The Astrophysical Journal, 687:726Y730, 2008 November 1 # 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.
A THEORETICAL STUDY OF THE PHOTODISSOCIATION MECHANISM OF CYANOACETYLENE IN ITS LOWEST SINGLET AND TRIPLET EXCITED STATES Cheng Luo, Wei-Na Du, Xue-Mei Duan, and Ze-Sheng Li Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, Changchun, 130023 Jilin, China; [email protected]
Received 2008 April 14; accepted 2008 June 25
ABSTRACT Cyanoacetylene (H5C4 C3C2 N1) is a minor constituent of the atmosphere of Titan, and its photochemistry plays an important role in the formation of the haze surrounding the satellite. In this paper, the complete active space self-consistent field (CASSCF) and multiconfigurational second-order perturbation (CASPT2) approaches are employed to investigate the photochemical processes for cyanoacetylene in its first singlet and triplet excited states with the cc-pVTZ basis set. Fissions of the C4H5 and C2C3 bonds in S1 yield H( 2S ) + CCCN(A 2) and HCC(A 2) + CN(X 2+), respectively. In T1, the corresponding dissociation products are H( 2S ) + CCCN(X 2+) and HCC(X 2) + CN(X 2+). At the CASPT2(14,13)//CASSCF(14,13) + ZPE level, the barriers for the adiabatic dissociation of the C4H5 and C2C3 bonds are 6.11 and 6.94 eV in S1 and 5.71 and 6.39 eV in T1, respectively, taking the energy of S0 minimum as reference. Based on the calculated potential energy surfaces, the existence of a metastable excited molecule is anticipated upon 260Y230 nm photoexcitation, which provides a probable approach for cyanoacetylene to polymerize. The internal conversion (IC) process through vibronic interaction followed by C4H5 fission in the ground state is found to account for the observed diffuse character in the UV absorption spectrum below 240 nm. Subject headingg s: astrochemistry — molecular processes — stars: atmospheres
Seki et al. (1996) determined the quantum yields for reactions (1), (2), and (4) at 193.3 nm to be 0.30 0.05, 0.02, and 0.70, respectively. A number of experiments have been undertaken to investigate the polymerization of HCCCN induced by photoexcitation (Carlini & Chien1984; Clarke & Ferris 1997; Ferris & Guillemin1990; Yuzhakova et al.1984). It has also been proposed that CA in its electronic exited state plays an important role in the formation of some polymers (Clarke & Ferris 1997). In this paper, the characteristics of the potential energy surfaces of the first singlet and triplet excited states are investigated. The mechanisms underlying the dissociation processes are determined on the basis of the calculated potential energy surfaces.
The photochemistry of cyanoacetylene (HC3N, hereafter CA) has received significant attention in recent years, as it provides clues to the origin of life ( Ferris et al. 2005). Because of its large absorption cross section in the UV region ( Bruston et al. 1989; Connors et al. 1974; Job & King 1966a, 1966b), the photochemistry of CA plays an important role in Titan’s atmosphere (Yung 1987; Yung et al. 1984), and its photolytic processes have been studied extensively in the laboratory (Clarke & Ferris 1995; Cody et al.1985; Halpern et al.1988,1990; Seki et al.1996; Titarchuk & Halpern 2000). Halpern et al. (1988) reported that cleaving of the CH bond is the major photodissociation pathway, with a reaction threshold of 244 8 nm, and that the quantum yield of the CC single bond fission is approximately 0.05 at 193 nm. Halpern et al. (1990) later proposed the following energetically accessible reaction processes at 193 nm: HC2 CN þ h ! C2 H þ CN;
HC2 CN þ h ! H þ C2 CN; HC2 CN þ h ! HCN þ C2 :
