Advertisement

Chemical Processes in the Interstellar Medium

  • Michael J. Pilling
Chapter
Part of the Physical Chemistry in Action book series (PCIA)

Abstract

Models of the chemical composition of the interstellar medium incorporate networks of chemical reactions. The rate coefficients and the products of these reactions are important components of the model. In this chapter I review the determinants of these components and the methods used to measure them experimentally and calculate them using theory. The bulk of the chapter is devoted to ion + neutral molecule and neutral molecule + neutral molecule reactions. I also briefly discuss radiative association, dissociative recombination and reactions occurring on surfaces. The conditions of low pressure and low temperature in the interstellar medium place considerable demands on experiment and theory, which are particularly severe for reactions between neutral species. Many reactions can be estimated with tolerable accuracy. Others require a combination of high level electronic structure calculations, coupled with detailed theory and low temperature experimental measurements.

Keywords

Transition State Rate Coefficient Phase Space Theory Variational Transition State Theory Master Equation Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I thank Dr. Stephen Klippenstein for helpful discussion of uncertainties in transition state energies in electronic structure calculations and Dr. Branko Ruscic for the provision of recent data for the Active Thermochemical Tables (ATcT).

References

  1. 1.
    Wakelam V, Smith IWM, Herbst E, Troe J, Geppert W, Linnartz H, Oberg K, Roueff E, Agundez M, Pernot P, Cuppen HM, Loison JC, Talbi D (2010) Reaction networks for interstellar chemical modelling: improvements and challenges. Space Sci Rev 156:13–72Google Scholar
  2. 2.
    Pilling MJ, Seakins PW (1995) Reaction kinetics. Oxford University Press, OxfordGoogle Scholar
  3. 3.
    Millar TJ, Rawlings JMC, Bennett A, Brown PD, Charnley SB (1991) Gas-phase reactions and rate coefficients for use in astrochemistry – the UMIST ratefile. Astron Astrophys Suppl Ser 87:585–619Google Scholar
  4. 4.
    Burke MP, Dryer FL, Ju YG (2011) Assessment of kinetic modeling for lean H(2)/CH(4)/O(2)/diluent flames at high pressures. Proc Combust Inst 33:905–912Google Scholar
  5. 5.
    Bloss C, Wagner V, Bonzanini A, Jenkin ME, Wirtz K, Martin-Reviejo M, Pilling MJ (2005) Evaluation of detailed aromatic mechanisms (MCMv3 and MCMv3.1) against environmental chamber data. Atmos Chem Phys 5:623–639Google Scholar
  6. 6.
    Bloss C, Wagner V, Jenkin ME, Volkamer R, Bloss WJ, Lee JD, Heard DE, Wirtz K, Martin-Reviejo M, Rea G, Wenger JC, Pilling MJ (2005) Development of a detailed chemical mechanism (MCMv3.1) for the atmospheric oxidation of aromatic hydrocarbons. Atmos Chem Phys 5:641–664Google Scholar
  7. 7.
    Wakelam V, Herbst E, Selsis F (2006) The effect of uncertainties on chemical models of dark clouds. Astron Astrophys 451:551–562Google Scholar
  8. 8.
    Wakelam V, Loison JC, Herbst E, Talbi D, Quan D, Caralp F (2009) A sensitivity study of the neutral-neutral reactions C + C(3) and C + C(5) in cold dense interstellar clouds. Astron Astrophys 495:513–521Google Scholar
  9. 9.
    Baulch DL, Bowman CT, Cobos CJ, Cox RA, Just T, Kerr JA, Pilling MJ, Stocker D, Troe J, Tsang W, Walker RW, Warnatz J (2005) Evaluated kinetic data for combustion modeling: supplement II. J Phys Chem Ref Data 34:757–1397Google Scholar
  10. 10.
    Crowley JN, Ammann M, Cox RA, Hynes RG, Jenkin ME, Mellouki A, Rossi MJ, Troe J, Wallington TJ (2010) Evaluated kinetic and photochemical data for atmospheric chemistry: Volume V – heterogeneous reactions on solid substrates. Atmos Chem Phys 10:9059–9223Google Scholar
  11. 11.
    Wakelam V et al (2012) A kinetic database for astrochemistry (KIDA). Astrophys J Suppl Ser 199:21. doi: 10.1088/0067-0049/199/1/21 Google Scholar
  12. 12.
