1. Modeling the influence of nuclear spin in the reaction of H 3 + with H 2 Kyle N. Crabtree, Brian A. Tom, and Benjamin J. McCall University of Illinois Kyle N. Crabtree, Brian A. Tom, and Benjamin J. McCall University of Illinois

2. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy2 Overview This talk: Modeling p-H 3 + fraction vs p-H 2 fraction to assess nuclear spin dependence of H 3 + + H 2 Next talk: Spectroscopic studies at 350 K and 135 K

3. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy3 Motivation Hydrogen- most abundant element in the Universe H 3 + is readily formed from H 2 H 2 + CR  H 2 + + CR¶ + e - H 2 + H 2 +  H 3 + + H Spectroscopic observations of H 3 + in astronomy have been used to measure: – Temperature – Density – Ionization rate – Object size – Ionosphere gas velocity Astronomer ’ s periodic table

4. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy4 Nuclear spin Observed lines: R(1,0), R(1,1) u, and R(1,1) l Nonthermal H 3 + in space To understand the ortho:para H 3 + ratio, the reaction H 3 + + H 2  H 2 + H 3 +, which interconverts the nuclear spin configurations of H 3 + and H 2, must be understood para-H 3 + ortho-H 3 + 1/23/2 For more on astronomy, see TF09, 160 MA, 3:52 pm

5. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy5 H 3 + + H 2  H 2 + H 3 + “ identity ” “ hop ” H5+H5+ “ exchange ” 3 11 6 Branching fractions: S id, S hop, S exch  ≡ S hop /S exch (3/6 = 0.5?) Conservation of nuclear spin angular momentum Strategy: ensure [H 2 ] >> [H 3 + ], ortho:para H 2 ratio constant

6. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy6 Mechanism-specific branching fractions id Reactantso-H 3 + p-H 3 + o-H 3 + + o-H 2 10 o-H 3 + + p-H 2 10 p-H 3 + + o-H 2 01 p-H 3 + + p-H 2 01 o-H 3 + + o-H 2 2/31/3 o-H 3 + + p-H 2 01 p-H 3 + + o-H 2 2/31/3 p-H 3 + + p-H 2 01 o-H 3 + + o-H 2 2/31/3 o-H 3 + + p-H 2 2/31/3 p-H 3 + + o-H 2 1/32/3 p-H 3 + + p-H 2 1/32/3 id exch hop

7. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy7 Steady state p-H 3 + fraction Write rate equation for p-H 3 +, assume ONLY H 3 + + H 2 rxn: Steady state; p 3 ≡ [p-H 3 + ]/[H 3 + ]; p 2 ≡ [p-H 2 ]/[H 2 ] Divide through by [H 3 + ][H 2 ]: Solve;  =k H /k E Write rate equation for p-H 3 +, assume ONLY H 3 + + H 2 rxn: Steady state; p 3 ≡ [p-H 3 + ]/[H 3 + ]; p 2 ≡ [p-H 2 ]/[H 2 ] Divide through by [H 3 + ][H 2 ]: Solve;  =k H /k E

8. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy8 “ High temperature ” model Spectroscopically measurable Experimentally controllable (n-H 2,n-H 3 + ) (p 2 =0.25, p 3 =0.5)

9. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy9 Three-body reactions High densities can lead to formation of larger H 2n+1 + clusters At lower pressures, can (H 5 + ) * clusters undergo proton scrambling with H 2 ? High densities can lead to formation of larger H 2n+1 + clusters At lower pressures, can (H 5 + ) * clusters undergo proton scrambling with H 2 ? H 3 + + H 2  (H 5 + ) *  H 3 + + H 2 H 5 + + H 2 + H 2 H 3 + + 2H 2  (H 7 + ) * ?

10. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy10 H 5 + + H 2  H 2 + H 5 + “ identity ” 11 “ hop ” 10 “ exchange ” 10 H7+H7+

11. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy11 “ 3-body high temperature model ”  2 = 2-body branching fraction  2,  3 = 2, 3-body hop:exchange ratio  2 = 2-body branching fraction  2,  3 = 2, 3-body hop:exchange ratio

12. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy12 Low temperature model High temperature models based on assumption that nuclear spin statistics exclusively determine reaction outcomes At low temperatures, some reaction channels are inhibited due to energetic considerations High temperature models based on assumption that nuclear spin statistics exclusively determine reaction outcomes At low temperatures, some reaction channels are inhibited due to energetic considerations p-H 2 ; J = 0 o-H 2 ; J = 1  E = 170 K

13. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy13 Low temperature model ParameterValue(s) T rot 10-160 K T coll 10-160 K S id 0.1-0.9 S hop 0-1 S exch 0-1 k oooo k ooop k oopo k oopp k opoo k opop k oppo k oppp k pooo k poop k popo k popp k ppoo k ppop k pppo k pppp f (T,S id,  )

14. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy14 T 160 K 140 K 120 K 100 K 80 K 60 K 40 K 20 K Low temperature model

15. 20 June 2011 66th OSU International Symposium on Molecular Spectroscopy15 Summary Measure p-H 3 + fraction in known p-H 2 fraction plasma High temperature models – Reaction outcomes governed by nuclear spin statistics – 2-body model: only H 3 + + H 2 reaction – 3-body model: additional scrambling via (H 7 + ) * Low temperature model – Only H 3 + + H 2 reaction – Conservation of nuclear spin, energetic considerations – Dependent on T and S id Next talk, application of models to experimental data More info: K. N. Crabtree, B. A. Tom, B. J. McCall, J. Chem. Phys. (2011), 134, 194310. Measure p-H 3 + fraction in known p-H 2 fraction plasma High temperature models – Reaction outcomes governed by nuclear spin statistics – 2-body model: only H 3 + + H 2 reaction – 3-body model: additional scrambling via (H 7 + ) * Low temperature model – Only H 3 + + H 2 reaction – Conservation of nuclear spin, energetic considerations – Dependent on T and S id Next talk, application of models to experimental data More info: K. N. Crabtree, B. A. Tom, B. J. McCall, J. Chem. Phys. (2011), 134, 194310.