Rotational excitation of protonated hydrogen cyanide (HCNH + ) by He atom at low temperature Rotational excitation of protonated hydrogen cyanide (HCNH + ) by He atom at low temperature

Rotational excitation of protonated hydrogen cyanide (HCNH+) by He atom at low temperature Christophe Nkem, Kamel Hammami, Idriss Yacoub Halalaw, Luc Calvin Owono Owono & Nejm-Eddine Jaidane Astrophysics and Space Science An International Journal of Astronomy, Astrophysics and Space Science ISSN 0004-640X Astrophys Space Sci DOI 10.1007/s10509-013-1600-5 1 23 Author's personal copy Astrophys Space Sci DOI 10.1007/s10509-013-1600-5 O R I G I N A L A RT I C L E Rotational excitation of protonated hydrogen cyanide (HCNH+ ) by He atom at low temperature Christophe Nkem · Kamel Hammami · Idriss Yacoub Halalaw · Luc Calvin Owono Owono · Nejm-Eddine Jaidane Received: 18 February 2013 / Accepted: 10 August 2013 © Springer Science+Business Media Dordrecht 2013 Abstract We report on ab initio coupled-cluster calculations of the interaction potential energy surface for the HCNH+ –He complex. The aug-cc-pVTZ Gaussian basis, to which is added a set of bond functions placed at middistance between HCNH+ center of mass and He atom is used. The HCNH+ bonds length are set to their values at the equilibrium geometry, i.e., re [HC] = 1.0780 Å, re [CN] = 1.1339 Å and re [NH] = 1.0126 Å. The interaction energy presents a global minimum located 266.9 cm−1 below the HCNH+ –He dissociation limit. Using the interaction potential obtained, we have computed rotational excitation cross sections in the close-coupling approach and downward rate coefficients at low temperature (T ≤ 120 K). It is expected that the data worked out in this study may be beneficial for further astrophysical investigations as well as laboratory experiments. Keywords CCSD(T) · PES · Collision · Cross sections · Rate coefficients C. Nkem · L.C. Owono Owono (B) Center for Atomic Molecular Physics and Quantum Optics, Faculty of Science, University of Douala, P.O. Box 8580, Douala, Cameroon e-mail: lcowono@yahoo.fr K. Hammami · N.-E. Jaidane Laboratory for Atomic Molecular Spectroscopy and Applications, Department of Physics, Faculty of Science, University Tunis El Manar, Campus Universitaire 1060 Tunis, Tunisia I.Y. Halalaw Faculty of Fundamental and Applied Sciences, University of Ndjamena, P.O. Box 1027, Ndjamena, Chad L.C. Owono Owono Department of Physics, Advanced Teacher Training College, University of Yaounde I, P.O. Box 47, Yaounde, Cameroon 1 Introduction The linear hydrogen cyanide molecular ion, HCNH+ , is one of the key species in the ion–molecule scheme of interstellar cloud chemistry (Herbst and Klemperer 1973, Herbst 1978, Watson 1974; Brown 1977; Brown and Rice 1981; Huntress and Mitchell 1978; Prasad and Huntress 1980; Capone et al. 1981). Its was reported for the first time as regards Sgr B2 by Ziurys and Turner (1986) who observed three rotational transitions: the J = 1 → 0 line at 74 GHz by using the National Radio Astronomy Observatory (NRAO) 12 meter antenna, the J = 2 → 1 and J = 3 → 2 transitions at 148 GHz and 222 GHz, measured with the Millimeter wave observatory (MWO) 4.9 meter dish. Later, i.e., in 1992, Ziurys et al. (1992) succeeded to detect HCNH+ toward TCM-1. The hyperfine structure of the J = 1 → 0 transition was then solved and the quadrupole coupling constant of the nitrogen nucleus