Theoretical study of ion-pair formation in electron recombination with H3

+

Royal Society Discussion meeting on Physics, Chemistry and Astronomy of H3

+

January 18-2006

Åsa Larson1, Johanna Roos1 and Ann E. Orel2

1Dept. of Applied Physics, Royal Institute of Technology, Stockholm, Sweden

2Dept. of Applied Science, UC Davis, Davis, California, USA

(Resonant) Ion-Pair formation in electron recombination (RIP)

eV 1.8EHHHeV 4.5HH

eV 0HHeV 0H H H

eH

-

-2

2-3 E

EE

High-energy resonant states for H3

The high-energy resonant states cannot explain the DR at low energies if not the taget ions are vibrationally excited.

The resonant states will produce a high-energy peak in the cross section of DR where both neutral and ionic fragments are formed (ion-pair formation).

1979, K. C. Kulander and M. F. Guest [1]

1984, H. H. Michels and R. H. Hobbs [2]

1D studies

[1] K. C. Kulander and M. F. Guest, J. Phys B: At. Mol. Phys, 12, L501 (1979)[2] H. H. Michels and R. H. Hobbs, Astrophys. J, 286, L27 (1984)

H2+ + H-

• 1994, A. E. Orel et al.2D study using the Complex Kohn Variational method

Resonance position Ei and width i

Triple intersection

More detailed calculations:

[1] A. E. Orel, K. C. Kulander and B. H. Lengsfield III, J. Chem. Phys. 100, 1756 (1994)

z (a0)

r z

C2v symmetry

High-energy peak in the DR cross section

• 1993, First experimental observation of the high-energy peak. (CRYRING) [1]

Neutral fragmants detected

• 1993, A. E. Orel et al. [2]Wave packet propagation in 2D assuming that everything dissociates into the neutral fragments (no couplings, potentials become flat).

[1] M. Larsson et al. Phys. Rev Lett., 70 430 (1993)[2] A. E. Orel and K. C. Kulander, Phys. Rev. Lett., 71 4315 (1993)

Measured cross section for ion-pair formation

[1] B. Peart et al. J. Phys. B, 12 3441 (1979)

[2] F. B. Yousif et al. J. Phys. B, 26, 4249 (1993)

[3] S. Kalhori et al. Phys. Rev. A, 69 022713-1 (2004)

•The H- fragments were detected (the two channels H2

+ + H- and H+ + H + H- cannot be seperated).

•Cross section depends on the vibrational excitation

•The magnitude of the cross section is about 2 ·10-18 cm2 in all experiments.

0 5 10 15 20

0

1

2

3H-+H++Hthreshold

H-+H+2

threshold

Yousif et al., Peart et al. (v>0, v=0, respectively) Kalhori et al. (v=0)

<v>

/v (1

0-18 c

m2 )

Collision Energy (eV)

H3+ vs H2

+

Potentials:

Lowest resonant state goes diabatically to the ion-pair limit

E = 5.4 eV

Potentials:

Lowest resonant state goes diabatically to the ion-pair limit

E = 1.91 eV

0 5 10 15 20 25 30 35 40-0,15

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20

0,25

0,30

HD+ X2g

+

1g

+ (2pu)2

1g

+ (1sgns

g)

1g

+ (1sgn'd

g)

Pote

ntia

l ene

rgy

(a.u

.)

Internuclear seperation (a.u.)

H3+ vs H2

+

Cross section for ion-pair formation:

2 % of total DR cross section

A ”bump” in the cross section

0 5 10 15 20-5,00E-019

0,00E+000

5,00E-019

1,00E-018

1,50E-018

2,00E-018

2,50E-018

CRYRING cross section

Cro

ss s

ectio

n (c

m2 )

Energy (eV)

Cross section for ion-pair formation:

5 % of total DR cross section

Resonant structure due to the quantum interference between competing pathways

0 2 4 6 8 10 12 14 160,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

Cro

ss se

ctio

n (1

0-19 c

m2 )

Electron Energy (eV)

Why are they so different?

