ISM: structuremolecular processes
121, 1997 November 1The ab initio molecular orbital method is applied to explore the possibility that neutral-neutral reactions lead to the formation of cyanoacetylene HC3N and its isomers HCCNC and HNCCC in interstellar space. Potential energy surfaces for the formation of the HC3N molecule are examined theoretically for the reactions of the CN radical with acetylene and the C2H radical with HCN and HNC. The calculated result shows that it is possible for HCCCN to be formed from C2H2 + CN and C2H + HNC, because these reactions are exothermic and have no energy barrier. It is not possible for the isomers of the HCCCN molecule to be formed by the neutral-neutral reactions studied here. The different reactivities are discussed by using frontier orbital theory.
Subject headings: ISM: moleculesISM: structuremolecular processes
The formation processes of the more than 100 molecules found in space are not well characterized. Because of the extremely low pressure (ca. 103104 molecules cm-3) and the low temperature (ca. 10 K), the chemical reactions in interstellar space must take place very efficiently to produce molecules when the reactants meet. The most probable processes for such reactions are ion-molecule reactions, which are initiated via either photoionization by stellar UV or ionization by Galactic cosmic-ray radiation (Herbst 1995; Smith 1992; Herbst 1985; Ferguson 1985; Prasad et al. 1987; Bohme 1987; Herbst 1987). When new interstellar species are identified, various reaction models are proposed mainly in terms of ion-molecule reactions, especially for dark clouds.
One of the important series of interstellar molecules observed in cold dark clouds and in carbon-rich circumstellar envelopes is the series of cyanopolyyne HCnN (n = 1, 2, 3, 5, 7, 9), which have carbon chains (Turner 1971; Morris et al. 1975; Broten et al. 1978; Kroto et al. 1978). This series of interstellar molecules has been considered to be mainly produced through ion-molecule reactions. Proposed mechanisms to produce HC3N molecule via ion-molecule reactions are as follows (Knight et al. 1986):
After forming HC3NH+ species, the final process to produce HC3N molecule is a dissociative recombination between HC3NH+ and electron.
Many theoretical simulations for cyanopolyyne formation have been presented to explain the abundances of these interstellar molecules based on reaction rates of various ion-molecule reactions (Herbst & Miller 1991). A satisfactory result, however, has not been obtained when the reaction scheme includes only ion-molecule reactions. Moreover, there is an ambiguity for assumed reaction rates used in the simulation because most of their rates have not been measured. Rate constants have been determined for several ion-molecule reactions to produce HC3NH+, such as the reactions (1)(3b) in the laboratory (Knight et al. 1986). The results of these studies indicate that reaction (1) is the main contributor to the ion-molecule schemes.
The final dissociative recombination process (Bates & Herbst 1987) of HC3NH+ with an electron can involve the following two channels:
The amount of HCCCN depends on the branching ratio between reactions (4) and (5). A similar dissociative recombination reaction occurs between HCNH+ and an electron to form HCN or HNC (Herbst 1978). The computed branching ratio for HCN/HNC is found to be nearly unity (Herbst 1978; Shiba et al. 1996). This result clearly explains the nearly equal observed abundances of HNC and HCN in many dark clouds (Ohishi, Irvine, & Kaifu 1992). If HC3N is formed via reactions (1)(4), the ratio between HCCCN and HNCCC caused by the processes (4) and (5) is expected to be not far from unity owing to the dissociative recombination of HCCCNH+. The observed abundance ratio in the Taurus molecular cloud 1 (TMC-1) (Kawaguchi 1994) is, however, totally different:
This evidence does not suggest that ion-molecule reaction schemes are enough to explain the formation process of the HCCCN molecule (Ohishi et al. 1992; Kawaguchi 1994).