determined. Indeed, HCNH+ is expected to be the main precursor of HCN, HNC, and CN via dissociative recombination with an electron (Herbst and Klemperer 1973, Watson 1973; Herbst 1978). The latter species have been observed in many interstellar clouds (Herbst and Klemperer 1973, Watson 1973). All the above clearly illustrate the importance of HCNH+ in the interstellar medium (ISM) and hence the effort devoted to conduct investigations on it. HCNH+ has been the subject of numerous studies of both theoretical and experimental interest (Lee and Schaefer 1984; DeFrees et al. 1982; DeFrees and McLean 1985; Pearson and Schaefer 1974; Summers and Tyrrell 1976; Saebq 1977; Allen et al. 1980, Dardi and Dykstra 1980; Del Bene et al. 1982; Hirao et al. 1982; Pople 1983; Ha and Nguyen 1983). On the experimental side, most of the efforts have been devoted to the observation of the infrared vibration–rotation spectrum of the ν1 (NH stretch), (Altman et al. 1984a), ν2 (CH stretch) (Altman et al. 1984b) and ν5 Author's personal copy Astrophys Space Sci (HNC bend), (Wing-Cheung Ho et al. 1987) bands. In addition, the dissociative recombination of HCNH+ has been studied at the heavy ion storage ring CRYRING, thus leading to the determination of absolute cross sections between 0.01 meV and 0.2 eV. The same study has made it possible to measure thermal rate coefficients as well as the branching ratio for different dissociation channels. In the same realm, the pure rotational transitions of HCNH+ have been measured up to 750 GHz and accurate molecular constants inferred (Amano et al. 2006). Concerning the theoretical predictions, calculations have mainly concentrated on the study of the equilibrium geometry (Botschwina 1986; Botschwina et al. 1994) and the prediction of pure rotational transition frequencies (Amano et al. 2006). A quantity of interest for microwave spectroscopy and radio astronomy, the electric dipole moment has also been determined (Lee and Schaefer 1984; Pearson and Schaefer 1974; Haese and Woods 1979; Dardi and Dykstra 1980; DeFrees et al. 1982). In the present study, we are interested in obtaining theoretical data for the rotational excitation of HCNH+ by He at low temperature. To the best of our knowledge, such excitation parameters have not yet been reported in the literature. To this end, a reliable potential energy surface (PES) is needed to enable the dynamics calculations of cross sections and rate coefficients. In Sect. 2, we present our two dimensional (2D) potential interaction energy and the corresponding computational details. This PES is fitted on a basis of Legendre polynomial functions and the fitting coefficients are used in Sect. 3 to compute the collision induced rotational excitation cross sections for J ranging from 0 to 10 and a total energy up to 640 cm−1 . The same section also discusses the rate coefficients for 10 K ≤ T ≤ 120 K. Our concluding remarks are presented in Sect. 4. 