Theoretical kinetic study of large species in the isomerization reaction HC n N HC n 1 NC (n = 7, 9 and 11)

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1 doi: /mnras/stu1963 Theoretical kinetic study of large species in the isomerization reaction HC n N HC n 1 NC (n = 7, 9 and 11) R. M. Vichietti and R. L. A. Haiduke Departamento de Química e Física Molecular, Instituto de Química de São Carlos, Universidade de São Paulo, CP 780, São Carlos, SP, Brazil. Accepted 2014 September 17. Received 2014 September 12; in original form 2014 July 28 1 INTRODUCTION Several molecules have been identified in the interstellar medium and circumstellar envelopes since the 1930s, reaching an amount of almost 200 of them, without considering isotopic varieties (Müller et al. 2001, 2005). These molecules can be composed from two to tens of atoms, and fullerenes (C 60 and C 70 ) are the largest ones observed in these environments nowadays (Cami et al. 2010). However, HC 11 N also occupied this position for some time since its first detection in 1997 (Bell et al. 1997). HC 11 N is a member of a group of linear molecules with alternation of single and triple bonds between carbon atoms, known as cyanopolyynes (HC n N, n = 1, 3, 5,... ). Interestingly, cyanopolyynes with n = 1 9 have already been identified in different sources, such as Heiles Cloud 2, IRC+10216, TMC 1and others (Snyder & Buhl 1971; Turner 1971; Avery et al. 1976; Broten et al. 1978; Kroto et al. 1978). Furthermore, there are some less common isomers of cyanopolyynes, which are called by isocyanopolyynes and have the structural formula HC n 1 NC. Unfortunately, only isocyanopolyynes with n = 1 and 3 have been identified in the interstellar medium and the first detections of these molecules ABSTRACT Cyanopolyynes (HC n N, n = 1, 3, 5,... ) with as many as 11 carbon atoms have already been identified in the interstellar medium. However, only the two smallest isocyanopolyynes (HC n 1 NC) were observed in such environment. This fact motivated the first kinetic study of the isomerization reaction between such long-chain species with n = 7, 9 and 11. In this sense, thermodynamic data, transition-state geometries and rate constants for these reactions were estimated by means of advanced quantum chemistry calculations at temperatures from to 3000 K. We show that the general conclusions are similar to the ones observed in a previous investigation for n = 1, 3 and 5. Thus, this reaction is exothermic and faster in the direction that leads to cyanopolyynes, favouring these isomers in colder environments. However, the ratio between forward and reverse rate constants for this isomerization approaches unit as the temperature is raised, suggesting that warmer environments, such as those found in the atmospheres of evolved carbon stars, are probable candidates for the detection of long-chain isocyanopolyynes. This study also indicates that the kinetic data at the highest temperatures considered show some unexpected variations with respect to chain-size increments caused by entropic contributions. Finally, parameterized equations were fitted to reproduce our rate constant data for reactions with n = 7 11 along the temperature range considered. Key words: astrochemistry molecular processes ISM: molecules. occurred in W51, NGC 2264 and TMC 1 (Snyder & Buhl 1972; Zuckerman et al. 1972; Kawaguchi et al. 1992). Cyanopolyynes are excellent molecules to be used as probes of the physical conditions in dark clouds (Winstanley & Nejad 1996). However, the formation of these long carbon chains in the interstellar medium is already a mystery, and several chemical mechanisms have been proposed to explain this process. The same authors suggest that ion molecule reactions are dominant in time-scales smaller than 10 4 yr and large cyanopolyynes could be formed in cold clouds by the following sequence: C n H + N C n N + H 2 HC n N + H 2 H 2 C n N + e HC n N (1.1) but, neutral neutral reactions become the most important ones for time-scales larger than 10 4 yr according to HCN and C 2H HC 3 N C 2H HC 5 N C 2H HC 7 N C 2H HC 9 N (1.2) C n H 2 + CN HC n+1 N + H (n = 4, 6 and 8), (1.3) haiduke@iqsc.usp.br where reactions (1.2) and (1.3) occur only when there are large abundances of C 2 HandC 2 H 2. C 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society