2. COMPUTATIONAL DETAILS Stationary structures for CA in the ground, first singlet, and triplet excited states were fully optimized by employing the complete active space self-consistent field (CASSCF) method (Roos 1987) with cc-pVTZ basis set ( Dunning1989). In order to consider the dynamic correlation energies, multiconfigurational second-order perturbation (CASPT2) theory (Finley et al. 1998) was applied for the single-point energy calculations. To confirm the right connective relationship between transition state and minimum (or dissociation product), the minimum-energy pathway (MEP) calculations were carried out at the CASSCF level. There are two degenerate sets of -type orbitals in the linear ground-state molecule. For convenience, we denote the () orbitals in each set as 1, 2, 3, and 4, in order of increasing energy. An active space containing 14 electrons in 13 orbitals, referred to as CASSCF(14,13) hereafter, was used for the calculations. The 13 orbitals include all the valence orbitals except the and orbitals of the C C and C N bonds. Calculations at the CASSCF(12,12) level, in which the lone pair orbital of the N atom is absent, were also performed for comparison. All the calculations mentioned above were carried out using the MOLCAS 6.2 program (Karlstro¨m et al. 2003). Unless otherwise noted, the
The thresholds of the three channels were suggested to be 200, 244, and 196 nm, respectively, according to the heats of formation given by Okabe (1978, p. 375). The possibility of reaction (3) was ruled out because of its large endothermicity and the large potential barrier for the linear molecule to rearrange. Clarke & Ferris (1995) found that the threshold of reaction (2) is 240 nm and that the quantum yield of H + CCCN, at a wavelength of 185 nm, is 0.09. Their experimental results also suggested that the major primary product upon photoexcitation from 185 to 254 nm is a metastable electronically excited molecule with a quantum yield of 0.86. This channel, with a threshold of 260 nm, is HC2 CN þ h ! HC2 CN :
PHOTODISSOCIATION OF CYANOACETYLENE TABLE 1 Bond Parameters for HCCCN, CCCN, HCC, and CN Obtained at the CASSCF/cc-pVTZ Level Bond Length (8) Structurea HCCCN: S0-MIN........................................... T1-cis-MIN ..................................... T1-cis-CHTS................................... T1-cis-CCTS................................... T1-trans-MIN.................................. T1-ISOTS ....................................... S1-MIN........................................... S1-CHTS ........................................ S1-CCTS......................................... CCCN(X 2+)..................................... CCCN(A 2) ...................................... HCC(X 2)......................................... HCC(A 2)......................................... CN(X 2+)..........................................
Bond Angle (deg)
Dihedral Angle (deg)
1.167 1.166 1.173 1.172 1.169 1.183 1.173 1.197 1.178 1.169 1.199 1.158 1.182 1.178 1.179 1.179 1.177 1.178 1.167 1.166 1.174 1.160 ... ... 1.170 1.157
1.383 1.384 1.398 1.398 1.386 1.387 2.305 1.321 1.381 1.384 1.321 2.513 1.396 1.381 1.352 1.350 2.059 2.039 1.382 1.382 1.366 1.363 ... ... ... ...
1.203 1.203 1.336 1.337 1.256 1.343 1.303 1.329 1.342 1.255 1.328 1.231 1.341 1.364 1.301 1.301 1.276 1.283 1.211 1.209 1.289 1.289 1.209 1.284 ... ...
1.074 1.073 1.099 1.099 1.980 1.069 1.068 1.096 1.091 1.977 1.096 1.079 1.103 1.107 1.657 1.658 1.080 1.059 ... ... ... ... 1.074 1.080 ... ...
180.0 180.0 174.8 174.9 177.2 172.5 176.9 179.4 173.8 177.5 178.9 173.3 172.4 173.5 178.7 179.3 152.3 151.1 180.0 180.0 180.0 180.0 ... ... ... ...
180.0 180.0 133.0 133.2 150.1 139.5 118.0 175.1 137.4 152.5 173.3 104.6 131.0 130.6 173.1 178.7 126.1 125.5 180.0 180.0 180.0 180.0 ... ... ... ...
180.0 180.0 128.2 128.3 114.4 130.4 138.0 129.5 129.9 114.8 129.7 159.7 124.1 119.7 114.1 114.0 176.4 172.1 ... ... ... ... 180.0 180.0 ... ...
... ... 180.0 180.0 179.8 179.8 133.5 138.7 179.9 180.0 146.2 170.7 179.4 176.8 180.0 179.6 126.2 145.2 ... ... ... ... ... ... ... ...
... ... 0.0 0.0 1.2 180.0 2.7 178.6 179.9 0.421 153.2 2.3 180.0 163.1 0.8 0.3 172.7 172.5 ... ... ... ... ... ... ... ...