2 Potential energy surface calculations The interaction potential energy of the HCNH+ –He van der Waals complex was calculated at the coupled-cluster [CCSD(T)] level of theory (Knowles et al. 1993, 2000) as it is implemented in MOLPRO molecular package (Werner et al. 2009) to account for electron correlation. The linear HCNH+ molecular ion was assumed to be fixed with its bond distances set to their experimental equilibrium ground X 1 Σ + state values re [HC] = 1.0780 Å, re [CN] = 1.1339 Å and re [NH] = 1.0126 Å (Botschwina et al. 1994). The radial coordinate R, i.e., the distance between He atom and the center of mass (c.m.) of HCNH+ was varied from 3.5 Bohr to 15.0 Bohr by steps of 0.25 Bohr. Additional points were added to the grid at 16.0, 17.0, 18.0, 19.0 Bohr, and 20.0 Bohr to allow for a better description of the separation limit. The values of the angle θ between the molecular axis Fig. 1 Contour plot of the HCNH+ –He potential energy surface as a function of R and θ with the bond separation held fixed at re (HC) = 1.0780 Å, re (CN) = 1.1339 Å and re (NH) = 1.0126 Å. The energies are in cm−1 . The zero of energy is taken as that of the HCNH+ –He asymptote and the R vector were chosen from 0◦ to 180◦ with a uniform step of 10◦ . This has resulted in a total number of 988 geometries to be calculated in the Cs symmetry point group. During the calculations, all the atoms were described by the aug-cc-pVTZ basis of Woon and Dunning (1994), to which was added a set of (3s3p2d1f ) bond functions optimized by Tao and Pan (1992) and placed at mid-distance between the c.m. of HCNH+ and He atom. Our total basis set thus included 190 contracted Gaussian basis functions. At all geometries, we have accounted for basis set superposition errors (BSSE) with the counterpoise procedure of Boys and Bernardi (1970). The contour plot of the potential energy surface is displayed in Fig. 1. It is clear from this figure that the global minimum of 266.9 cm−1 occurred at R = 6.5 Bohr and θ = 0◦ . A secondary minimum exists for θ = 180◦ . To appreciate the shape of our PES, we have illustrated in Fig. 2 the cuts of the PES corresponding to three values of θ for different He approach. θ = 0◦ , [HCNH+ ] . . . He stretch; θ = 90◦ , T-shaped geometry; and θ = 180◦ , He . . . [HCNH+ ] stretch. As one can see, the two minima corresponding to θ = 90◦ and θ = 180◦ lie well above the global minimum. Concerning the long-range expansion of the PES, the procedure described and used recently by Ajili and Hammami (2013) was applied in the present work. Figure 3 displays a comparison of the ab initio values with the analytical expansion for θ = 90°. As one can see, there is good agreement between the two sets of data. In order to carry out faithfully the calculations of the dynamics, we have first obtained an analytic representation of the PES by using the fitting procedure described by Werner et al. (1988) and applied successfully in our previous works Author's personal copy Astrophys Space Sci Table 1 Potential energies obtained from ab initio calculations and the corresponding fitted values obtained from the Vλ coefficients θ (◦ ) R Bohr Ab initio potential energy (cm−1 ) Potential energy λmax = 12 (cm−1 ) 10 50 100 180 λmax = 18 (cm−1 ) 4 36317.530 36388.722 36387.525 5 2956.320 2956.848 2956.749 7 −208.160 −208.161 −208.162 10 −29.180 −29.165 −29.170 4 4894.51 4882.491 4892.591 5 331.21 330.820 330.819 7 −91.340 −91.343 −91.342 10 −18.740 −18.730 −18.735 4 2000.360 2007.983 2009.883 5 52.480 52.637 52.486 7 −66.080 −66.084 −66.083 10 −15.310 −15.305 −15.307 4 112925.860 112960.608 112967.708 5 10346.60 10316.574 10316.575 7 −159.220 −159.208 −159.210 10 −33.480 −33.456 −33.455 Fig. 2 Cuts of the potential energy surface of HCNH+ –He as a function of R for three He orientation (θ = 0◦ , θ = 90◦ and θ = 180◦ ) Fig. 