1. “Rotational Energy Transfer in o - / p -H 2 + HD” Renat A. Sultanov and Dennis Guster BCRL, St. Cloud State University St. Cloud, MN June 20, 2007 OSU International Symposium on Molecular Spectroscopy, June 18-22, 2007

2. http://www.bcrl.stcloudstate.edu/

3. ABSTRACT Rotational energy transfer in molecular hydrogen ortho- /para- H 2 +HD collisions are computed. The low temperature limit is investigated, which is of significant astrophysical interest in regard to the cooling of primordial gas and ISM. The newest global H 2 -H 2 PES from A.I. Boothroyd, P.G. Martin, W.J. Keogh, M.J. Peterson, JCP 116 (2002) 666 (BMKP PES) is appropriately adopted to the current system and applied. Sharp resonance have been reproduced in cross sections at very low collision energies: v ~10 m/sec (~10E-7 eV). Very accurate H 2 -H 2 surface(rigid rotor model) from P. Diep and K. Johnson JCP 113, 3480 (2000) (DJ PES) as far as some results for H 2 +H 2 collision are also presented. Cross sections and rate coefficients are calculated using a close coupling quantum-mechanical approach.

4. The 4 -ATOMIC COLLISIONS ● H 2 (v 1,j 1 ) + H 2 (v 2,j 2 ) -> H 2 (v' 1,j' 1 ) + H 2 (v' 2,j' 2 ) ● H 2 (v 1,j 1 ) + HD(v 2,j 2 ) -> H 2 (v' 1,j' 1 ) + HD(v' 2,j' 2 ) ● Astrophysics: cooling primordial gas ● Low number of electrons: high precision PESs ● The benchmark systems: semiclassical time - dependent, wave-packet studies and quantum- mechanical time -independent.

5. ASTROPHYSICAL APPLICATION S ● H2/HD play important role in astrophysics ● Simplest and most abundant molecules ● Energy transfer involving HD / H 2 governs the evolution of PDRs in ISM ● Cooling of primordial gas ● Shock wave-induced heating in ISM ● To model the thermal balance and kinetics in ISM one needs accurate rates k vj-v'j' ( T ) ● Collisional rates are important: contribute to molecular excitation/de-excitation in competition with radiative processes.

6. HD COOLING of astrophysical media ● Primordial D abundance is small: N( D ) / N( H ) ~ 4.0E-5 ● Due chemical fractionation: N( HD ) / N( H 2 ) ~ 1.0E-3 ● Permanent dipole moment of HD molecules for cooling ● Smaller rotational constant of HD molecules relative to H 2 molecules ● T~100 K: HD cooling is very important !

7. DJ PES ● Vibrationally averaged rigid monomer model; ● Bond length 1.449 a. u.; ● 4-term spherical harmonics expansion model was chosen to fit the surface; ● Defined by the center-of-mass intermolecular distance R and 3 angles; ● Calculated from only 2.0 to 10.0 A; ● Functional form of the potential represents an expansion on Legendre polynomials.

8. H 2 + H 2

9. BMKP PES ● BMKP PES - global six-dimensional surface for two hydrogen molecules; ● Constructed to represent the whole interaction of the four-atomic H 2 -H 2 system; ● To provide an accurate as possible estimate of the van der Waals well; ● Fits the van der Waals well to an accuracy about 5% rms error of 1.43 millihartree relative to the 48180 ab initio energies.

10. 4- atomic system HD+H 2

11. DJ and BMKP PESs at angular configuration: 60 o, 60 o and 0 o

12. DJ and BMKP PESs at angular configuration: 90 o, 0 o and 0 o

13. DJ and BMKP PESs at angular configuration: 90 o, 90 o and 0 o

14. BASIC EQUATIONS

16. REFERENCES ● S. Green, JCP 62, 2271 (1975): [Theory] ● J.M. Hutson, S. Green, MOLSCAT Ver. 1(1994) CCP6, Darsbury Lab. UK: [Manual] ● Shih-I Chu, JCP 62, 4089 (1975): [H 2 +HD effective potential formalism] ● D.W. Schwenke, JCP 89, 2076 (1988): [PES] ● J. Schaefer, Astron. Astrophys. Suppl. Ser. 85, 1101 (1990): [HD+H2, T ~ 10m/sec] ● E. Roueff, D.R. Flower, Mon. Not. R. Astron. Soc., 305, 353 (1999): [HD+H 2, T ~ 300 m/sec]