Another defect of the ion-molecule reaction scheme concerning HC3N formation arises from the recent observation of the 13C isotopic species of HC3N in TMC-1 (Takano et al. 1997). This result shows that H13CCCN and HC13CCN have a similar intensity in their spectral line but that HCC13CN has a stronger intensity than those of other isotopic species; i.e., [HCC13CN] > [H13CCCN], [HC13CCN]. The relative intensity ratio H13CCCN : HC13CCN : HCC13CN is obtained as ca. 1.0 : 1.0 : 1.4 (Takano et al. 1997). If HC3N is produced mainly by the ion-molecule reaction (1), the abundances of these three isotopic species should be almost identical because all three carbon atoms in cyclic-C
H
cannot be distinguished. This observed evidence, however, shows that the C atom of CN substituent in the HCCCN molecule has a different origin from the other C atoms. Considering these facts, one would expect that the HCCCN molecule is not mainly produced by ion-molecule reactions but by another type of reaction.
According to the experimental study by Sims et al. (1993), the rate constants of neutral-neutral reactions involving the CN radical become large at ultralow temperatures down to 25 K (Sims & Smith 1995; Lichtin & Lin 1986). This fact suggests that neutral-neutral reactions are also important in addition to ion-molecule reactions in interstellar space. Many new models, including neutral-neutral reactions, have been proposed to explain the abundances of hydrocarbons and cyanopolyynes (Millar & Herbst 1994; Bettens, Lee, & Herbst 1995; Herbst et al. 1994; Herbst & Leung 1990; Cherchneff & Glassgold 1993). Herbst et al. (1994) have suggested that the reaction CN + C2H2 could be the dominant formation route of HC3N in both interstellar and circumstellar clouds, if this reaction is rapid at low temperature. Some reaction networks incorporating the neutral-neutral reactions between the CN radical and acetylene give reasonable agreement for the observed abundance of HCCCN (Herbst & Leung 1990; Cherchneff, Glassgold, & Mamon 1993).
In the present study, we have explored the potential energy surfaces of several neutral-neutral reactions to form HCCCN molecule theoretically, in order to confirm whether such types of reactions are really possible in interstellar space. We have calculated the minimum energy pathway of the reaction between C2H2 and the CN radical by using the ab initio molecular orbital method. We have also studied the potential energy surfaces of the neutral-neutral reactions for the formation of HNCCC (Kawaguchi et al. 1992b) and HCCNC (Kawaguchi et al. 1992a), which are the observed isomers of HC3N. These species are much less abundant than HC3N.
All calculations were performed with the GAUSSIAN 92 and GAUSSIAN 94 programs (Frisch et al. 1995). Geometries were optimized by using the Hartree-Fock (HF) method, and the configuration interaction method including all single and double excitations (CISD) (Pople, Seeger, & Krishnan 1977) with a double-zeta plus polarization (DZ+P) basis set (Huzinaga 1965; Dunning 1970). Coupled cluster singles and doubles with a perturbative estimate of triple excitations (CCSD(T)) (Raghavachari et al. 1989) were employed to evaluate the relative energies with DZ+P and a triple-zeta plus polarization quality basis cc-pVTZ (Dunning 1989). Vibrational frequencies were calculated with the analytical derivative method based on the HF wave function and numerical differentiation of analytic gradients based on the CISD wave function. All structures have been confirmed as to whether they are located at energy minima or saddle points (transition states) from vibrational analyses. We use the notation "method/basis set" as the description of the computational method and the basis set used to obtain the optimized geometries. For example, CCSD(T)/cc-pVTZ//CISD/DZ+P means that the energy is evaluated with the CCSD(T) method by using a cc-pVTZ basis set at the molecular structure calculated by using the CISD method with a DZ+P basis set. Since the electron correlation is very important for the system studied here, the values used in the text are obtained with the CISD/DZ+P method unless otherwise stated. The problem of size consistency arises when we use the CISD method to evaluate the reaction energies. In order to avoid this problem, we have calculated the energies of reactions or products by putting each species at 10 Å separation.