2 Kinetic of HC n N HC n 1 NC (n = 7, 9 and 11) 3611 On the other hand, Chapman et al. (2009) believed that cyanopolyynes can also be formed in hot-core regions ( 200 K) and presented important chemical routes that could explain the formation of HC 5 N, HC 7 NandHC 9 N in these environments. They mention that the abundance of these systems depends directly on acetylene, which is very abundant in the early stages of the core evolution. So, these authors also consider reactions (1.3) as important routes for the formation of large cyanopolyynes in hot sources, and C n H 2 (n = 6 and 8) in these reactions are, respectively, originated by C n 4 H 2 + C 4 H C n H 2 + H (1.4) and C n 2 H 2 + C 2 H C n H 2 + H. (1.5) Chapman et al. (2009) also conclude that cyanopolyynes are short lived. However, this fact suggests that cyanopolyynes do behave like chemical clocks, which allows us to determine the age of hot cores according to their abundances. Nevertheless, a large variety of molecules with long carbon chain can also be observed in circumstellar shells and dust grains that surround carbon-rich stars, such as in IRC ( 2500 K; Winnewisser & Walmsley 1979). Moreover, they point out that this kind of molecules is synthetized from acetylene (as mentioned above by Chapman et al. 2009) or diacetylene, C 4 H 2,andthefirst ones have been discovered in the shell of carbon-rich stars with abundance comparable to that of carbon monoxide. Laboratory experiment carried out by Vasile & Smolinsky (1977) showed that reaction C 2 H + X + C 2H 2 C 4 H + Y + C 2H 2 C 6 H + Z + C 2H 2... (1.6) forms long polyacetylenes under acetylene discharge. On the other hand, these species can react with CN and HCN to form cyanopolyynes, although Broten et al. (1978) noticed that the abundances of these systems decline as the chain length increases, which was observed at least in Heiles Cloud 2. Until now, many possibilities that could explain the formation of large cyanopolyynes outside Earth have been discussed, but similar studies are lacking for isocyanopolyynes, to the best of our knowledge. Hence, the aim of this work is to investigate whether the formation of large isocyanopolyynes in the interstellar medium can take place from cyanopolyynes by means of the isomerization reaction between these systems. Thus, transition-state geometries, activation enthalpies, Gibbs free energies of activation and rate constants for these forward and reverse isomerization reactions are determined for n = 7, 9 and 11. We used a similar combined quantum chemical treatment to the one carried out in our previous study (Vichietti & Haiduke 2014) that considered smaller (iso)cyanopolyynes with n = 1, 3 and 5. 2 METHODOLOGY All electronic structure calculations were performed with the GAUSSIAN 03 package (Frisch et al. 2004) and rate constants are derived from the transition state theory (TST; Evans & Polanyi 1935). The difficulties in the description of electron correlation along with very large basis sets led to the creation of practical procedures to obtain molecular energies in the limit of a complete basis set, E CBS, by means of extrapolation strategies from calculations carried out with finite-size basis sets (Nixon et al. 2012; Spada et al. 2013; Vichietti & Haiduke 2014). Moreover, all the required energy contributions for theoretical studies of chemical kinetics are usually obtained in two distinct steps (Simón & Goodman 2011), in which one selects a combination of methods and basis sets that does not lead to a very high computational demand and still provides as accurate results as those obtained with more advanced methods associated with large basis sets. This study considered temperatures of , 500, 700, 1000 and 3000 K. So, in step 1, geometries, zero-point energies and thermal corrections of thermodynamic quantities (enthalpy and Gibbs free energy, for example) for chemical species that participate in the reaction (reactants, products and transition states) are found with the same density functional theory (DFT) methods used to treat this kind of reaction for n = 1, 3 and 5 (Vichietti & Haiduke 2014), B3LYP and MPW1K. However, a smaller basis set was employed for the large systems considered in this paper (n = 7, 9 and 11), aug-cc-pvtz. Moreover, in step 2, electronic energy calculations are performed in the optimized geometries determined in step 1 (minimum points associated with reactants, products and transition states) by means of the most advanced levels as possible. Here, the CCSD(T)/augcc-pVmZ (m = D and T) levels were chosen to treat these large systems. For comparison, the isomerization of smaller members was investigated with the same method but considered larger basis sets (Vichietti & Haiduke 2014). Next, the electronic energy results obtained at these two levels are extrapolated according to a mathematical expression that provides an estimate of E CBS. The following extrapolation equation was adopted here (Nixon et al. 2012; Spada et al. 2013; Vichietti & Haiduke 2014), E CBS = [E(n b) n 3 b E(n a) n 3 a ] [n 3 b n3 a ], (2.1) where n a = 2 for aug-cc-pvdz and n b = 3 for aug-cc-pvtz. E(n a ) and E(n b ) are electronic energies given by levels with m = D and T, respectively. Thus, electronic energy results provided by equation (2.1) are added to zero-point energies and thermal corrections found in step 1 providing a combined estimate of thermodynamic quantities (enthalpies and Gibbs free energies). So, the nomenclature method/basis set (step 1)//method/basis set (step 2) will be used in the following discussions to represent all the choices made. Thus, the Gibbs free energy of activation provided by this combined treatment is employed in an expression derived from TST that determines rate constants, k, for unimolecular reactions (Wynne- Jones & Eyring 1935; Garret & Truhlar 1979). So, this theory is adequate for forward and reverse isomerization reactions HC n N HC n 1 NC (n = 7, 9 and 11) and k is obtained by k = k BT h e Gact RT, (2.2) with k B being the Boltzmann constant, h represents the Planck constant, G act indicates the Gibbs free energy of activation, R is the ideal gas constant and T refers to temperature. Besides, quantum tunnelling effects should be considered to provide more realistic data for rate constants, especially at low temperatures. We chose a semiclassical approximation known by Wigner factor (Wigner 1932; Buchowiecki & Vanicek 2010; Nixon et al. 2012). This factor should be multiplied by equation (2.2) to provide a Wigner rate constant, k w, which is described by [ k w = k ( ) ] hc ωi 2, (2.3) 24 k B T