    Solomon PM, Werner MW (1971) Low-energy cosmic rays and abundance of atomic hydrogen in dark clouds. Astrophys J 165:41–49Google Scholar
  13. 13.
    Herbst E, Klemperer W (1973) Formation and depletion of molecules in dense interstellar clouds. Astrophys J 185:505–533Google Scholar
  14. 14.
    Barlow SE, Luine JA, Dunn GH (1986) Measurement of ion molecule reactions between 10 K and 20 K. Int J Mass Spectrom 74:97–128Google Scholar
  15. 15.
    Klippenstein SJ, Georgievskii Y, McCall BJ (2010) Temperature dependence of two key interstellar reactions of H3+: O(3P) + H3+ and CO + H3+. J Phys Chem A 114:278–290Google Scholar
  16. 16.
    McMahon TB, Beaucham JI (1972) Versatile trapped ion cell for ion-cyclotron resonance spectroscopy. Rev Sci Instrum 43:509–512Google Scholar
  17. 17.
    Fehsenfeld FC, Schmeltekopf AL, Goldan PD, Schiff HI, Ferguson EE (1966) Thermal energy ion-neutral reaction rates. I. Some reactions of helium ions. J Chem Phys 44:4087–4094Google Scholar
  18. 18.
    Dunkin DB, Fehsenfeld FC, Schmeltekopf AL, Ferguson EE (1968) Ion-molecule reaction studies from 300 to 600 K in a temperature-controlled flowing afterglow system. J Chem Phys 49:1365–1371Google Scholar
  19. 19.
    Barlow SE, Dunn GH, Schauer M (1984) Radiative association of CH3+ and H2 at 13 K. Phys Rev Lett 52:902–905Google Scholar
  20. 20.
    Asvany O, Savic I, Schlemmer S, Gerlich D (2004) Variable temperature ion trap studies of CH4++H2, HD and D2: negative temperature dependence and significant isotope effect. Chem Phys 298:97–105Google Scholar
  21. 21.
    Adams NG, Smith D (1976) Selected ion flow tube (sift) – technique for studying ion-neutral reactions. Int J Mass Spectrom 21:349–359Google Scholar
  22. 22.
    Snow TP, Bierbaum VM (2008) Ion chemistry in the interstellar medium. Annu Rev Anal Chem 1:229–259Google Scholar
  23. 23.
    Rowe BR, Dupeyrat G, Marquette JB, Gaucherel P (1984) Study of the reactions N2+ + 2 N2 → N4+ + N2 and O2+ + 2O2 → O4+ + O2 from 20 to 160 K by the CRESU technique. J Chem Phys 80:4915–4921Google Scholar
  24. 24.
    Rowe BR, Marquette JB (1987) CRESU studies of ion molecule reactions. Int J Mass Spectrom 80:239–254Google Scholar
  25. 25.
    Chesnavich WJ, Su T, Bowers MT (1980) Collisions in a non-central field – variational and trajectory investigation of ion-dipole capture. J Chem Phys 72:2641–2655Google Scholar
  26. 26.
    Su T, Chesnavich WJ (1982) Parametrization of the ion-polar molecule collision rate-constant by trajectory calculations. J Chem Phys 76:5183–5185Google Scholar
  27. 27.
    Woon DE, Herbst E (2009) Quantum chemical predictions of the properties of known and postulated neutral interstellar molecules. Astrophys J Suppl Ser 185:273–288Google Scholar
  28. 28.
    Maergoiz AI, Nikitin EE, Troe J, Ushakov VG (1996) Classical trajectory and adiabatic channel study of the transition from adiabatic to sudden capture dynamics. 1. Ion-dipole capture. J Chem Phys 105:6263–6269Google Scholar
  29. 29.
    Maergoiz AI, Nikitin EE, Troe J, Ushakov VG (1996) Classical trajectory and adiabatic channel study of the transition from adiabatic to sudden capture dynamics. 2. Ion-quadrupole capture. J Chem Phys 105:6270–6276Google Scholar
  30. 30.
    Maergoiz AI, Nikitin EE, Troe J, Ushakov VG (1996) Classical trajectory and adiabatic channel study of the transition from adiabatic to sudden capture dynamics. 3. Dipole-dipole capture. J Chem Phys 105:6277–6284Google Scholar
  31. 31.
    Pechukas P, Light JC (1965) On detailed balancing and statistical theories of chemical kinetics. J Chem Phys 42:3281–3291Google Scholar
  32. 32.