Theoretical study of the ion-pair formation

0 2 4 6 8 10 12 14-1,5

-1,4

-1,3

-1,2

-1,1

-1,0

ion potential

Adiabatic A1 resonant states

r = 1.65 a0

Pot

entia

l ene

rgy

(H)

z (a0)

1. Calculate the resonant states using the Complex Kohn Variational method → ),( ,),( zrzrE i

adi

Note:

all ca

lculat

ions

are

carri

ed ou

t in 2

D!

Theoretical study of the ion-pair formation2. Calculate the ionic and neutral adiabatic potentials using CI with a

basis set including diffuse orbitals to describe Rydberg states.

0 2 4 6 8 10 12 14-1,5

-1,4

-1,3

-1,2

-1,1

-1,0

ion potential

adiabatic A1 Rydberg states

r = 1.65 a0

Pot

entia

l ene

rgy

(H)

z (a0)

3. Transform from the adiabatic to the corresponding diabatic states using the CI coefficients. Calculate also the couplings beween the neutral states. →

Theoretical study of the ion-pair formation

0 2 4 6 8 10 12 14-1,5

-1,4

-1,3

-1,2

-1,1

-1,0

r = 1.65 a0

Pot

entia

l ene

rgy

(H)

z (a0)

),( ,),( zrczrE ijdi

0 2 4 6 8 10 12 14-1,5

-1,4

-1,3

-1,2

-1,1

-1,0

r = 1.65 a0

Pot

entia

l ene

rgy

(H)

z (a0)

Initiate wave packets on the resonant states (electron recombination)

Include autoionization using complex resonant potentials.

Theoretical study of the ion-pair formation4. Study the dynamics using wave packets.

),(2

),(),,0( ', zrXzrzrt vv

di

i

2

1

121

121

2

1

ˆˆ

VTccVT

ti

Propagate the wavepackets on coupled potentials

2),(),(),( zrizrEzrV

did

ii

0 2 4 6 8 10 12 14-1,5

-1,4

-1,3

-1,2

-1,1

-1,0

r = 1.65 a0

Pot

entia

l ene

rgy

(H)

z (a0)

Theoretical study of the ion-pair formation5. Calculate the cross section for ion-pair formation by analyzing the

dissociating flux [1].

22

01

),()(

),,()(),(

v z

v

rstopviEt

EvTE

gE

dtzrtreEvT

zstop

[1] D. J. Haxton et al., Phys. Rev A., 69 062714-1 (2004);

G. G. Balint-Kurti et al., Comp. Phys. Comm. 63 126 (1991)

1D studyIon-pair state alone. Autoionization is included and lowest vibrational level of the ion is assumed.

0 2 4 6 8 10 12 140,00E+000

2,00E-018

4,00E-018

6,00E-018

8,00E-018

1,00E-017

1,20E-017

1,40E-017

1,60E-017

Cro

ss s

ectio

n (c

m2 )

Energy (eV)0 5 10 15 20 25 30

-0,1

0,0

0,1

0,2

0,3

0,4

0,5

Pot

entia

l ene

rgy

(a.u

.)

z (a.u.)

Include the second resonance and the direct and indirect couplings between them.

0 2 4 6 8 10 12 140,00E+000

2,00E-018

4,00E-018

6,00E-018

8,00E-018

1,00E-017

1,20E-017

1,40E-017

1,60E-017

Cro

ss s

ectio

n (c

m2 )

Energy (eV)

indirect

0 5 10 15 20 25 30

-0,1

0,0

0,1

0,2

0,3

0,4

0,5

Pot

entia

l ene

rgy

(a.u

.)

z (a0)

1D study

Add the couplings to the Rydbergs at small z.

