Global fit of the states of

the six isotopologues of oxygen

Shanshan Yu, Charles E Miller, Brian DrouinJet Propulsion Laboratory, California Institute of Technology, USA

Holger MüllerI. Physikalisches Institut, Universität zu Köln, 50937 Köln, Germany

Copyright 2011. All rights reserved.

uggg

BbaX 3113 and,,

Carry out band-band fit for all data to check bad measurements and misassignments

Fit all 16O2 data with the Dunham model (including highly accurate MW transitions) for Extrapolate rotational energies for unobserved vibrational levels

Provide predictions for unobserved bands

Employ mass relationship to add minor isotopologue data to the fit Determine Born-Oppenheimer breakdown parameters

Provide predictions for unobserved isotopologue bands

Derive Dunham-type potentials from obtained parameters

Project procedures and goals

Low-lying electronic states of O2 below 6.1 eV

Figure and table taken from Slanger et al. Chem. Rev. 103, 4733 (2003)

**

***

Systems included in our fit

* ( not shown in the figure)

Schumann-Runge 49356

*

16O16O 5 electronic states; v=0-29 for each electronic state Total 150 vibrational quanta Total 4728 transitions collected for these states

Five minor isotopologues 3 electronic states; v=0-29 for each electronic state Total 450 vibrational quanta Total 4295 transitions collected for these states

SPFIT Vibrational quantum numbers

  16O16O 16O17O 16O18O 17O17O 17O18O 18O18OX 3Sg

– V=0-29 0-29 300-329 400-429 500-529 600-629 700-729a 1Dg

V=0-29 30-59 330-359 430-459 530-559 630-659 730-759b 1Sg

+ V=0-29 60-89 360-389 460-489 560-589 660-689 760-789B 3Su

– V=0-29 100-129        A’ 3Du

V=0-29 130-159        

13031 61

Lab data

Levels and transitions for 16O16O

X 3Sg–

3938373635343332

40

a 1Dg

118117116115114113112111110109108107106105104103102101100

B 3Su–

139138137136135134133132131130

7574737271706968676665646362

60

18171615141312111098765432

b 1Sg+ A’ 3Du

V=0

MW&IR data available

IR data unconnected to the rest levels

Limited rotational levels observed

UV data with fine structures unresolved

IR or UV data available

Nightglow data Bad data

Chamberlain26346 cm-1

Schumann-Runge

49356 cm-1Atmospheric13122 cm-1

Noxon5233 cm-1

Herzberg III34387 cm-1

IR atmospheric7889 cm-1

700701

600

500

400

300

a 1Dg b 1Sg+ X 3Sg

–

530531

533532

563562561560

503502501

16O17O

a 1Dg b 1Sg+ X 3Sg

–

330331

333332

363362361360

303302301

16O17O

430431

433432

463462461460

403402401

16O18O630631

633632

663662661660

603602601

17O18O

730731

733732

763762761760

703702

18O18O

Levels and transitions for minor isotopologues

MW&IR data available

Solar data

Lab data

Rotational parameters are expanded in (N(N+1) - l2)

1

1

1

1

1

  Mass(u)  16O 15.994 914 619 56(16) AME200317O 16.999 131 756 6(9) Phys. Rev. A 81, 064501 (2010)18O 17.999 159 613 0(13) Phys. Rev. A 79, 012507 (2009)

Dunham-type expansions

Parameter Identifier

Parameter ValueParameter

UncertaintyComments

0 23683467.0956274 1.00E+37 /16O16O Y1,0/2

-1001 71050401.2868814 1.00E-37 /*3-2002 118417335.4781370 1.00E-37 /*5-3003 165784269.6693910 1.00E-37 /*7-4004 213151203.8606470 1.00E-37 /*9-5005 260518138.0519010 1.00E-37 /*11-6006 307885072.2431550 1.00E-37 /*13-7007 355252006.4344090 1.00E-37 /*15-8008 402618940.6256630 1.00E-37 /*17-9009 449985874.8169180 1.00E-37 /*19

-10010 497352809.0081710 1.00E-37 /*21-11011 544719743.1994260 1.00E-37 /*23-12012 592086677.3906790 1.00E-37 /*25-13013 639453611.5819330 1.00E-37 /*27-14014 686820545.7731870 1.00E-37 /*29-15015 734187479.9644420 1.00E-37 /*31-16016 781554414.1556970 1.00E-37 /*33

