laboratory spectroscopy of h 3 + ben mccall oka ion factory tm university of chicago

Laboratory spectroscopy of H3+

Ben McCall

Oka Ion FactoryTM

University of Chicago

Motivations

Astronomical

– obtain frequencies for detection & use as probe

Quantum Mechanical

– study structure of this fundamental ion

– refine theoretical calculations of polyatomics

Formation of H3+

H2+ + H2 H3

+ + H

H2cosmic ray

interstellarmedium

H2e- impact

laboratoryplasma

Rate constant: k ~ 2 × 10-9 cm3 s-1

Exothermicity: H ~ 1.7 eV

H2 Proton Affinity:~ 4.4 eV~ 100 kcal/mol~ D(H2)

Laboratory Plasma

Types of Molecular Spectroscopy

Electronic (visible)e e

Rotational (microwave)

Vibrational (infrared)

Poster: Friedrich & Alijah××

Vibrational Modes of H3+

Degenerate

any linear combination

Infraredinactive

Infrared active

1 2x 2y

Vibrational Modes of H3+

1 2x 2y

2+

vibrationalangular

momentum

Angular momentum– I — nuclear spin

Quantum Numbers for H3+

I=3/2ortho

I=1/2para

– J — nuclear motion» k = projection of J ; K = |k|

– l2 — vibration

“l-resonance”: states with same |k-l2| mixed

– G |k-l2| — rotational part of J

Symmetry requirements– G=3n ortho, G3n para– Pauli: certain levels forbidden (J=even, G=0)

600

500

400

300

200

100

0

Ene

rgy

(cm

-1)

3210G

1

3

3

1

22

33

0

2

The 2 0 fundamental band

G0 1 2 3

grou

nd s

tate

2800

2700

2600

2500

Ene

rgy

(cm

-1)

0 11 21

2222

2 s

tate

ortho orthopara para

J (J,G) {u,l}

Q(1,0) R(1,0) R(1,1)l R(1,1)u P(3,3)

Experimental work on 2 0

Oka

1981

30

Wat

son

et a

l. 19

84

46

Initial Detection (Oka 1980)– search over two years, over 500 cm-1

– 15 lines, few percent deep

– assigned by Watson overnight 2 = 2521 cm-1

Maj

ewsk

iet

al.

1994

206

FTIR

emis

sion

Nak

anag

aet

al.

1990

FTIR

abso

rpti

on

McK

ella

r &

Wat

son

1998

FTIR

abs

orpt

ion

wid

e-ba

nd

Maj

ewsk

iet

al.

1987

113

FTIR

emis

sion

J=9

Uy

et a

l. 19

94

151J=15

Joo

et a

l. 20

00

207

Low

est f

requ

ency

1546

.901

cm

-1

Lin

dsay

et a

l. 20

00

217

Con

tinu

ous

scan

3000

– 3

600

cm-1

Oka

1980

15

The 2 0 band as a probe of H3+

Laboratory– H3

+ electron recombination rate (Amano 1988)

– spin conversion of H3+ in reactions (Uy et al. 1997)

– ambipolar diffusion in plasmas (Lindsay, poster)

Astronomy– probe of planetary ionospheres (Connerney, Miller)– confirmation of interstellar chemistry (Herbst)– measurements of interstellar clouds (Geballe)

1.0

0.8

0.6

0.4

0.2

0.0

Rel

ativ

e In

tens

ity

3200300028002600240022002000Frequency (cm

-1)

1234567 1 2 3 4 5 6

1 2 3 4 5 6 7 8

0 1R(J)

u

R(J)l

Q

P(J)u

The fundamental band

No R(0) line three equivalent spin 1/2 fermions

equilateral triangle geometry

T=400 K

2:1 intensity ratiosreflect spin statisticalweights (ortho/para)

Spacing illustrates large rotational constants

(B ~ 44 cm-1)

QR(J)u

R(J)l

P(J)u

Understanding the 2 Spectrum

For low energies, use perturbation approach:– E” = BJ(J+1) + (C-B)K2 - DJKJ(J+1)K2 + ...

– E’ = 2 + B’J’(J’+1) + (C’-B’)K’2 - 2C’K’l + ...

– use observed transitions to fit molecular constants

– For higher vibrational energies, this approach completely breaks down

Variational calculations based on an ab initio potential energy surface!