3 3612 R. M. Vichietti and R. L. A. Haiduke where c is the speed of light (in cm s 1 )andω i denotes the imaginary frequency (in cm 1 ) of the transition state. Finally, a modified Arrhenius equation (McElroy et al. 2013), given by k = α ( T 300 ) β ( ) γ exp, (2.4) T was used to fit our Wigner rate constant results for both forward and reverse reactions HC n N HC n 1 NC (n = 7, 9 and 11) from to 3000 K, providing values for α, β and γ parameters. 3 RESULTS AND DISCUSSION 3.1 Validation of the methodology In order to validate our kinetic results for reactions with n = 7,9and 11 at the CCSD(T)/CBS and MPW1K/augcc-pVTZ//CCSD(T)/CBS levels, we also applied the entire procedure proposed here for the isomerization reactions of smaller systems with n = 1, 3 and 5, in which cases there are more experimental and theoretical results for comparison. The geometric results for these small cyanopolyynes and isocyanopolyynes are shown, respectively, in Tables 1 and 2. Fortunately, all bond length results obtained by B3LYP and MPW1K functionals with the aug-cc-pvtz basis set are in nice agreement with experimental data and the maximum deviation is smaller than 2 per cent. Furthermore, several of these results are even better than those from a larger aug-cc-pvqz set (Vichietti & Haiduke 2014) with respect to experimental data (Costain 1958; Alexander, Kroto & Walton 1976; Krüger et al. 1991; Okabayashi & Tanimoto 1993; McCarthy & Thaddeus 2001). Obviously, this fact is explained owing to more efficient error cancellations between DFT methods and the aug-cc-pvtz set. Besides, results of bond lengths and angles of transition states from the augcc-pvtz basis set (Table 3) for these small systems are also close to the ones obtained in B3LYP/aug-cc-pVQZ and MPW1K/aug-ccpVQZ calculations (Vichietti & Haiduke 2014) and to data found by Van Mourik et al. (2001) with much more advanced levels, CCSD(T)/cc-pCVTZ and CCSD(T)/cc-pCVQZ, for the reaction HCN HNC. Moreover, we analysed imaginary frequencies of the transition states furnished by B3LYP and MPW1K methods with the aug-cc-pvtz basis set and their results are available in Table 4. These values are compared with those obtained by the aug-ccpvqz basis set (Vichietti & Haiduke 2014) and one can see that they are in excellent agreement, with a maximum deviation of 0.7 per cent. Zero-point energies and thermal corrections are also almost insensitive to the exchange of aug-cc-pvtz for aug-ccpvqz sets in step 1 at temperatures of and 3000 K (see Tables A1 and A2 in the appendix, available online as Supporting Information). Finally, Table 5 was elaborated to evaluate the effect of a reduction of the basis set size in step 2, as proposed for the larger systems investigated here when compared to our previous study (Vichietti & Haiduke 2014). In this table, electronic energy differences among reagents, products and transition states are derived from CBS1 (given by aug-cc-pvmz levels, m = DandT)and CBS2 (m = T and Q) alternative extrapolations for n = 1, 3 and 5. Differences between values from CBS1 and CBS2 are not higher than 0.7 kcal mol 1, no matter which method was chosen to step 1 Table 1. Bond lengths (Å) of small cyanopolyynes calculated at B3LYP/aug-cc-pVTZ and MPW1K/aug-cc-pVTZ levels. a Bond B3LYP/aug-cc-pVTZ MPW1K/aug-cc-pVTZ HCN HC 3 N HC 5 N HCN HC 3 N HC 5 N H C ( 0.24) (0.60) ( 0.53) (0.12) (0.91) ( 0.23) C1 C (0.21) (0.28) (1.02) (1.12) C2 C (0.76) (0.56) (0.71) (0.37) C3 C (0.91) (1.88) C4 C (0.22) (0.07) C n N b (0.67) (0.30) (0.28) (1.49) (1.30) (1.34) Note: a The values in parentheses are the standard deviations (per cent) in relation to experimental data (Costain 1958; Alexander et al. 1976; McCarthy & Thaddeus 2001). b Here, n is 1, 3 and 5, respectively, for each one of the listed levels. Table 2. Bond lengths (Å) of small isocyanopolyynes calculated at B3LYP/aug-cc-pVTZ and MPW1K/aug-cc-pVTZ levels. a Bond B3LYP/aug-cc-pVTZ MPW1K/aug-cc-pVTZ HNC HC 2 NC HC 4 NC HNC HC 2 NC HC 4 NC H N ( 0.08) (0.62) H C ( 0.59) ( 0.28) C1 C (0.34) (1.12) C2 C C3 C C n 1 N b (0.82) (1.10) N C (0.31) ( 0.15) (1.07) (0.77) Note: a The values in parentheses are the standard deviations (per cent) in relation to experimental data (Krüger et al. 1991; Okabayashi & Tanimoto 1993). b Here, n is 3 and 5, respectively, for each one of the listed levels.