…

Parameter Identifier

Parameter ValueParameter

UncertaintyComments

0 23683467.0956274 1.00E+37 /16O16O Y1,0/2

-1001 71050401.2868814 1.00E-37 /*3-2002 118417335.4781370 1.00E-37 /*5

…

-300300 23331072.4780496 1.00E-37 /16O17O Y1,0/2

-301301 69993217.4341492 1.00E-37 /*3…

-400400 23014724.3513394 1.00E-37 /16O18O Y1,0/2

-401401 69044173.0540186 1.00E-37 /*3…

-500500 22973272.9989080 1.00E-37 /17O17O Y1,0/2

-501501 68919818.9967241 1.00E-37 /*3…

-600600 22651928.5332284 1.00E-37 /17O18O Y1,0/2

-601601 67955785.5996850 1.00E-37 /*3…

-700700 22325959.3358630 1.00E-37 /18O18O Y1,0/2

-701701 66977878.0075893 1.00E-37 /*3…

O2 ground state Y1,0(V+1/2) expansion

17O hyperfine structure (hfs) parameters

5 hfs parameters can be determined a, bF, c, eQq1: mass independent

CI : m-1

hfs parameters excluded when fitting hfs unresolved lines

Itot basis used for 17O17O

989100 989150 989200989100 989150 989200Frequency (M H z)

x5

989100 989150 989200

Results before and after our global fit

16O17O a 1Dg V=0, J = 12 ← 11, DF = DJ = +1 (left) DF = 0 (inset). The I = 5/2 nuclear spin of 17O splits the DF = 1 transitions into a sextuplet and the DF = 0 into a pentuplet.

  (Vmax=18) (Vmax=10) (Vmax=12)

Te 0 237576991( 33) 395594758(150)

Te(BOB) 0 8919( 50) 25636(151)

Y1,0/2 23683467(169) 22625647(178) 21474459( 75)

Y1,0(BOB)/2 1561(169) 1543(172) 1040( 74)

Y2,0/4 -89235.0( 38) -98161.6(262) -104788.2( 93)

Y3,0/8 126.30( 44) 74.45(239) 23.68( 89)

Y4,0/16 -0.8113(184) -3.700( 64) -4.4950(236)

Y5,0/32 -0.015451(245)    

Obtained values (MHz) for 16O2 Yl,0

 

Y0,1 43343.5189(131) 42766.691( 65) 41988.255( 68)

Y0,1(BOB) -5.1403( 99) -4.734( 33) -6.084( 34)

Y1,1/2 -238.2570(202) -256.968(130) -273.410(104)

Y2,1/4 0.3301( 49) 0.163( 39) -0.1161(172)

Y3,1/8 -6.192(100)E-03 -0.01760(200) -0.01867( 71)

Y0,2 -0.1452056(100) -0.1526708(154) -0.160518( 70)

Y1,2/2 0.0779(127)E-03 -0.3032(149)E-03 -0.506( 71)E-03

Y2,2/4 -0.01710(312)E-03    

Y0,3 0.0819( 34)E-06    

Obtained values (MHz) for 16O2 Yl,1, Yl,2, Yl,3

 

l0,0237713.386( 88) g0,0 -252.28957( 68)

l0,0(BOB) 27.425( 53) g0,0(BOB) 0.01019( 72)

l1,0/2 256.274(114) g1,0/2 -0.306501( 56)

l2,0/4 8.2969(295) g0,1 -0.245505(116)E-03

l0,1 0.218066(163)

l0,1(BOB) 5.570(175)E-03

l1,1/2 9.7568(188)E-03

l0,2 1.2600(219)E-06

Obtained values (MHz) for 16O2 ll,m and gl,m

9023 transitions collected and fitted for O2 (8840 fitted to 3 , swith a reduced RMS=1.04 )

111 independent parameters (12021 parameters defined) determined for fives electronic states of six O2 isotopologues