Variational Calculations

10000

5000

0

Ene

rgy

(cm

-1)

3.02.52.01.51.00.5(rad)

0

2

22

32

42

52

1+2

1+22

1

1+32

1+42

21+2

21

21+22

31

31+2

21+32

ZeroPointVibrationalEnergy

RR

Vibrational Band Types

10000

5000

0

Ene

rgy

(cm

-1)

3.02.52.01.51.00.5(rad)

0

2

22

32

42

52

1+2

1+22

1

1+32

1+42

21+2

21

21+22

31

31+2

21+32

Fundamental: 2 0

Overtones: n2 0

Hot band: 22 2

Forbidden: 1 0

Combination: 1 + 22 0

100008000600040002000

Frequency (cm-1

)

0.001

0.01

0.1

1

Rel

ativ

e In

tens

ityVibrational Overview

2 0

22 0

32 0

42 0

52 0

1+22 0

21+2 01+2 0

1 2

22 2

1+2 1

32 2

100008000600040002000

Frequency (cm-1

)

0.001

0.01

0.1

1

Rel

ativ

e In

tens

ityVibrational Overview

2 0

22 0

32 0

42 0

52 0

1+22 0

21+2 01+2 0

1 2

22 2

1+2 1

32 2

Ti:Sapphire (1 W)

Diodes (8 mW)FCL (30 mW)

D.F. (LiNbO3) (0.1 mW)

D.F. (LiIO3) (20 µW)

100008000600040002000

Frequency (cm-1

)

0.001

0.01

0.1

1

Rel

ativ

e In

tens

ityVibrational Overview

2 0

22 0

32 0

42 0

52 0

1+22 0

21+2 01+2 0

1 2

22 2

1+2 1

32 2

Ti:Sapphire (1 W)

Diodes (8 mW)FCL (30 mW)

D.F. (LiNbO3) (0.1 mW)

D.F. (LiIO3) (20 µW)

Hot Bands

At 600 K, ~200 times weaker than fundamental He dominated discharge only 50 times weaker Bawendi et al. (1990)

– 72 lines of 222 2

– 14 lines of 220 2

– 21 lines of 1+2 1

Variational calculations essential in assignment– Sutcliffe 1983; Miller & Tennyson 1988, 1989

0

2

22

32

1+2

1+22

1

21+2

21

First Overtone Band: 22 0

First overtone (22 0) usually orders of magnitude weaker than fundamental

In H3+, only about 7 times weaker

Discovery:– (in hindsight) Majewski et al. (1987)– Jupiter (Trafton et al. 1989, Drossart et al. 1989)– Assigned by Watson (with aid of hot bands)– Majewski et al. (1989) – 47 transitions, FTIR– Xu et al. (1990) – transitions observed in absorption

0

2

22

32

1+2

1+22

1

21+2

21

Absolute Energy Levels

Fundamental: G = 0

G=0 G=1 G=2

01

2

G=3

P(2,1)

Q(1,1)

nP(2,2)

E12

Hot bands: G = 0

Overtone band: G = ±3– (n G = -3, t G = +3)

Absolute energy levels

0

122

2

0

12

Second Overtone Band: 32 0

~ 200 times weaker than fundamental Band origin ~ 7000 cm-1

Tunable diode lasers Lee et al. (1991), Ventrudo et al. (1994) 15 transitions observed

Assigned based on variational calculations– Miller & Tennyson (1988, 1989)

0

2

22

32

1+2

1+22

1

21+2

21

Forbidden Band 1 0

1 mode totally symmetric infrared inactive

1 0 very forbidden since 1 & 2 not coupled

First mixing term: “Birss resonance”– mixes levels in 1 & 2 with same J, G=3

– effective for accidental degeneracies (fairly high J) Xu et al. (1992)

– 9 lines 1 = 3178 cm-1

Lindsay et al. (2000)– 10 new lines

4000

3000

2000

1000

0

6543210 543210

J=5

J=5G=2 G=5

ground stateJ=4

2 state1 state

Forbidden Band 1+2 2

Not as forbidden as 1 0

– anharmonicity of potential mixes 1+2 withother states (e.g. 22

2)

1+2 2 can “borrow” intensity from allowed bands (e.g. 22

2 2)

Xu et al. (1992) observed 21 lines

0

2

22

32

1+2

1+22

1

21+2

21

Combination Bands

1+222 0

0

2

22

32

1+2

1+22

1

21+2

21 Highest energy band Weakest allowed band

– 270 times weaker than 2

Tunable diode laser– 7780 – 8168 cm-1

Observed Spectrum

1.0

0.8

0.6

0.4

0.2

Re

lativ

e In

ten

sity

8100800079007800Frequency (cm

-1)

tQ(1,0)

tR(1,0)

tR(3,3)

tR(2,2) t

R(1,1)nP(3,3)

nP(2,2)

nQ(1,1) t

R(2,1)tR(3,0)

nQ(3,3)

nQ(2,2)

tQ(3,0)

nP(1,1)

nR(1,1)

tR(3,2)t

R(4,3)

nQ(2,1)

nP(4,4)

l

P(6,6) P(5,5)

nQ(3,2)