4 Kinetic of HC n N HC n 1 NC (n = 7, 9 and 11) 3613 Table 3. Transition-state bond lengths (Å) and angles (degrees) for the reactions HC n N HC n 1 NC (n = 1, 3 and 5) calculated at B3LYP/augcc-pVTZ and MPW1K/aug-cc-pVTZ levels. Bond/angle a B3LYP/aug-cc-pVTZ MPW1K/aug-cc-pVTZ n = 1 H Cl Cl N N H H C1 N b H N C1 b n = 3 H C C1 C C2 C C3 N N C C1 C2 C3 b C1 C2 N b C2 C3 N b n = 5 H C C1 C C2 C C3 C C4 C C5 N N C C1 C2 C3 b C3 C4 C5 b C3 C4 N b C4 C5 N b Note: a The dotted lines indicate bonds that are being broken/formed along the reaction coordinate. b Angle originating from the central atom. Table 4. Comparison of imaginary frequencies (cm 1 ) for the transition state of reactions with n = 1, 3 and 5 obtained at B3LYP/aug-cc-pVmZ and MPW1K/aug-cc-pVmZ (m = T and Q) levels. Level n = 1 n = 3 n = 5 B3LYP/aug-cc-pVTZ 1126i 420i 430i B3LYP/aug-cc-pVQZ a 1126i 422i 433i MPW1K/aug-cc-pVTZ 1165i 495i 509i MPW1K/aug-cc-pVQZ a 1166i 496i 510i Note: a Values obtained by Vichietti & Haiduke (2014). (B3LYP or MPW1K). Thus, these overall results of bond lengths, imaginary frequencies, zero-point energies, thermal corrections and electronic energy differences presented by the combined approach DFT/aug-cc-pVTZ//CCSD(T)/CBS1 for reactions with n = 1, 3 and 5 assure that this choice is also indicated for the larger systems investigated in this work. 3.2 Kinetic results for the isomerization of large (iso)cyanopolyynes Tables 6 and 7 show, respectively, bond lengths of cyanopolyynes and isocyanopolyynes obtained at B3LYP/aug-cc-pVTZ and MPW1K/aug-cc-pVTZ levels for systems with n = 7, 9 and 11. Experimental bond lengths are available only for large cyanopolyynes (McCarthy & Thaddeus 2001). The B3LYP treatment predicts triple-bond distances in closer agreement with these experimental results while MPW1K is better to describe simple bonds. In general cases, our theoretical results underestimate the experimental data (positive values between parenthesis), but these deviations do not reach 2 per cent. In addition, it is possible to notice that triple bonds given by the B3LYP/aug-cc-pVTZ level are a little longer than those furnished by MPW1K/aug-cc-pVTZ, while the opposite usually occurs for single bonds in both (iso)cyanopolyynes. Ultimately, Table 8 provides bond distances and angles for the transition states of the isomerization reactions HC n N HC n 1 NC (n = 7, 9 and 11) at the same levels previously mentioned. The transition-state geometries present a typical triangular structure formed by nitrogen and the two closest carbon atoms, C α and C β. This configuration can be seen in Fig. 1. Besides, one can see that this triangular structure is formed mainly by a sudden displacement of nitrogen towards C β, which is also bound to nitrogen at the end of the reaction. Here, a similar fact related with geometries contained in Tables 6 and 7 also occurs and B3LYP/aug-cc-pVTZ level presents larger triple-bond lengths than MPW1K/aug-cc-pVTZ, while the opposite tends to be observed for single ones. The MPW1K method overestimates their angle results in relation to those obtained by the B3LYP treatment (Table 8), with deviations up to 2 between these two levels. Furthermore, the B3LYP/aug-cc-pVTZ level provides imaginary frequencies for the transition states of 441i, 447i and 450i cm 1, respectively, for the reactions with n = 7, 9 and 11. On the other hand, MPW1K/aug-cc-pVTZ level presents