600 vibrational states calculated

modeled well with Dunham model

not modeled well with Dunham model; now modeled with band-by-band parameters

High vibration excitation lab data needed to replace nightglow data for b-X

b(1)-X(1) or a(0)-X(1) isotopologue transitions needed to clarify the existing problem fitting 17O18O X(1)-X(0) data

Conclusions

Fit statistics on Edwards et al., 1976, 1978,1981

Band#

bad lines

# good lines

N' srmsrms(cm-1)

AVG (cm-1)

 P (Torr)

Shift (cm-1)

16O17O 0-0 4 50 3-20 1.767 0.009 0.002 300

16O18O 0-0 4 43 3-20 2.381 0.012 -0.009 750

17O17O 0-0 4 53 3-21 1.788 0.009 -0.002 300

18O18O 0-0 2 42 3-31 1.630 0.008 0.000 750

               

16O16O 1-0 1 69 1-19 0.911 0.014 -0.010 550

17O17O 1-0 3 61 1-13 2.230 0.033 -0.031 550

17O18O 1-0 75 0 1-17 12.290 0.184 0.182 55018O18O 1-0 6 70 1-19 1.027 0.015 0.006 550

Fit statistics on 16O16O b-X lab data

Reference#

bad lines

# good lines

N' srmsrms(cm-1)

AVG (cm-1)

 P (Torr)

Shift (cm-1)

0-0, Robichaud et al. , 2008 2 30 2-30 1.364 0.000 0.000 0  

0-0, Brown et al., 2000 0 44 0-22 0.830 0.001 0.000 4 -

0.0006

0-0, Cheah et al., 2000 4 57 0-30 0.594 0.006 -0.002 0 0.0014

0-0, O'Brien et al., 2001 2 34 22-40 1.149 0.006 0.002 0.8

0-0, van Leeuwen et al., 2004 0 12 34-44 0.683 0.014 -0.011 300  

1-1, van Leeuwen et al., 2004 1 58 0-32 0.532 0.011 -0.003 300  

1-0, Cheah et al., 2000 1 57 0-30 0.420 0.005 0.000 0  

2-0 Naus et al., 1999 0 49 0-26 0.906 0.009 0.001 60  

2-0, Cheah et al., 2000 1 43 0-24 1.108 0.012 0.008 0  

3-0, Biennier et al., 1998 1 42 0-24 1.225 0.013 0.006 600  

3-0, Naus et al., 1999 1 42 0-22 1.444 0.010 -0.008 183  

Fit statistics on 16O16O ground state MW lab data

Reference#

bad lines

# good lines

N' srmsrms(MH

z)AVG

(MHz) P

(Torr)

V=0, Endo et al., 1982 0 8 31-39 1.140 0.031 -0.031  

V=1 Endo et al., 1982 0 19 1-19 0.889 0.016 0.002  

V=0, Zink & Mizushima, 1987 1 4 5-15 2.063 0.185 0.116  

V=0 Brown et al., 1992 (CARS) 0 30 3-21 0.173 25.905 12.677 70

V=0, Park et al., 1996 1 1 9,15 0.395 0.015 0.015  

V=0, Golubiatnikov et al., 2003 0 8 3-7 1.221 0.024 -0.010  

V=0, Tretyakov et al., 2005 0 27 1-27 0.694 0.005 0.000  

V=0, Drouin et al., 2010 0 5 5-11 0.835 0.033 -0.017  

Fit statistics on 16O16O b-X nightglow (Cosby2006)

Band# bad lines

# good lines

N' srmsrms

(cm-1)AVG (cm-1)

0-0 0 8 28-40 0.884 0.088 0.0370-1 0 42 0-24 0.903 0.090 0.0891-1 0 52 2-34 1.195 0.120 0.0802-1 0 27 2-18 1.215 0.122 0.1043-1 0 1 10 0.815 0.082 0.0820-2 0 3 2-8 0.345 0.034 0.0252-2 0 37 0-20 1.040 0.104 0.0873-2 0 39 0-20 1.070 0.107 0.0944-2 0 1 6 1.777 0.178 0.1782-3 0 5 4-10 0.875 0.087 0.0783-3 0 31 0-20 0.870 0.087 0.0774-3 0 39 0-24 0.764 0.076 0.0505-3 0 4 4-14 0.965 0.096 0.0393-4 0 29 0-18 0.682 0.068 0.056

…