u

28 transitions of 1+222 0

2 of 21+21 0

Table of Results

Predictionsfrom

J. K. G. Watson

Symbol Obs Calc o-c J' <G'> o/p n' <v1'> <v2'> <l2'> J" k"tQ(3,0) 7785.233 7785.264 -0.032 3 3.0 - o 12 1.0 2.0 -2.0 3 0tQ(1,0) 7785.701 7785.340 0.361 1 3.0 - o 5 1.0 2.0 -2.0 1 0tR(3,3) 7789.878 7790.025 -0.147 4 5.9 + o 9 1.0 2.0 -2.0 3 3nP(1,1) 7805.893 7805.851 0.043 0 2.0 + p 5 1.0 2.0 2.0 1 1nP(2,2) 7820.239 7819.980 0.259 1 1.0 - p 12 1.0 2.0 2.0 2 2tR(2,2) 7822.375 7822.250 0.125 3 5.0 - p 18 1.0 2.0 -2.0 2 2nP(3,3) 7826.739 7826.679 0.060 2 0.0 + o 6 1.0 2.0 2.0 3 3nP(4,4)l 7833.249 7833.444 -0.195 3 1.1 - p 21 1.0 2.0 1.8 4 4tR(1,1) 7850.959 7850.677 0.283 2 4.0 + p 15 1.0 2.0 -2.0 1 1tR(4,3) 7880.921 7881.443 -0.522 5 5.9 + o 13 1.0 2.0 -2.0 4 3nQ(1,1) 7894.711 7894.378 0.333 1 2.0 + p 5 1.0 2.0 2.0 1 1nQ(2,1) 7898.371 7898.187 0.183 2 2.0 + p 17 1.0 2.0 2.0 2 1nQ(3,1) 7905.717 7905.891 -0.174 3 2.0 + p 17 1.0 2.0 1.9 3 1tR(3,2) 7912.047 7912.196 -0.148 4 4.9 - p 18 1.0 2.0 -2.0 3 2tR(2,1) 7939.619 7939.499 0.120 3 4.0 + p 15 1.0 2.0 -2.0 2 1tR(1,0) 7970.413 7970.124 0.288 2 3.0 - o 5 1.0 2.0 -2.0 1 0nQ(2,2) 7998.890 7998.754 0.136 2 1.0 - p 12 1.0 2.0 2.0 2 2tR(4,2) 8005.582 8006.441 -0.858 5 4.8 - p 30 1.0 2.0 -1.9 4 2

nQ(3,2)u 8007.410 8007.628 -0.218 3 1.0 - p 22 1.0 2.0 1.9 3 2nQ(4,2)u 8022.012 8022.693 -0.681 4 1.0 - p 22 1.0 2.0 1.7 4 2tR(3,1) 8027.840 8028.337 -0.497 4 3.5 + p 26 1.0 2.0 -1.8 3 1nR(3,1)l 8037.673 8038.191 -0.518 4 2.4 + p 27 0.9 2.1 1.7 3 1P(6,6) 8053.382 8054.810 -1.428 5 5.5 - o 17 1.8 1.2 -1.2 6 6

nR(1,1) 8071.617 8071.414 0.203 2 2.0 + p 17 1.0 2.0 2.0 1 1nQ(4,3) 8089.406 8090.282 -0.876 4 0.1 + o 11 1.0 2.0 2.0 4 3nQ(3,3) 8110.069 8110.202 -0.133 3 0.0 + o 11 1.0 2.0 1.8 3 3P(5,5) 8123.128 8123.985 -0.857 4 4.8 + p 30 1.9 1.1 -1.1 5 5tR(4,1) 8128.280 8129.331 -1.051 5 3.4 + p 27 0.9 2.1 -1.8 4 1nR(2,1) 8163.129 8163.294 -0.165 3 2.0 + p 17 1.0 2.0 1.9 2 1tR(3,0) 8162.653 8163.319 -0.666 4 2.9 - o 12 1.0 2.0 -1.9 3 0