We have considered the following five neutral-neutral reactions which form the HCCCN molecule and its isomers, HNCCC and HCCNC:
Since interstellar space is extremely cold and has low density, two conditions are required for the chemical reaction to proceed. One is that the reactions be exothermic. The other is that there be no activation barrier during the reaction course except in cases where proton tunneling is involved. We will discuss each of the potential energy surfaces for reactions (6)(10), which are illustrated in Figures (1)(4).
HC3N + HMany discussions concerning reaction (6) have been presented based on either laboratory measurements (Sims et al. 1993; Lichtin & Lin 1986) or theoretical simulations (Herbst et al. 1994; Herbst & Leung 1990; Cherchneff et al. 1993; Liao & Herbst 1995) for the formation processes of cyanopolyyne. Radical-molecule reactions with a radical in a nonsinglet electronic state are generally considered to occur relatively easily compared to the reactions between two closed-shell molecules. The amounts of acetylene molecules are thought to be large in interstellar space, and CN is one of the most numerous interstellar molecules involving a nitrogen atom (Ohishi et al. 1992). In order to explore whether reaction (6) is really capable of forming HC3N in an interstellar environment, we have calculated the potential energy surface for reaction (6).
As shown in Figure 1, CN approaches the 
-orbital of acetylene in the first stage of the reaction. There is a small energy barrier after forming of the van der Waals complex between C2H2 and the CN radical. The energy of this transition state (TS1) is calculated to be lower than that of the reactants (relative energy of TS1 = -2.5 kcal mol-1). After the formation of the intermediate HCCHCN species, the reaction proceeds via the second transition state (TS2), in which the hydrogen atom is eliminated. The energy of this transition state is calculated to be -5.7 kcal mol-1 lower than that of the reactants. The overall reaction energy is 22.1 kcal mol-1 exothermic. Woon & Herbst (1997) have obtained a similar potential energy surface for reaction (6) in a parallel study. Their results also show the intermediate HCCHCN species and the transition state in the exit channels, while there is no van der Waals complex and no transition state in the entrance channel. This feature of the potential energy surface agrees with our highest level of calculation, CCSD(T)/cc-pVTZ//CISD/DZ+P, where the van der Waals complex and TS1 disappear.
Fig. 1
The potential energy surface depicted in Figure 1 is very similar to the one in most cases of ion-molecule reactions in its absence of a positive activation energy barrier. Ion-molecule reactions are generally exothermic and also have no positive energy barrier, owing to the attractive interaction between ion and neutral species caused by dielectric polarization. High reactivity in the case of reaction (6) seems to be a result of the unpaired electron of the CN radical which attacks the -orbital of acetylene. After creation of a CC 
-bond, elimination of the hydrogen atom from the intermediate species leads to the formation of a conjugated -bond in HC3N. Consequently, reaction (6) is possible in interstellar space because of the lack of a positive barrier in spite of the neutral-neutral reaction.
HC3N + H Since the system C2H2 + CN is isoelectronic with HCN + C2H, the reaction between HCN and C2H might have a similar potential profile to the reaction between C2H2 and CN. In order to look for another process to produce the HC3N molecule, we have also explored reaction (7) (Becker & Hong 1983). This reaction might be feasible in interstellar space owing to the following two pieces of evidence. One is that the abundance of HCN lies at the same order of magnitude as does that of CN by radio observation (Ohishi et al. 1992). The other fact is that C2H is the most abundant species in the series of hydrocarbon chain molecules CnH (n = 18) in dark clouds and in circumstellar envelopes (Ohishi et al. 1992).
