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O 2 ENERGY LEVELS, BAND CONSTANTS, POTENTIALS, FRANCK- CONDON FACTORS AND LINELISTS INVOLVING THE X 3  g, a 1  g AND b 1  + g STATES SHANSHAN YU, BRIAN.

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Presentation on theme: "O 2 ENERGY LEVELS, BAND CONSTANTS, POTENTIALS, FRANCK- CONDON FACTORS AND LINELISTS INVOLVING THE X 3  g, a 1  g AND b 1  + g STATES SHANSHAN YU, BRIAN."— Presentation transcript:

1 O 2 ENERGY LEVELS, BAND CONSTANTS, POTENTIALS, FRANCK- CONDON FACTORS AND LINELISTS INVOLVING THE X 3  g, a 1  g AND b 1  + g STATES SHANSHAN YU, BRIAN DROUIN, CHARLES MILLER, IOULI GORDON Jet Propulsion Laboratory, California Institute of Technology Harvard-Smithsonian Center for Astrophysics 6/17/20141TI14 Image courtesy of: www.executionandstrategy.com

2 What is needed for comprehensive linelist? Energy level(s) Line position Degeneracy Intensity o Spin moments o Electronic correlations o Eigenfunction overlaps o Partition sums Lineshapes 6/17/2014TI142 Energy level(s) Line position Degeneracy Intensity – Spin moments – Electronic correlations – Eigenfunction overlaps – Partition sums Lineshapes Source:web.sahra.arizona.edu

3 2012 TA04  Simultaneously fit MW, THz, infrared, visible and UV transitions of 16 O 16 O, 16 O 17 O, 16 O 18 O, 17 O 17 O, 17 O 18 O, 18 O 18 O  Treat all six O 2 isotopologues as the same molecule using well- known reduced mass relationships  Leverage experimental information from one isotopologue to accurately predict the spectra of any other isotopologue  Derive potentials from obtained parameters 6/17/2014TI143

4 Isotope Invariant Parameter Set (1) 6/17/2014TI144 (V max =31) (V max =10) (V max =12) TeTe 237577161( 52)395594904(149) 9100( 66)25556(149) GvGv 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

5 6/17/2014TI145 (V max =31) (V max =10) (V max =12) BvBv 43343.5117(110)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 DvDv -0.1450753( 43)-0.1526375(167)-0.1604358( 59) -0.0515( 48)E-03-0.3310(166)E-03-0.5031( 49)E-03 0.01241(112)E-03 -0.5865(226)E-06 HvHv -1.34E-09 a -0.0652E-06 a -0.135E-06 a 4.52( 73)E-09 Isotope Invariant Parameter Set (2)

6 6/17/2014TI146 (V max =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 Isotope Invariant Parameter Set (3)

7 Method for deriving band parameters Math is straightforward But tedious for 6 isotopes, with 70 vibronic states each Especially if error propagation is desired! 6/17/2014TI147

8 Method for generating potentials 6/17/2014TI148 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

9 6/17/2014TI149

10 What is needed for comprehensive linelist? Energy level(s) Line position Degeneracy Intensity o Spin moments o Electronic correlations o Eigenfunction overlaps o Partition sums Lineshapes 6/17/2014 TI1410 http://www4.ncsu.edu/~franzen/public_html/CH433/workshop/fc/fc.html

11 Partition Sums Only need Degeneracy d i & Energy E i Then calculate as a function of temperature Total Internal Partition Sums from HITRAN Our calculations disagreed by 10 -4 error in Boltzmann constant for 16 O 2 and by d 0 for asymmetric isotopologues 6/17/2014TI1411

12 Partition Sums 6/17/2014TI1412

13 What is needed for comprehensive linelist? Energy level(s) Line position Degeneracy (quantum assignment) Intensity o Spin moments o Electronic correlations o Eigenfunction overlaps o Partition sums Lineshapes 6/17/2014TI1413

14 Theory for transition moments in O 2 6/17/2014TI1414 O = O 33 11 11  N = 2  S = 1,  L = 2  N = 0,+1,+2  S = 0  L = 2  N = 0,+2 =  spin D rot  S = 1,  L = 0  N = 0,+1,+2,+3  N = 1 = Q elec D rot

15 Transition Moments 6/17/2014TI1415

16 Transition Intensities 6/17/2014TI1416 Flat lines indicate scaling factor Siedways ‘w’s indicate Herman-Wallis factor

17 Conclusion Predictions from literature, SPCAT, RKR1 SPCAT predictions for all O2 states below 15000 cm- 1 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 6/17/2014TI1417

18 Acknowledgements NASA ACLR OCO-2 ABSCO Herb Pickett 6/17/2014TI1418 © 2014 California Institute of Technology. Government sponsorship acknowledged.

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