MICROWAVE SPECTRUM OF 12C16O

S.A. TASHKUN and S.N. MIKHAILENKO, Laboratory of Theoretical Spectroscopy,

V.E. Zuev Institute of Atmospheric Optics, Zuev square 1,

634021, Tomsk, RUSSIA

Motivation• Calculate microwave rotational transition frequencies

with confidence intervals up to J = 50 for the 0-0, 1-1, 2-2, and 3-3 bands using experimental energy levels derived from measured transition frequencies

• Compare them with data in COLOGNE1, JPL2, NIST3, and HITRAN4 databanks

1) H.S.P. Muller et al, J Mol Struct 742 215–227 (2005)2) H.M. Pickett et al, JPL Catalog (2000) , spec.jpl.nasa.gov3) F.J. Lovas, www.nist.gov/physlab/data/msd-di/index.cfm4) L.S. Rothman et al, JQSRT, 110, 553 (2009)

Experimental energy levelsMeasured transition frequencies and

measurement uncertainties collected from the literature

s s si j i j i jc v E E

exp exp, { , }, i iE E C

exp exp

exp 2 exp 2 exp exp( ) ( ) 2

i j i j

i j i j ij i j

v E E

v E E C E E

Derivation of energy levelsi j i jv E E Ideally:

s s s si j i j i j i jc v E E In reality:

More detail in S.A. Tashkun et al JQSRT 111, 1106 (2010)

cs – correction factors for some spectra (for microwave spectra cs=0)si j - measurement uncertaintysi j - pressure induced shift

s s si j i j i jc v E E Finally: cs , {E} are unknowns

Portrait of the correlation matrixValues and uncertainties of experimental energy levels Ntra = 15797

Nlev = 2247Χ = 0.71

assign RITZ(MHz) unc(KHz) COLOGNE(MHz) unc(KHz) JPL(MHz) unc(KHz) NIST(MHz) unc(KHz) 1 0 115271.2017 0.3 115271.2018 0.5 115271.2018 0.5 115271.202 2.0 2 1 230538.0001 0.4 230538.0000 0.5 230538.0000 0.5 230538.000 2.0 3 2 345795.9902 0.4 345795.9899 0.5 345795.9899 0.5 345795.991 2.0 4 3 461040.7682 0.3 461040.7682 0.5 461040.7682 0.5 461040.770 2.0 5 4 576267.9304 0.3 576267.9305 0.5 576267.9305 0.5 576267.922 32.0 6 5 691473.0765 0.4 691473.0763 0.5 691473.0763 0.5 691473.090 12.0 7 6 806651.8057 3.2 806651.806 5.0 806651.806 5.0 806651.719 10.0 8 7 921799.7027 3.1 921799.700 5.0 921799.700 5.0 921799.711 10.0 9 8 1036912.3958 3.1 1036912.393 5.0 1036912.393 5.0 1036912.403 10.010 9 1151985.4533 5.5 1151985.452 11.0 1151985.452 1.0 1151985.454 11.01110 1267014.4895 3.2 1267014.486 5.0 1267014.486 5.0 1267014.504 10.01211 1381995.1069 6.4 1381995.105 13.0 1381995.105 13.0 1381995.110 13.01312 1496922.9122 6.0 1496922.909 12.0 1496922.909 12.0 1496922.915 12.01413 1611793.5178 5.6 1611793.518 11.0 1611793.518 11.0 1611793.517 11.01514 1726602.5082 40.5 1726602.507 1.51615 1841345.5091 5.5 1841345.506 11.0 1841345.506 11.0 1841345.512 11.01716 1956018.1407 5.5 1956018.139 11.0 1956018.139 11.0 1956018.142 11.01817 2070615.9957 7.0 2070615.993 14.0 2070615.993 14.0 2070615.998 14.01918 2185134.6823 6.5 2185134.680 13.0 2185134.680 13.0 2185134.685 13.02019 2299569.8435 5.0 2299569.842 10.0 2299569.842 10.0 2299569.865 10.02120 2413917.1158 5.5 2413917.113 11.0 2413917.113 11.0 2413917.118 11.02221 2528172.0603 5.5 2528172.060 11.0 2528172.060 11.0 2528172.060 11.02322 2642330.5358 356. 2642330.346 3.72423 2756387.5871 8.5 2756387.584 17.0 2756387.584 17.0 2756387.590 17.02524 2870339.4106 6.5 2870339.407 13.0 2870339.407 13.0 2870339.414 13.02625 2984181.4585 7.0 2984181.455 14.0 2984181.455 14.0 2984181.461 14.02726 3097909.3640 8.5 3097909.361 17.0 3097909.361 17.0 3097909.360 17.02827 3211518.6908 851. 3211518.750 4.22928 3325011.0883 1020. 3325005.282 4.23029 3438364.6145 5.0 3438364.611 10.0 3438364.611 10.0 3438364.618 10.03130 3551592.3631 5.0 3551592.361 10.0 3551592.361 10.0 3551592.365 10.03231 3664685.1208 1406. 3664684.179 5.03332 3777635.7295 8.0 3777635.728 16.0 3777635.728 16.0 3777635.731 16.03433 3890442.7214 6.5 3890442.717 13.0 3890442.717 13.0 3890442.744 13.03534 4003102.9236 1681. 4003100.789 8.93635 4115605.5887 11.0 4115605.585 22.0 4115605.585 22.0 4115605.592 22.03736 4227955.2821 1743. 4227952.780 14.038 37 4340138.1181 22.0 4340138.112 43.0 4340138.112 43.0 4340138.124 43.0