Notes.—The values in roman type for HCCCN, CCCN, HCC, and CN were obtained at the CASSCF(14,13), CASSCF(13,12), CASSCF(7,7), and CASSCF(7,6) levels, respectively, while the values in italics for HCCCN, CCCN, and CN were obtained at CASSCF(12,12), CASSCF(11,11), and CASSCF(5,5) levels, respectively. The atom labels for HCCCN are given as H5C4 C3C2 N1. The labels for the fragments are associated with the parent molecule. a The optimizations of HCCCN were entirely carried out adopting the C1 symmetry point group except for S0-MIN, with C2v symmetry. The CCCN, HCC, and CN radicals were all optimized with C2v symmetry, and the frequency analysis shows that there exists no imaginary frequency at the converged geometries.
CASSCF(14,13) geometries and CASPT2(14,13)//CASSCF(14,13)/ cc-pVTZ energies with zero-point energy (ZPE) correction are used throughout. We attempted to locate the surface intersections in the FranckCondon region using a reduced active space, CASSCF(8,8). The optimizations of the crossing points were carried out using the program Gaussian 03 ( Frisch et al. 2003) and MOLCAS 6.2. 3. RESULTS AND DISCUSSION 3.1. The C4H5 and C2C3 Bond Fissions on the Singlet Surfaces (S0 and S1) The bond parameters for CA at its stationary points are presented in Table 1. The equilibrium geometry of ground-state CA has previously been investigated in detail both experimentally and theoretically (Botschwina 2005; Botschwina et al.1993; Job & King1963; Westenberg & Wilson1950). Our calculated bond parameters are in good agreement with Botschwina’s recent results (Botschwina 2005). In the ground state, no transition state was found on either the C4H5 or C2C3 dissociation pathway. The C4H5 and C2 C3 fissions adiabatically produce H( 2S ) + CCCN(X 2+) and HCC(X 2) + CN(X 2+), respectively. The relative energy of H( 2S ) + CCCN(X 2+) is 5.65 eV, which does not deviate much from the previously determined values of 6.00 0.09 eV by Francisco & Richardson (1994) and 5.52 eV by Yang et al. (2006). The dissociation thresholds experimentally observed are 5.08 eV
(244 nm) from Halpern et al. (1988, 1990) and 5.17 eV (240 nm) from Clarke & Ferris (1995), respectively. Our CASPT2 result slightly overestimates the C4H5 bond energy. The C2C3 dissociation energy is 6.39 eV, which is energetically inaccessible by photoexcitation at wavelengths longer than 194 nm. This energy was estimated to be 6.37 0.09 eV by Francisco & Richardson (1994) and 6.06 eV by Yang et al. (2006). The reaction threshold of the C2C3 fission is experimentally observed to range from 184.4 nm ( Yung et al. 1984) to 200 nm ( Halpern et al. 1988), values that bracket our result. Before discussing the CH and CC single bond fissions in S1, we focus on the S1 equilibrium geometry. Early theoretical results (Fischer & Ross 2003) showed that the S1 minimum (‘‘S1-MIN’’) has a planar structure. However, our CASSCF(14,13) calculation reveals that the optimization of S1-MIN with the Cs symmetry constraint leads to an imaginary frequency of 492i cm1 (a 0 0 symmetry) at the converged geometry. The global minimum, with no imaginary frequency, was finally located with C1 symmetry. As shown in Table 1, S1-MIN presents a quasi-planar geometry. The N1C2, C2C3, and C3C4 distances in S1-MIN become 1.182, 1.396, and 1.341 8, respectively, while the NCC, CCC, and CCH angles are 172.4 , 131.0 , and 124.1 , respectively. These structural changes can be attributed to the 3 2 transition. It should be pointed out that although the 2 and 3 orbitals among the heavy atoms have a delocalized tendency to cover the whole molecular backbone, the electronic transition is mainly localized on the C3C4 moiety. The S1 adiabatic excitation
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TABLE 2 Vertical Excitation Energies of Cyanoacetylene Obtained at the CASPT2 + ZPE Level State
1 1A1(X 1+) ..................... 1 1A2(A 1).....................
0.90 0.87 0.87 0.87 0.86 0.87 0.86
0 6.76 6.92 7.16 7.32 7.16 7.32
0 5.46 5.46 5.81 5.78 5.81 5.78
... 0.0 0.0 0.0 0.0 0.0 0.0
... 2 ! 3 2 ! 3 2 ! 3 2 ! 3 2 ! 3 2 ! 3
... 5.48 ... 5.80 ... 5.80 ...