It is noticeable that the energy of the reactants C2H + HCN is only 0.1 kcal mol-1 higher than the reactants of reaction (6), C2H2 + CN, with the CISD/DZ+P method. Since this energy difference is calculated to be ca. 6 kcal mol-1 with the highest level of theory studied here, the systems C2H + HCN and C2H2 + CN are nearly degenerate. Because the products of reaction (7) are the same as those of reaction (6), reaction (7) is also an exothermic reaction, and its exothermicity is 22.4 kcal mol-1 with the CISD/DZ+P method. When the C2H radical approaches the -orbital of the carbon atom of HCN, there is a transition state between the reactants and the intermediate species, as shown in Figure 2. This energy barrier is calculated to be ca. 6 kcal mol-1 with the HF and CISD methods. In the highest level of calculation for the transition state, we have obtained a lower energy barrier (1.6 kcal mol-1 with CCSD(T)/cc-pVTZ//CISD/DZ+P). Recalling that the temperature is about 10 K in dark clouds and that 1 kcal mol-1 corresponds to 500 K, this energy barrier height is large enough to prohibit the reaction in interstellar clouds. There is also a second transition state between the intermediate species and the products, but its energy is found to be lower than that of the reactants. Consequently, the formation of the HC3N molecule via reaction (7) seems to be impossible in interstellar space even if the first energy barrier is small. We will discuss the different reactivity between reactions (6) and (7) based on the frontier orbital consideration in the last section.
Fig. 2
Let us consider the third reaction, between C2H and HNC, where HNC, the isomer of HCN, is 14.7 kcal mol-1 less stable than HCN, and the energy barrier from HNC to HCN is calculated to be 33.5 kcal mol-1 using a CCSD(T) level calculation (Bowman et al. 1993). If the system HCN
HNC is in chemical equilibrium, the abundance of HNC is expected to be much less than that of HCN. It is, however, noticeable that the amount of HNC is similar to that of HCN in interstellar clouds (Ohishi et al. 1992). Moreover, one could expect that HNC is more reactive than HCN because it is an energetically high species. In this respect, the reaction between the C2H radical and the HNC molecule may be a better candidate to produce HC3N than the reaction between C2H and HCN.
There are three kinds of possible products from the reaction between the C2H radical and HNC : HC3N + H (reaction [8]), HNC3 + H (reaction [9]), and HCCNC + H (reaction [10]). In the first stage of reactions (8) and (9), the radical center of C2H attacks the carbon atom of HNC to form the common intermediate HCCCNH. Reaction (10) involves CN bond formation between C2H and HNC.
As shown in Figure 3, reaction (8) experiences a weak van der Waals complex in the initial stage, the first transition state (TS1), the intermediate HCCCNH, and the second transition state (TS2) before reaching products. The exothermicity of reaction (8) is calculated to be 35.4 kcal mol-1. The energies of two transition states, TS1 and TS2, are found to be below the energy of reactants (-0.7 and -15.7 kcal mol-1, respectively). The potential energy surface of reaction (8), illustrated in Figure 3, is calculated to be similar to the case of reaction (6). Therefore, it is possible in interstellar space to form HC3N by the reaction of C2H + HNC owing to the reactivity of HNC, whereas reaction is impossible between C2H + HCN.
Fig. 3
In reaction (9), the hydrogen atom dissociates from the carbon atom of the intermediate HCCCNH. This process leads to the formation of HNCCC molecule, which is an observed species (Kawaguchi et al. 1992b). As is shown in Figure 3, this path is calculated to have a high energy barrier (+22.9 kcal mol-1) for CH bond cleavage, and furthermore to be 19.1 kcal mol-1 endothermic. Consequently, the HNC3 molecule cannot be produced by neutral-neutral reaction (9).
When the C2H radical attacks the N atom of HNC, reaction (10) may take place to produce HCCNC via an HCCNHC intermediate. Figure 4 depicts the potential energy surface for reaction (10). There are two transition states before and after forming the intermediate, and both energies are relatively high (+14.0 and +13.6 kcal mol-1). Therefore, when C2H and HNC react, only HC3N formation is probable in interstellar space.
Fig. 4
Because the abundance ratio [HCCCN]/[HCCNC] is 2060 in TMC-1 (Kawaguchi et al. 1992a), the mechanism of HCCNC formation seems to be different from that of HC3N formation. In other words, we suggest that HCCCN can be produced by neutral-neutral reactions such as reaction (6), but HCCNC can only be produced by ion-molecule reactions.
