Laboratory spectroscopy of H 3 + Ben McCall Oka Ion Factory TM University of Chicago.
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Transcript of Laboratory spectroscopy of H 3 + Ben McCall Oka Ion Factory TM University of Chicago.
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Laboratory spectroscopy of H3+
Ben McCall
Oka Ion FactoryTM
University of Chicago
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Motivations
Astronomical
– obtain frequencies for detection & use as probe
Quantum Mechanical
– study structure of this fundamental ion
– refine theoretical calculations of polyatomics
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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)
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Laboratory Plasma
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Types of Molecular Spectroscopy
Electronic (visible)e e
Rotational (microwave)
Vibrational (infrared)
Poster: Friedrich & Alijah××
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Vibrational Modes of H3+
Degenerate
any linear combination
Infraredinactive
Infrared active
1 2x 2y
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Vibrational Modes of H3+
1 2x 2y
2+
vibrationalangular
momentum
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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)
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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)
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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
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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)
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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
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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!
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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
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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
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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
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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)
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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>
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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
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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??
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Acknowledgements
Oka
J. K. G. Watson
Fannie and John Hertz Foundation
NSF
NASA
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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!