... 5.10 ... ... ... ... ...
2 1A1(B 1) ...................... 2 1A2(B 1) ......................
Note.—Entries in roman type show the CASPT2(14,13) + ZPE results, and italics show the CASPT2(12,12) + ZPE results. a Reference weight. b Relative CASSCF/cc-pVTZ + ZPE energies in eV. c Relative CASPT2/cc-pVTZ + ZPE energies in eV, with the level-shift value equal to 0.0 hartrees. d Oscillator strength in atomic units. e Previous theoretical results at the CASPT2 level ( B. O. Roos, unpublished). f Experimental result from Job & King (1966a).
energy is 4.71 eV, in good agreement with the experimental value of 4.77 eV (260 nm), which was found to be the threshold for the formation of the metastable HCCCN. The H and CN moieties in S1-MIN are clearly trans oriented with respect to the C3C4 bond, and all the optimizations from cis-oriented structures result in the trans-oriented S1-MIN. On the C4H5 and C2C3 fission pathways in S1, the respective transition states S1-CHTS and S1-CCTS were located. The MEP calculations confirm that S1-CHTS connects S1-MIN and H( 2S ) + CCCN(A 2), while S1-CCTS connects S1-MIN and HCC(A 2) + CN(X 2+). The relative energy of S1-CHTS is 6.11 eV with respect to the S0 zero level and only 0.06 eV higher than that of H( 2S ) + CCCN(A 2). At the CASSCF(14,13) + ZPE level, S1-CCTS lies 0.27 eV above HCC(A 2) + CN(X 2+); however, it lies 0.11 eV below HCC(A 2) + CN(X 2+) at the CASPT2(14,13)//CASSCF(14,13) + ZPE level. Given that the difference also exists between CASSCF(12,12) + ZPE and CASPT2(12,12)//CASSCF(12,12) + ZPE levels, the results with CASPT2 verification should be taken seriously. According to Page & Olivucci’s (2003) test calculations, the CASPT2//CASSCF and CASPT2//CASPT2 profiles are almost identical. It is reasonable to consider that the C2C3 fission in S1 is a process without a transition state and that the dissociation barrier is 6.94 eV, which is the relative energy of HCC(A 2) + CN(X 2+) with respect to S0-MIN at the CASPT2(14,13)//CASSCF(14,13) + ZPE level. From the energy viewpoint, in either the S0 or S1 state the C4H5 cleavage is superior to the C2C3 fission, which indicates that the C4H5 bond, the weakest in the ground state, is still the most fragile following photoexcitation. Given the relative energies of S1-CHTS and HCC(A 2) + CN(X 2+), direct dissociation of the C4H5 and C2C3 single bonds in S1 should occur if the wavelengths of the absorbed photon are shorter than 203 and 179 nm, respectively. However, as listed in Table 2, the vertical excitation energy of the S2 state (B 1) is 5.80 eV (214 nm), which means that such short wavelengths would lead the molecule to the S2, or even higher, electronic excited state. 3.2. The C4H5 and C2C3 Bond Fissions on the Triplet Surface (T1) As opposed to the case of S1, there are two minima in T1, one trans oriented ( T1-trans-MIN ) and the other cis oriented ( T1-cis-MIN ). Both are close to S1-MIN in structure, except for the CCH angle and the CCCH dihedral angle. This structural similarity can be seen as a result of the fact that the S1 and T1 states both originate from the same 3 2 transition. T1-cis-MIN is
energetically more stable than T1-trans-MIN by 0.14 eV. At the CASSCF(14,13) + ZPE level, the transition state T1-ISOTS connecting T1-cis-MIN and T1-trans-MIN is found and predicted to lie 0.30 eV above T1-cis-MIN and 0.08 eV above T1-trans-MIN. However, the CASPT2(14,13) calculations show that this energy barrier disappears, which indicates that T1-trans-MIN could easily isomerize to the more stable T1-cis-MIN. The C4H5 and C2C3 bond fissions in T1 yield H( 2S ) + CCCN(X 2+) via T1-cis-CHTS and HCC(X 2) + CN(X 2+) via T1-cis-CCTS, respectively. T1-cis-CHTS lies 5.70 eV above the S0 minimum and only 0.05 eVabove H( 2S ) + CCCN(X 2+). At the CASSCF(14,13) + ZPE level, T1-CCTS lies 0.23 eVabove HCC(X 2) + CN(X 2+); however, it turns out to be 0.05 eV below at the CASPT2(14,13)//CASSCF(14,13) + ZPE level. According to El Sayed’s rule (El-Sayed 1968; Lower & ElSayed1966), the rate of intersystem crossing is relatively small if the nonradiative decay does not involve a change of orbital type. In this case, both S1 and T1 states originate from the transition, which indicates a small chance for the formation of T1-cis-MIN through intersystem crossing ( ISC), under the condition that the ISC point between S1 and T1 is absent. 