slightly larger values of 515i, 518i and 520i cm 1, respectively, for the same reactions. Activation enthalpies for reactions HC n N HC n 1 NC (n = 7to 11) are available in Table 9 for all selected temperatures. These activation enthalpies were calculated according to the theoretical procedure described above, in which the CBS extrapolation is estimated from CCSD(T)/aug-cc-pVmZ and CCSD(T)/aug-cc-pVmZ (m = D and T) levels, whose values can be found from Table A3 A5 (in the appendix available online as Supporting Information). The CCSD(T)/CBS level always provides results of enthalpies for forward and reverse reactions, H f and H r, slightly higher than those obtained with MPW1K geometries for all analysed temperatures. In this sense, the maximum difference between these two levels is not higher than 0.7 kcal mol 1. All these enthalpy values do not vary significantly with chain-size increments, with maximum deviations of only 0.4 kcal mol 1. Furthermore, the largest difference from n = 3 (Vichietti & Haiduke 2014) to 11 is around 1 kcal mol 1. Moreover, there is a gradual decrease for H f and H r values as temperature increases. The H values become larger in high temperatures but the variation is less significant than the ones for H f and H r, resulting in a difference of only 0.9 kcal mol 1 between results at and 3000 K. This fact suggests that enthalpy for the transition-state geometry is more sensitive to temperature changes than enthalpies for reactants and products. Finally, one can notice that isomerization reactions are exothermic in the reverse direction, which produces cyanopolyynes. Gibbs free energies of activation carried out at the CCSD(T)/CBS and MPW1K/aug-ccpVTZ//CCSD(T)/CBS levels for the reactions HC n N HC n 1 NC (n = 7, 9 and 11) are shown in Table 10 for the same temperature range ( K). Results that were extrapolated to generate CBS values (CCSD(T)/aug-cc-pVmZ and CCSD(T)/aug-cc-pVmZ, with m = Dand T) are available in Tables A6 A8 (in the appendix available online

5 3614 R. M. Vichietti and R. L. A. Haiduke Table 5. Electronic energy differences (kcal mol 1 ) among reagents (HC n N), products (HC n 1 NC) and transition states (TS n ) for reactions with n = 1, 3 and 5 obtained by alternative CBS extrapolations. m/aug-cc-pvqz//ccsd(t)/cbs1 a m/aug-cc-pvqz//ccsd(t)/cbs2 b m = B3LYP m = MPW1K m = B3LYP m = MPW1K TS 1 HCN TS 1 HNC HNC HCN TS 3 HC 3 N TS 3 HC 2 NC HC 2 NC HC 3 N TS 5 HC 5 N TS 5 HC 4 NC HC 4 NC HC 5 N Note: a CBS1 refers to the extrapolation equation given by aug-cc-pvdz and aug-cc-pvtz basis sets. b CBS2 refers to the extrapolation equation given by aug-cc-pvtz and aug-cc-pvqz basis sets. Table 6. Bond lengths (Å) of cyanopolyynes calculated at B3LYP/aug-cc-pVTZ and MPW1K/aug-cc-pVTZ levels. a Bond B3LYP/aug-cc-pVTZ MPW1K/aug-cc-pVTZ HC 7 N HC 9 N HC 11 N HC 7 N HC 9 N HC 11 N H C ( 0.50) ( 0.48) ( 0.48) ( 0.19) ( 0.19) ( 0.19) C1 C (0.26) (0.28) (0.17) (1.14) (1.18) (1.08) C2 C (0.69) (0.74) (0.79) (0.46) (0.46) (0.48) C3 C ( 0.24) ( 0.18) ( 0.18) (0.83) (0.95) (0.98) C4 C (1.26) (0.79) (1.01) (0.95) (0.37) (0.53) C5 C (0.01) (0.62) ( 0.56) (1.08) (1.79) (0.69) C6 C (0.52) (0.64) (1.82) (0.33) (0.22) (1.31) C7 C (0.05) ( 0.34) (1.18) (0.90) C8 C (0.64) (0.82) (0.39) (0.36) C9 C ( 0.01) (1.15) C10 C (0.59) (0.34) C n N b (0.24) (0.19) (0.17) (1.34) (1.30) (1.30) Note: a The values in parentheses are the standard deviations (per cent) in