0 2 4 6 8 10 12 140,00E+000

2,00E-018

4,00E-018

6,00E-018

8,00E-018

1,00E-017

1,20E-017

1,40E-017

Cro

ss s

ectio

n (c

m2 )

Energy (eV)

0 5 10 15 20 25 30

-0,1

0,0

0,1

0,2

0,3

0,4

0,5

Pot

entia

l ene

rgy

(a.u

.)

z (a.u.)

Add also the couplings to the Rydbergs at large z

0 5 10 15 20 25 30

-0,1

0,0

0,1

0,2

0,3

0,4

0,5

Pot

entia

l ene

rgy

(a.u

.)

z (a.u.) 0 2 4 6 8 10 12 140,00E+000

2,00E-018

4,00E-018

6,00E-018

8,00E-018

1,00E-017

Cro

ss s

ectio

n (c

m2 )

Energy (eV)

1D study

Compare with experimental cross section:

0 2 4 6 8 10 12 14 16 18 20

0,00E+000

2,00E-018

4,00E-018

6,00E-018

8,00E-018

1,00E-017

Cro

ss s

ectio

n (c

m2 )

Energy (eV)

Questions:

•Why is the shape so different ?

•Why is the magnitude a factor 5 too large?

Perform 2D wave packet calculation!

2D study

0 5 10 15 200,00E+000

2,00E-018

4,00E-018

6,00E-018

8,00E-018

1,00E-017

1,20E-017

Cro

ss s

ectio

n (c

m2 )

Energy (eV)

Diabatic ion-pair state alone

Much better shape of the cross section!

Add the couplings to the second resonance

The 2nd dimension will smear out the interference effects between the two resonant states.

z r

Pote

ntia

l ene

rgy

(H)

0 5 10 15 200,00E+000

2,00E-018

4,00E-018

6,00E-018

8,00E-018

1,00E-017

1,20E-017

Cro

ss s

ectio

n (c

m2 )

Energy (eV)

• In the 1D study the couplings to the Rydberg states reduced the cross section about 40 %, assume the same is true in the 2D study.

Add the effects from the Rydberg states (plan B)

0 5 10 15 200,00E+000

2,00E-018

4,00E-018

6,00E-018

8,00E-018

1,00E-017

1,20E-017

Cro

ss s

ectio

n (c

m2 )

Energy (eV)

0 5 10 15 200,00E+000

2,00E-018

4,00E-018

6,00E-018

8,00E-018

1,00E-017

1,20E-017

Cro

ss s

ectio

n (c

m2 )

Energy (eV)

0 5 10 15 200,00E+000

2,00E-018

4,00E-018

6,00E-018

8,00E-018

1,00E-017

1,20E-017

Cro

ss s

ectio

n (c

m2 )

Energy (eV)

0 2 4 6 8 10 12 14 16-1,50

-1,45

-1,40

-1,35

-1,30

-1,25

-1,20

-1,15

-1,10 Potentials along the classical trajectory

Pot

entia

l ene

rgy

(au)

z (au)0 5 10 15 20

0,00E+000

2,00E-018

4,00E-018

6,00E-018

8,00E-018

1,00E-017

1,20E-017

Cro

ss s

ectio

n (c

m2 )

Energy (eV)

Use the Landau-Zener model to estimate the loss of flux to the Rydberg states. Define the ”reaction path” as the classical path on the ion-pair state.

•Assume the flux coupled to the Rydberg state is lost.

•Assume the flux can jump back to the ion-pair state.

Summary

• To describe the ion-pair formation in H3+ it is crucial to

include at least two dimensions in the dynamics.• The second dimension will smear out the interference effects.• Flux will be lost due to the couplings to the Rydberg states.

To do …• The wave packets propagating on 6 coupled potentials (two

resonant states and 4 Rydberg states) are running now.• Study the effects from vibrational excitation of the ion.• Study the reaction for other isotopologous: D3

+, HD2+ , H2D+