17. REFERENCES ● D.R. Flower, E. Roueff, J. Phys. B 31, 2935 (1998): [HD+H 2, T ~ 300 m/s] ● D.R. Flower, J. Le Bourlot, G. Pineau des Forets, and E. Roueff, Mon. Not. R. Astron. Soc. 314, 753 (2000): [HD cooling function] ● R.A. Sultanov, D. Guster, Chem. Phys. Lett. 436, 19 (2007): [ p-H2+HD, T ~ 10 m/sec]

18. REFERENCES ● E. Roueff, M. Gerin, Space Science Review 106, 61 (2003): [Review of observational studies] ● S.Y. Lin, H. Guo, Chem. Phys. 289, 191 (2002):[H 2 +H 2, time-dependent approach] ● B. Mate et al., JCP 122, 064313 (2005): [State resolved cross sections & rates: Experiment] ● F. Gatti et al., JCP 123, 174311 (2005): [H 2 +H 2, wave packet studies] ● R.A. Sultanov, D. Guster, Chem. Phys. Lett. 428, 227 (2006): [H 2 +H 2 with DJ and BMKP PESs] ● R.A. Sultanov, D. Guster, Chem. Phys. 326, 641 (2006): [H 2 +H 2 ]

19. Rotational state resolved integral cross sections for HD(j 1 =1) + para-H 2 (j 2 =0) BMKP PES: (10)-(00) & (20)-(10)

20. HD(j 1 =1) + para-H 2 (j 2 =0): (10)-(00)

21. HD(j 1 ) + para-H 2 (j 2 ): (20)-(00) & (12)-(02)

22. HD(j 1 ) + para-H 2 (j 2 ): (12)-(20), (12)-(10) & (12)-(00)

23. HD(j 1 ) + para-H 2 (j 2 ): (12)-(20)

24. HD(j 1 ) + para-H 2 (j 2 ): Elastic

25. HD(j 1 ) + ortho-H 2 (j 2 ): Elastic

26. HD(j 1 ) + ortho-H 2 (j 2 ): (11)-(01)

27. HD(j 1 ) + ortho-H 2 (j 2 ): (21) - (01)

28. HD(j 1 ) + ortho-H 2 (j 2 ): (21) - (11)

29. Rate k(T): HD(j 1 ) + para-H 2 (j 2 ): (10) - (00)

30. Rate k(T): HD(j 1 ) + para-H 2 (j 2 ): (20) - (10)

31. Rate k(T): HD(j 1 ) + para-H 2 (j 2 ): (20) - (00)

32. Rate k(T): HD(j 1 ) + ortho-H 2 (j 2 ): (11) - (01)

33. Rate k(T): HD(j 1 ) + ortho-H 2 (j 2 ): (21) - (11)

34. Integral elastic cross sections calculated with the BMKP and DJ PESs

35. Temperature dependence of the state- resolved thermal rates for 00 => 20, 22, 40 & 42. Results with the BMKP & DJ PESs

36. Rotational state resolved cross sections for elastic p-/p-H 2 and o-/o-H 2 and transitions 00=>22 & 11=>13

37. Rotational state resolved integral cross sections calculated with the BMKP and DJ surfaces: 00 =>20, 22, 40, 42 & 44 R.A. Sultanov, D. Guster, Chemical Physics 326, 641 (2006)

38. Temperature dependence of thermal rates calculated with the DJ surface: 00=>22, 02=>22, 20=>00 & 11-13

39. Temperature dependence of the 00=>20 state resolved thermal rate and its cross section calculated with the BMKP&DJ PESs

40. 00 => 20 cross section: experiment and theory

41. Cross sections for 00=>42 transition: this work with BMKP PES and Lin & Guo results: JCP 117, 5183 (2002)

42. Cross sections for 00=>44 transition: this work with BMKP PES and Lin & Guo results: JCP 117 5183 (2002)

43. State resolved rates for rotational transitions: 00=>20, 22 & 40 (DJ PES)