C2H + HCN There might be another pathway in the reaction between C2H2 and CN. If the CN radical approaches linearly toward the hydrogen atom of C2H2, the hydrogen abstraction reaction may take place to produce the C2H radical and HCN. According to a paper by Bair and Dunning, the reaction barrier of a similar reaction, H2 + CN H + HCN, was calculated to be 16 kcal mol-1 (Bair & Dunning 1985). Since the energy difference between C2H2 + CN and C2H + HCN is extremely small, as stated in § 3.2, one would expect that this hydrogen abstraction reaction has an energy barrier. Figure 5 illustrates the molecular geometries at the stationary points during the reaction obtained with the HF/DZ+P method. The calculated energy barrier (26 kcal mol-1) for hydrogen transfer is substantially high, and such a hydrogen abstraction reaction can be expected not to occur in interstellar space. Therefore, HC3N and H are concluded to be the only products of the reaction between C2H2 and the CN radical.
Fig. 5
(10) We have studied the potential energy surfaces for reactions (6)(10) with various methods. Table 1 summarizes the relative energies obtained by using the HF, CISD, and CCSD(T) methods for all reactions studied in this paper. All the product energies calculated with various methods relative to the energy of reactants show negative values except for reaction (9). The relative energies of the transition states tend to be overestimated at the HF level of theory in general because of the lack of electron correlation. There is not so much difference for the optimized structures between HF and CISD methods, but there is a clear difference as to whether an energy barrier exists or not. The existence of an energy barrier is very critical for reactions in the interstellar medium.
In reaction (6), the result of the HF/DZ+P calculation shows that there is an extremely small energy barrier (0.1 kcal mol-1) between the reactants and the intermediate. Moreover, the HF method does not give a van der Waals complex at the early stage of reaction (6). When we used methods including electron correlation, such as the CISD or CCSD(T) methods, we found the weakly bound complex between the CN radical and C2H2. The energy of TS1 calculated with the CCSD(T)/cc-pVTZ method at the CISD/DZ+P optimized geometry turns out to be lower than that of the van der Waals complex, and the energy barrier for the overall reaction disappears. In reaction (7), the value of the energy barrier (TS1) decreases drastically from 6.3 to 1.6 kcal mol-1 when we increase the level of calculation. We, however, infer the existence of this positive energy barrier, since the result indicating a small energy barrier in the entrance channel persists when using the highest level of calculation. The energy barrier (TS1) for reaction (8) is significantly large at the HF level (+4.8 kcal mol-1) but decreases with the inclusion of electron correlation to negative values (-0.7 kcal mol-1 at CISD/DZ+P and -3.2 kcal mol-1 at CCSD(T)/cc-pVTZ). In the case of reaction (10), there are two high energy barriers that definitely prohibit reaction in interstellar space.
The relative energies corrected for zero-point vibrational energies at all stationary points are shown in parentheses in Table 1. The features of the potential energy surfaces are not changed by the zero-point energy corrections.
There seems to be no reason that reactions (6) and (8) have no energy barrier and reactions (7), (9), and (10) have barriers. The frontier orbital theory (Fukui 1964; Fukui 1971) may help us to understand the difference in reactivities among these reactions.
Figure 6 shows the orbital energy diagram of the frontier orbitals for reactants calculated with the restricted Hartree-Fock (RHF) method. Since the HOMO (highest occupied molecular orbital)LUMO (lowest unoccupied molecular orbital) separation of C2H2 is smaller than that of HCN, C2H2 is a reactive species to be attacked by radical species. As a result, the reaction between the CN radical and C2H2 is more favorable than that between the C2H radical and HCN. Although the energy of the singly occupied molecular orbital (SOMO) of C2H is relatively higher than that of the CN radical, both HCN and HNC molecules are expected to have low reactivity owing to the large HOMO-LUMO gap in reactions (7)(10). It is not clear, however, that the C2H radical reacts with HNC but not with HCN, since the energies of HOMO and LUMO are lying at near levels for both HCN and HNC molecules. This evidence may be understood by considering the frontier orbital interactions on the bond formation.
