The ortho:para Ratio of HThe ortho:para Ratio of H33

++

in in Laboratory and Astrophysical PlasmasLaboratory and Astrophysical Plasmas

Ben McCallBen McCall

Dept. of Chemistry Dept. of Astronomy

Nick Indriolo

Kyle Crabtree

Holger

Kreckel

Metallurgical and Chemical EngineeringVol. IX, No. 6, p.298 (1911)

Richard Payne (Arizona Astrophotography)

Interstellar gas ~1/6th

of mass!

~1066

molecules

~half in diffuse clouds

Interstellar Cloud ClassificationInterstellar Cloud Classification

T. P. Snow and B. J. McCall, Annu. Rev. Astron. Astrophys. (2006), 44, 367-414.T. P. Snow and B. J. McCall, Annu. Rev. Astron. Astrophys. (2006), 44, 367-414.

n ~ 101–103

cm-3[~10-15

Torr]T ~ 60 K

PerseiPersei

Photo: Jose Fernandez Garcia

Diffuse Molecular CloudsDiffuse Molecular Clouds

B. L. Rachford

et al., Astrophys. J. 577, 221 (2002)

1.00

0.96

0.92

0.88

8780877087608750Wavelength (Å)

R6

R4

R2R0

Q2Q4

P2

Q6 Q8P4Q10 P6

HD 204827

C2

H2H2

J=0 (para) & J=1 (ortho)thermalized by proton swap

H2

+ H+

→ H2

+ H+

Importance of HImportance of H22

& H& H33

++

He

C N O Ne

Mg

Fe

Si S Ar

8

7

6

5

4

3

N

O2H2

ON2

CO2CH4

OHCC2

H2

O

H2

COCH

NH2

SiNH3

CO

Pro

ton

Affi

nity

(eV

)

HH33

++: Cornerstone of Interstellar Chemistry: Cornerstone of Interstellar Chemistry

8

7

6

5

4

3

N

O2H2

ON2

CO2CH4

OHCC2

H2

O

H2

COCH

NH2

SiNH3

CO

Pro

ton

Affi

nity

(eV

)

H2+

H3+CH+

CH2+

CH3+

CH5+CH4

C2

H3+C2

H2

C3

H+

C3

H3+C4

H2+

C4

H3+

C6

H5+

C6

H7+ C6

H6

H2

H2

H2

H2

H2

C

e

C+

e

C+

C

H

C2

H2

H2e

OH+H2

O+H3

O+H2

O

OHe

OH2

H2HCO+

CO

HCNCH3

NH2

CH3

CN

C2

H5

CN

N, eNH3, e

HCN, eCH3C

N, e

eCO, e

H2O, e

CH3OH, e

CHCH2

CO

CH3

OH

CH3

OCH3

CH3+C2

H5+e

C2

H4

eC3

H2e

C3

H

eC2

H

HH22

TemperatureTemperature

B. L. Rachford

et al., ApJ (2002), 577, 221-244.B. L. Rachford

et al., ApJ (2002), 577, 221-244.

p-H2 ; J = 0

o-H2 ; J = 1

E170 K

•

UV measurementsof H2

absorption•

99% of H2

in J=0 (para) and J=1 (ortho) levels•

Profile fitting gives accurate column densities for N(0) and N(1) T01

•

UV measurementsof H2

absorption•

99% of H2

in J=0 (para) and J=1 (ortho) levels•

Profile fitting gives accurate column densities for N(0) and N(1) T01

ortho and ortho and parapara

HH33

++

+

orthoI = 3/2

paraI = 1/2

+

NoNp

gogp

e-ΔE/kT(H3+)=

ΔE

R(1,0) R(1,1)

Temperature DiscrepancyTemperature Discrepancy•

Average T01

in diffuse molecular clouds: 70 K (N = 66)•

Average T(H3

+) in diffuse molecular clouds: 30 K (N = 18)•

Only 2 sight lines in common

•

Recent observations expand this number to 6

•

Average T01

in diffuse molecular clouds: 70 K (N = 66)•

Average T(H3+) in diffuse molecular clouds: 30 K (N = 18)

•

Only 2 sight lines in common•

Recent observations expand this number to 6

Target Obs. p3 p2 T(H3+) T01 T

Per UKIRT 0.65(4) 0.68(6) 25(3) 58(6) 33

X Per UKIRT 0.66(5) 0.69(4) 24(4) 57(4) 33

HD 154368 Gem. S. 0.69(6) 0.76(7) 22(4) 51(8) 29

HD 73882 VLT 0.67(4) 0.76(5) 23(3) 51(6) 28HD 110432 VLT 0.60(2) 0.57(3) 30(2) 68(5) 38

Cep UKIRT/ Keck

0.57(7) 0.54(3) 34(10) 73(4) 39

Rate = ke

[H3+] [e-]

