Temperature dependence of rotational excitation rate coefficients of OH(X2Π) in collision with He

Chemical Physics Letters 445 (2007) 12–16 www.elsevier.com/locate/cplett

Temperature dependence of rotational excitation rate coefficients of OH(X2P) in collision with He J. Kłos *, F. Lique, M.H. Alexander Department of Chemistry and Biochemistry and Institute for Physical Sciences and Technology, University of Maryland, College Park, MD 20742-2021, USA Received 12 June 2007; in final form 17 July 2007 Available online 21 July 2007

Abstract We report fully-quantum, close-coupling (CC) calculations of inelastic integral cross sections of hydroxyl radical collisions with He, based on a recent RCCSD(T) potential energy surface. We compare with experimental calculated integral cross sections for a collision energy of 394 cm1. The excellent agreement confirms the accuracy of the potential energy surfaces. Scattering calculations, which take into account the fine-structure of the OH radical, are done on a grid of collision energies large enough to ensure converged state-to-state rate coefficients for temperatures ranging from 1 K up to 500 K. The calculated cross sections and rate coefficients exhibit sizeable, parity-dependent propensities.  2007 Elsevier B.V. All rights reserved.

1. Introduction The experimental and theoretical study of collisioninduced rotational energy transfer has received much attention during the past 30 years. This has been motivated by the development of combined molecular beam, laser techniques and the improvement of techniques for fullyquantum treatments of the collision dynamics based on accurate potential energy surfaces. Now, collisions of both closed- and open-shell diatomic radicals with close-shell partners can be treated routinely. Modeling of the scattering process of radicals with closed shell targets is very important from the point of view of atmospheric and interstellar chemistry since both atmospheric and interstellar clouds contain simple radicals like OH, NO or CN. Among these, the OH(X2P) radical is of particular interest since it is one of the most detected interstellar molecules [1,2]. In addition, several interstellar OH masers have been detected. In these masers the required population inversion is induced by heavy particle (He and H2) impact [3]. The kinetic models for this processes are based *

Corresponding author. E-mail address: [email protected] (J. Kłos).

0009-2614/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.07.035

on theoretical predictions that collisions will excite preferentially the upper K-doublet levels of rotationally excited states in the lower (2P3/2) spin–orbit ladder [4]. It is thus of great importance to provide accurate rate coefficients for OH(X2P) molecules in collisions with He and H2. Theoretical study of the excitation of OH in collisions with H2, in particular rate coefficients, have been reported by Flower et al. [5] (and references therein) and more recently by Offer et al. [6]. However, although OH–He has been the object of several experimental and theoretical studies, to our knowledge no complete set of collisional rate coefficients exist for the excitation of OH in collisions with He. Schreel et al. [7] have measured state-to-state cross sections for excitation of OH(X2P, m = 0) in collision with He at a collision energy of 394 cm1. Hickson et al. [9,10] have reported rotational rate coefficients for collisions of OH(X2P, m = 1) with He at room temperature. From a theoretical point of view, Degli-Esposti and coworkers [11] have studied OH–He rotational excitation using a PES calculated at the coupled electron pair approximation (CEPA) level. They determined cross sections at 394 cm1 but did not calculate rate coefficients. Although these studies have provided important knowledge on the the rotational excitation of OH in collisions with He, theoretical data are