Fig. 6
Figure 7 illustrates the frontier orbital interactions between the CN radical and acetylene in reaction (6). An electron delocalization from SOMO of the CN radical to LUMO of C2H2 is more important than that from HOMO of C2H2 to SOMO of the CN radical in the initial stage of radical-neutral reaction. Since both of these interactions simultaneously occur at the identical site, this makes CC -bond formation favorable.
Fig. 7
Frontier orbital interactions for reaction (7) are shown in Figure 8. SOMO-LUMO interaction between the C2H radical and HCN is favorable to form a CC -bond because the orbital coefficient of LUMO is dominant on the C atom of HCN. On the other hand, HOMO-SOMO interaction is less favorable owing to the lesser density of HOMO on the carbon atom of HCN. Consequently, reaction (7) is predicted to be unfavorable to form a CC -bond leading to the HCCCHN intermediate.
Fig. 8
In the formation of the CC bond between the C2H radical and HNC (reaction [8]), both HOMO-SOMO and SOMO-LUMO interactions occur in one center on the C atom of HNC, as is shown in Figure 9. Both interactions make the CC bond formation between HNC and C2H favorable. This means that the C2H radical prefers to approach the middle angle of HOMO and LUMO of HNC, and the CCN angle is expected to be about 135° in the initial stage of reaction (8). This consideration is consistent with the result of the calculated structure of the transition state (TS1) depicted in Figure 3, where the calculated CCN angle is 131°.
Fig. 9
In the first stage of reaction (10), the CN -bond must be formed between the C2H radical and HNC. Figure 10 illustrates the scheme of frontier orbital interactions for reaction (10). Since the -orbital coefficient of LUMO on the nitrogen atom is smaller than that on the carbon atom in HNC, SOMO-LUMO interaction in reaction (10) is less favorable than in the case of reaction (8). Moreover, the electron transfer from the HNC molecule to the SOMO of C2H does not occur easily because HOMO is the lone-pair orbital on the carbon atom, and we have to use the next HOMO (HOMO-1) in order to form the NC bond. Considering both frontier interactions, we can conclude that the CN -bond formation is energetically less favorable in reaction (10).
Fig. 10
Such frontier orbital consideration backs up our understanding of the reason why both reactions (6) and (8) are possible and reactions (7) and (10) are unfavorable.
For each of the five neutral-neutral reactions (6)(10), ab initio molecular orbital calculations were carried out to seek possible pathways to form HC3N and its isomers, because the large amount of interstellar HC3N molecules cannot be explained only by ion-molecule reactions. Using the potential energy surfaces, we can decide whether or not the reactions can occur in interstellar space.
All reactions were found to have similar features in their potential energy surface, i.e., a transition state (TS1) in the initial stage, a stable intermediate, and a second transition state (TS2) dissociating the hydrogen atom from the intermediate. The potential energy surfaces of reaction (6), C2H2 + CN, and reaction (8), C2H + HNC, indicate that they are exothermic reactions and have no energy barrier. These results lead to the conclusion that both neutral-neutral reactions (6) and (8) form HCCCN in interstellar space. These two potential surfaces are very similar to the case of ion-molecule reactions. Another three reactions(7), (9), and (10)forming HCCCN, HNCCC, and HCCNC, respectively, are impossible in interstellar space owing to the presence of activation energy barriers or because they are endothermic. Of all the reactions (6)(10) studied in this paper, only the HCCCN molecule can be produced by neutral-neutral reactions, and neither of the formation pathways to HNCCC and HCCNC seems to be plausible via neutral-neutral reactions. According to the calculation by Woon & Herbst (1997), the rate coefficient for reaction (6), with the phase-space approach based on an ab initio potential energy surface, gives good agreement with experiment and suggests the contribution of reaction (6) under interstellar conditions.
