SYSTEMATIC THEORETICAL STUDY ON THE INTERSTELLAR CARBON CHAIN MOLECULES

Apart from their importance in astrophysics, astrochemistry, and astrobiology, pure carbon chain molecules such as C₂, C₃, and C₅ are of great interest to the combustion chemistry, particularly for application in flames and propellants. Table 1 shows the enthalpy of formation and the current astronomical status of the carbon chain (C_n) molecules considered in this study. Rotational spectroscopy has been the dominant tool in the chemical examination of interstellar and circumstellar media with about 90% of all known interstellar and circumstellar molecules observed via their rotational transitions. However, the application of rotational spectroscopy in this field is hampered by the fact that it is limited to molecules with a permanent dipole moment (Etim & Arunan 2015). The C_n chain molecules have no permanent dipole moment; hence, their pure rotational transitions cannot be measured. All the known interstellar C_n chain molecules have been observed in the infrared region through their vibrational transitions.

As can be seen from Table 1, there is a steady increase in the enthalpy of formation of the C_n chains as the chain length increases. C₄ is the exception, as it is yet to be observed. All the lower members of the chains with lower enthalpies of formation have been detected (Souza & Lutz 1977; Hinkle et al. 1988; Bernath et al. 1989; Cernicharo et al. 2000). With respect to the effect of thermodynamics, the lower members of the chains with lower enthalpies of formation are more stable than the higher members of the chains with higher enthalpies of formation. Figure 1 shows the plot of the enthalpy of formation of the C_n chain molecules estimated at the G4 level. The lower members of the chains remain the most likely candidates for astronomical observation compared to the higher members of the chains. As C₄ is yet to be observed and C₅ has already been observed, it is likely that C_7, which has a larger enthalpy of formation, may be observed before C_6, which has a lower enthalpy of formation.

Zoom In Zoom Out Reset image size

The C_nO group presents an interesting set of carbon chain molecules containing two (carbon and oxygen) of the four most important biological elements. Unlike the C_n chains, which lack a permanent dipole moment, the C_nO chains all possess a permanent dipole moment. Hence, all the known interstellar/circumstellar C_nO molecules have been observed via their rotational transition spectra. The enthalpy of formation and current astronomical status for all the C_nO molecules considered in this study are presented in Table 2, while Figure 2 depicts the plot of the enthalpy of formation for these molecules. Of the six molecules considered in the C_nO group, the first three (n = 1–3) have been astronomically observed (Smith & Stecher 1971; Matthews et al. 1984; Ohishi et al. 1991). The trend of the enthalpy of formation is the same as in the case of the C_n chain molecules. The odd-numbered carbon chain molecules are found to be more stable (lower enthalpy of formation value) than their corresponding even-numbered ones. The interstellar chemistry of oxygen and sulfur is well coupled, with over 80% of all the known S-containing interstellar molecules having their corresponding O-containing molecules as known interstellar molecules. Also, in most of the cases, the abundance of the S-compound relative to its O-analog is approximately equal to the cosmic S/O ratio (Frerking et al. 1979; Linke et al. 1979). The high probability of C₅O as an interstellar molecule stems from two important facts; C₅O has lower enthalpy of formation compared with C₄O and C₆O, and consequently, it is more stable in interstellar medium (ISM), and can thus possibly be observed. Second, C₅S, the sulfur analog of C₅O, has recently been observed (Agúndez et al. 2014) and the O-containing molecules are known to be more abundant in ISM than in their corresponding S-analog. Hence, astronomical observation of C₅S is a clear indication of the presence of C₅O in detectable abundance in ISM.