[H2

]

parapara--HH33

++

Fraction on FormationFraction on Formation

H2

H2+

+ e-H2

+ H2+

H3+

+ H

cosmic ray

H3+

+ e-

H + H2

or 3H

Rate =

Formation

Destruction

M. Quack, Mol. Phys. 34, 477 (1977)T. Oka, JMS 228, 635 (2004)

H2 H2+ ortho-H3+ para-H3+

ortho ortho 2/3 1/3

ortho para 1/3 2/3

para ortho 1/3 2/3

para para 0 1

(1-p2

)2

(1-p2

)p2p2

(1-p2

)

p22

(1-p2

)2

(1-p2

)p2p2

(1-p2

)

p22

+

+

+

(1/3 + 2/3 p2

) = p3 (p2

= 0.68)

Observedpara-H3+

fractionp3

~ 0.62

?= 0.79

B. A. Tom, V. Zhaunerchyk, M. B.Wiczer, …, M. Larsson, R. D. Thomas, & B. J. McCall, J. Chem. Phys. 130, 031101 (2009)

parapara--HH33

++

+ e+ e-- vs. orthovs. ortho--HH33

++

+ e+ e--

CRYRING

S.F. dos Santos, V. Kokoouline, and C. H. Greene, J. Chem. Phys. 127, 124309 (2007)

para-H3+

ortho-H3+

theory

T(K)

The Life of an HThe Life of an H33

++

•

Birth rate:

n(H2

) ~ 3×10-14

cm-3

s-1–

in 1 mL, birth once every million years

–

once per second in cube ~300m on a side–

demographics: 79% para, 21% ortho

•

Collision rate with H2

: k n(H2

) ~ 1×10-7

s-1–

once every ~100 days

–

happens 1052

s-1

in our galaxy!–

influence on ortho:para ????

•

Lifetime: 1/[ke

n(e)] ~ 5×108

s ~ 16 years

HH33

++

+ H+ H22 →→

(H(H55

++)* )* →→

HH2 2 + H+ H33

++

“identity”

“hop”

“exchange”

H5+

1

3

6what is branching ratio? α

= Shop/Sexch

3/6 ? T-dependent?

•

simplest bimolecular reaction involving a polyatomic

•

most common bimolecular reaction in the universe! Sid

Shop

Sexch

Dynamics of ReactionDynamics of Reaction

C2v

D2d C2v

“hop”

“exchange”

Not obvious that “statistical” hop/exchange = 0.5 is valid!

~300

0 cm

-1

~50 cm-1~1500 cm-1

PES: Z. Xie, B. J. Braams, & J. M. Bowman,J. Chem. Phys. 122, 224307 (2005)

HighHigh--T Statistical Model (Oka)T Statistical Model (Oka)•

Adopt constant α

(ignore PES)

•

Ortho & para

as two species (ignore J,K)•

Assume all pathways energetically possible

•

Use “nuclear spin branching ratios”

as k’s

Cordonnier

et al., J. Chem. Phys. 113, 3181 (2000)

H3+ H2 proton hop hydrogen exchange

ortho-H3+ para-H3+ ortho-H3+ para-H3+

ortho ortho 2/3 1/3 2/3 1/3

ortho para 0 1 2/3 1/3

para ortho 2/3 1/3 1/3 2/3

para para 0 1 1/3 2/3

Our HighOur High--T ModelT Model

•

Assumptions:–

Gas has constant p2

[p-H2

]/[H2

]•

Laboratory: p2

established by preparation•

Diffuse clouds: p2

fixed by reaction with H+

–

Steady state (reached in a few collisions)•

Results independent of H3+

formation, destruction

•

Results:–

p3

[p-H3+]/[H3+] =

–

If p2

= ¼, p3

= ½

for all α•

n-H2

→ n-H3+

α+1+2αp23α+2

p2

p3

¼

½

HighHigh--T Model PredictionsT Model Predictions

n-H2 p-H2

full thermalequilibrium

Low Temperature EffectsLow Temperature Effects•

Angular momentum restrictions–

p-H3+

+ p-H2

→ o-H3+

+

p-H2–

p-H3+

+ p-H2

→ o-H3+

+

o-H2•

At low T in enriched p-H2

, slower p-H3+

→ o-H3+

orthoI = 3/2

paraI = 1/2

paraI = 0

orthoI = 1

170 K

1/2

0 ↔ 3/2

0

Low Temperature Statistical ModelLow Temperature Statistical Model

•

Still requires α

as input parameter (no PES)•

Does consider rotational states & energies

•

Rate constants from ground state

reactantse.g. koppo

(Trot

,Tkin

)

k(o-H3+

+ p-H2

→ p-H3+

+ o-H2

)

SteadySteady--State Model PredictionsState Model Predictions

n-H2 p-H2

•

Really should use state-to-state rate coefficients

•

No reason α

must be constant•

Quantum reactive scattering calculations highly desirable!

Oka Group ExperimentsOka Group ExperimentsCordonnier

et al. JCP 113, 3181 (2000)

o-H3+

p-H3+

n-H2 p-H2

hopexch ~2.4

T ~ 400 K

α

= ≠

0.5!

