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 H3

+ with H2

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

Kyle N. Crabtree, Brian A. Tom, and Benjamin J. McCall

University of Illinois

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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OverviewOverview

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

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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MotivationMotivation• 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

• 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

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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Nuclear spinNuclear spin

• 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

para-H3+ ortho-H3

+

1/2 3/2

For more on astronomy, see TF09, 160 MA, 3:52 pm

For more on astronomy, see TF09, 160 MA, 3:52 pm

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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H3+ + H2 H2 + H3

+H3+ + H2 H2 + H3

+

“identity”

“hop”

H5+

“exchange”

3

1111

6

Branching fractions: Sid, Shop, Sexch

≡ Shop/Sexch (3/6 = 0.5?)Conservation of nuclear spinangular momentum

Strategy: ensure [H2]>>[H3+],

ortho:para H2 ratio constant

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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Mechanism-specific branching fractionsMechanism-specific branching fractions

id

Reactants o-H3+ p-H3

+

o-H3+ + o-H2 1 0

o-H3+ + p-H2 1 0

p-H3+ + o-H2 0 1

p-H3+ + p-H2 0 1

o-H3+ + o-H2 2/3 1/3

o-H3+ + p-H2 0 1

p-H3+ + o-H2 2/3 1/3

p-H3+ + p-H2 0 1

o-H3+ + o-H2 2/3 1/3

o-H3+ + p-H2 2/3 1/3

p-H3+ + o-H2 1/3 2/3

p-H3+ + p-H2 1/3 2/3

id

exch

hop

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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Steady state p-H3+ fractionSteady 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; =kH/kE

• 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; =kH/kE

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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“High temperature” model“High temperature” model

Spectroscopically measurable

Experimentally controllable

(n-H2,n-H3+)

(p2=0.25, p3=0.5)

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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Three-body reactionsThree-body reactions

• High densities can lead to formation of larger H2n+1

+ clusters

• At lower pressures, can (H5

+)* clusters undergo proton scrambling with H2?

• 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

H5+ + H2

+ H2

H3+ + 2H2 (H7

+)*

?

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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H5+ + H2 H2 + H5

+H5+ + H2 H2 + H5

+

“identity”

1111

“hop”

10

“exchange”

10

H7+

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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“3-body high temperature model”“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

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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Low temperature modelLow 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-H2; J = 0

o-H2; J = 1

E = 170 K

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Low temperature modelLow temperature model

Parameter Value(s)

Trot 10-160 K

Tcoll 10-160 K

Sid 0.1-0.9

Shop 0-1

Sexch 0-1

koooo kooop koopo koopp

kopoo kopop koppo koppp

kpooo kpoop kpopo kpopp

kppoo kppop kpppo kpppp

f (T,Sid,)

20 June 2011 66th OSU International Symposium on Molecular Spectroscopy

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T

160 K

140 K

120 K

100 K

80 K

60 K

40 K

20 K

Low temperature modelLow temperature model

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SummarySummary

• 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.

• 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.