Temperature dependence of rotational excitation rate coefficients of C2H− in collision with He

Chemical Physics Letters 533 (2012) 6–9

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Temperature dependence of rotational excitation rate coefficients of C2H in collision with He F. Dumouchel a,⇑, A. Spielfiedel b, M.L. Senent c, N. Feautrier b a

Laboratoire d’ondes et Milieu Complexe, FRE 3102, 25 Rue Ph Lebon, 76600 Le Havre, France LERMA et UMR 8112, CNRS, Observatoire de Paris-Meudon, 5 Place Jules Janssen, 92195 Meudon Cedex, France c Departmento de Quimica y Fisica Teóricas, Instituto de Estructura de la Materia, IEM-CSIC, Calle Serrano 121, 28006 Madrid, Spain b

a r t i c l e

i n f o

Article history: Received 3 December 2011 In final form 2 March 2012 Available online 10 March 2012

a b s t r a c t From a new two-dimensional Potential Energy Surface (PES), rotational excitation of the C2H(X1R+) anion by collision with He is investigated. PES is obtained in the supermolecular approach based on a single and double-excitation coupled cluster method with perturbative contributions from triple excitations (CCSD(T)). Fully-quantum close-coupling calculations of inelastic integral cross sections are done on a grid of collision energies large enough to insure converged state-to-state rate coefficients for the 13 first rotational levels of C2H and temperatures ranging from 5 to 100 K. For this collisional system, rate coefficients exhibit a strong propensity in favor of even DN transitions. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction The recent discovery of carbon chain anions in interstellar and circumstellar media has instigated many theoretical and experimental works on these species [1,2]. Their structures as well as the importance of their role in the interstellar chemistry and in gas phase ion–molecule reactions are the object of many recent studies [3–5]. Although the existence of anions in astrophysical sources was first predicted theoretically and early considered in chemical models [6,7], the first negative hydrocarbon C6H was detected in 2006 [8] solving the problem of the unidentified lines discovered by Kawaguchi et al. [9]. The C6H identification was followed by the detection of other negatively charged species like C4H [10], C8H [11,12], C3N [13], C5N [4] and CN [14]. Many of these species were first detected in IRC+10216. Hydrocarbon anions were also discovered later in other molecular clouds [15]. The search for interstellar anions persists. Some species, like C2H, are expected to be discovered with the new astrophysical instruments such as ALMA. Although C2H has been already observed at the laboratory level [16,17] and the parent neutral form C2H is a well known astrophysical molecule discovered in 1974 [18], the C2H anion seems to be a very low abundant species. This fact has been justified in terms of reactivity. Actual models predict large carbon chain anion formation to be more probable than small chains [19]. However, how the CnH species are produced in astro-

physical environments is a question that is not already solved. It is generally accepted that gas-phase processes are crucial. Hydrocarbon radicals CnH may be the main precursors of the CnH anions through electron attachment or association processes whereas  associative detachment processes (C n þ H ! Cn H þ e ) contributes to the generation of neutral CnH. A new mechanism for the C2H formation from C2H2 has been recently proposed [1]. Astrophysical abundances have to be understood in terms of molecular stabilities, reaction probabilities and radiative and collisional excitations. All these facts can determine the existence of a molecule and the probability of being observed. Stabilities and spectroscopic properties of C2H have been studied theoretically using very accurate ab initio methods [20]. The modeling of molecular emission requires collisional rate coefficients with the most abundant interstellar species like He and H2. To our knowledge, no collisional data exists for C2H and other anions. For this reason, we report in this Letter a first collisional study of (C2H) with He at low temperatures trying to understand the particular behavior of negatively charged species during collisions and how they compare with neutral forms [21]. In the next section, we present details of the ab initio calculations of the C2H-He Potential Energy Surface (PES) and we give some theoretical aspects of the scattering calculations. State-to-state collisional cross sections and rate coefficients are reported in Section 3. The results are discussed and propensity rules are given. Concluding remarks are in Section 4. 2. Potential Energy Surface and scattering calculations

⇑ Corresponding author. E-mail addresses: [email protected] (F. Dumouchel), annie. spielfi[email protected] (A. Spielfiedel). 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2012.03.006

In this Letter we consider the C2H anion as a rigid system, neglecting in particular possible excitation of the bending mode

