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
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!