    Quack M, Troe J (1975) Complex-formation in reactive and inelastic-scattering – statistical adiabatic channel model of unimolecular processes III. Ber Bunsenges Phys Chem Chem Phys 79:170–183Google Scholar
  33. 33.
    Clary DC (1984) Rates of chemical-reactions dominated by long-range intermolecular forces. Mol Phys 53:3–21Google Scholar
  34. 34.
    Troe J (1987) Statistical adiabatic channel model for ion molecule capture processes. J Chem Phys 87:2773–2780Google Scholar
  35. 35.
    Troe J (1996) Statistical adiabatic channel model for ion-molecule capture processes. 2. Analytical treatment of ion-dipole capture. J Chem Phys 105:6249–6262Google Scholar
  36. 36.
    Georgievskii Y, Klippenstein SJ (2005) Long-range transition state theory. J Chem Phys 122(194103):1–17Google Scholar
  37. 37.
    Fehsenfeld FC (1976) Ion reactions with atomic oxygen and atomic nitrogen of astrophysical importance. Astrophys J 209:638–639Google Scholar
  38. 38.
    Milligan DB, McEwan MJ (2000) H3+ + O: an experimental study. Chem Phys Lett 319:482–485Google Scholar
  39. 39.
    Bettens RPA, Hansen TA, Collins MA (1999) Interpolated potential energy surface and reaction dynamics for O(3P) + H3+(1A1′) and OH+(3Σ) + H2(1Σg+). J Chem Phys 111:6322–6332Google Scholar
  40. 40.
    Tanner SD, Mackay GI, Hopkinson AC, Bohme DK (1979) Proton-transfer reactions of HCO+ at 298 K. Int J Mass Spectrom 29:153–169Google Scholar
  41. 41.
    Kim JK, Theard LP, Huntress WT (1975) Proton-transfer reactions from H3+ ions to N2, O2, and CO molecules. Chem Phys Lett 32:610–614Google Scholar
  42. 42.
    Burt JA, Dunn JL, McEwan MJ, Sutton MM, Roche AE, Schiff HI (1970) Some ion-molecule reactions of H3+ and proton affinity of H2. J Chem Phys 52:6062–6075Google Scholar
  43. 43.
    Ryan KR (1974) Ionic collision processes in simple gas mixtures containing hydrogen. J Chem Phys 61:1559–1570Google Scholar
  44. 44.
    Bohme DK, Mackay GI, Schiff HI (1980) Determination of proton affinities from the kinetics of proton-transfer reactions. 7. The proton affinities of O2, H2, Kr, O, N2, Xe, CO2, CH4, N2O, and CO. J Chem Phys 73:4976–4986Google Scholar
  45. 45.
    Adams NG, Smith D (1981) A laboratory study of the reaction H3+ + HD ↔ H2D+ + H2 – the electron-densities and the temperatures in inter-stellar clouds. Astrophys J 248:373–379Google Scholar
  46. 46.
    Rakshit AB (1982) A drift-chamber mass-spectrometric study of the interaction of H3+ ions with neutral molecules at 300 K. Int J Mass Spectrom 41:185–197Google Scholar
  47. 47.
    Marquette JB, Rebrion C, Rowe BR (1989) Proton-transfer reactions of H3+ with molecular neutrals at 30 K. Astron Astrophys 213:L29–L32Google Scholar
  48. 48.
    Gannon KL, Glowacki DR, Blitz MA, Hughes KJ, Pilling MJ, Seakins PW (2007) H atom yields from the reactions of CN radicals with C2H2, C2H4, C3H6, trans-2-C4H8, and iso-C4H8. J Phys Chem A 111:6679–6692Google Scholar
  49. 49.
    Blitz MA, Pesa M, Pilling MJ, Seakins PW (1999) Reaction of CH with H2O: temperature dependence and isotope effect. J Phys Chem A 103:5699–5704Google Scholar
  50. 50.
    Wollenhaupt M, Carl SA, Horowitz A, Crowley JN (2000) Rate coefficients for reaction of OH with acetone between 202 and 395 K. J Phys Chem A 104:2695–2705Google Scholar
  51. 51.
    Brown SS, Ravishankara AR, Stark H (2000) Simultaneous kinetics and ring-down: rate coefficients from single cavity loss temporal profiles. J Phys Chem A 104:7044–7052Google Scholar
  52. 52.