3 Comparison between the long-range ab initio and analytical potential energies for θ = 90◦ (Hammami et al. 2008a, 2008b, 2008c; Nkem et al. 2009) and by other authors (see for example Lique et al. 2007). Thus, we have performed separate fits of potential energies vs. angle, each at one value of R. This was done by projections using quadrature. In each fit, we have fitted 13 ab initio points on a basis of Legendre polynomial functions according to the formula with λmax = 12. To test the potential expansion, we have started from the above 13 values of θ for each radial distance R and deduced the 19 ones using a cubic spline routine. Figure 4 displays plots of the first Vλ (R) values. The other numbers are available as online material from the BASECOL website (see http://www.obspm.fr/basecol). Over the entire grid, the mean relative difference between the analytic fit and the ab initio calculations is lower than 1 % (see Table 1). From an analysis of Figs. 1–4, we found that the scattering calculations may be carried out faithfully for R starting from 3.5 Bohr. This value provides sufficiently repulsive potential V (r = re , R, θ ) = λ max λ=0 Vλ (R)Pλ (cos θ ), (1) Author's personal copy Astrophys Space Sci Table 2 Wavelengths values λ (in mm) for the transitions considered in this work Table 3 Energy dependence of selected He–HCNH+ rotational excitation cross sections as functions of the Jmax parameter (units: Å2 ) Line λ Line λ Energy Transition Jmax = 17 Jmax = 19 Jmax = 21 Jmax = 23 1→0 4.045 8→0 0.112 50 cm−1 0→1 38.619 38.619 38.619 38.619 2→0 1.348 8→1 0.115 1→2 27.782 27.781 27.781 27.781 2→1 2.022 8→2 0.122 2→5 4.257 4.258 4.258 4.258 3→0 0.674 8→3 0.135 3→5 13.413 13.413 13.413 13.413 300 cm−1 0 → 1 13.056 13.056 13.056 13.056 1→2 9.636 9.636 9.636 9.636 2→5 1.507 1.507 1.507 1.507 5→7 9.050 9.050 9.050 9.050 7→9 8.201 8.202 8.202 8.202 8 → 10 7.615 7.615 7.615 7.615 9 → 10 8.861 8.860 8.859 8.859 3→1 0.809 8→4 0.155 3→2 1.348 8→5 0.193 4→0 4→1 0.404 0.449 8→6 8→7 0.269 0.506 4→2 0.578 9→0 0.090 4→3 1.011 9→1 0.092 5→0 0.269 9→2 0.096 5→1 0.289 9→3 0.104 5→2 0.337 9→4 0.115 640 cm−1 0 → 1 7.528 7.528 7.528 7.528 5→3 0.449 9→5 0.135 1→2 6.334 6.334 6.334 6.334 5→4 0.809 9→6 0.168 2→5 2.165 2.165 2.165 2.165 6→0 0.193 9→7 0.238 5→7 6.164 6.164 6.164 6.164 6→1 0.202 9→8 0.449 7→9 5.855 5.855 5.855 5.855 6→2 0.225 10 → 0 0.073 8 → 10 5.713 5.712 5.072 5.072 6→3 0.269 10 → 1 0.075 9 → 10 5.093 5.096 5.096 5.096 6→4 0.368 10 → 2 0.078 6→5 0.674 10 → 3 0.082 7→0 0.144 10 → 4 0.090 7→1 0.150 10 → 5 0.101 7→2 0.162 10 → 6 0.119 7→3 0.184 10 → 7 7→4 0.225 7→5 0.311 7→6 0.578 Table 4 MOLSCAT parameters used in the present calculations INTFL = 6 STEPS = 20, 10 OTOL = 0.001 0.150 DTOL = 0.01 Jmax = 17, 19, 23 Rmin = 3.5 Bohr 10 → 8 0.213 Be = 1.236032 cm−1 De = 1.608893 × 10−6 cm−1 Rmax = 50 Bohr 10 → 9 0.405 for all orientations. During the calculations, an interpolation was performed with the POTENL module of the MOLSCAT package (Hutson and Green 1994) to obtain Vλ (R) at other values of R. We present also in Table 2 the wavelengths of the transitions of interest. This includes the J = 1 → 0, J = 2 → 1, and J = 3 → 2 lines observed by Ziurys and Turner (1986). 