich systems, so the result is rather
tentative and, unlike O-rich conditions, not very dependent on time
past ‘early time’.
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How significant are the differences among our various calculations? It is of some interest to determine the uncertainties in the
calculated abundances as a result of uncertainties in the rate coefficients utilized in the networks. This task is a most difficult one and,
to our knowledge, has been accomplished only twice with interstellar networks for dense clouds. The method utilized was to vary
the rate coefficients randomly within their measured or estimated
uncertainties and look at the effects on calculated abundances at
steady-state. Roueff, Le Bourlot & Pineau des Forets (1996) were
mainly concerned with how random variation in the rate coefficients in the parameter space where bistability occurs could shift
the solution from one phase to another. They also noted uncertainties of factors of perhaps 2–5 for the ionization fraction and C/CO
ratio at steady-state for each individual phase. In the more recent
attempt, Markwick (2002) used a subset of the latest UMIST network for a dense cloud 60 000 times and determined the following
results: (i) most small molecules are determined to within a factor of 2–5; (ii) HC 5 N and HC 7 N are known to within a factor of
10; and (iii) most species with more than six carbon atoms have
uncertainties exceeding one order of magnitude. It is unlikely that
such a massive calculation undertaken by us would achieve different results at steady-state. Assuming, then, that Markwick’s results
pertain at least crudely to our early-time calculations as well, there
is a particular need for caution in comparing network results for the
largest species. The fact that virtually all of the complex molecules
have lower abundances when the osu.2003 network is used is an
argument, however, that the deviations are not purely statistical in
nature.
4 S P E C I F I C R E AC T I O N S
The changed agreement between calculated and observed abundances in TMC-1 when the osu.2003 network is substituted for the
nsm network stems directly from the use of rapid neutral–neutral
reactions. Among the unstudied reactions of this class, there may
be some critical ones with poorly determined rate coefficients. To
determine if our changed results can be traced back to such a small
group of reaction rates, we have looked carefully at some prime
candidates. Our initial investigations, based on the dominant reactions for formation and destruction of assorted species determined
by our model code, led to eight critical reactions, which are listed
in the upper half of Table 4. For each reaction, we have tabulated
the rate coefficient used in the nsm and the new osu.2003 models.
Of the eight reactions, five are neutral–neutral reactions leading to
two products, while three are radiative association reactions not included at all in the nsm network. The reaction rate coefficients are
all uncertain.
The two reactions involving the CN radical are the only ones to
have been studied in the laboratory. The importance of these two
reactions lies in their ability to destroy CN rapidly so that the radical is not available to form the cyanopolyynes. If neither reaction
involving CN occurs, cyanopolyynes may be boosted significantly
in abundance. But, the amount of CN may then grow too large, as
occurs for other models with large cyanopolyyne abundances. The
reactions involving O and C 2 , C 4 , and C 6 are critical in destroying
carbon clusters, which would otherwise lead to hydrocarbons. Lowering their rates thus may enhance the production of hydrocarbons.
Finally, the three radiative association reactions involving atomic C
and carbon clusters could be important in the destruction of atomic
C, which is a critical reagent in the growth of large molecules. Reducing their rates, or removing them completely as in the nsm, may
help in the production of many complex systems.
328
I. W. M. Smith, E. Herbst and Q. Chang
Table 3. Calculated fractional abundances with respect to H 2 at 1.0 105 yr compared with observed values for
TMC-1 (CP).