J. Kłos et al. / Chemical Physics Letters 445 (2007) 12–16

always needed and especially for the thermal dependence of the rotational excitation rate coefficients of OH(2P) in collision with He. We present here a new study of rotational excitation of the OH molecule in its ground vibrational state in collisions with He. Our work is motivated by the astrophysical need for rates coefficients with He, the second most abundant species, and by recent experimental measurement of rate coefficients by Marinakis et al. [12]. Collisional cross sections are obtained using the recently published potential energy surface (PES) of Lee et al. [13]. State-resolved inelastic cross sections are obtained for collision energies from 0.2 to 3000 cm1 which yield, after a Boltzmann thermal average, rate coefficients up to 500 K. Finally, cross sections and rate coefficients obtained in the present study are compared with the available experiments in order to check the quality of the set of rate coefficients obtained. The Letter is organized as follows: Section 1 describes the ab initio potential energy surface used in this work. Section 2 provides a brief description of the theory and of the calculations. In Section 3, we present and discuss the results. Concluding remarks are drawn in Section 4. 2. Potential energy surface and scattering calculations The open-shell OH molecule in its ground X2P electronic state is split into a lower (labelled F1) and upper (F2) spin–orbit manifold [8]. In Hund’s case (a) these correspond, for a molecule with a negative spin–orbit constant – as OH – to projection quantum numbers of the sum of the electronic orbital and spin angular momenta X = 3/2 and X = 1/2, respectively. Each rotational level j is further split into two close lying K-doublet levels, which are labelled e and f. For a state of doublet multiplicy, the total parity is +(1)J1/2 for the e-labelled states and (1)j1/2 for the f-labelled states [14]. The energies of the rotational levels of the OH molecule, including the spin–orbit and K-doubling fine structure are given by 1 e Ej;X¼3=2;e ¼ Aso þ B0 ½jðj þ 1Þ  7=4 þ ðB0 =Aso Þ 2 2 ð2q þ pB0 =Aso Þðj  1=2Þðj þ 1=2Þðj þ 3=2Þ 1 e Ej;X¼1=2;e ¼  Aso þ B0 ½jðj þ 1Þ þ 1=4 þ pðj þ 1=2Þ 2 2

13

When the OH(X2P) radical interacts with a spherical structureless target, the doubly-degenerate P electronic state is split into two states, one of A 0 symmetry and one of the A00 symmetry. These correspond, respectively, to the singly occupied p orbital lying in, or perpendicular to, the triatomic plane [18–20]. In the scattering calculations it is more appropriate [17] to use the average 1 V sum ¼ ðV A00 þ V A0 Þ 2

ð2Þ

and half-difference1. 1 V dif ¼ ðV A00  V A0 Þ ð3Þ 2 of these two potential energy surfaces. In the pure Hund’s case (a) limit, it is Vsum which is responsible for inducing inelastic collisions within a given spin–orbit manifold, and Vdif which induce inelastic collisions between the two (X = 3/2) and (X = 1/2) spin–orbit manifold. In our calculations we used the results of prior ab initio calculations – and the fit thereto – of Lee et al. [13]. Scattering calculations were done with the HIBRIDON suite of programs [16]. Note that we use the full quantum close-coupling (CC) method, rather than the computationally less intensive, but more approximate coupled-states (CS) method. The channel basis was chosen to ensure convergence of the integral cross sections for all j, Fi ! j 0 , F0i transitions with j, j 0 6 11.5. At each collision energy, the maximum value of the total angular momentum J was set large enough (Jmax = 100) that the inelastic cross sec˚ 2. tions were converged to within 0.01 A 3. Results Fully-quantum, close-coupling calculations of integral cross sections were carried out for collision energies ranging from 0.2 to 3000 cm1. The calculated cross sections are used then in subsequent calculations of state-selected, temperature-dependent excitation and de-excitation rate coefficients. We also compare cross sections at a collision energy of 394 cm1 to earlier experimental results of Schreel et al. [7]. 3.1. Integral cross sections

ð1Þ where e = +1 for the e-labelled and 1 for the f-labelled levels. Here B0 is the rotational constant in the lowest vibrational manifold of OH (B0 = 19.5487 cm1), Aso is the spin–orbit constant (Aso =  139.21 cm1) and the two K doubling parameters are p = 2.35 · 101 cm1 and q =  3.910 · 102 cm1 [15]. In the scattering calculations reported here we assume that the value of the SO constant is not altered by approach of the He atom. This is certainly a valid approximation at the moderate-to-large OH–He distances of importance in low energy collisions.

The variation with collision energy of integral cross sections for transitions out of the lowest (j = 1.5, e) rotational level in the ground (F1) spin–orbit manifold to several rotational levels in the F1 and F2 spin–orbit manifolds is shown in Figs. 1 and 2, respectively. For spin–orbit-changing transitions (Fig. 2) we see a clear propensity for total parity conserving transitions, that is, transitions with even Dj which conserve the e/f label or with odd Dj which change 1

Note that the authors of Ref. [13] define the difference potential as  V A00 Þ, which is opposite to the standard convention; see Ref. [17].