3 Scattering calculations 3.1 Cross sections Fig. 4 Vλ expansion coefficients for the HCNH+ –He interaction potential energy surface (λ = 0, 1, 2, 3, 4) as functions of R State to state rotational integral cross sections for the excitation of HCNH+ by the helium atom were computed by using the quantum mechanical close-coupling approach formulated in 1960 by Arthurs and Dalgarno (1960) and implemented in the MOLSCAT package for dynamics calculations (Hutson and Green 1994). The values of J range from Author's personal copy Astrophys Space Sci Fig. 5 Collisional excitation cross sections of HCNH+ by He from the ground level (a) and for J = 1 (b) and J = 2 (c) as a function of the kinetic energy 0 to 10 and the total energy up to 640 cm−1 . The rotational levels of HCNH+ may be obtained from the usual expansion with the spectroscopic constants Be = 1.236032 cm−1 and De = 1.608893 × 10−6 cm−1 (Amano et al. 2006). To account for resonances during the calculations, the energy range was carefully spanned as follows. Below 50 cm−1 , the step was set to 0.1 cm−1 . From 50 cm−1 to 100 cm−1 , it was set to 0.2 cm−1 , from 100 cm−1 to 200 cm−1 to 0.5 cm−1 , from 200 cm−1 to 300 cm−1 to 1 cm−1 , from 300 cm−1 to 500 cm−1 to 5 cm−1 , and from 500 cm−1 to 640 cm−1 to 10 cm−1 . In addition, we have set Jmax = 17 for E < 300 cm−1 , Jmax = 19 for 300 cm−1 ≤ E ≤ 500 cm−1 , and Jmax = 23 for E > 500 cm−1 . These values were obtained after we had performed some convergence tests as illustrated in Table 3. These values provide us with rota- tional basis sets of adequate size for a good accuracy in the calculated cross sections. The integration step was lowered such that for E < 300 cm−1 , STEPS = 20 and for E ≥ 300 cm−1 , STEPS = 10. To allow the cross sections to converge to within 0.001 Å2 for off diagonal terms and 0.01 Å2 for diagonal ones, the maximum value of the total angular momentum was set to Jtot = 147 for E < 100 cm−1 , Jtot = 211 for 100 cm−1 ≤ E ≤ 500 cm−1 , and Jtot = 237 for 500 cm−1 ≤ E ≤ 640 cm−1 . The other parameters required for MOLSCAT calculations are displayed in Table 4. The coupled equations were solved with the propagator of Manolopoulos (1986). Figure 5 displays the collisional excitation cross sections of HCNH+ by He atom as a function of the kinetic energy from the first level (panel a) and for J = 1 and 2 Author's personal copy Astrophys Space Sci Fig. 6 Collisional excitation cross sections of the HCNH+ by He as functions of J ′ for selected values of energy Fig. 7 Calculated downward rate coefficients at selected temperatures for the collision of HCNH+ with He as a function of J ′ Author's personal copy Astrophys Space Sci Table 5 Rate coefficients (given as a(b) = a.10b ) for de-excitation of HCNH+ rotational levels in collision with He as functions of kinetic temperature (in units of cm3 s−1 ) Rate coefficients (cm3 s−1 ) Levels Initial Final J J′ 10 K 20 K 50 K 80 K 100 K 120 K 1 0 1.1016(−10) 9.3665(−11) 7.7148(−11) 7.2057(−11) 7.0202(−11) 6.8806(−11) 2 0 4.4429(−11) 4.2533(−11) 4.3902(−11) 4.6847(−11) 4.8437(−11) 4.9634(−11) 2 1 1.5397(−10) 1.3956(−10) 1.1480(−10) 1.0397(−10) 9.9724(−11) 9.6635(−11) 3 0 1.5593(−11) 1.3515(−11) 9.2158(−12) 7.2621(−12) 6.5600(−12) 6.1218(−12) 3 1 7.1942(−11) 7.3766(−11) 7.5330(−11) 7.7277(−11) 7.8296(−11) 7.8977(−11) 3 2 1.4941(−10) 1.3912(−10) 1.1970(−10) 1.1035(−10) 1.0645(−10) 1.0350(−10) 4 0 1.1032(−11) 1.1471(−11) 1.0633(−11) 9.8038(−12) 9.3521(−12) 8.9618(−12) 4 1 1.9395(−11) 1.8137(−11) 1.4086(−11) 1.1919(−11) 1.1117(−11) 1.0625(−11) 4 2 6.7862(−11) 7.2804(−11) 7.6802(−11) 