Species
TMC-1a
osu.2003b
C/H = 7.3E−05
C/O = 0.42
nsm
7.3E−05
0.42
osu.2003
7.3E−05
1.2
osu.2003
1.46E−05
0.8
C2
CH
CN
CO
CS
NO
OH
SO
C2H
C2S
C2O
H2S
HCN
HNC
OCS
SO2
C3H
C3N
C3O
C3S
H2CO
H2CS
NH3
CH2CN
CH2CO
C3H2
C4H
HCOOH
HC2NC
HC3N
HNC3
CH3CN
C4H2
C5H
CH3OH
CH3CHO
C2H3CN
C3H4
C6H
HC5N
C6H2
CH3C3N
CH3C4H
HC7N
HC9N
HCO+
HCS+
N2H+
H2CN+
C3H2N+
5E−08
2E−08
5E−09
8E−05
4E−09
3E−08
2E−07
2E−09
2E−08
8E−09
6E−11
5E−10
2E−08
2E−08
2E−09
1E−09
1E−08
6E−10
1E−10
1E−09
5E−08
7E−10
2E−08
5E−09
6E−10
1E−08
9E−08
2E−10
5E−10
2E−08
6E−11
6E−10
1E−09
6E−10
3E−09
6E−10
4E−09
6E−09
2E−10
4E−09
5E−11
8E−11
4E−10
1E−09
5E−10
8E−09
4E−10
4E−10
2E−09
1E−10
5.5E−10
1.6E−09
2.3E−09
1.3E−04
5.0E−09
8.2E−09
1.1E−08
4.8E−09
5.7E−09
2.7E−09
1.2E−12
3.2E−11
2.7E−09
2.3E−09
2.3E−10
3.3E−10
5.2E−09
3.9E−10
1.2E−09
9.4E−10
6.3E−09
3.1E−10
1.1E−08
2.9E−10
3.0E−09
1.9E−08
3.0E−09
4.6E−10
8.4E−12
1.2E−10
1.1E−11
2.3E−12
4.3E−09
1.2E−09
1.9E−11
6.7E−13
1.6E−14
1.8E−10
1.2E−09
1.5E−10
4.4E−10
1.9E−12
5.5E−11
4.6E−11
7.5E−12
6.1E−09
1.1E−11
1.1E−10
3.4E−11
1.8E−12
1.1E−08
2.9E−08
1.0E−07
8.1E−05
5.7E−09
2.1E−08
4.9E−09
9.5E−10
3.0E−08
2.8E−09
1.3E−10
2.3E−11
5.9E−08
6.8E−08
3.0E−10
1.6E−10
2.5E−08
3.6E−09
3.4E−11
5.5E−10
1.3E−07
5.1E−10
5.4E−09
2.2E−08
2.7E−08
2.6E−08
5.0E−09
6.8E−10
2.0E−10
5.8E−09
4.4E−11
2.5E−09
1.4E−08
1.1E−09
2.7E−09
2.5E−12
1.1E−12
2.8E−09
8.3E−10
2.3E−09
3.2E−09
8.4E−11
2.4E−09
2.9E−10
4.8E−11
4.5E−09
9.8E−12
1.1E−12
5.6E−10
3.8E−11
6.5E−08
1.9E−08
2.0E−07
1.2E−04
3.5E−08
7.4E−08
1.7E−08
8.2E−10
3.2E−08
2.7E−09
5.4E−12
1.7E−10
1.2E−07
1.2E−07
3.0E−10
7.8E−12
3.6E−08
1.7E−09
1.5E−10
8.7E−10
2.4E−08
2.8E−09
7.3E−08
1.6E−09
3.1E−09
3.6E−08
1.0E−07
2.8E−11
2.2E−10
6.2E−09
2.6E−10
3.6E−10
1.2E−08
4.4E−09
6.3E−12
1.2E−13
5.5E−12
1.0E−09
1.3E−08
1.3E−09
1.5E−09
3.7E−12
8.6E−10
1.8E−10
4.0E−11
6.7E−09
5.5E−10
4.1E−10
1.4E−09
3.9E−11
5.8E−09
7.0E−09
2.8E−08
2.1E−05
4.0E−09
5.6E−08
3.3E−08
1.6E−09
1.1E−08
9.9E−10
2.4E−12
3.0E−10
4.7E−08
4.4E−08
1.2E−10
2.2E−11
1.6E−08
2.3E−09
1.7E−10
2.8E−10
2.7E−08
6.4E−10
1.9E−07
1.1E−09
3.4E−09
1.8E−08
1.5E−08
3.6E−11
3.4E−11
3.8E−10
6.1E−11
1.2E−10
2.0E−09
7.8E−10
1.3E−11
1.2E−13
2.5E−13
1.6E−10
1.5E−09
1.2E−10
2.1E−10
1.6E−12
5.9E−11
2.6E−11
2.9E−12
3.4E−09
7.7E−11
1.4E−09
8.2E−10
9.5E−12
7.0E−08c
7.7E−08d
3.0E−07
5.4E−06
9.3E−07
3.7E−08
1.4E−08
4.7E−08
7.8E−08
5.1E−07
H2O
O2
a See
text for sources.