Zoom In Zoom Out Reset image size

IRC+10216, the carbon-star envelope, has emerged as one of the richest sources of molecules, with over eighty different molecular species so far observed in it. Alongside other molecular clouds, all the known C_nS molecules were observed in IRC+10216. As discussed in the previous section, the interstellar chemistry of oxygen and sulfur is very similar in many ways. Of the four (CS, C₂S, C₃S, C₅S) observed molecules in the C_nS group (Penzias et al. 1971; Cernicharo et al. 1987; Saito et al. 1987; Yamamoto et al. 1987; Agúndez et al. 2014), 3 (CS, C₂S, C₃S), three have the corresponding O-analogs known as interstellar molecules. However, C₅S has been astronomically observed, but not C₄S and C₆S. This could be correlated with its enthalpy of formation value (Table 3) compared to those of C₄S and C₆S. As shown in Table 3 and Figure 3, all the odd-numbered C_nS chains have lower enthalpy of formation than their corresponding even-numbered C_nS chains. Hence they are more stable and likely more abundant, and can thus be more easily observed than their even-numbered counterparts.

Zoom In Zoom Out Reset image size

The long carbon chain radicals like C_nN have long been thought to be present in the interstellar and circumstellar media in detectable abundance and supposed to play an important role in astrophysics. A number of fundamental interstellar molecules were first detected in space before being observed in the gas phase in the terrestrial laboratory. These include HCO⁺, C₂H, HNC, and ${{{\rm{HN}}}_{2}}^{+}$ (Guélin & Thaddeus 1977) among others, and thus most of them were termed "non-terrestrial." The cyanoethynyl radical, C₃N, is one such molecule whose identification was guided by the electron spin resonance spectrum of a related species, C₄H (butadinyl radical). The astronomical observations of C₂N and C₅N were hindered by the lack of accurate spectroscopic data. Their astronomical observations became possible immediately after their laboratory microwave spectra were measured (Jefferts et al. 1970; Friberg et al. 1980; Guélin et al. 1998; Anderson & Ziurys 2014). Table 4 and Figure 4 indicate a constant gradual increase in the enthalpy of formation of the C_nN chain molecules. A good correlation between the observations of the lower chains (except for C₄N) with the enthalpy of formation can be seen.

Zoom In Zoom Out Reset image size

Every unique astronomical observation of molecule(s) in the interstellar or circumstellar medium has always been a concerted effort between the laboratory spectroscopists and the astrophysicists. The successful detection (after a number of failed attempts) of SiC in IRC+10216 (Cernicharo et al. 1989), came immediately after the successful measurements of its laboratory spectrum. Whether cyclic molecules are chemically less abundant than their related linear species in the interstellar or circumstellar medium has been the question for decades, due to the fact that of about 200 known interstellar and circumstellar molecules, only about ten are cyclic. However, of the four known C_nSi molecules, two are cyclic. The ground-state geometry of SiC₂ is shown to have a compact symmetric (C_2v) ring, in contrast to the earlier belief that SiC₂ is linear. The proper elucidation of its ground-state geometry became instrumental for its astronomical observation (Thaddeus et al. 1984). Figure 5 shows the most stable geometry for the SiC₃ molecule, which is the rhomboidal isomer. The experimentally determined bond lengths of c-SiC₃ through isotopic substitution measurement (Apponi et al. 1999) and the theoretically calculated bond lengths at the G4 level are in good agreement, as shown in Figures 5(A) and (B), respectively. Table 5 and Figure 6 show the enthalpies of formation for all the C_nSi molecules considered in this study. There is a steady increase in the enthalpy of formation value as the carbon chain increases, except for c-C₂Si. The observed molecules are also the most stable molecules (Thaddeus et al. 1984; Cernicharo et al. 1989; Ohishi et al. 1989; Apponi et al. 1999). The enthalpy of formation for the linear C₃Si molecule, 221.687 kcal/mol, is about 10 kcal/mol higher than the most stable isomer, which is cyclic in structure. The detection of more silicon–carbon molecules in IRC+10216 in particular (where all C_nSi chains have been observed) and other astronomical sources await laboratory spectra of such molecules.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The largest claimed interstellar linear molecule, the cyanopolyne HC₁₁N, belongs to the HC_nN chains. The enthalpies of formation of these molecules follow a unique trend, with the odd-numbered carbon chains being more stable than their preceding and the next even-numbered carbon chains, as shown in Table 6. For instance, HC₃N is more stable than both HC₂N and HC₄N; HC₅N is more stable than both HC₄N and HC₆N, etc. Figure 7 depicts the zigzag pattern of the enthalpies of formation of the HC_nN chains. Of the eight molecules belonging to the HC_nN carbon chain, which have been detected in interstellar and circumstellar media (Snyder & Buhl 1971; Turner 1971; Avery et al. 1976; Broten et al. 1978; Kroto et al. 1978; Guélin & Cernicharo 1991; Bell et al. 1997; Cernicharo et al. 2004), only two (HC₂N and HC₄N) are even-numbered carbon chains, while the remaining six are odd-numbered (HCN, HC₃N, HC₅N, HC₇N, HC₉N, and HC₁₁N). A very good correlation between the observations of more odd-numbered HC_nN chains and their enthalpy of formation values, in comparison to the even-numbered HC_nN chains, can be seen. The odd-numbered HC_nN chains are found to be more stable, and thus may be more easily observed compared to the even-numbered HC_nN chains. From this analogy, HC₁₃N is a more probable candidate for astronomical observation than both HC₁₂N and HC₁₄N. Accurate laboratory rest frequencies of HC₁₃N will be crucial for its astronomical searches and possible detection.