    DeSain JD, Clifford EP, Taatjes CA (2001) Infrared frequency-modulation probing of product formation in alkyl plus O2 reactions: II. The reaction of C3H7 with O2 between 296 and 683 K. J Phys Chem A 105:3205–3213Google Scholar
  53. 53.
    Blitz MA, Goddard A, Ingham T, Pilling MJ (2007) Time-of-flight mass spectrometry for time-resolved measurements. Rev Sci Instrum 78:034103.1–034103.9Google Scholar
  54. 54.
    Meloni G, Selby TM, Osborn DL, Taatjes CA (2008) Enol formation and ring-opening in OH-initiated oxidation of cycloalkenes. J Phys Chem A 112:13444–13451Google Scholar
  55. 55.
    Mullen C, Smith MA (2005) Low temperature NH(X 3Σ) radical reactions with NO, saturated, and unsaturated hydrocarbons studied in a pulsed supersonic laval nozzle flow reactor between 53 and 188 K. J Phys Chem A 109:1391–1399Google Scholar
  56. 56.
    Smith IWM (2011) Laboratory astrochemistry: gas-phase processes. Annu Rev Astron Astrophys 49(49):29–66Google Scholar
  57. 57.
    Tyndall GS, Staffelbach TA, Orlando JJ, Calvert JG (1995) Rate coefficients for the reactions of OH radicals with methylglyoxal and acetaldehyde. Int J Chem Kinet 27:1009–1020Google Scholar
  58. 58.
    Dransfield TJ, Donahue NM, Anderson JG (2001) High-pressure flow reactor product study of the reactions of HO(X) + NO2: the role of vibrationally excited intermediates. J Phys Chem A 105:1507–1514Google Scholar
  59. 59.
    Wardlaw DM, Marcus RA (1986) Unimolecular reaction-rate theory for transition-states of any looseness. 3. Application to methyl radical recombination. J Phys Chem 90:5383–5393Google Scholar
  60. 60.
    Harding LB, Klippenstein SJ, Jasper AW (2007) Ab initio methods for reactive potential surfaces. Phys Chem Chem Phys 9:4055–4070Google Scholar
  61. 61.
    Sims IR, Smith IWM (1988) Pulsed laser photolysis laser-induced fluorescence measurements on the kinetics of CN(v = 0) and CN(v = 1) with O2, NH3 and NO between 294 and 761 K. J Chem Soc Faraday Trans II 84:527–539Google Scholar
  62. 62.
    Sims IR, Queffelec JL, Defrance A, Rebrionrowe C, Travers D, Rowe BR, Smith IWM (1992) Ultra-low temperature kinetics of neutral-neutral reactions – the reaction CN + O2 down to 26 K. J Chem Phys 97:8798–8800Google Scholar
  63. 63.
    Sims IR, Queffelec JL, Defrance A, Rebrionrowe C, Travers D, Bocherel P, Rowe BR, Smith IWM (1994) Ultralow temperature kinetics of neutral-neutral reactions – the technique and results for the reactions CN + O2 down to 13 K and CN + NH3 down to 25 K. J Chem Phys 100:4229–4241Google Scholar
  64. 64.
    Feng WH, Hershberger JF (2009) Reinvestigation of the branching ratio of the CN + O2 reaction. J Phys Chem A 113:3523–3527Google Scholar
  65. 65.
    Klippenstein SJ, Kim YW (1993) Variational statistical study of the CN + O2 reaction employing ab-initio determined properties for the transition-state. J Chem Phys 99:5790–5799Google Scholar
  66. 66.
    Stoecklin T, Dateo CE, Clary DC (1991) Rate-constant calculations on fast diatom-diatom reactions. J Chem Soc Faraday Trans 87:1667–1679Google Scholar
  67. 67.
    Greenwald EE, North SW, Georgievskii Y, Klippenstein SJ (2005) A two transition state model for radical-molecule reactions: a case study of the addition of OH to C2H4. J Phys Chem A 109:6031–6044Google Scholar
  68. 68.
    Sabbah H, Biennier L, Sims IR, Georgievskii Y, Klippenstein SJ, Smith IWM (2007) Understanding reactivity at very low temperatures: the reactions of oxygen atoms with alkenes. Science 317:102–105Google Scholar
  69. 69.