1 0 2 ðV A

14

J. Kłos et al. / Chemical Physics Letters 445 (2007) 12–16

K-doublet level of the j = 1.5, F1 state at a collision energy of 394 cm1 with the experimental results of Schreel et al. [7]. These are shown in Fig. 3. As discussed in Table 1 of Ref. [7], the displayed cross sections include a 15% contribution from cross sections for scattering out of the j = 2.5, F1, f initial state which is fractionally present in the OH beam. The experimental cross sections are scaled so that the sum of all the experimental cross sections is equal to the sum of the corresponding calculated cross sections. Except for transitions to the j 0 = 4.5 levels, the agreement is everywhere excellent, nearly within the experimental uncertainty.

1

10

j =2.5 e F1

j =3.5 e F1

j =1.5 f F1 0

2

σij (A )

10

j =2.5 f F1

j =3.5 f F1

-1

10

5

j =1.5 e F1 0

500

1000

1500

2000

F1,f (expt.)

4.5

Ecol (cm-1)

F1,f (theory)

4

F1,e (expt.) F1,e (theory)

3.5

Fig. 1. Dependence on the collision energy of cross sections for Ficonserving (spin–orbit conserving) rotational transitions out of the j = 1.5, e, F1 state.

F2,f (expt.) F2,f (theory)

2

σ (A )

3

F2,e (expt.)

2.5

F2,e (theory)

2

1

10

1.5

j =1.5 e F1

1

j =0.5 f F2

0.5 j =1.5 e F2

0

2

σij (A )

10

0

0.5

1.5

2.5

j =2.5 f F2

3.5

4.5

j’

j =1.5 f F2

Fig. 3. Comparison of integral cross sections at Ecol = 394 cm1 for spin– orbit-conserving (black, solid line) and spin–orbit-changing (red, dashed line) transitions out of the j = 1.5, F1, f level from the present work and from recent experiments of Schreel et al. The latter values were scaled to match the sum of the theoretical cross sections. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

-1

10

j =2.5 e F2 j =0.5 e F2

-2

10

0

500

1000

E

col

1500

2000

-1

(cm )

Fig. 2. Dependence on the collision energy of cross sections for Fichanging (spin–orbit changing) transitions out of the j = 1.5, e, F1 state.

the e/f label. By contrast, for spin–orbit-conserving transitions, for a given final j the relative magnitudes of the cross sections into the two K-doublet levels varies with the collision energy, so a similar propensity toward parity conservation does not emerge. At low collision energy, the excitation (Dj > 0) cross sections show a propensity to populate e final levels, while the de-excitation (Dj < 0) cross sections show, predominately, a propensity for conservation of the total parity as observed previously by Degli-Esposti et al. [11] (and references therein). At high energy the largest cross sections correspond to parity conserving transitions regardless of the e/f label of the initial state. To check the accuracy of the present calculations we have compared cross sections for transitions out of the f

Table 1 Comparison of experimental and theoretical cross sectionsa from the present calculations based on a RCCSD(T) potential energy surface and from previous calculationsb based on a CEPA potential energy surface j0

e0

F0i

Expc

RCCSD(T)

CEPA

2.5 3.5 4.5 1.5 2.5 3.5 4.5

f f f e e e e

F1 F1 F1 F1 F1 F1 F1

0.603 ± 0.080 0.262 ± 0.034 0.034 ± 0.011 0.956 ± 0.068 4.452 ± 0.148 0.968 ± 0.080 0.216 ± 0.023

0.503 0.184 0.004 0.925 4.700 0.723 0.059

0.316 0.131 0.002 0.574 4.484 0.481 0.030

0.5 1.5 2.5 0.5 1.5

f f f e e

F2 F2 F2 F2 F2

0.103 ± 0.034 1.082 ± 0.125 0.114 ± 0.046 3.131 ± 0.114 0.273 ± 0.091

0.105 1.531 0.133 3.000 0.328

0.105 1.360 0.082 2.866 0.281

Ecol = 394 cm1. a ˚ 2. To simulate the experiments, the tabulated theoretical Units of A cross sections are a weighted average of cross sections out of the j = 1.5, f, F1 (weight = 0.935) and out of the j = 2.5, f, F1 (weight = 0.065) levels. b Ref. [11]. c Ref. [7]. Results scaled as described in the text.