Zoom In Zoom Out Reset image size

Discoveries of cyanopolynes set the pace for the recognition of long chain molecules in space, such as C_nH, C_nH⁻, etc. The acetylenic chain (C_nH) radicals from n = 1 to n = 8 have all been observed in space, (Swings & Rosenfeld 1937; Tucker et al. 1974; Guélin et al. 1978; Thaddeus et al. 1985a; Cernicharo et al. 1986; Suzuki et al. 1986; Cernicharo & Guélin 1996; Guélin et al. 1997). The steady increase in the enthalpy of formation of these chains, as the carbon chain increases, is shown in Table 7 and Figure 8. Most of the C_nH radicals could be termed "non-terrestrial", as they were first observed in space using the results from quantum chemical calculations prior to being studied in the laboratory. They are believed to grow steadily in the recombination phase of the interstellar medium (Suzuki 1983). In the carbon-rich astronomical sources, such as TMC and IRC+10216, where all the known C_nH chain radicals have been detected, successive members of the C_nH chains (n > 8) are more likely to exist.

Zoom In Zoom Out Reset image size

Just like sulfur and oxygen, phosphorus (the 18th most cosmically abundant element) and nitrogen are in the same group in the periodic table. Whereas the similarity between the interstellar molecules of sulfur and oxygen is well established with almost all S-containing interstellar molecules having the O-analog as a known interstellar molecule, this is not the case in terms of the interstellar chemistry of N-containing molecules and the P-analog, with only very few known P-containing molecules compared with the large number of N-containing interstellar/circumstellar molecules. This is due to the cosmic ratio of phosphorus and nitrogen compared with the cosmic ratio of sulfur and oxygen. Table 8 and Figure 9 display the enthalpy of formation for all the C_nP chains considered in this study. The only two astronomically observed molecules in this group, CP and C₂P (Guélin et al. 1990; Halfen et al. 2008), are also the most stable, and thus they may be detectable. As with the C_nH chains, there is a corresponding increase in the enthalpy of formation value for every successive increase in the carbon chain.

Zoom In Zoom Out Reset image size

Interstellar acetylene is a well known starting material in the formation processes of many interstellar and circumstellar species (Ridgway et al. 1976; Lacy et al. 1989). For the molecules with the empirical formula, H₂C₃, both the linear and the cyclic isomers have been observed in the Taurus molecular cloud, i.e., TMC-1 (Thaddeus et al. 1985b; Cernicharo et al. 1991). The cyclic isomer is now recognized as a common feature of many molecular clouds/astronomical sources. The polyacetylenic chains, C₄H₂ and C₆H_2, have been observed in the proto-planetary nebula CRL 618 (Cernicharo et al. 2001) via their infrared vibrational spectra. The first three carbon chains in the H₂C_n group have been astronomically observed, as shown in Table 9 and Figure 10. The next most likely observable member of this group is neither H₂C₅ nor H₂C₇, but rather H₂C₆.The even-numbered carbon chains in H₂C_n are more stable than their corresponding odd-numbered carbon counterparts, thus probably accounting for the astronomical observation of more even-numbered than odd-numbered carbon chains in this group.