F. Dumouchel et al. / Chemical Physics Letters 533 (2012) 6–9

for energies larger than 502.0 cm-1 [20]. Indeed, from QCT studies of rotational excitation of H2O by H2, it was shown [22] that the coupling between the rotational excitation and the bending may be neglected for temperatures up to 5000 K. Moreover, it was also shown by Faure et al. [23], in the particular case of the H2O–H2 system, that the 5D-PES calculated at the experimental ground vibrational state geometry and the full 9D-PES averaged over the ground vibrational state are very similar (see also Lique et al. [24] for the CS–He system). These results suggest that the use of a rigid body 2D-PES is sufficient as long as bending and vibrational excitation are not considered. In the ground electronic state, C2H is a linear singlet (X1 Rþ ). The C2H–He system can be described by the usual Jacobi coordinates: R, the distance between the He atom and the C2H molecule center of mass, r ¼ r 1 þ r 2 with r1 the C–C distance and r 2 the C–H distance in the C2H molecule and h, the angle between R and r. We assume that C2H is placed along the z-axis and the C2H–He system lies in the xz plane. In our convention h ¼ 0 corresponds to the He atom approaching the carbon atom. The PES was calculated in the supermolecular approach based on a single and double-excitation coupled cluster method with perturbative contributions from triple excitations (CCSD(T)) ([26,27]). We used the aug-cc-pVQZ (hereafter denoted aVQZ) basis set of Woon and Dunning [28] for the three atoms, augmented by the bond functions optimized by Cybulski and Toczylowski [29] placed at mid-distance between the C2H center of mass and He. At all geometries the Boys and Bernardi [30] counterpoise procedure was used to correct for basis set superposition error (BSSE). All the calculations were carried out using the MOLPRO 2006 package [31]. Calculations were performed on a total of 1254 geometries. The values of R ranged from 4.00 to 15.0 bohr in steps of 0.25, from 15.0 to 23.0 bohr in steps of 0.5, plus the values 24, 25, 27, 30, 35 and 40 bohr. The angular grid was uniform with a 10 ° spacing from 0 to 180 °. An analytic representation of the present 2D PES suitable for dynamics calculations, was obtained using the procedure described by Eqs. 12–16 of Werner et al. [32] for the CN–He system. In order to perform the scattering calculations, this PES was expanded in terms of Legendre polynomials as:

Vðr ¼ r e ; R; hÞ ¼

P V k ðRÞP k ðcoshÞ

ð1Þ

k

Terms with k up to 19 were included in the expansion. Figure 1 displays the contour plot of the 2D Vðr ¼ r e ; R; hÞ PES. For this van der Waals system, the global minimum was found to be 37:764 cm1 at R ¼ 7:91 bohr, h ¼ 72:38°.

Figure 1. Contour plot of the C2H–He PES as a function of R and h. h ¼ 0 corresponds to colinear He—CCH .

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For an anion–He system, the asymptotic part of the potential should behave as a sum of C 4 =R4 and C 6 =R6 terms which account for induction and dispersion contributions [25]. To check the quality of the calculated PES, we have calculated the theoretical C th 40 and C th 60 coefficients of the isotropic part of the potential and compared ab them to their counterparts (C ab 40 and C 60 ) obtained from a fit of the long range part of the V 0 ab initio data. We found: C th 40 ¼ th ab 0:6915; C ab 40 ¼ 0:6888; C 60 ¼ 29:715; C 60 ¼ 29:224 (in atomic units) which is very satisfactory. The fitted C2H–He 2D-PES was used to calculate state-to-state cross sections and rate coefficients. The full close coupling approach (CC hereafter), first introduced by Arthurs & Dalgarno [33] was used for the calculations of the state-to-state cross sections between the 13 first rotational levels. The energies of the rotational levels were computed from the following C2H spectroscopic constants: B0 ¼ 1:3889354 cm1 and D0 ¼ 3:2345 106 cm1 [16]. The scattering calculations were carried out with the MOLSCAT code [34]. Calculations were performed for energies ranging from 3.0 to 1000 cm1 . The integration parameters were chosen to ensure convergence of the cross sections over this range. At the highest considered total energy (1000 cm1 ), the C2H rotational basis included channels up to N ¼ 20 to ensure convergence of the excitation cross sections for transitions including up to the N ¼ 12 rotational level. We carefully spanned the energy grid to take into account the presence of resonances. The energy steps are 0:1 cm1 below 100 cm1 ; 0:2 cm1 from 100 to 250 cm1 ; 0:5 cm1 between 250 and 300 cm1 ; 1 cm1 between 300 and 500 cm1 and 2.0 cm1 between 500 and 1000 cm1. From the calculated cross sections, one can obtain the corresponding state-to-state rate coefficients by Boltzmann averaging:

kN!N0 ðTÞ ¼

 1  2 Z 1 Ek 8kB T 2 1  Ek rN!N0 ðEk Þe kB T dEk kB T pl 0

ð2Þ

where kB is the Boltzmann constant and Ek the kinetic energy. The total energy range considered in this Letter allows us to determine rate coefficients for temperatures up to 100 K. 3. Results 3.1. Integral cross sections Fully-quantum close-coupling calculations of integral cross sections were carried out for values of total energies ranging from 3.0 to 1000 cm1 . The variation of integral cross sections for a few selected N ! N 0 rotational transitions with collision energy is

Figure 2. Rotational de-excitation N ! N 0 cross sections of C2H in collision with He as a function of the relative kinetic energy.