7.9706(−11) 8.1214(−11) 8.2299(−11) 4 3 1.4589(−10) 1.3729(−10) 1.2236(−10) 1.1416(−10) 1.1040(−10) 1.0741(−10) 5 0 2.3556(−12) 2.4188(−12) 2.0723(−12) 1.8237(−12) 1.7286(−12) 1.6712(−12) 5 1 1.3576(−11) 1.5274(−11) 1.5707(−11) 1.5005(−11) 1.4501(−11) 1.4024(−11) 5 2 1.5419(−11) 1.6313(−11) 1.4845(−11) 1.3291(−11) 1.2652(−11) 1.2254(−11) 5 3 6.3670(−11) 6.9575(−11) 7.6680(−11) 8.0562(−11) 8.2384(−11) 8.3681(−11) 5 4 1.4320(−10) 1.3681(−10) 1.2285(−10) 1.1511(−10) 1.1151(−10) 1.0859(−10) 6 0 8.5243(−13) 1.2205(−12) 1.4537(−12) 1.3763(−12) 1.3136(−12) 1.2590(−12) 6 1 2.8308(−12) 3.1930(−12) 3.0893(−12) 2.8614(−12) 2.7802(−12) 2.7446(−12) 6 2 1.1790(−11) 1.4631(−11) 1.7461(−11) 1.7450(−11) 1.7087(−11) 1.6649(−11) 6 3 1.3474(−11) 1.4645(−11) 1.4334(−11) 1.3489(−11) 1.3132(−11) 1.2925(−11) 6 4 6.1315(−11) 6.6200(−11) 7.4086(−11) 7.8860(−11) 8.1091(−11) 8.2691(−11) 6 5 1.4264(−10) 1.3775(−10) 1.2322(−10) 1.1534(−10) 1.1175(−10) 1.0884(−10) 7 0 1.0931(−13) 1.7246(−13) 2.1923(−13) 2.2915(−13) 2.3988(−13) 2.5433(−13) 7 1 9.3345(−13) 1.6305(−12) 2.4310(−12) 2.4524(−12) 2.3861(−12) 2.3129(−12) 7 2 2.6484(−12) 3.1692(−12) 3.4792(−12) 3.3839(−12) 3.3394(−12) 3.3248(−12) 7 3 9.9139(−12) 1.2519(−11) 1.6255(−11) 1.7221(−11) 1.7278(−11) 1.7125(−11) 7 4 1.1796(−11) 1.2872(−11) 1.2996(−11) 1.2794(−11) 1.2774(−11) 1.2827(−11) 7 5 5.9885(−11) 6.3709(−11) 7.2108(−11) 7.7561(−11) 8.0040(−11) 8.1784(−11) 7 6 1.4658(−10) 1.4124(−10) 1.2514(−10) 1.1663(−10) 1.1280(−10) 1.0970(−10) 8 0 3.0662(−14) 7.0093(−14) 1.2368(−13) 1.3283(−13) 1.3556(−13) 1.3868(−13) 8 1 1.3542(−13) 2.4869(−13) 3.8865(−13) 4.2813(−13) 4.5351(−13) 4.8260(−13) 8 2 8.1540(−13) 1.4163(−12) 2.5068(−12) 2.7722(−12) 2.7921(−12) 2.7687(−12) 8 3 2.4691(−12) 2.8794(−12) 3.2149(−12) 3.2752(−12) 3.3210(−12) 3.3788(−12) 8 4 8.2897(−12) 1.0593(−11) 1.4960(−11) 1.6706(−11) 1.7115(−11) 1.7209(−11) 8 5 1.1305(−11) 1.2335(−11) 1.2720(−11) 1.2861(−11) 1.3028(−11) 1.3225(−11) 8 6 5.7532(−11) 6.1404(−11) 6.9373(−11) 7.5013(−11) 7.7651(−11) 7.9518(−11) 8 7 1.4410(−10) 1.4208(−10) 1.2684(−10) 1.1800(−10) 1.1397(−10) 1.1068(−10) 9 0 9.5632(−15) 1.5833(−14) 2.6236(−14) 3.1837(−14) 3.6378(−14) 4.1611(−14) 9 1 4.0947(−14) 8.4961(−14) 1.9133(−13) 2.3021(−13) 2.4458(−13) 2.5643(−13) 9 2 1.5617(−13) 2.4046(−13) 3.9340(−13) 4.7194(−13) 5.1949(−13) 5.6661(−13) 9 3 8.7518(−13) 1.2913(−12) 2.4531(−12) 2.9122(−12) 3.0165(−12) 3.0476(−12) 9 4 2.6659(−12) 2.8835(−12) 3.1501(−12) 3.2953(−12) 3.3993(−12) 3.5048(−12) 9 5 7.6377(−12) 9.3368(−12) 1.3377(−11) 1.5489(−11) 1.6156(−11) 1.6466(−11) 9 6 1.1802(−11) 1.2775(−11) 1.3194(−11) 1.3502(−11) 1.3770(−11) 1.4039(−11) 9 7 5.6540(−11) 6.0069(−11) 6.6827(−11) 7.2054(−11) 7.4618(−11) 7.6454(−11) 9 8 1.5980(−10) 1.4999(−10) 1.3032(−10) 1.2014(−10) 1.1560(−10) 1.1191(−10) Author's personal copy Astrophys Space Sci Table 5 (Continued) Rate coefficients (cm3 s−1 ) Levels Initial Final J J′ 10 K 20 K 50 K 80 K 100 K 120 K 10 0 4.4092(−15) 5.1679(−15) 9.1298(−15) 1.2355(−14) 1.4683(−14) 1.7144(−14) 10 1 1.8214(−14) 2.4035(−14) 4.2297(−14) 5.6275(−14) 6.6449(−14) 7.7187(−14) 10 2 5.3322(−14) 8.6609(−14) 2.1758(−13) 2.8519(−13) 3.1175(−13) 3.3165(−13) 10 3 2.1597(−13) 2.6658(−13) 4.1892(−13) 5.2930(−13) 5.9510(−13) 6.5599(−13) 10 4 1.0545(−12) 1.2590(−12) 2.2141(−12) 2.7460(−12) 2.9155(−12) 3.0020(−12) 10 5 3.1126(−12) 3.1010(−12) 3.2671(−12) 3.4686(−12) 3.6117(−12) 3.7462(−12) 10 6 7.2463(−12) 8.4030(−12) 1.1742(−11) 1.3841(−11) 1.4626(−11) 1.5070(−11) 10 7 1.3761(−11) 1.4080(−11) 1.4159(−11) 1.4443(−11) 1.4729(−11) 1.5007(−11) 10 8 5.7904(−11) 5.9167(−11) 6.4062(−11) 6.8756(−11) 7.1168(−11) 7.2899(−11) 10 9 1.6659(−10) 1.5351(−10) 1.3236(−10) 1.2148(−10) 1.1660(−10) 1.1259(−10) except at low energies E < 100 cm−1 , there is an overall propensity towards J = 2 transitions. 