How does p3vary with p2

,or α

with T?

pump Liquid-nitrogen cooled hollow cathode

TakayoshiAmano

(p2

) p-H2

+ (1-p2

) o-H2

ortho-H3+ para-H3+measure steady state p3

[p-H3+]/[H3+] vs

p2

Experimental ApproachExperimental Approach

Experimental ResultsExperimental Results

Pulse on Pulse off

FrequencyA

bs. Tkin

H3+

H5+

T ~ 130 K

K. Crabtree, C. Kauffman, B. Tom, E. Becka, B. McGuire, & B. J. McCall, J. Chem. Phys., 134, 194311 (2011)

o/po/p--HH33

++

vs. o/pvs. o/p--HH22

K. Crabtree, C. Kauffman, B. Tom, E. Becka, B. McGuire, & B. J. McCall, J. Chem. Phys., 134, 194311 (2011)

o/po/p--HH33

++

vs. o/pvs. o/p--HH22

K. Crabtree, C. Kauffman, B. Tom, E. Becka, B. McGuire, & B. J. McCall, J. Chem. Phys., 134, 194311 (2011)

o/po/p--HH33

++

vs. o/pvs. o/p--HH22

T↓ → complex

↑ more scrambling

K. Crabtree, C. Kauffman, B. Tom, E. Becka, B. McGuire, & B. J. McCall, J. Chem. Phys., 134, 194311 (2011)

IsotopicallyIsotopically

Substituted SystemSubstituted System

•

Higher energy → hop dominant

•

Lower energy → more statistical

•

Endothermic!Dieter Gerlich,J. Chem. Soc. Farad. Trans.89, 2199 (1993)

D3+

+ H2H2

D+

+ D2

HD2+

+ HD

hop

exch.

hop/

exch

ange

New Astronomical ObservationsNew Astronomical Observations

K. Crabtree, N. Indriolo, H, Kreckel, B. A. Tom, & B. J. McCall, Astrophys. J., 729, 15 (2011)

HH33

++

+ H+ H22

Reaction ResultsReaction Results

K. Crabtree, N. Indriolo, H, Kreckel, B. A. Tom, & B. J. McCall, Astrophys. J., 729, 15 (2011)

Sid=0.1

Sid=0.9

No agreement; H3+

+ H2

reaction not solely responsible for T discrepancy

10 K

20 K

30 K40 K

50 K60 K70 K80 Ketc Note:p2

= p2

(T)

Steady State Model RevisitedSteady State Model Revisited•

Include formation

and destruction

reactions:

•

Assume steady state, simplify:

K. Crabtree, N. Indriolo, H, Kreckel, B. A. Tom, & B. J. McCall, Astrophys. J., 729, 15 (2011)

Model Results for Model Results for kke,pe,p

= = kke,oe,oRate Coefficients from McCall et al., PRA 2004, 70, 052716

K. Crabtree, N. Indriolo, H, Kreckel, B. A. Tom, & B. J. McCall, Astrophys. J., 729, 15 (2011)

Sid=0.1

Sid=0.9

Agree

ment

for S

id ~0.9!

Incompletethermalization by H3+

+ H2beforeDR

Model Results for Model Results for kke,pe,p

>>

kke,oe,oRate Coefficients from dos Santos et al., JCP 2007, 127, 124309

K. Crabtree, N. Indriolo, H, Kreckel, B. A. Tom, & B. J. McCall, Astrophys. J., 729, 15 (2011)

No ag

reeme

nt!

Future WorkFuture Work•

Experiments–

Cold o/p

DR in storage ring (CSR?)

–

H3+

+ H2

in 22-pole ion trap (MPIK, Cologne)•

test low temperature model

•

measure Sid

•

Observations (VLT)–

Additional sightlines

•

Theory–

State-to-state model

–

Quantum reactive scattering calculations?

Acknowledgments: Part 1Acknowledgments: Part 1

http://bjm.scs.illinois.edu

Nick Indriolo

Kyle Crabtree

Holger

Kreckel

Brian Tom

Kisam

Park

Acknowledgments: Part 2Acknowledgments: Part 2

The ortho:para Ratio of H3+ in Laboratory and Astrophysical PlasmasSlide Number 2Slide Number 3Interstellar Cloud ClassificationDiffuse Molecular CloudsImportance of H2 & H3+H3+: Cornerstone of Interstellar ChemistryH2 Temperatureortho and para H3+Temperature Discrepancypara-H3+ Fraction on FormationSlide Number 12The Life of an H3+H3+ + H2 → (H5+)* → H2 + H3+Dynamics of ReactionHigh-T Statistical Model (Oka)Our High-T ModelHigh-T Model PredictionsLow Temperature EffectsLow Temperature Statistical ModelSteady-State Model PredictionsOka Group ExperimentsExperimental ApproachExperimental Resultso/p-H3+ vs. o/p-H2o/p-H3+ vs. o/p-H2o/p-H3+ vs. o/p-H2Isotopically Substituted SystemNew Astronomical ObservationsH3+ + H2 Reaction ResultsSteady State Model RevisitedModel Results for ke,p = ke,oModel Results for ke,p > ke,oFuture WorkAcknowledgments: Part 1Acknowledgments: Part 2