The HNCCC and HCCNC molecules are thought to be mainly produced by ion-molecule reactions because of their low abundances. The present results support the observed abundance ratio between HCCCN and HNCCC, if reactions (6) and (8) contribute to the formation of HC3N in interstellar clouds. We can conclude that neutral-neutral reactions are very important in the formation of HCCCN but not in that of its isomers. This result suggests that the longer carbon-chain molecules, cyanopolyyne HC2n-1N (n = 15), may also be formed via similar types of neutral-neutral reactions, which are now under consideration.
We thank K. Kawaguchi and M. Ohishi of the Nobeyama Radio Observatory, S. Yamamoto of the University of Tokyo, and S. Takano of the University of Köln for helpful comments and discussions. Computer resources were provided by the Power Challenge XL at Nobeyama Radio Observatory. This research was supported by the Grants-in-Aid for General Scientific Research (07640686) and for Scientific Research on Priority Areas (04233103) from the Ministry of Education, Science, and Culture, Japan.
. 1989, J. Chem. Phys., 90, 1007 First citation in article | Crossref | ADS. 1971, Accounts Chem. Res., 4, 57 First citation in article | Crossref. 1985, in Molecular Astrophysics, ed. G. H. F. Diercksen, W. F. Huebner, & L. P. W. Langhoff (NATO ASI Ser. C, Vol. 157; Dordrecht: Reidel), 237 First citation in article | Crossref | ADS. 1987, in Rate Coefficients in Astrochemistry, ed. T. J. Millar & D. A. Williams (Dordrecht: Kluwer), 239 First citation in article. 1995, Annu. Rev. Phys. Chem., 46, 27 First citation in article | Crossref
Full image (34kb) | Discussion in textPotential energy surface for neutral-neutral reaction (6) (CN + C2H2) calculated with the CISD/DZ+P method. The potential curve (dotted line) and the relative energies in parentheses are obtained with the CCSD(T)/cc-pVTZ//CISD/DZ+P method.
Full image (34kb) | Discussion in textPotential energy surface for neutral-neutral reaction (7) (C2H + HCN) calculated with the CISD/DZ+P method. The relative energies shown in parentheses are obtained with the CCSD(T)/cc-pVTZ//CISD/DZ+P method.
Full image (42kb) | Discussion in textPotential energy surface for neutral-neutral reactions (8) and (9) (C2H + HNC) calculated with the CISD/DZ+P method. The potential curve (dotted line) and the relative energies in parentheses are obtained with the CCSD(T)/cc-pVTZ//CISD/DZ+P method.
Full image (31kb) | Discussion in textPotential energy surface for neutral-neutral reaction (10) (C2H + HNC) calculated with the CISD/DZ+P method. The relative energies shown in parentheses are obtained with the CCSD(T)/cc-pVTZ//CISD/DZ+P method.
Full image (20kb) | Discussion in textOptimized structures and relative energies of the reactants, transition state, and products for the hydrogen abstraction reaction C2H2 + CN C2H + HCN calculated with the HF/DZ+P method. Distances are shown in angstroms.
Full image (20kb) | Discussion in textOrbital energy diagram of the frontier orbitals for various reactants; the CN radical, C2H2, the C2H radical, and HNC calculated with the RHF/DZ+P method.
Full image (17kb) | Discussion in textFrontier orbital interactions for reaction (6), C2H2 + CN HC3N + H.
Full image (13kb) | Discussion in textFrontier orbital interactions for reaction (7), C2H + HCN HC3N + H.
Full image (15kb) | Discussion in textFrontier orbital interactions for reaction (8), C2H + HNC HC3N + H.
