Xinchuan Huang,1 David W. Schwenke,2 Timothy J. Lee2

1 SETI Institute, Mountain View, CA 94043, USA2 NASA Ames Research Center, Moffett Field, CA 94035, USA

Columbus, Ohio

June 25, 2010

The 65th International Symposium on Molecular Spectroscopy

Toward Accurate Rovibrational Energy Levels of 12C16O2

--- Start-up for CO2 IR Linelist Project

2Funding

Venus Express Supporting Investigator2

Motivation Venus Express data analysisSpectrum analysis/simulation for Venus environment

Goal: High energy & high temperature IR Linelists (up to 20,000 cm-1 above ZPE, 750K, 100bar) (Position: 0.03 cm-1; Intensity: 90%; line shape) Can make reliable predictions with SAME Accuracy!

Research Strategy: Refine high-quality ab initio PES/DMS with high-res experimental data --- Best Theory + High-res Exp

3

14NH3: Two-orders-of-magnitude Improvement

0 1500 3000 4500 6000

0

2

4

6

Cal

c -

Exp

/ c

m-1

Rovibrational levels / cm-1

0 1500 3000 4500 6000

0.0

0.2

0.4

0.6

Cal

c -

Exp

/ c

m-1

Rovibrational levels / cm-1

0 1500 3000 4500 6000

0.0

0.2

0.4

0.6

Rovibrational levels / cm-1

Cal

c -

Exp

/ c

m-1

Pure ab initio (published) HSL-0, RMS= 2-3 cm-1

1st refinement (published)HSL-1, RMS= 0.1-0.3 cm-1

2nd refinement (submitted) HSL-2, RMS= 0.01-0.02 cm-1

0 1000 2000 3000 4000 5000-1

0

1

2

3

4

5

6

J=0 J=1 J=2 J=3 J=4

Calc - E

xp

/ cm

-1

Rovibrational levels / cm-1

E / cm-1 E / cm-1 E / cm-1

0 1000 2000 3000 4000 5000-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06J=0 J=1 J=2 J=3

J=4 J=5 J=6

Calc - E

xp / cm

-1

Rovibrational levels / cm-1

0 1000 2000 3000 4000 5000-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06J=0 J=1 J=2 J=3

J=4 J=5 J=6

Calc - E

xp / cm

-1

Rovibrational levels / cm-1

6 0.6 0.6

JNo. of All IR States

No. of HITRAN States

No. of Missing States

RMS

(s/a)(cm-1)

RMS

(splits)(cm-1)

0-6 1030 1005 25 0.015 0.0117 315 294 21 0.020 0.0148 357 328 29 0.023 0.0159 399 329 70 <0.028 <0.022

10 441 341 100 <0.039 <0.02912 525 274 251 <0.043 <0.032

J“Cold” band Lines

RMS

(cm-1)

Hot-band Lines

RMS

(cm-1)

0-6 3087 0.017 1011 0.0390-7 4662 0.018 1385 0.0400-8 6002 0.020 1790 0.042

50-75% HITRAN levels and 31% transitions have been analyzed!new Bands; 15NH3; new assignments; …

4

HITRAN2008 data for 12C16O2

Thank all the contributors, for your invaluable work! Otherwise we can NEVER imagine a “refinement”!

Incomplete List of references ……

Rothman et al --J. Quant. Spectrosc. Rad. Transfer 48 (1992) 537Miller & Brown -- J. Mol. Spectrosc. 228 (2004) 329Perevalov & Tashkun, “CDSD-296 (Carbon Dioxide Spectroscopic Databank): Updated and Enlarged Version for Atmospheric Applications,” 10th HITRAN Database Conference, Cambridge MA, USA (2008). Rothman et al -- J. Quant. Spectrosc. Rad. Transfer 110 (2009) 572

……

Accuracy will depend on and are limited by high-res data

No. of transitions: 128,117 (CDSD2008-296 incorporated)No. of energy levels: 14,809 0 – 14320 cm-1, J = 0 – 125 291 vib states (lower J = 0 – 39)

5

HITRAN08 is great! but not enough …

0 25 50 75 100 1250

100

200

300

4000 25 50 75 100 125

J

No.