b Boldface signifies a theoretical value low by more than an order of magnitude, while italic indicates a theoretical
value high by this amount.
c SWAS result – see Snell et al. 2000.
d NH peak; Odin result – see Pagani et al. 2003.
3
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2004 RAS, MNRAS 350, 323–330
A new interstellar network
329
Table 4. Critical neutral–neutral reactions.
Reactant
Reactant
Product
Product
k(nsm)
cm3 s−1
k(osu.2003)
cm3 s−1
N
O
N
O
O
O
C
C
C
CN
CN
C2
C4
C6
C3
C5
C7
CO
N2
CO
CO
CO
C4
C6
C8
N
C
C
C3
C5
1.8E−11(T/300)0.5
1.5E−13(T/300)0.5
5.0E−11(T/300)0.5
5.0E−11(T/300)0.5
5.0E−11(T/300)0.5
–
–
–
4.0E−11
3.0E−10
1.0E−10
1.0E−10
1.0E−10
1.0E−10
1.0E−10
1.0E−10
22
18
1
34
15
36
24
7
C
C
N
N
N
N
O
O
O
O
C
O2
CH2
OH
C3
C4
C6
OH
C2H
CH2
C3H
H2
CO
C2H
NO
CN
CN
CN
O2
CO
products
C2H
CH2
O
H
H
C2
C3
C5
H
CH
4.7E−11(T/300)−0.34
5.0E−11(T/300)0.5
7.6E−11(T/300)−0.17
–
–
–
9.4E−11(T/300)−0.24
1.7E−11
2.0E−10
1.7E−11
1.0E−17
4.7E−11(T/300)−0.34
1.0E−10
7.5E−11(T/300)−0.18
1.0E−13
1.0E−10
1.0E−10
7.5E−11(T/300)−0.25
1.7E−11
2.0E−10
1.7E−11
1.0E−17
10
15
16
13
24
11
14
25
37
24
25
CO
As a complementary approach to finding critical reactions, we
tried a different criterion that simply measures the sensitivity of results to individual reactions (Wakelam et al., in preparation). For
all neutral–neutral reactions in the osu.2003 network, we individually increased the rate coefficients by a perturbative factor of 1.1 and
looked at the effect on molecular abundances at early time for species
detected in TMC-1. If we simply total the number of abundances
changed by 5 per cent or more, we can get some idea concerning
the influence of each particular reaction. The results of this analysis
are also shown in Table 4, where the column headed by N stands
for the number of abundances so changed. This analysis yielded
17 reactions affecting 10 or more abundances. Although the second
analysis agrees in part with our initial one, in that six of the eight reactions possess a value of N > 10, eleven additional reactions were
shown to be important. These are shown in the lower half of Table 4.
Some of these reactions are actually well-studied in the laboratory;
those that have poorly determined rate coefficients include N + C 3 ,
N + C 4 , N + C 6 , O + C 3 H, and the radiative association between
C and H 2 .