    Smith IWM, Sage AM, Donahue NM, Herbst E, Quan D (2006) The temperature-dependence of rapid low temperature reactions: experiment, understanding and prediction. Faraday Discuss 133:137–156Google Scholar
  70. 70.
    Clarke JS, Kroll JH, Donahue NM, Anderson JG (1998) Testing frontier orbital control: kinetics of OH with ethane, propane, and cyclopropane from 180 to 360 K. J Phys Chem A 102:9847–9857Google Scholar
  71. 71.
    Miller JA, Klippenstein SJ (2006) Master equation methods in gas phase chemical kinetics. J Phys Chem A 110:10528–10544Google Scholar
  72. 72.
    Robertson SH, Pilling MJ, Jitariu LC, Hillier IH (2007) Master equation methods for multiple well systems: application to the 1-,2-pentyl system. Phys Chem Chem Phys 9:4085–4097Google Scholar
  73. 73.
    Bohland T, Temps F (1984) Direct determination of the rate-constant for the reaction CH2 + H → CH + H2. Ber Bunsenges Phys Chem 88:459–461Google Scholar
  74. 74.
    Bohland T, Temps F, Wagner HG (1987) A direct study of the reactions of CH2(X3B1) radicals with H and D atoms. J Phys Chem 91:1205–1209Google Scholar
  75. 75.
    Boullart W, Peeters J (1992) Product distributions of the C2H2 + O and HCCO + H reactions – rate-constant of CH2(X3B1) + H. J Phys Chem 96:9810–9816Google Scholar
  76. 76.
    Devriendt K, Vanpoppel M, Boullart W, Peeters J (1995) Kinetic investigation of the CH2(X3B1) + H → CH(X2Π) + H2 reaction in the temperature-range 400 K > T >1,000 K. J Phys Chem 99:16953–16959Google Scholar
  77. 77.
    Brownsword RA, Canosa A, Rowe BR, Sims IR, Smith IWM, Stewart DWA, Symonds AC, Travers D (1997) Kinetics over a wide range of temperature (13–744 K): rate constants for the reactions of CH(ν = 0) with H2 and D2 and for the removal of CH(ν = 1) by H2 and D2. J Chem Phys 106:7662–7677Google Scholar
  78. 78.
    Fulle D, Hippler H (1997) The temperature and pressure dependence of the reaction CH + H2 → CH3 → CH2 + H. J Chem Phys 106:8691–8698Google Scholar
  79. 79.
    Ruscic B (2012) Private communication of unpublished ATcT datum for ver. 1.112 od ATcT TNGoogle Scholar
  80. 80.
    Ruscic B, Pinzon RE, Morton ML, von Laszevski G, Bittner SJ, Nijsure SG, Amin KA, Minkoff M, Wagner AF (2004) Introduction to active thermochemical tables: several “key” enthalpies of formation revisited. J Phys Chem A 108:9979–9997Google Scholar
  81. 81.
    Ruscic B, Pinzon RE, von Laszewski G, Kodeboyina D, Burcat A, Leahy D, Montoya D, Wagner AF (2005) Active thermochemical tables: thermochemistry for the 21st century. In: Conference on scientific discovery through advanced computing (SciDAC 2005), vol 16. San Francisco, pp 561–570Google Scholar
  82. 82.
    Medvedev DM, Harding LB, Gray SK (2006) Methyl radical: ab initio global potential surface, vibrational levels and partition function. Mol Phys 104:73–81Google Scholar
  83. 83.
    Meads RF, MacLagan RGAR, Phillips LF (1993) Kinetics, energetics, and dynamics of the reactions of CN with NH3 and ND3. J Phys Chem 97:3257–3265Google Scholar
  84. 84.
    Herbst E, Lee HH, Howe DA, Millar TJ (1994) The effect of rapid neutral-neutral reactions on chemical-models of dense interstellar clouds. Mon Not R Astron Soc 268:335–344Google Scholar
  85. 85.
    Bettens RPA, Lee HH, Herbst E (1995) The importance of classes of neutral-neutral reactions in the production of complex interstellar-molecules. Astrophys J 443:664–674Google Scholar
  86. 86.
    Talbi D, Smith IWM (2009) A theoretical analysis of the reaction between CN radicals and NH3. Phys Chem Chem Phys 11:8477–8483Google Scholar
  87. 87.
    Blitz MA, Seakins PW, Smith IWM (2009) An experimental confirmation of the products of the reaction between CN radicals and NH3. Phys Chem Chem Phys 11:10824–10826Google Scholar
  88. 88.