relation to experimental data (McCarthy & Thaddeus 2001). b Here, n is 7, 9 and 11, respectively, for each one of the listed levels. Table 7. Bond lengths (Å) of isocyanopolyynes calculated at B3LYP/aug-cc-pVTZ and MPW1K/aug-cc-pVTZ levels. Bond B3LYP/aug-cc-pVTZ MPW1K/aug-cc-pVTZ HC 6 NC HC 8 NC HC 10 NC HC 6 NC HC 8 NC HC 10 NC H C C1 C C2 C C3 C C4 C C5 C C6-C C7 C C8 C C9 C C n 1 N a N C Note: a Here, n is 7, 9 and 11, respectively, for each one of the listed levels. as Supporting Information). First, we notice that the values in Table 10 are consistent with those for smaller isocyanopolyynes with n = 3and5(Vichietti&Haiduke2014). The Gibbs free energy of activation for forward and reverse reactions, G f and G r, decreases along with temperature increments, except for many of these values from 1000 to 3000 K. Gibbs free energies of isomerization, G, also decrease as the temperature increases, resulting in a maximum difference of 3.2, 6.8 and 1.8 kcal mol 1,

6 Kinetic of HC n N HC n 1 NC (n = 7, 9 and 11) 3615 Table 8. Transition-state bond lengths (Å) and angles (degrees) for the reactions HC n N HC n 1 NC (n = 7, 9 and 11) calculated at B3LYP/aug-cc-pVTZ and MPW1K/aug-cc-pVTZ levels. Bond/angle a B3LYP/aug-cc-pVTZ MPW1K/aug-cc-pVTZ n = 7 n = 9 n = 11 n = 7 n = 9 n = 11 H C C1 C C2 C C3 C C4 C C5 C C6 C C7 C C8 C C9 C C6 C C7 N N C C5 C6 C7 b C5 C6 N b C6 C7 N b C8 C C9 N N C C7 C8 C9 b C7 C8 N b C8 C9 N b respectively, for reactions with n = 7, 9 and 11 between and 3000 K. However, although G f, G r and G from smaller temperatures are similar for reactions with n = 7, 9 and 11, the discrepancies increase in larger temperatures. Thus, there is a clear distinction between the results of the reaction with n = 9in relation to the other ones for the highest temperatures investigated, including small (iso)cyanopolyynes with n = 3 and 5 (Vichietti & Haiduke 2014), which should be caused by a difference in the thermal contribution associated with vibrational modes. Approximately, the results for n = 9 at 3000 K indicate 10 per cent larger G r values together with per cent smaller G ones than those for n = 7 and 11. Therefore, since enthalpy values from Table 9 do not exhibit such a discrepancy for n = 9 values, we can conclude that this is a direct result of entropic contributions to Gibbs free energies. ThedatainTable10 are used to determine rate constants for the reactions with n = 7, 9 and 11 by means of equation (2.2), whose results can be found from Tables Only for comparison, the rate constants obtained without CBS extrapolations are presented from Tables A9 A11 (in the appendix available online as Supporting Information). In general, CCSD(T)/CBS and CCSD(T)/CBS results show the same order of magnitude for rate constants of these reactions in each C10 C C11 N N C C9 C10 C11 b C9 C10 N b C10 C11 N b Note: a The dotted lines indicate bonds that are being broken/formed along the reaction coordinate. b Angle originating from the central atom. temperature and the values obtained at B3LYP/aug-cc-pVTZ geometries are always lower than those arising from MPW1K/aug-ccpVTZ ones. A significant increase of these quantities is observed when the temperature is raised. This increase of rate constants is Figure 1. Transition-state geometries for the reactions (a) HC 7 N HC 6 NC, (b) HC 9 N HC 8 NC and (c) HC 11 N HC 10 NC plotted with MOLDEN 5.0 (Schaftenaar & Noordik 2000).

