1TI14

O2 ENERGY LEVELS, BAND CONSTANTS, POTENTIALS,

FRANCK-CONDON 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 TechnologyHarvard-Smithsonian Center for Astrophysics

6/17/2014Image courtesy of: www.executionandstrategy.com

TI14 2

What is needed for comprehensive linelist?• Energy level(s)• Line position• Degeneracy• Intensity

o Spin momentso Electronic correlationso Eigenfunction overlapso Partition sums

• Lineshapes

6/17/2014

• Energy level(s)• Line position• Degeneracy • Intensity

– Spin moments– Electronic correlations– Eigenfunction overlaps– Partition sums

• Lineshapes

Source:web.sahra.arizona.edu

TI14 3

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 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

6/17/2014

TI14 4

Isotope Invariant Parameter Set (1)

6/17/2014

  (Vmax=31) (Vmax=10) (Vmax=12)

Te   237577161( 52) 395594904(149)

  9100( 66) 25556(149)

Gv

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

TI14 56/17/2014

  (Vmax=31) (Vmax=10) (Vmax=12)

Bv

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

Dv-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-06Hv -1.34E-09a -0.0652E-06a -0.135E-06a

4.52( 73)E-09

Isotope Invariant Parameter Set (2)

TI14 66/17/2014

  (Vmax=31) (Vmax=31)

237726.55( 40) -252.28822( 55)

31.328(109) 8.31( 60)E-03226.24( 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)

TI14 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!

6/17/2014

TI14 8

Method for generating potentials

6/17/2014

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

TI14 96/17/2014

TI14 10

What is needed for comprehensive linelist?• Energy level(s)• Line position• Degeneracy• Intensity

o Spin momentso Electronic correlationso Eigenfunction overlapso Partition sums

• Lineshapes

6/17/2014

http://www4.ncsu.edu/~franzen/public_html/CH433/workshop/fc/fc.html

TI14 11

Partition SumsOnly needDegeneracy di

&Energy Ei

Then calculate as a function of temperatureTotal Internal Partition Sums from HITRAN

Our calculations disagreed by 10-4 error in Boltzmann constant for 16O2 and by d0 for asymmetric isotopologues

6/17/2014

TI14 12

Partition Sums

6/17/2014

TI14 13

What is needed for comprehensive linelist?• Energy level(s)• Line position• Degeneracy (quantum assignment)• Intensity

o Spin momentso Electronic correlationso Eigenfunction overlapso Partition sums

• Lineshapes

6/17/2014

TI14 14

Theory for transition moments in O2

6/17/2014

O = O 3S

O = O 1D

O = O 1S

DN = 2DS = 1, DL = 2DN = 0,+1,+2

DS = 0 DL = 2DN = 0,+2

<fi|L+2S+N|fj> = <fi|fi>MspinDrot

DS = 1, DL = 0DN = 0,+1,+2,+3

DN = 1

<fi|Q+N|fj> = <fi|fi>QelecDrot

TI14 15

Transition Moments

6/17/2014

TI14 16

Transition Intensities

6/17/2014

Flat lines indicate scaling factorSiedways ‘w’s indicate Herman-Wallis factor

TI14 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

6/17/2014

TI14 18

Acknowledgements• NASA ACLR• OCO-2 ABSCO• Herb Pickett

6/17/2014

© 2014 California Institute of Technology. Government sponsorship acknowledged.