Pure rotational spectrumBlue – measured frequencies; red – calculated frequencies

Pure rotational spectrum (extrapolation)

assign RITZ(MHz) unc(KHz) JPL(MHz) unc(KHz) RITZ - JPL(KHz)3938 4452159.358 2327. 4452157.136 21.2 2223.4039 4564002.889 3170. 4564005.660 25.8 -2772.4140 4675677.306 4584. 4675679.336 30.9 -2029.4241 4787169.751 5590. 4787173.860 36.9 -4109.4342 4898488.830 5723. 4898484.933 43.5 3897.4443 5009605.681 6255. 5009608.264 51.0 -2583.4544 5120550.571 6714. 5120539.564 59.4 11006.4645 5231255.602 7003. 5231274.551 68.8 -18949.4746 5341799.211 7102. 5341808.947 79.2 -9736.4847 5452151.699 7585. 5452138.482 90.8 13217.4948 5562363.412 9337. 5562258.888 103.5 104524.5049 5672073.401 10045. 5672165.908 117.5 -92507.

Energy levels:E0,49 = 4673.54169 ± 0.00048 cm-1 Ntra = 6 Refs: a b c d e fE0,48 = 4488.00156 ± 0.00046 cm-1 Ntra = 10 Refs: a b c d e f g

a 1.0 R. Farrenq et al, JMS 149, 375 (1991); FT/solar absorption filter 2b 0.99999990 R. Farrenq et al, JMS 149, 375 (1991); FT/solar absorption filter 3c 0.99999990 R. Farrenq et al, JMS 149, 375 (1991); FT/solar absorption filter 4d 1.0 G. Guelachvili et al, JMS 98, 64 (1983) FT/set Ce 1.0 A.W. Mantz and J.P. Maillard, JMS 53, 466 (1974); FT/emission f 1.00000030 D.H. Rank et al, JMS 18, 418 (1965)g 0.99999980 D.H. Rank et al, JMS 4, 518 (1960)

Consider: 49 48 5562363.412 9337. 5562258.888 103.5 104524.

F.J. Lovas, NIST recommended rest frequencies for observed inter-stellar molecular microwave transitions-2002 revision. J. Phys. Chem. Ref. Data, 33, 177 (2004)

RITZ vs HITRAN-2008

Residuals Uncertainties

zoom

100 microwave transitionsspectral range 3.8 – 189.2 cm-1

intensity range 3.19 10-33 - 1.45 10-21 cm/moleculeposition uncertainty 10-4 – 10-5 cm-1

Conclusions• Microwave transition frequencies of the 0-0,1-1,2-2,

and 3-3 bands up to J=50 calculated from experimental energy levels* were presented.

• Each frequency is given together with 99% confidence interval.

• A comparison of calculated data and data from COLOGNE, JPL, NIST, and HITRAN databanks revealed a number of discrepancies which should be removed in future releases of these databanks

*) S.A. Tashkun et al JQSRT 111, 1106 (2010)

Financial supportWe acknowledge support from a joint RFBR (09-05-92508-ИК_а) and CRDF (RUG1-2954-TO-09) grant.