J. Kłos et al. / Chemical Physics Letters 445 (2007) 12–16

3.2. Rate coefficients By averaging over a Maxwell distribution of collision velocities, we used the CC cross section described in Section 3.1 to obtain excitation and de-excitation thermal rate coefficients for transitions between fine structure levels of OH. The representative variation with temperature of these state-to-state rate coefficients is illustrated in Figs. 4 and 5 for spin–orbit-conserving and spin–orbit changing transitions out of the j = 1.5, F1, e level. -11

2.5

jf=1.5 f

f

jf=3.5 e

3

kij (cm /molecule×s)

jf=2.5 e j =3.5 f

1

0.5

0

0

jf=0.5 f jf=0.5 e 2

j =1.5 f f

j =1.5 e f

jf=2.5 f

1.5

j =2.5 e

3

f

1

0.5

0

0

100

200

300

400

500

T (K) Fig. 5. Temperature dependence of state-to-state rate coefficients for spin– orbit-changing transitions out of the j = 1.5, F1, elevel.

The rate coefficients obviously display the same propensity rules seen in the integral cross sections. The rate coefficients for transfer from F1 to F2 are the same order of magnitude as the corresponding rate coefficients for transitions within the F1 manifold. The complete set of (de)excitation rate coefficients with j, j 0 6 11.5 is available on-line from the BASECOL website2. Excitation rate coefficients can be easily obtained by detailed balance: k j!j0 ðT Þ ¼ k j0 !j ðT Þ

2j0 þ 1 exp½ðej0  ej Þ=kT  2j þ 1

ð4Þ

where ej and ej 0 are, respectively, the energies of the rotational levels j and j 0 . Our room temperature rate coefficients have been used in a recent comparison with experimental results from polarization spectroscopy [12].

We have used quantum scattering calculations to investigate rotational energy transfer in collisions of OH(X2P) with He atoms. The calculations are based on a recent, highly-correlated 2D potential energy surface [13]. Closecoupling cross sections were obtained for collision energies ranging from 0 to 3000 cm1. Excellent agreement between theoretical and experimental cross sections of Schreel et al. [7] was found for transitions out of j = 1.5, F1, e/f level at a collision energy of 394 cm1. Rate coefficients for transitions involving the lowest 28 fine structure levels of the OH molecule were determined for temperatures ranging from 1 to 500 K.

jf=2.5 f

1.5

x 10

4. Conclusions

x 10

2

-11

2.5

kij (cm /molecule×s)

In Table 1 we compare numerical values of the present calculated cross sections with experiment (scaled as described above) and the results of the previous CC calculations of Degli-Esposti et al. [11], based on a CEPA potential energy surface. As can be seen, in most of the cases the present results agree better with experiment than these earlier calculations. This shows that the highly-correlated potential energy surface of Lee et al. [13] is likely more accurate than the earlier CEPA potential energy surface used by Degli-Esposti et al. [11]. We note that the theoretical results [calculated on both the CEPA and RCCSD(T) PESs] for transitions into the j 0 = 4.5 levels are approximately an order of magnitude smaller than the experimental values. A similar discrepancy is seen in the results of Schreel et al. [7] for the Ar–OH system. At a collision energy of 394 cm1 the j 0 = 4.5, F1 level is open (energetically allowed) by only 40 cm1. Calculations show that the cross section into both K-doublet components of this level increase rapidly as Ecol increases beyond 394 cm1. At a collision energy of 460 cm1 the cross sections into j 0 = 4.5, F1, e and j 0 = 4.5, F1, f have risen to ˚ 2, respectively. Thus, it is likely that the 0.15 and 0.01 A experimental cross sections into j 0 = 4.5, F1 shown in Table 1 are biased by higher energy components in the experimental beam, which has a width, in collision energy, of 70 ± 20 cm1 [21].

15

100

200

300

400

500

T (K) Fig. 4. Temperature dependence of state-to-state rate coefficients for spin– orbit-conserving transitions out of the j = 1.5, F1, e level.