    Gerlich D (2008) In: Smith IWM (ed) Low temperatures and cold molecules. Imperial College Press, London, pp 121–174Google Scholar
  89. 89.
    Herbst E (1982) A reinvestigation of the rate of the C+ + H2 radiative association reaction. Astrophys J 252:810–813Google Scholar
  90. 90.
    Smith IWM (1989) Effects of quantum-mechanical tunneling on rates of radiative association. Astrophys J 347:282–288Google Scholar
  91. 91.
    Smith IWM (1989) Radiative association in collisions between neutral free-radicals. Chem Phys 131:391–401Google Scholar
  92. 92.
    Geppert WD, Larsson M (2008) Dissociative recombination in the interstellar medium and planetary ionospheres. Mol Phys 106:2199–2226Google Scholar
  93. 93.
    Vidali G, Pirronello V, Liu C, Shen LY (1998) Experimental studies of chemical reactions on surfaces of astrophysical interest. Astrophys Lett Commun 35:423–447Google Scholar
  94. 94.
    Vidali G, Roser JE, Manico G, Pirronello V (2004) Laboratory studies of formation of molecules on dust grain analogues under ISM conditions. J Geophys Res Planets 109:E07S14, doi: 10.1029/2003JE002189 Google Scholar
  95. 95.
    Hornekaer L, Baurichter A, Petrunin VV, Luntz AC, Kay BD, Al-Halabi A (2005) Influence of surface morphology on D2 desorption kinetics from amorphous solid water. J Chem Phys 122:124701Google Scholar
  96. 96.
    Zecho T, Guttler A, Sha XW, Lemoine D, Jackson B, Kuppers J (2002) Abstraction of D chemisorbed on graphite(0001) with gaseous H atoms. Chem Phys Lett 366:188–195Google Scholar
  97. 97.
    Islam F, Latimer ER, Price SD (2007) The formation of vibrationally excited HD from atomic recombination on cold graphite surfaces. J Chem Phys 127:064701Google Scholar
  98. 98.
    Williams DA, Brown WA, Price SD, Rawlings JMC, Viti S (2007) Molecules, ices and astronomy. Astron Geophys 48:25–34Google Scholar
  99. 99.
    Latimer ER, Islam F, Price SD (2008) Studies of HD formed in excited vibrational states from atomic recombination on cold graphite surfaces. Chem Phys Lett 455:174–177Google Scholar
  100. 100.
    Hidaka H, Watanabe M, Kouchi A, Watanabe N (2009) Reaction routes in the CO-H2CO-CH3OH system, clarified from H(D) exposure on solid formaldehyde at low temperatures. Astrophys J 702:291–300Google Scholar
  101. 101.
    Hidaka H, Watanabe N, Shiraki T, Nagaoka A, Kouchi A (2004) Conversion of H2CO to CH3OH by reactions of cold atomic hydrogen on ice surfaces below 20 K. Astrophys J 614:1124–1131Google Scholar
  102. 102.
    Watanabe N, Nagaoka A, Shiraki T, Kouchi A (2004) Hydrogenation of CO on pure solid CO and CO-H2O mixed ice. Astrophys J 616:638–642Google Scholar
  103. 103.
    Ward MD, Price SD (2011) Thermal reactions of oxygen atoms with alkenes at low temperatures on interstellar dust. Astrophys J 741:121Google Scholar
  104. 104.
    Tielens AGGM, Hagen W (1982) Model-calculations of the molecular composition of inter-stellar grain mantles. Astron Astrophys 114:245–260Google Scholar
  105. 105.
    Charnley SB (2001) Stochastic theory of molecule formation on dust. Astrophys J 562:L99–L102Google Scholar
  106. 106.
    Green NJB, Toniazzo T, Pilling MJ, Ruffle DP, Bell N, Hartquist TW (2001) A stochastic approach to grain surface chemical kinetics. Astron Astrophys 375:1111–1119Google Scholar
  107. 107.
    Biham O, Furman I, Pirronello V, Vidali G (2001) Master equation for hydrogen recombination on grain surfaces. Astrophys J 553:595–603Google Scholar
  108. 108.
    Caselli P, Hasegawa TI, Herbst E (1998) A proposed modification of the rate equations for reactions on grain surfaces. Astrophys J 495:309–316Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of ChemistryUniversity of LeedsLeedsUK

Personalised recommendations