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F. Dumouchel et al. / Chemical Physics Letters 533 (2012) 6–9

Figure 3. Temperature dependence of state-to-state rate coefficients.

shown in Figure 2. For collisional energies below 30 cm1 many resonances occur. This is a consequence of the attractive potential well with a depth of 37:76 cm1 . At low energy, the He atom can be temporarily trapped in quasibound states [35,36] which arise both from tunneling through the centrifugal barrier (shape resonances) and from excitation of C2H to a higher rotational level which is energetically allowed in the well (Feshbach resonances). Except for the 2–0 first transition, we see, beyond the resonance zone, a propensity for DN ¼ N  N 0 ¼ 2 transitions. This effect was first explained by McCurdy and Miller [37] as a consequence of the near-homonuclear symmetry of the PES. Indeed, we observe on the contour plot that the repulsive wall of the PES, which is dominant at the higher energies is quite symmetrical. Some anisotropy appears around the well depth which may induce a different trend of the cross sections at lower energies. Figure 4. C2H–He de-excitation rate coefficients from the N = 12 initial level at 10 and 100 K.

3.2. Rate coefficients From calculated cross sections, one can obtain the corresponding state-to-state rate coefficients by Boltzmann averaging. The total energy range considered in this Letter allows us to determine rate coefficients for temperatures up to 100 K. The representative variation with temperature of de-excitation rate coefficients from an initial level N to a final level N 0 is shown in Figure 3 for DN ¼ 1 (left) and DN ¼ 2 (right) transitions. The rate coefficients obviously display the same propensity than the integral cross sections. Figure 4 presents for 10 and 100 K downward rotational rate coefficients of C2H (N = 12) level as a function of the final N 0 level. This plot confirms the DN ¼ 2 even propensity. The same behavior was found for the isoelectronic HCN molecule ([38]) and for C2H ([21]) in collision with He. However, one notices that He rate coefficients for the C2H anion are larger by factors varying from 2 to 5 than the corresponding rates for HCN. It seems interesting to compare He-rate coefficients of the C2H anion with those of the neutral (C2H) ([21]). For this comparison, the C2H–He rate coefficients between fine structure levels are averaged and summed over initial and final electronic spin quantum numbers, respectively:

P kN!N ðTÞ ¼ 0

jj0 kN j !Nj0 ðTÞ 0

2

ð3Þ

Figure 5 displays the temperature variation of C2H–He de-excitation rate coefficients ([21]). One can easily see by comparing those coefficients with the corresponding C2H–He coefficients (Figure 3, right) that, at a given temperature, the de-excitation rate coefficients for DN ¼ 2 transitions (dominant for both systems)

Figure 5. Temperature variation of de-excitation electronic spin averaged C2 H—HeN ! N 0 rate coefficients with DN ¼ 2 ([21]).

increase for increasing initial N. However, rate coefficients for the C2H anion are larger by factors generally of the order of 3 to 5 than the corresponding coefficients for the C2H neutral radical, depending on the transitions and the temperature. This difference

F. Dumouchel et al. / Chemical Physics Letters 533 (2012) 6–9

could be partly due to the asymptotic dependence of the PESs which varies as R6 and R4 for C2H–He and C2H–He, respectively. As was already mentioned by Klos and Lique [39], the impact of collision will be more important for interstellar anions than for neutral species and thus neutral species cannot be used for modeling of interstellar line emission of anions. The complete set of de-excitation rate coefficients with N; N 0 6 13 will be available on-line from the BASECOL website.1 Excitation rate coefficients can be easily obtained by detailed balance.

4. Summary and conclusion We have used quantum scattering calculations to investigate energy transfer in collisions of C2H with He atoms. The calculations are based on a new, highly correlated 2D PES calculated at the RCCSD(T) level using large basis sets. Close coupling calculations were performed for collision energies ranging from 3.0 to 1000 cm1 . Rate coefficients for transitions involving the 13 first rotational levels of the C2H anion were determined for temperature ranging from 5 to 100 K. The rate coefficients show a strong propensity for even DN, mainly DN ¼ 2. A comparison with the spin-averaged He-rate coefficients of the related neutral C2H molecule points out the relatively large difference between the anion and the neutral species, rate coefficients for C2H being larger by factor 2–5 than the corresponding rates for C2H. Similar trend was found recently by Klos and Lique [39] for CN . We expect that the present set of rate coefficients will help to enable accurate modeling of He–C2H collisions in astrophysical environments.

Acknowledgments This work was supported by the CNRS national program ‘Physique et Chimie du Milieu Interstellaire’. M.L. Senent acknowledges the MICINN (Spain) for the Grant No. AYA2008-00446 and Computing resources of CESGA. Part of the calculations were performed at the IDRIS-CNRS French national computing center (Institut de Développement et des Ressources en Informatique Scientifique du Centre National de la Recherche Scientifique) under Project No. 2010040883 and on Siolino work stations at the Centre Informatique of Paris Observatory. We would like to thank François Lique and Fabrice Dayou for fruitful discussions.

1

http://www.obspm.fr/basecol/.

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