Zoom In Zoom Out Reset image size

Among the ion molecules in interstellar and circumstellar media, the positive ions have long been known and observed, while the negative ions have only been known for less than a decade. Of the eight C_nN⁻ chains considered here, only three have been astronomically observed; CN⁻, C₃N⁻, and C₅N⁻ (Cernicharo et al. 2008; Thaddeus et al. 2008; Agúndez et al. 2010). The observed molecules (odd-numbered carbon chains) are found to be more stable than the others. CN⁻ is more stable than C₂N⁻; C₃N⁻ is more stable than both C₂N⁻ and C₄N⁻; and C₅N⁻ is more stable than both C₄N⁻ and C₆N⁻ (Table 10). Figure 11 depicts the plot of the enthalpy of formation of these molecules, which shows a zigzag pattern as noted in the case of the HC_nN chains. Following the order of their astronomical observations, C₇N can be considered as the next probable candidate as it is more stable than both C₆N⁻ and C₈N⁻.

Zoom In Zoom Out Reset image size

Molecular anions have long been predicted to be detectable in astronomical sources, and are currently estimated by chemical formation models to be in higher abundance than their neutral counterparts. The first known interstellar molecular anion, C₆H⁻, was shown to be the carrier of the unidentified series of lines of IRC+10216 via laboratory measurements of its rotational spectrum. The astronomical observations of C₄H⁻ and C₈H⁻ came immediately after the successful measurements of their rotational spectra (McCarthy et al. 2006; Brünken et al. 2007a; Cernicharo et al. 2007). Theoretically estimated enthalpy of formation for the C_nH⁻ (n = 1–10) chains using the G4 composite method is presented in Table 11. The same is also displayed in Figure 12. The even-numbered carbons chains are more stable than the preceding and the next odd-numbered carbon chains; C₂H⁻ is more stable than CH⁻ and C₃H, C₄H⁻ is more stable than C₃H⁻ and C₅H⁻, and so on. The rotational spectrum of C₂H⁻ is known (Brünken et al. 2007b), and its astronomical observation is a function of time. The three astronomically detected C_nH⁻ carbon chains are all even-numbered. These are the most stable, which might account for their observation, rather than the preceding and the next odd-numbered chain in each case, which have not been observed.

Zoom In Zoom Out Reset image size

Table 12 gives the summary of all the different carbon chains, which have been considered in this study. It is obvious from the table, that in each group the number of odd- and even-numbered carbon chains observed depends on the trend of the enthalpy of formation of the molecules in that group. The odd-numbered carbon chains are found to be more stable than their corresponding even-numbered carbon chains in most of the group (Figure 13). This might have resulted in the observation of more interstellar odd-numbered (60%) than the even-numbered carbon chains.

