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Modeling the influence of nuclear spin in the reaction of H 3 + with H 2

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. Overview. This talk : Modeling p-H 3 + fraction vs p-H 2 fraction to assess nuclear spin dependence of H 3 + + H 2.

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Modeling the influence of nuclear spin in the reaction of H 3 + with H 2

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  1. Modeling the influence of nuclear spin in the reaction of H3+ with H2 Kyle N. Crabtree, Brian A. Tom, and Benjamin J. McCall University of Illinois

  2. Overview This talk: Modeling p-H3+ fraction vs p-H2 fraction to assess nuclear spin dependence of H3+ + H2 Next talk: Spectroscopic studies at 350 K and 135 K 66th OSU International Symposium on Molecular Spectroscopy

  3. Motivation • Hydrogen- most abundant element in the Universe • H3+ is readily formed from H2 H2 + CR  H2+ + CR¶ + e- H2 + H2+  H3+ + H • Spectroscopic observations of H3+ in astronomy have been used to measure: • Temperature • Density • Ionization rate • Object size • Ionosphere gas velocity Astronomer’s periodic table 66th OSU International Symposium on Molecular Spectroscopy

  4. 1/2 3/2 para-H3+ ortho-H3+ Nuclear spin For more on astronomy, see TF09, 160 MA, 3:52 pm • Observed lines: R(1,0), R(1,1)u, and R(1,1)l • Nonthermal H3+ in space • To understand the ortho:para H3+ ratio, the reaction H3+ + H2 H2 + H3+, which interconverts the nuclear spin configurations of H3+ and H2, must be understood 66th OSU International Symposium on Molecular Spectroscopy

  5. H3+ + H2 H2 + H3+ Branching fractions: Sid, Shop, Sexch a ≡ Shop/Sexch (3/6 = 0.5?) Conservation of nuclear spin angular momentum 1 “identity” H5+ 3 “hop” Strategy: ensure [H2]>>[H3+], ortho:para H2 ratio constant 6 “exchange” 66th OSU International Symposium on Molecular Spectroscopy

  6. Mechanism-specific branching fractions id id hop exch 66th OSU International Symposium on Molecular Spectroscopy

  7. Steady state p-H3+ fraction • Write rate equation for p-H3+, assume ONLY H3+ + H2 rxn: • Steady state; p3 ≡ [p-H3+]/[H3+]; p2 ≡ [p-H2]/[H2] • Divide through by [H3+][H2]: • Solve; a=kH/kE 66th OSU International Symposium on Molecular Spectroscopy

  8. “High temperature” model Spectroscopically measurable (n-H2,n-H3+) (p2=0.25, p3=0.5) Experimentally controllable 66th OSU International Symposium on Molecular Spectroscopy

  9. Three-body reactions • High densities can lead to formation of larger H2n+1+ clusters • At lower pressures, can (H5+)* clusters undergo proton scrambling with H2? ? H3+ + H2 (H5+)*  H3+ + H2 + H2 H5+ + H2 H3+ + 2H2  (H7+)* 66th OSU International Symposium on Molecular Spectroscopy

  10. 1 “identity” H7+ 10 “hop” 10 “exchange” H5+ + H2 H2 + H5+ 66th OSU International Symposium on Molecular Spectroscopy

  11. “3-body high temperature model” • F2 = 2-body branching fraction • a2, a3 = 2, 3-body hop:exchange ratio 66th OSU International Symposium on Molecular Spectroscopy

  12. o-H2; J = 1 DE = 170 K p-H2; J = 0 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 66th OSU International Symposium on Molecular Spectroscopy

  13. Low temperature model f (T,Sid,) 66th OSU International Symposium on Molecular Spectroscopy

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

  15. Summary • Measure p-H3+ fraction in known p-H2 fraction plasma • High temperature models • Reaction outcomes governed by nuclear spin statistics • 2-body model: only H3+ + H2 reaction • 3-body model: additional scrambling via (H7+)* • Low temperature model • Only H3+ + H2 reaction • Conservation of nuclear spin, energetic considerations • Dependent on T and Sid • 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. 66th OSU International Symposium on Molecular Spectroscopy

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