Table of Results

Predictionsfrom

J. K. G. Watson

Symbol Obs Calc o-c J' <G'> o/p n' <v1'> <v2'> <l2'> J" k"tQ(3,0) 7785.233 7785.264 -0.032 3 3.0 - o 12 1.0 2.0 -2.0 3 0tQ(1,0) 7785.701 7785.340 0.361 1 3.0 - o 5 1.0 2.0 -2.0 1 0tR(3,3) 7789.878 7790.025 -0.147 4 5.9 + o 9 1.0 2.0 -2.0 3 3nP(1,1) 7805.893 7805.851 0.043 0 2.0 + p 5 1.0 2.0 2.0 1 1nP(2,2) 7820.239 7819.980 0.259 1 1.0 - p 12 1.0 2.0 2.0 2 2tR(2,2) 7822.375 7822.250 0.125 3 5.0 - p 18 1.0 2.0 -2.0 2 2nP(3,3) 7826.739 7826.679 0.060 2 0.0 + o 6 1.0 2.0 2.0 3 3nP(4,4)l 7833.249 7833.444 -0.195 3 1.1 - p 21 1.0 2.0 1.8 4 4tR(1,1) 7850.959 7850.677 0.283 2 4.0 + p 15 1.0 2.0 -2.0 1 1tR(4,3) 7880.921 7881.443 -0.522 5 5.9 + o 13 1.0 2.0 -2.0 4 3nQ(1,1) 7894.711 7894.378 0.333 1 2.0 + p 5 1.0 2.0 2.0 1 1nQ(2,1) 7898.371 7898.187 0.183 2 2.0 + p 17 1.0 2.0 2.0 2 1nQ(3,1) 7905.717 7905.891 -0.174 3 2.0 + p 17 1.0 2.0 1.9 3 1tR(3,2) 7912.047 7912.196 -0.148 4 4.9 - p 18 1.0 2.0 -2.0 3 2tR(2,1) 7939.619 7939.499 0.120 3 4.0 + p 15 1.0 2.0 -2.0 2 1tR(1,0) 7970.413 7970.124 0.288 2 3.0 - o 5 1.0 2.0 -2.0 1 0nQ(2,2) 7998.890 7998.754 0.136 2 1.0 - p 12 1.0 2.0 2.0 2 2tR(4,2) 8005.582 8006.441 -0.858 5 4.8 - p 30 1.0 2.0 -1.9 4 2

nQ(3,2)u 8007.410 8007.628 -0.218 3 1.0 - p 22 1.0 2.0 1.9 3 2nQ(4,2)u 8022.012 8022.693 -0.681 4 1.0 - p 22 1.0 2.0 1.7 4 2tR(3,1) 8027.840 8028.337 -0.497 4 3.5 + p 26 1.0 2.0 -1.8 3 1nR(3,1)l 8037.673 8038.191 -0.518 4 2.4 + p 27 0.9 2.1 1.7 3 1P(6,6) 8053.382 8054.810 -1.428 5 5.5 - o 17 1.8 1.2 -1.2 6 6

nR(1,1) 8071.617 8071.414 0.203 2 2.0 + p 17 1.0 2.0 2.0 1 1nQ(4,3) 8089.406 8090.282 -0.876 4 0.1 + o 11 1.0 2.0 2.0 4 3nQ(3,3) 8110.069 8110.202 -0.133 3 0.0 + o 11 1.0 2.0 1.8 3 3P(5,5) 8123.128 8123.985 -0.857 4 4.8 + p 30 1.9 1.1 -1.1 5 5tR(4,1) 8128.280 8129.331 -1.051 5 3.4 + p 27 0.9 2.1 -1.8 4 1nR(2,1) 8163.129 8163.294 -0.165 3 2.0 + p 17 1.0 2.0 1.9 2 1tR(3,0) 8162.653 8163.319 -0.666 4 2.9 - o 12 1.0 2.0 -1.9 3 0

1+222 Energy Levels

9000

8800

8600

8400

8200

8000

Up

pe

r S

tate

En

erg

y (c

m-1)

876543210<G>

0 12

11 3

24

222 3

33 4

33 3

44 5

4

454

5

2.00 -2.00

-2.00

2.002.00 -1.99

-2.00

-1.981.991.99

1.97 -1.99

-1.961.81 -1.99

1.931.76 1.89

-1.811.67 -1.98

-1.91

2.00-1.92

1.75

-1.79

6

6

5 54

4

5

-1.96

-1.93

1.51 2.00

1.84

1.81

-1.96

2 3

4

21 5

3

620

1 4

31 5

20 1

42 6

3

05

1

4

7

8

2 3

2

1

7

JG*

<l2>

Breaking the Barrier to Linearity

10000

5000

0

Ene

rgy

(cm

-1)

3.02.52.01.51.00.5(rad)

0

2

22

32

42

52

1+2

1+22

1

1+32

1+42

21+2

21

21+22

31

31+2

21+32

Future Prospects

Improvements in Theory– Hyperspherical coordinates for linearity (Watson)– Relativistic effects (Jaquet)– Non-adiabatic effects (Polyansky & Tennyson 1999)

Experimental Advances– Titanium:Sapphire laser, Dye laser– New techniques (heterodyne, cavities?)

– 42 0, 52 0 on the horizon

– ... 102 0 in the future??

Acknowledgements

Oka

J. K. G. Watson

Fannie and John Hertz Foundation

NSF

NASA

Column Density of H3+

(concentration) × (path length) Column Density

Laboratory: 1011 cm-3 103 cm 1014 cm-2× =

MolecularCloud:

10-4 cm-3 1018 cm 1014 cm-2× =

Laboratory and astronomical spectroscopy progressing together!