Zoom In Zoom Out Reset image size

The effect of kinetics on the formation of carbon chain species both in the terrestrial laboratory and in the interstellar medium cannot be overemphasized. Although there is hardly consensus as to how any molecule (especially the complex ones with six atoms and above) is formed in the interstellar medium, C₂ addition is the widely acclaimed route for the formation of the linear carbon chains. In the terrestrial laboratory, unsaturated molecules like acetylene, diacetylene, etc., are used as the source of the C₂ in producing the carbon chains, while in the interstellar medium, acetylene, which produces the C₂ is generally accepted as the starting material for the formation of these carbon chains (Cherchneff et al. 1993; Cherchneff & Glassgold 1993; McCarthy et al. 1997; Thaddeus et al. 1998). With respect to the carbon chains discussed here, a good correlation between the enthalpy of formation and observed abundances has been seen. For instance, in the C_nO chains, where the odd-numbered carbon chains are more stable than their progressive even-numbered chains, C₂ addition to the lower chains to form the higher chains, clearly favors the odd-numbered chains compared to their corresponding even-numbered chains. A C₂ addition to CO to form C₃O is likely to have a lower barrier compared to C₂ addition to C₂O to form C₄O, which could account for the delayed observation of C₄O. This is also applicable to the C_nS chains, where a C₂ addition to C₃S to form C₅S (astronomically observed) is more favorable than a C₂ addition to C₂S to form C₄S (yet to be observed). And this continues to the higher members of the chains. Also, in the HC_nN and C_nN⁻ chains, C₂ addition to form higher members of the chains is likely to favor the odd-numbered carbon chains compared to the even-numbered ones, which explains the trends in the astronomical observation of these species. In the case of C_nSi, H₂C_n, and C_nH⁻ chains, where the even-numbered are more stable than their corresponding odd-numbered chains, it is crystal clear that C₂ addition to the lower members of the chains is more likely to favor the even-numbered carbon chains compared to their odd-numbered counterparts. For instance, a C₂ addition to HC₅N to form HC₇N is could be more favorable than C₂ addition to HC₄N to form HC₆N, which has not been detected. Correlation between the effects of kinetics on the formation of these species can be seen even for the chains with a linear increase in the enthalpy of formation such as in the C_nH, C_nP, C_nN and C_n chains.

The correlation between the thermodynamics and observation of the linear interstellar carbon chains has been discussed in the previous sections. Here, it is also correlated with the chemical reactivity indices such as global hardness (η) and softness (S). Soft species are more reactive and unstable in comparison to the hard species. Larger values of S indicate that the species are more unstable, and larger values of η indicate that the species are more stable. All the parameters are pointed out in Table 13. For the sake of simplicity, in Figure 14, we have shown the softness values for the carbon chain species.

Zoom In Zoom Out Reset image size

3.13.1. Chemical Modeling

3.13.2. Physical Aspects

Chemical enrichment of a molecular cloud is interrelated with the surrounding physical conditions and age of the cloud. Depending on the densities (n_H), temperatures (T) and visual extinction (A_V) parameters, Snow & McCall (2006) classified various types of clouds. Das et al. (2016) also assumed these classifications in their model. For the diffuse cloud region, they considered that n_H may vary between 100–500 cm⁻³, T may vary between 30–100 K and A_V = 0.2, for the translucent cloud region, we used n_H =  501–10,000 cm⁻³, T = 15–30 K, A_V = 1–2, and for the dense cloud region, we used n_H = 10,001–1,000,000 cm⁻³, T = 10 K, and A_V = 5–10. In order to consider a more realistic condition, they considered different temperatures and extinction parameters for various regions of the clouds. They used constant slopes for T and A_V in respective number density windows. In diffuse and translucent cloud regions, gas and grains are not well coupled. So, temperature between these two phases might vary. However, in dense cloud regions, gas and grains are strongly coupled and the temperature would be more or less the same for both phases. They assumed that the grain temperature is always fixed at 10 K for all the clouds and for the gas temperature (T_gas), we assume T_gas = T. Here, we present the results for the dense and translucent cloud regions. Following Das et al. (2015a), we use n_H = 2 × 10⁴ cm⁻³, T_gas = 10 K, T_gr = 10 K, A_V = 5.05 for dense cloud and n_H = 5 × 10³ cm⁻³, T_gas = 22.89 K, T_gr = 10 K, and A_V = 1.47 for translucent cloud.

We assume that initially most of the hydrogen was in the form of molecular hydrogen. Our adopted initial condition is shown in Table 14. The choice of our initial condition was based on the study of Leung et al. (1984). These initial low-metalicity elemental abundances are often used to calculate molecular abundances in cold, dense clouds. Gas-phase species are allowed to accrete on the grains with a sticking coefficient of 0.3. Surface species are allowed to migrate through the grain surface, depending upon their binding energies. Binding energies of the surface species are taken from some past studies (Allen & Robinson 1977; Tielens & Allamandola 1987; Hasegawa & Herbst 1993; Hasegawa et al. 1992).

