O2 ENERGY LEVELS, BAND
CONSTANTS, POTENTIALS, FRANCKCONDON FACTORS AND LINELISTS
INVOLVING THE X3Sg , a1Dg AND b1S+g
STATES
SHANSHAN YU, BRIAN DROUIN, CHARLES MILLER, IOULI
GORDON
Jet Propulsion Laboratory, California Institute of Technology
Harvard-Smithsonian Center for Astrophysics
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Image courtesy of: www.executionandstrategy.com
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What is needed for
comprehensive linelist?
•
•
•
•
Energy level(s)
Line position
Degeneracy
Intensity
–
o
o
–
o
–
o
–
Spin moments
Electronic correlations
Eigenfunction overlaps
Partition sums
• Lineshapes
Source:web.sahra.arizona.edu
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2012 TA04
 Simultaneously fit MW, THz,
infrared,
visible
and
UV
transitions of 16O16O, 16O17O,
16O18O, 17O17O, 17O18O, 18O18O
 Treat all six O2 isotopologues as
the same molecule using wellknown reduced mass relationships
 Leverage
experimental
information
from
one
isotopologue to accurately predict
the spectra of any other
isotopologue
 Derive potentials from obtained
parameters
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Isotope Invariant
Parameter Set (1)
(Vmax=31)
(Vmax=10)
(Vmax=12)
237577161( 52) 395594904(149)
Te
Gv
9100( 66)
25556(149)
23683150(166)
22624892(173)
21473929( 68)
2009(165)
1905(171)
1590( 60)
-89298.8( 67)
-98029.5(229)
-104798.0( 75)
137.94( 99)
63.28(217)
25.09( 81)
-1.591( 56)
-3.436( 61)
-4.5355(226)
6.31(134)E-03
-0.2165(114)E-03
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Isotope Invariant Parameter Set (2)
(Vmax=31)
43343.5117(110)
Bv
(Vmax=10)
(Vmax=12)
42766.1783(198) 41988.2188(256)
-5.1592( 91)
-5.6158(165)
-6.1443(213)
-238.2546(158)
-255.8725(282)
-273.320( 36)
0.3600( 39)
-0.1679( 70)
-0.1302(105)
-0.015555(271)
-0.01875( 56)
0.4723( 73)E-03
-6.602( 62)E-06
-0.1450753( 43)
-0.1526375(167)
-0.1604358( 59)
-0.0515( 48)E-03 -0.3310(166)E-03 -0.5031( 49)E-03
Dv
0.01241(112)E-03
-0.5865(226)E-06
-1.34E-09a
Hv
-0.0652E-06a
-0.135E-06a
4.52( 73)E-09
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Isotope Invariant Parameter Set (3)
(Vmax=31)
(Vmax=31)
237726.55( 40)
-252.28822( 55)
31.328(109)
8.31( 60)E-03
226.24( 89)
-0.306488( 52)
23.89( 46)
-0.243777(283)E-03
-2.661( 79)
-1.113(210)E-09
0.05798(124)
0.21107( 39)
0.02681( 54)
-4.500(142)E-03
1.064( 62)E-06
0.086( 39)E-09
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Method for deriving band
parameters
• Math is straightforward
• But tedious for 6
isotopes, with 70
vibronic states each
• Especially if error
propagation is desired!
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Method for generating
potentials
R.J. Le Roy, RKR1 2.0, A computer program
implementing the first-order RKR method
for determining diatomic molecule
potential energy function, University of
Waterloo, Chemical Physics Research
Report CP-657R(2004); see
http://leroy.uwaterloo.ca/programs
Band Parameters 6 isotopes, 3 electronic states
RKR turning points 6 isotopes, 3 electronic states
Vibrational wavefunctions, Franck-Condon Factors
6 isotopes, 3 electronic states, 3 transitions
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What is needed for
comprehensive linelist?
•
•
•
•
Energy level(s)
Line position
Degeneracy
Intensity
o
o
o
o
Spin moments
Electronic correlations
Eigenfunction overlaps
Partition sums
• Lineshapes
http://www4.ncsu.edu/~franzen/public_html/CH433/workshop/fc/fc.html
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Partition Sums
Only need
Degeneracy di
&
Energy Ei
Then calculate as a function of temperature
Total Internal Partition Sums from HITRAN
Our calculations disagreed by 10-4 error in Boltzmann
constant for 16O2 and by d0 for asymmetric
isotopologues
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Partition Sums
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What is needed for
comprehensive linelist?
•
•
•
•
Energy level(s)
Line position
Degeneracy (quantum assignment)
Intensity
o
o
o
o
Spin moments
Electronic correlations
Eigenfunction overlaps
Partition sums
• Lineshapes
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Theory for transition
moments in O2
DS = 1, DL = 2
DN = 0,+1,+2
DN = 1
O=O
O=O
3S
DS = 1, DL = 0
DN = 0,+1,+2,+3
1D
DS = 0 DL = 2
DN = 0,+2
DN = 2
O=O
1S
<fi|L+2S+N|fj> = <fi|fi>MspinDrot
<fi|Q+N|fj> = <fi|fi>QelecDrot
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Transition Moments
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Transition Intensities
Flat lines indicate scaling factor
Siedways ‘w’s indicate Herman-Wallis factor
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Conclusion
• Predictions from literature, SPCAT, RKR1
• SPCAT predictions for all O2 states below 15000 cm1 are almost as good as HITRAN12
• Details of J dependence of intensity still an issue for
‘A-band’
• Lineshape is not part of SPCAT, need to apply
alternate method
• Method produces ‘good’ extrapolative listings of
isotopes, hot bands, difference bands
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Acknowledgements
• NASA ACLR
• OCO-2 ABSCO
• Herb Pickett
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© 2014 California Institute of Technology.
Government sponsorship acknowledged.
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