3.3. The Dissociation Mechanism and Implications for the Atmosphere of Titan On the adiabatic surface of S1, neither the CH nor the CC single bond fission is energetically accessible upon one-photon absorption in the wavelength range from 230 to 260 nm. We endeavored to locate the surface crossing point in the FranckCondon region where radiationless decay from S1 to S0 or T1 would take place efficiently. Although various initial structures (the equilibrium geometries in S0, S1, and T1, and two points in the MEPs) were used, no intersection was found, which indicates that radiationless decay via a surface intersection is unlikely to occur. In addition, the CASSCF(14,13) calculations provide an oscillator strength of approximately 0.005 from S1 to S0 at S1-MIN, which indicates a low radiative transition rate. Accordingly, a high quantum yield and a long lifetime of the metastable excited molecule HCCCN can be anticipated from photoexcitation between 230 and 260 nm. In fact, HCCCN was experimentally detected as the major product in the primary photochemical process by Clarke & Ferris (1995) and by Seki et al. (1996). The existence of the metastable HCCCN has significant consequences for the atmosphere of Titan. The molecular equilibrium geometry, which is originally linear in S0, becomes bent and distorted in S1. The C3C4 distance of 1.341 8 in S1-MIN is close
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PHOTODISSOCIATION OF CYANOACETYLENE
to the typical carbon-carbon double bond. The CCC (131.0 ) and CCH (124.1 ) angles both approach the typical bond angle between the sp2 hybrid orbitals. These structural characteristics of S1-MIN make it easy for CA to undergo addition reactions involving the unsaturated C3C4 bond, leading to different products when attacked by different reagents. In Titan’s atmosphere, large amounts of various hydrocarbons and cyanides act as attacking reagents to induce addition reactions for CA. Clarke & Ferris (1997) investigated experimentally the photopolymerization processes of pure CA and HC3N/C2H6, HC3N/CO, and HC3N/ C2H2 mixtures at 254 nm. Through infrared, elemental, and thermal analyses, they suggested that the C = C double bonds in the possible polymers that were previously determined to be cis oriented by Yuzhakova et al. (1984) are very likely trans oriented. Consistent with Clarke & Ferris’s experiments, the equilibrium geometry in S1 is trans oriented rather than cis oriented, as already mentioned, in our calculations. From the structural point of view, a cis orientation in the polymer could give rise to a rotation process with respect to the C3C4 bond or a bending process of the CCH (or CCC) bond angle, either of which would make the metastable S1-MIN overcome an energy barrier to reach another structure. Therefore, it can be expected that the trans orientations of the nitrile groups and hydrogen atoms would be predominant in such polymers. In isolation, CA in its S1 state, HCCCN, would undergo relaxation to produce a rovibrationally hot ground-state molecule. With the exception of radiative decay, the relaxation from S1 to S0 is mainly through the vibronic interaction between the two electronic states. The 3 2 transition from S0 to S1, which results in a bent and distorted S1 equilibrium geometry, leads not only to the displacement and the distortion but also to the mixing of the normal modes. The frequency analysis shows that the normal modes 4 (C2C3 stretching mode) and 5 (CCC bending mode) in S0 mix with each other in S1. As suggested by Mebel transitions in molecules of small or interet al. (1999), for mediate size, the change of frequencies and the mixing of normal modes would increase the rate of the nonradiative transition process. Nonradiative transitions in our system are well suited to play a significant role according to Mebel et al.’s theory. The relatively large rate at which the molecule in the S1 state can go back to the S0 state through nonradiative transitions necessitates a detailed discussion of reactions in the ground state. The amount of energy that the hot molecule accumulates depends on the wavelength of the absorbed photon. Once the accumulated energy transcends the dissociative threshold of CA in the ground state, a dissociation reaction will take place in the ground state. From the energy analysis, CH bond fission is the most probable dissociation channel in S0. The threshold for the CH fission is 5.65 eV, which seems to be the predominant barrier for the dissociation process. The channel for the CH fission can be summarized as follows, with the relative energies in parentheses: h
Fig. 1.— Potential energy surfaces of the S1, T1, and S0 states for the dissociation of the C4H5 and C2C3 single bonds of HCCCN obtained at the CASPT2(14,13)/ cc-pVTZ//CASSCF(14,13)/cc-pVTZ + ZPE, CASSCF(14,13)/cc-pVTZ + ZPE, CASPT2(12,12)/cc-pVTZ//CASSCF(12,12)/cc-pVTZ + ZPE, and CASSCF(12,12)/ cc-pVTZ + ZPE levels. Energies are in eV.