Table 14.  Initial Abundances

Species	Abundance w.r.t. total H
H2	5.00 × 10−01
He	1.00 × 10−01
N	2.14 × 10−05
O	1.76 × 10−04
H3+	1.00 × 10−11
C+	7.30 × 10−05
S+	8.00 × 10−08
Si+	8.00 × 10−09
Fe+	3.00 × 10−09
Na+	2.00 × 10−09
Mg+	7.00 × 10−09
P+	3.00 × 10−09
Cl+	4.00 × 10−09
e-	7.31 × 10−05
HD	1.60 × 10−05

Download table as:  ASCIITypeset image

Chemical evolution of the carbon chain molecules is shown in Figure 15 (for the dense cloud region) and Figure 16 (for the translucent cloud region). For the dense cloud region, gas-phase abundances of the carbon chain molecules are decreased at the latter stages (∼10⁶ years). This happened due to the heavy depletion of the gas-phase species. Since the depletion timescale is inversely proportional to the number density of a cloud, for the translucent cloud region no such depletion is prominent around the latter stages. The abundance of interstellar species is not driven by the thermodynamic stability of that species. It primarily depends on some other factors like: formation and destruction rate of the species, relative concentration of the interacting species, size of the species (here it depends on the number of carbons in it), etc. For example, for the formation of C_nX, it would require some extra reaction steps in comparison to the formation of C_n-1X. So, while comparing the abundances of any species with the effect of thermodynamics, it should be with the appropriate weighted average. The peak and final abundances of these species after 10⁶ years are shown in Table 15. Keeping in mind all these aspects, the abundances might be correlated with the energy and stability values of several carbon chain species. Few prominent examples of these correlations could be seen from Figures 15 and 16 and Table 15. Some examples are:

• (a)  
  From Figure 12, it can be seen that C₆H⁻ is more stable than C₅H⁻, C₇H⁻, C₈H⁻, C₉H⁻, and C₁₀H⁻ and in Figures 15 and 16, and Table 15, we find that C₆H⁻ is comparatively more abundant, as expected.
• (b)  
  From Figure 10, it is evident that H₂C₆ is more stable than H₂C₅, H₂C₇, and H₂C₈. This is also prominent from Figures 15 and 16 and Table 15.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Table 15.  Abundances of Carbon Chain Molecules