Full image (12kb) | Discussion in textFrontier orbital interactions for reaction (10), C2H + HNC HCCNC + H.
| REACTION | METHOD FOR ENERGY EVALUATION | |||
| HF/DZ+P | CISD/DZ+P | CCSD(T)/DZ+P a | CCSD(T)/cc-pVTZ a | |
| Reaction (6): | ||||
| Total energy of reactants (hartrees)... | -169.0504 | -169.4932 | -169.6023 | -169.7524 |
| C2H2 + CN: | ||||
| Reactants... | 0.0 (0.0) | 0.0 (0.0) | 0.0 | 0.0 |
| Van der Waals complex... |  |
-3.1 (-2.4) | -2.3 | -2.7 |
| Transition state 1 (TS1)... | 0.1 (-0.1) | -2.5 (-1.2) | -1.8 | -2.9 |
| Intermediate... | -64.1 (-62.3) | -65.0 (-60.9) | -57.0 | -55.9 |
| Transition state 2 (TS2)... | -6.0 (-10.9) | -5.7 (-7.4) | -3.2 | -7.4 |
| HC3N + H products... | -11.4 (-13.9) | -22.1 (-25.6) | -14.7 | -16.5 |
| Reaction (7): | ||||
| Total energy of reactants (hartrees)... | -169.0522 | -169.4929 | -169.5935 | -169.7424 |
| C2H + HCN: | ||||
| Reactants... | 0.0 (0.0) | 0.0 (0.0) | 0.0 | 0.0 |
| Van der Waals complex... | |
|
|
|
| Transition state 1 (TS1)... | 6.0 (5.6) | 6.3 (7.3) | 2.6 | 1.6 |
| Intermediate... | -52.2 (-49.4) | -50.2 (-46.6) | -46.3 | -48.8 |
| Transition state 2 (TS2)... | -3.5 (-7.3) | -4.0 (-5.3) | -7.0 | -12.0 |
| HC3N + H products... | -10.3 (-12.2) | -22.4 (-25.7) | -20.2 | -22.7 |
| Reaction (8): | ||||
| Total energy of reactants (hartrees)... | -169.0369 | -169.4720 | -169.5698 | -169.7186 |
| C2H + HNC: | ||||
| Reactants... | 0.0 (0.0) | 0.0 (0.0) | 0.0 | 0.0 |
| Van der Waals complex... | |
-1.6 (-1.2) | -2.1 | -1.2 |
| Transition state 1 (TS1)... | 4.8 (5.5) | -0.7 (-0.1) | -3.2 | -3.2 |
| Intermediate... | -48.0 (-45.8) | -55.3 (-51.2) | -57.5 | -60.4 |
| Transition state 2 (TS2)... | -9.8 (-13.8) | -15.7 (-17.4) | -21.2 | -27.7 |
| HC3N + H products... | -19.9 (-21.5) | -35.4 (-38.6) | -35.0 | -37.7 |
| Reaction (9): | ||||
| Transition state 2 (TS2)... | 34.8 (31.9) | 22.9 (19.5) | 20.8 | 15.3 |
| HNC3 + H products... | 31.2 (27.8) | 19.1 (14.1) | 17.7 | 14.7 |
| Reaction (10): | ||||
| Total energy of reactants (hartrees)... | -169.0369 | -169.4720 | -169.5698 | -169.7186 |
| C2H + HNC: | ||||
| Reactants... | 0.0 (0.0) | 0.0 (0.0) | 0.0 | 0.0 |
| Van der Waals complex... | |
|
|
|
| Transition state 1 (TS1)... | 22.8 (23.6) | 14.0 (15.2) | 9.1 | 8.6 |
| Intermediate... | -14.4 (-9.5) | -25.0 (-21.5) | -20.2 | -20.7 |
| Transition state 2 (TS2)... | 26.3 (24.8) | 13.6 (12.2) | 11.6 | 8.8 |
| HCCNC + H products... | -1.4 (-4.0) | -13.7 (-16.9) | -11.3 | -10.6 |
The relative energies are shown in kcal mol-1. The numbers shown in parentheses are the relative energies corrected for the zero-point vibrational energies.