3.2 Rate coefficients Fig. 8 Calculated downward rate coefficients for selected transitions as functions of the kinetic temperatures (panels b and c, respectively). It is obvious that for collision energies below 100 cm−1 , many resonances occur in the cross sections. A similar behavior of the cross sections has been observed and explained in papers by Lique et al. (2006), Hammami et al. (2008a, 2008b, 2008c), and Nkem et al. (2009). Figure 6 presents cross sections as a function of J ′ for selected energies. From Fig. 4(a), it is clear that the 0 → 1 transition predominates up to an energy of 100 cm−1 , at which transition 0 → 2 become dominant. For J = 1 (Fig. 4(b)), the magnitude of the cross sections for the 1 → 2 transition is greater than that of the other transitions over the entire range of energy. The magnitude of the J = 2 transitions (Fig. 4(c)) follows the hierarchy 1 → 3 > 2 → 4 > 3 → 5 > 4 → 6. Figure 6 illustrates the dependence of the cross sections on J = J ′ and J = J ′ − 1 at various energies. As one can see, the 0 → 2 transition is dominant. Thus Downward rate coefficients were computed using the same procedure as done previously by Hammami et al. (2008a, 2008b, 2008c), Nkem et al. (2009) and Gotoum et al. (2011), i.e., by averaging the cross sections over a Maxwell– Boltzmann distribution of kinetic energies. The corresponding values for all the transitions investigated are listed in Table 5 for selected temperatures. Additional numbers may be obtained upon request from the authors. Figure 7 shows the behavior of the rate coefficients with J ′ for different values of J and temperatures. As one can see, all the quantities exhibit almost the same trend for a given J with increasing temperature. The overall propensity towards J = 2 transitions already noticed in the cross sections remains. From Fig. 8, which displays the dependence of collision rates on temperature, it is clear that these quantities are smooth varying functions of the temperature. It should be pointed out that the IOS and statistical hyperfine rate coefficients may be retrieved from our rotational rate coefficients by using the procedure described by Faure and Lique (2012), which is well adapted for both closed and open shell rigid rotors of 1 Σ or 2 Σ electronic symmetry in collision with the electron, He and para H2 (j = 0). 4 Concluding remarks A reliable ab initio potential interaction energy for the HCNH+ –He van der Waals complex was obtained with an aug-cc-pVTZ Gaussian basis set at the CCSD(T) level of theory. Bond functions that have proven to give a correct description of the intersystem correlation energy were Author's personal copy Astrophys Space Sci employed. The PES was then used to compute rotational integral cross sections in the quantum mechanical closecoupling approach. These cross sections were averaged over a Maxwell–Boltzmann distribution of kinetic energies to infer downward rate coefficients for T ≤ 120 K. 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