This process would not occur upon photoexcitation from 230 to 260 nm. Titan’s surface temperature is about 178 C, which is too low to significantly influence the reaction mechanisms. The principal energy source in Titan’s atmosphere is the solar UV irradiation, which is also the primary driving force responsible for the creation and the destruction of various species. According to our calculations, once a photon whose wavelength is shorter than 263 nm (4.71 eV) is absorbed by HCCCN, it is likely to yield the metastable HCCCN, which can subsequently react with other molecules or radicals to form species with large molecular weight. On the other hand, in each of the three considered states (S0, S1, and T1) the formation of the CA molecule, either from HCC + CN or from H + CCCN, is a process that has no energy barrier or one less than 0.1 eV, accompanied by the release of a large amount of heat.
S0 -MIN (0:0 eV) ! S1 -MIN (4:71 eV) ! S0 -MIN ( hot) ! H( 2 S ) þ CCCN(X 2 þ ) (5:65 eV): This mechanism provides a rational explanation for the diffuse nature exhibited in the UV absorption bands below 240 nm; that is, following the absorption of a photon at 240 nm, the molecule will have enough energy to dissociate along the CH bond in the ground state. The most possible channel for the CC single bond fission is h
S0 -MIN (0:0 eV ) ! S1 -MIN (4:71 eV ) ! S0 -MIN ( hot) ! HCC(X 2 ) þ CN(X 2 þ ) (6:39 eV ):
4. CONCLUSION The mechanism of the photodissociation of CA has been studied at both the CASPT2(14,13)//CASSCF(14,13) + ZPE and the CASPT2(12,12)//CASSCF(12,12) + ZPE levels. The energy differences between the CASPT2(14,13) and CASPT2(12,12) levels are less than 0.15 eV. It can be concluded that the absence of the lone pair orbital of the nitrogen atom in the active space has a marginal influence on the description of the reaction pathways for C4H5 and C2C3 fissions. As shown in Figure 1, on the S1 surface of CA, when the excitation energy is more than 4.71 eV, the metastable state S1-MIN is the most probable primary product. In the energy range from 5.65 to 6.11 eV, direct S1 dissociations
LUO ET AL.
are energetically inaccessible, but internal conversion by means of vibronic interaction followed by CH fission in the ground state is a most probable dissociation channel. When the excitation energy is higher than 6.11 eV, the S1 adiabatic dissociation to H( 2S ) + CCCN(A 2) and IC followed by CH fission in S0 are both likely to occur. The HCC and CN radicals will not be produced if the excitation energy is less than 6.39 eV. Our calculations show that photoexcitation provides the main possibilities for the small nitrogen-containing molecule HC3N to yield species with large molecular weight rather than dissociating into small radicals, indicating that HCCCN, as one of the minor constituents of the reductive atmosphere, which is considered necessary for the origin of life, is not extremely vulnerable
to falling apart under the condition of UV illumination but has the ability to undergo polymerizations. Our theoretical results are consistent with the corresponding experiments and may be useful for further experimental studies about cyanoacetylene and other relevant molecules.
This work was supported by the National Natural Science Foundation of China (grants 20333050, 20673044), the Program for Changjiang Scholars and Innovative Research Teams (grant IRT0625), and the program Key Subject of Science and Technology by Jilin Province.
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