Carbon Chains	Peak Abundance (Final Abundance) with Respect to Total H in all Forms
	Translucent Cloud	Dense Cloud
C2	5.32E-08(4.53E-08)	4.62E-08 (4.94E-12)
C3	1.58E-13 (1.17E-13)	3.97E-10 (3.44E-16)
C4	1.51E-11 (2.03E-12)	1.32E-10 (2.31E-14)
C5	1.69E-11 (1.17E-11)	8.62E-11 (1.23E-13)
C6	1.23E-12 (7.90E-13)	3.69E-12 (4.40E-14)
C7	7.68E-15 (6.90E-15)	5.37E-13 (3.66E-18)
C8	2.40E-20 (7.91E-21)	4.86E-15 (3.29E-25)
CO	6.26E-06 (1.08E-07)	2.93E-05 (1.09E-07)
C2O	2.46E-11 (1.23E-13)	1.67E-10 (7.85E-16)
C3O	5.07E-16 (5.35E-18)	1.43E-13 (5.85E-18)
CH	2.22E-07 (5.68E-08)	3.72E-07 (5.43E-10)
C2H	1.19E-09 (2.98E-10)	2.89E-09 (1.13E-13)
C3H	2.88E-11 (1.12E-11)	2.97E-10 (2.49E-14)
C4H	2.97E-11 (5.16E-12)	3.51E-10 (1.86E-13)
C5H	4.86E-12 (1.45E-12)	2.79E-11 (9.76E-14)
C6H	3.49E-11 (3.40E-11)	1.51E-11 (1.96E-13)
C7H	9.51E-15 (5.67E-15)	1.23E-12 (2.73E-17)
C8H	2.08E-17 (6.61E-18)	1.04E-12 (2.76E-20)
CN	3.60E-07 (1.58E-09)	4.25E-06 (4.08E-10)
C2N	1.29E-11 (4.14E-14)	8.32E-10 (3.19E-14)
C3N	5.88E-13 (7.75E-15)	3.45E-11 (5.93E-13)
C4N	2.68E-13 (3.21E-16)	5.90E-11 (4.11E-15)
C5N	1.53E-14 (7.44E-16)	4.14E-13 (2.63E-16)
C6N
C7N	4.16E-16 (1.62E-17)	1.61E-12 (4.86E-13)
C9N	1.19E-21(2.54E-23)	4.64E-14(7.61E-17)
CP	2.53E-12 (2.53E-12)	7.83E-12 (1.63E-14)
C2P	9.57E-16 (3.55E-16)	1.79E-13 (1.21E-17)
C3P	1.82E-20 (9.47E-21)	1.31E-17 (6.57E-22)
C4P	4.83E-20 (3.27E-20)	4.45E-17 (9.13E-23)
C5P
C6P
HCN	1.06E-10 (2.06E-12)	1.33E-07 (1.27E-11)
HC2N	3.06E-14 (4.14E-17)	1.21E-12 (1.23E-17)
HC3N	1.13E-14 (5.67E-17)	2.46E-09 (3.28E-14)
HC5N	1.66E-14 (2.67E-16)	8.37E-13 (1.10E-14)
HC7N	2.37E-15 (1.06E-16)	4.86E-12 (1.35E-15)
HC9N	1.17E-20 (2.36E-22)	1.53E-14 (1.03E-19)
H2C2	1.76E-11 (4.77E-12)	2.75E-10 (8.38E-13)
H2C3	2.33E-11(7.51E-11)	4.48E-10 (4.95E-14)
H2C4	1.21E-14 (2.87E-15)	1.69E-12 (3.58E-17)
H2C5	8.96E-12 (9.26E-13)	5.64E-11 (1.05E-12)
H2C6	1.90E-11 (7.85E-12)	2.11E-11 (2.05E-12)
H2C7	3.18E-14 (5.86E-15)	5.77E-12 (1.06E-15)
H2C8	8.27E-17 (1.71E-17)	1.93E-12 (1.22E-18)
H2C9	4.73E-18 (1.21E-18)	1.42E-12(5.32E-21)
CSi	1.47E-12 (1.47E-12)	1.51E-12 (1.97E-14)
C2Si	1.04E-14 (1.04E-14)	2.14E-12 (1.64E-19)
C3Si	1.48E-14 (1.07E-14)	3.57E-16 (5.17E-18)
C4Si	4.04E-19 (1.73E-19)	3.57E-16 (1.32E-22)
CS	1.79E-10 (9.97E-11)	1.58E-08 (7.11E-12)
C2S	2.32E-15 (2.32E-15)	1.93E-12 (2.46E-16)
C3S	2.24E-16 (2.19E-16)	3.53E-13 (3.98E-17)
C4S	1.07E-20 (1.04E-20)	1.27E-17 (5.04E-21)
CN−	4.71E-16 (1.82E-18)	1.85E-14 (2.52E-22)
C3N−	2.03E-15 (6.99E-18)	1.07E-13 (5.09E-16)
C5N−	2.12E-14 (2.01E-16)	3.46E-13 (1.04E-16)
CH−	6.46E-19 (8.64E-23)	1.30E-16 (1.80E-28)
C2H−	1.65E-16 (1.34E-18)	1.07E-14 (7.42E-22)
C3H−	2.24E-14 (1.49E-17)	6.53E-13 (4.20E-21)
C4H−	3.32E-12 (1.29E-13)	4.46E-11 (6.74E-15)
C5H−	1.58E-12 (1.35E-13)	1.31E-11 (1.32E-14)
C6H−	1.00E-11 (4.81E-12)	1.02E-11 (4.01E-14)
C7H−	1.11E-14 (2.44E-15)	2.81E-12 (1.71E-17)
C8H−	7.99E-18 (8.47E-19)	7.78E-13 (5.64E-21)
C9H−	1.01E-18 (5.61E-23)	3.05E-13 (2.93E-19)

Download table as:  ASCIITypeset images: 1 2