of

leve

ls in

HIT

RA

N08

No. of 12C16O2 levels

at every single J

Highest energy

at every single J

0

4000

8000

12000

16000 Highest E

nergy at each J /cm-1

Distribution of HITRAN08 Energy levels

6

Ab initio PES/DMS

CCSD(T)/ACPF/MRCI for energiesCCSD(T) and ACPF for dipole(aug-)cc-pC(V)XZ basis, X=T,Q,5

E = Long-range terms (Morse-type) + Short-range terms * damping func

219 unique coeffs, i,j,k 8, i+j+k 12, i j 551 selected geometriesHigher weights on 472 points < 40,000 cm-1

REQ(CO) = 1.159080 Å (grid) 1.161287 Å (initial PES) 1.159179 Å (1st refined PES) 1.160239 Å (2nd refined PES) ……

Final DMS: CCSD(T)/aug-cc-pVQZ

Fitting error distribution

7

Dipole is ready! Now find a best starting PES

8

Before and after 1st refinement with J=0-4 levels

0 5000 10000 15000 20000 25000 30000-15

0

15

30

45 Starting PES 1st refinement

(J=0-4 included)

Cal

c -

Exp

/ c

m-1

Experimental Levels / cm-1

Fit J=0 only: rms = 0.003 cm-1

for 31 levels

Fit J=0-4 only --- 1st

rms = 0.016 cm-1

for 553 levels

All higher energy band origins (observed & predicted) in Rothman et al (1992) can be included except for 3 bands above 20,000 cm-1

coeff changes < 1%

Exact Variational rovibrational CI for all calculations

HITRAN08

Rothman et al 1992

9

Compare to present HITRAN database --- should we go to J=100 next?

0 3000 6000 9000 12000 15000-4

-2

0

2

4

J = 0 - 4 J = 0, 5, 10, 15, ..., 95

1st r

efin

ed P

ES

- H

ITR

AN

/ c

m-1

HITRAN Levels / cm-1

10

2nd refinement: after many failures …

0 3000 6000 9000 12000 15000-4

-2

0

2

4

J = 0 - 10 J = 0, 5, 10, 15, ..., 95

HITRAN Levels / cm-1

2nd

refin

ed P

ES

- H

ITR

AN

/ c

m-1 Can NOT include

ALL levels derived from HITRAN08 if J > 40

Outliers around ~9000 cm-1:(1) convergence in our calculations(2) predictions in HITRAN models

J=0-10 data completely included, rms = 0.015 cm-1 on 1804+24 levels

Approximately, 3-4% HITRAN levels were excluded from J=0 – 95 statistics

11

Identify outliers / convergence defects

~800 levels0.079 cm-1

0.015cm-1

~2800 levels0.090 cm-1

J=0,5,…50~2000 levels0.036 cm-1

J=51-95~3100 levels0.136 cm-1

Remove Outliers & Convergence Defects!

Overall 0.071 cm-1

12

Agreement on n3 overtones, n=0-5

-0.45 -0.30 -0.15 0.000

3000

6000

9000

12000

15000-0.45 -0.30 -0.15 0.00

Calc - HITRAN / cm-1

Ene

rgy

/ cm

-1

50

60

70

80

90

100J

53

43

33

3

23

GS

13

Data Selection for 3rd refinement

50 65 80 95-6

-4

-2

0

2

4

6

Cal

c -

HIT

RA

N /

cm-1

J

Safe pool: 3094 of 4293 levels 50<J95 72.1% + 1990 of 2037 levels J=0,5,..,50 97.7%

14

Goal Accurate high-energy & high-temperature IR line list for all

CO2 isotopomers including line shape parameters

Current Stage 0.015 / 0.036 cm-1 agreements for J = 0 – 10/50 0.07 cm-1 overall accuracy for J up to 95.

Future work Use experimentally measured transitions/levels ONLY Higher energy/J refinement with careful selection, ~9000 cm-1 Nonadiabatic corrections may be necessary for

isotopologues IR Intensity will be done as soon as J up to 40 are

solved! 14

Summary & Next Step