5 DISCUSSION
We have constructed a new gas-phase network differing from previous networks mainly in the rate coefficients and numbers of lowtemperature neutral–neutral reactions. In the network, laboratory
work on rapid neutral–neutral reactions at low temperatures has
been generalized to systems not studied. We assume reactions to be
rapid at very low temperature either if they are known to be rapid
at room temperature or below, or they are analogous to rapid systems studied at or below room temperature. Based on intuition and
analogy, we use two different types of temperature dependence: (i)
no dependence at all, and (ii) a weak inverse dependence. A third
type of temperature dependence measured in the laboratory – a
weak inverse dependence down to approximately 50 K followed by
a small positive dependence at still lower temperatures – has only
been utilized for systems actually found to have such a temperature
dependence.
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2004 RAS, MNRAS 350, 323–330
We have used the new network, which we designate as osu.2003,
in a simple model of the rich gas-phase chemistry of the pre-stellar
condensation TMC-1 (CP) with the assumption that the source possesses a fixed density and temperature. With commonly used gasphase elemental abundances, we find that a model of TMC-1 with
our network does not produce sufficiently large abundances of organic species, especially cyanopolyynes, to agree with observations.
This result is contrary to what is obtained with more standard networks such as those from UMIST (Millar et al. 1997; Le Teuff et al.
1999) and the nsm network from Ohio State (Terzieva & Herbst
1998). Some improvement can be obtained with carbon-rich abundances or with reduced carbon and oxygen abundances. For the
commonly used abundances, it appears that there is a small number of critical reactions that either lead to the poor agreement or
just affect a large number of species. While recognizing the difficulty, we suggest that these reactions be studied further if their
rate coefficients are not accurately known. Equally importantly, as
kindly suggested by one of our two referees, a major problem lies
in the poorly determined uncertainty of our calculated abundances
and the related statistical significance of differences between results
for the new and older networks. We plan to look at this problem in
more detail in the future if we can devise a more subtle approach
than that used by Markwick (2002) that, in addition, contains time
dependence.
Nevertheless, our negative results indicate that the whole scenario
for the gas-phase models may be oversimplified. One oversimplification is the neglect of surface chemistry. In cold condensations
such as TMC-1, the role of surface chemistry in explaining gas-phase
abundances is unclear. Certainly the molecular hydrogen found in
these sources is formed on grains, but it is not obvious how heavier species would be able to come off the grains efficiently if the
temperature remains low (Ruffle & Herbst 2000). Since the grain
adsorption time for a cloud of density 104 cm−3 is 105−6 yr, the
main effect of inclusion of the grains is the serious depletion from
the gas of condensible molecules at times longer than this despite
the fact that cosmic rays do help to maintain a minimal presence
in the gas of heavy molecules. Yet, depletion of some molecules
330
I. W. M. Smith, E. Herbst and Q. Chang
slows destruction pathways for others remaining in the gas, and the
net result is sensitive to poorly understood desorption rates.
A second oversimplification concerns initial conditions. In most
gas-phase and gas-grain models of cold dark clouds, the initial conditions include a gas of atoms and molecular hydrogen, and the
chemistry is followed through one long cycle, which may end with
most heavy species in the solid phase. One can imagine a far different scenario, in which multiple cycles occur, each of which is
started by either a rise in temperature, as in hot cores, or by sputtering of material off grains due to the existence of periodic shock
waves or turbulence (Viti, Natarajan & Williams 2002). Following
the ejection of material into the gas, a completely different cycle
of gas-phase or gas-grain chemistry can occur (Markwick et al.
2000; Charnley, Rodgers & Ehrenfreund 2001; Markwick, Millar
& Charnley 2001). It will be of some interest to use the new network
in such multicyclic studies.
AC K N OW L E D G M E N T S
EH wishes to thank the National Science Foundation (US) for support of his research programme in astrochemistry. We also thank
the Ohio Supercomputer Center for time on their SV1 machine.
IWMS acknowledges support for this work by the European Union
both through a TMR Research Network grant ‘Astrophysical chemistry: Experiments, calculations and astrophysical consequences
of reactions at low temperatures’ under Contract FMRX-CT970132(DG12-MIHT) and through the award of a Descartes prize in
2000.
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