2

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

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J. Kłos et al. / Chemical Physics Letters 445 (2007) 12–16

We anticipate that the rate coefficients determined in the present study would also be useful in the interpretation of collision experiments at very low temperature. In addition, recent studies [22,23] have shown that modeling studies based on inaccurate collisional excitation rates can lead to important errors in the determination of molecular abundances in molecular clouds. We expect that the present set of rate coefficients will help to enable more accurate modelling of He–OH collisions in astrophysical environments. In particular, the present data will help in the interpretation of astrophysical observations and determination of physical conditions in interstellar clouds probed by planned ground-based and space-based missions, like the Herschel satellite3 or the ALMA interferometer4. These will open up high spectral and spatial resolution studies of the universe at infrared and submillimeter wavelengths. Acknowledgement The authors acknowledge financial support from the US National Science Foundation under grant CHE-0413743. We thank Dr. Sarandis Marinakis for valuable discussions which prompted our interest in this study. References [1] S. Weinreb, A.H. Barrett, M.L. Meeks, J.C. Henry, Nature 200 (1963) 829. [2] V.L. Fish, L.K. Zschaechner, L.O. Sjouwerman, Y.M. Pihlstroem, M.J. Claussen, Astrophys. J. 653 (2006) L45. [3] M. Bertojo, A.C. Cheung, C.H. Townes, Astrophys. J. 208 (1976) 914. [4] G. Herzberg, The Spectra and Structures of Simple Free Radicals, Dover, New York, 1971.

[5] D.P. Dewangan, D.R. Flower, M.H. Alexander, MNRAS 226 (1987) 505, and references therein. [6] A.R. Offer, M.C. van Hemert, E.F. van Dishoeck, J. Chem. Phys. 100 (1994) 362. [7] K. Schreel, J. Schleipen, A. Eppink, J. ter Meulen, J. Chem. Phys. 99 (1993) 8713. [8] G. Herzberg, Spectra of Diatomic Molecules, Princeton, Van Nostrand, 1968. [9] K.M. Hickson, C.M. Sadowski, I.W.M. Smith, J. Phys. Chem. A 106 (2002) 8442. [10] K.M. Hickson, C.M. Sadowski, I.W.M. Smith, Phys. Chem. Chem. Phys. 4 (2002) 5613. [11] A. Degli-Esposti, A. Berning, H.-J. Werner, J. Chem. Phys. 103 (1995) 2067. [12] S. Marinakis, G. Paterson, J. Kłos, M.L. Costen, K.G. McKendrick, Phys. Chem. Chem. Phys. (2007), doi:10.1039/b703909c, Advance article. [13] H.-S. Lee, A. McCoy, R. Toczyłowski, S. Cybulski, J. Chem. Phys. 113 (2000) 5736. [14] J.M. Brown et al., J. Mol. Spectrosc. 55 (1975) 500. [15] J.P. Maillard, J. Chauville, A.W. Mantz, J. Mol. Spectrosc. 63 (1976) 120. [16] The HIBRIDON package was written by M.H. Alexander, D.E. Manolopoulos, H.-J. Werner, B. Follmeg, with contributions by P.F. Vohralik, D. Lemoine, G. Corey, R. Gordon, B. Johnson, T. Orlikowski, A. Berning, A. Degli-Esposti, C. Rist, P. Dagdigian, B. Pouilly, G. van der Sanden, M. Yang, F. de Weerd, S. Gregurick, J. Kłos. [17] M.H. Alexander, Chem. Phys. 92 (1985) 337. [18] M.H. Alexander, S. Stolte, J. Chem. Phys. 112 (2000) 8017. [19] W.B. Zeimen, G.C. Groenenboom, A. van der Avoird, J. Chem. Phys. 119 (2003) 31. [20] W.B. Zeimen, G.C. Groenenboom, A. van der Avoird, J. Chem. Phys. 119 (2003) 141. [21] H. ter Meulen, private communication, 2007. [22] F. Lique, J. Cernicharo, P. Cox, Astrophys. J. 653 (2006) 1342. [23] F. Daniel, J. Cernicharo, M.-L. Dubernet, Astrophys. J. 648 (2006) 461.