7 3616 R. M. Vichietti and R. L. A. Haiduke Table 9. Activation enthalpy for the forward and reverse reactions, H f and H r, and enthalpy changes, H, (in kcal mol 1 ) of the reaction HC n N HC n 1 NC (n = 7, 9 and 11) in different temperatures, T (in K). T CCSD(T)/CBS CCSD(T)/CBS n = 7 n = 9 n = 11 n = 7 n = 9 n = H f H r H H f H r H H f H r H H f H r H H f H r H Table 10. Gibbs free energy of activation for the forward and reverse reactions, G f and G r, and Gibbs free energy changes, G, (in kcal mol 1 ) of the reaction HC n N HC n 1 NC (n = 7, 9 and 11) in different temperatures, T (in K). T CCSD(T)/CBS CCSD(T)/CBS n = 7 n = 9 n = 11 n = 7 n = 9 n = G f G r G G f G r G G f G r G G f G r G G f G r G much faster from to 1000 K and becomes less significant above this range. Rate constants for forward reactions, k f,arealways lower than those for reverse one, k r, although the relative difference between these two constants becomes small in high temperatures. This fact supports the affirmations of Tsuji (1964), which point out that conditions in carbon-star atmospheres are able to overcome activation energies of reactions and chemical equilibrium can be achieved. Moreover, results for rate constants obtained with inclusion of the Wigner correction, k w, are also available in Tables and it is possible to notice that the tunnel effect increases rate constants, especially at lower temperatures. The result of a larger Gibbs free energy of activation for the reverse reaction of n = 9 at 3000 K compared to the ones for n = 7 and 11 is a decrease of the respective rate constant to roughly half. Finally, these rate constants with Wigner s corrections for forward and reverse reactions with n = 7 11 were fitted according to equation (2.4) within the temperature range from to 3000 K and their parameters (α, β and γ ) are shown in Table 14. The maximum deviations between values provided by these equations (for both forward and reverse reactions) and

8 Kinetic of HC n N HC n 1 NC (n = 7, 9 and 11) 3617 Table 11. Forward and reverse rate constants, k f and k r (in s 1 ), for the reaction HC 7 N HC 6 NC in different temperatures, T (in K). a T CCSD(T)/CBS CCSD(T)/CBS k k w k k w k f (10 32 ) k r (10 13 ) k f (10 14 ) k r (10 2 ) k f (10 6 ) k r (10 2 ) k f (10 0 ) k r (10 6 ) k f (10 9 ) k r (10 11 ) Note: a The values of k f and k r must be multiplied by the powers of 10 indicated between parentheses. Table 12. Forward and reverse rate constants, k f and k r (in s 1 ), for the reaction HC 9 N HC 8 NC in different temperatures, T (in K). a T CCSD(T)/CBS CCSD(T)/CBS k k w k k w k f (10 32 ) k r (10 13 ) k f (10 14 ) k r (10 2 ) k f (10 6 ) k r (10 2 ) k f (10 0 ) k r (10 5 ) k f (10 9 ) k r (10 11 ) Note: a The values of k f and k r must be multiplied by the powers of 10 indicated between parentheses. Table 13. Forward and reverse rate constants, k f and k r (in s 1 ), for the reaction HC 11 N HC 10 NC in different temperatures, T (in K). a T CCSD(T)/CBS CCSD(T)/CBS k k w k k w k f (10 32 ) k r (10 12 ) k f (10 14 ) k r (10 2 ) k f (10 6 ) k r (10 2 ) k f (10 0 ) k r (10 6 ) k f (10 9 ) k r (10 11 ) Note: a The values of k f and k r must be multiplied by the powers of 10 indicated between parentheses.

9 3618 R. M. Vichietti and R. L. A. Haiduke Table 14. Fitted parameters (α, β and γ ) to be used in the modified Arrhenius equation for forward, f, and reverse, r, reactions HC n N HC n 1 NC (n = 7, 9 and 11) obtained at the B3LYP/aug-ccpVTZ//CCSD(T)/CBS and CCSD(T)/CBS level. Reaction CCSD(T)/CBS CCSD(T)/CBS α (s 1 ) β γ (K) α (s 1 ) β γ (K) n = 7 f r n = 9 f r n = 11 f r our CCSD(T)/CBS and MPW1K/aug-ccpVTZ//CCSD(T)/CBS results are, respectively, less than 2.9 and 3.5 per cent. If the experience acquired with the smallest systems (Vichietti & Haiduke 2014) was taken into account, B3LYP/augcc-pVTZ//CCSD(T)/CBS values could be indicated as the best ones in this study. However, due to the lack of more experimental data to compare these alternatives, we also decided to present the results given at the CCSD(T)/ CBS level. 4 CONCLUSIONS Kinetic calculations were performed for forward and reverse isomerization reactions HC n N HC n 1 NC with n = 7, 9 and 11 at CCSD(T)/CBS and MPW1K/augcc-pVTZ//CCSD(T)/CBS levels for different temperatures (from to 3000 K), in which CBS estimates are obtained by extrapolations of aug-cc-pvmz (m = D and T) results. This methodology was fully validated from additional calculations performed for the same reactions with n = 1, 3 and 5. The agreement with experimental data and other more advanced theoretical results available in the case of these small systems allows us to conclude that the proposed combined treatment should be satisfactory for large (iso)cyanopolyynes. Enthalpies and Gibbs free energies of activation for these large systems are consistent with the values previously determined for the reactions with n = 1, 3 and 5 (Vichietti & Haiduke 2014). However, the Gibbs free energies obtained at the highest temperatures for n = 9 differ significantly from the values of systems with n = 7 and 11 and this is due to entropic contributions probably associated with their vibrational levels. Results also indicate that isomerization reactions are exothermic and faster in the direction that leads to cyanopolyynes, favouring the conversion to this isomer in colder regions of the interstellar medium. Finally, forward and reverse rate constants for n = 7, 9 and 11 show similar orders of magnitude when compared with reactions where n is 3 and 5 (Vichietti & Haiduke 2014) along the whole temperature range considered. There is a drastic increase of rate constant values from to 1000 K, which becomes more subtle above this range. Relative differences between the k f and k r results become smaller as the temperature raises, indicating that isocyanopolyynes are more likely to be observed in hotter environments, like in carbon-rich stars. This is the first study that presents kinetic data for the isomerization reaction between large cyanopolyynes and isocyanopolyynes with n = 7, 9 and 11. ACKNOWLEDGEMENTS The authors thank FAPESP for financial support (grant number 2010/ ). RMV also thanks Capes for a doctoral fellowship. REFERENCES Alexander A. J., Kroto H. W., Walton D. R. M., 1976, J. Mol. Spectrosc., 62, 175 Avery L. W., Broten N. W., MacLeod J. M., Oka T., 1976, ApJ, 205, L173 Bell M. B., Feldman P. A., Travers M. J., McCarthy M. C., Gottlieb C. A., Thaddeus P., 1997, ApJ, 483, L61 Broten N. W., Oka T., Avery L. W., MacLeod J. M., Kroto H. W., 1978, ApJ, 223, L105 Buchowiecki M., Vanicek J., 2010, J. Chem. Phys., 132, Cami J., Bernard-Salas J., Peeters E., Malek S. E., 2010, Science, 329, 1180 Chapman J. 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10 Kinetic of HC n N HC n 1 NC (n = 7, 9 and 11) 3619 Vichietti R. M., Haiduke R. L. A., 2014, MNRAS, 437, 2351 Wigner E. P., 1932, Z. Phys. Chem. Abt. B, 19, 203 Winnewisser G., Walmsley C. M., 1979, Ap&SS, 65, 83 Winstanley N., Nejad L. A. M., 1996, Ap&SS, 240, 13 Wynne-Jones W. F. K., Eyring H., 1935, J. Chem. Phys., 3, 492 Zuckerman B., Morris M., Palmer P., Turner B. E., 1972, ApJ, 173, L125 SUPPORTING INFORMATION Additional Supporting Information may be found in the online version of this article. Table A1. Zero-point energies (E ZPE ) and thermal corrections for enthalpy (H corr ) and Gibbs free energy (G corr ) at K (in kcal mol 1 ). Table A2. Zero-point energies (E ZPE ) and thermal corrections for enthalpy (H corr ) and Gibbs free energy (G corr ) at 3000 K (in kcal mol 1 ). Table A3. Activation enthalpy for the forward and reverse reactions, H f and H r, and enthalpy changes, H, (in kcal mol 1 )ofthe reaction HC 7 N HC 6 NC in different temperatures, T (in K). Table A4. Activation enthalpy for the forward and reverse reactions, H f and H r, and enthalpy changes, H, (in kcal mol 1 )ofthe reaction HC 9 N HC 8 NC in different temperatures, T (in K). Table A5. Activation enthalpy for the forward and reverse reactions, H f and H r, and enthalpy changes, H, (in kcal mol 1 )ofthe reaction HC 11 N HC 10 NC in different temperatures, T (in K). Table A6. Gibbs free energy of activation for the forward and reverse reactions, G f and G r, and Gibbs free energy changes, G, (in kcal mol 1 ) of the reaction HC 7 N HC 6 NC in different temperatures, T (in K). Table A7. Gibbs free energy of activation for the forward and reverse reactions, G f and G r, and Gibbs free energy changes, G, (in kcal mol 1 ) of the reaction HC 9 N HC 8 NC in different temperatures, T (in K). Table A8. Gibbs free energy of activation for the forward and reverse reactions, G f and G r, and Gibbs free energy changes, G, (in kcal mol 1 ) of the reaction HC 11 N HC 10 NC in different temperatures, T (in K). Table A9. Forward and reverse rate constants, k f and k r (in s 1 ), for the reaction HC 7 N HC 6 NC in different temperatures, T (in K). a Table A10. Forward and reverse rate constants, k f and k r (in s 1 ), for the reaction HC 9 N HC 8 NC in different temperatures, T (in K). a Table A11. Forward and reverse rate constants, k f and k r (in s 1 ), for the reaction HC 11 N HC 10 NC in different temperatures, T (in K) ( stu1963/-/dc1). Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the paper. This paper has been typeset from a Microsoft Word file prepared by the author.