1. Molecular Spectroscopy Symposium 2010 21-25 June 2010 Can the Inversion-Vibration-Rotation Problem in the 4 and 2 2 States of NH 3 be solved to Experimental Accuracy? J.C. Pearson, S. Yu & B.J. Drouin Jet Propulsion Laboratory, California Institute of Technology, Pasadena CA 91109 O. Pirali, M.-A. Martin, M. Vervloet & D. Balcon Ligne Ailes-Synchrotron SOLEIL, L’Ormes de Merisiers Saint- Aubin, 91192 Gif-sur-Yvette, France C.P. Enders I. Physikalisches Insitut, Universität zu Köln, 50937 Köln, Germany

2. 2 Molecular Spectroscopy Symposium 2010 21-25 June 2010 Motivation Coupling between Large Amplitude (LAM) and Small Amplitude Vibrational motions is an incompletely solved problem – C 3V case cannot achieve experimental accuracy  Series do not converge  Unclear if there is a numerically practical solution NH 3 inversion-normal vibration quantum mechanics worked out in detail – Simpler than 3-fold motion – See Urban, 1988, JMS 131, 133 and references therein Two previous global attempts ignored 169 microwave transitions and did not achieve experimental accuracy (factor of ~10) – Sasada et al., 1992, JMS 151, 33 – Cottaz et al., 2000, JMS 203, 285 It was not apparent that the LAM-normal vibration problem could be solved to experimental accuracy – higher NH 3 states are even more problematic Previous NH 3 attempts also had problems with convergence – Basis set issue or incompletely characterized interactions?

3. 3 Molecular Spectroscopy Symposium 2010 21-25 June 2010 2 2 and 4 GS- 4 band is strong, while GS-2 2 is weak with the S-A part being very weak Hot band 2 2 - 2 and 2 2 -2 2 are strong S state of 2 2 is strongly mixed with 4 A state of 2 2 is free of 4 at low J Ground State and 2 known to high J

4. 4 Molecular Spectroscopy Symposium 2010 21-25 June 2010 Data Sets Historical 2 2 and 4 band data –Cottaz et al., 2000, JMS 203, 285 –Sasada et al., 1992, JMS 151, 33 (inc microwave lines) –Lellouch et al., 1987, JMS 124, 333 (inc new assignments) –Papoušek et al., 1986, J. Mol. Struct. 141, 361 –Urban et al., 1984, Can. J. Phys 62, 1775 –Weber et al., 1984, JMS 107, 405 Historical Hot band 2 2 - 2 data –D’Cunha, 1987, JMS 122, 130 –Hermanussen, Bizzarri & Baldacchini, 1986, JMS 119, 291 (inc new assignments) –Sasada et al., 1986, JMS 117, 317 Historical laser measurements –Chu, Li, & Cheo, 1994, JSQRT 51, 591 –Hillman, Jennings, & Faris, 1979, Appl. Opt. 18, 1808 –Kostiuk et al., 1977, IR Phys. 17, 431 –Sattler et al., 1981, JMS 88, 347 & JMS 90, 297 –Nereson, 1978, JMS 69, 489 –Bischel, Kelly, & Rhodes, 1976, Phys. Rev. A 13, 1829

5. 5 Molecular Spectroscopy Symposium 2010 21-25 June 2010 New Data AC Discharge Emission Spectrum 20-650cm -1 –Pirali & Vervloet, 2006, Chem. Phys. Lett. 423, 376 Long path low pressure Synchrotron absorption Spectrum 20-650cm -1 ~2000 new lines assigned –Rotation-Inversion 2 2 -2 2, 4 -2 2, 4 - 4 –Hot bands 4 - 2 & 2 2 - 2 10 6 -10 7 2 2 S- 4 S l =1 10 1 -9 1 4 A-S l =-1 11 6 -10 5 4 S l =1-2 2 S 10 7 -9 8 2 2 S- 4 S l =1 11 7 -10 6 2 2 S- 4 S l =1 10 5 -10 4 4 S l =1-2 2 S 10 8 -9 9 2 2 S- 4 S l =1 12 7 -11 7 2 S-A

6. 6 Molecular Spectroscopy Symposium 2010 21-25 June 2010 Symmetry Allowed Interactions Coriolis Interaction 2 2 - 4 (K- l )=0,6,12,… (A-S or S-A)   K=  l =±1 in Hamiltonian   K=+/-5,  l =-/+1 &  K=+/-7,  l =+/-1 and higher are not in Hamiltonian L-type Interaction 4 - 4 (K- l )=0 (A-A or S-S)   K=  l =±2 in Hamiltonian K-type Interaction 4 - 4 (K- l )=6,12,… (A-A or S-S)   K=+/-4,  l =-/+2 &  K=+/-8,  l =-/+2 in Hamiltonian   K=+/-10,  l =-/+2 &  K=+/-14,  l =-/+2 and higher are not in Hamiltonian  K=3 Interaction 2 2 -2 2 & 4 - 4 (K-( l =0))=3,9,… (A-S or S-A)   K=+/-1,  l =-/+2 &  K=3,  l =0 in Hamiltonian   K=+/-5,  l =+/-2 &  K=+/-7,  l =-/+2 and higher are not in Hamiltonian  K=3 Interaction 2 2 - 4 (K- l )=3,9,… (A-A or S-S)   K=+/-2,  l =-/+1 &  K=+/-4,  l =+/-1 in Hamiltonian   K=+/-8,  l =-/+1 &  K=+/-10,  l =-/+1 and higher are not in Hamiltonian

7. 7 Molecular Spectroscopy Symposium 2010 21-25 June 2010 Hamiltonian Matrix 2 2 S Rot  K=6,12 2 2 A Rot  K=6,12 4 S l =1 Rot  K=6,12 4 S l =-1 Rot  K=6,12 4 A l =1 Rot  K=6,12 4 A l =-1 Rot  K=6,12  K=3,9  l =0 (K- l )=0,6 (K- l )=3,9  K=3,9  l =0  K=3,9  l =0 (K- l )=3,9 (K- l )=0,6 Rotation Inversion Hamiltonian elements Same Colors are same Matrix elements

8. 8 Molecular Spectroscopy Symposium 2010 21-25 June 2010 What is in the available data 1/3? Interactions 2 2, S with 4  K=-8,-2,4,10 with 4, S, l =1   K=-2, K= 3 & 1, 4 & 2, 5 & 3, 6 & 4 starting at J=16 and progressing to higher J’s   K=-8,4,10 do not cross below J=20  K=-4,2,8 with 4, S, l =-1   K=2 K= 0 & 2 cross at J=13   K=-4 will start crossing at J>20  K=-5,1,7 with 4, A, l =1 (  K=1 dominates J=9-11)   K=1 Crossings K=1&2 J=11, K=2&3 J=11, K=3&4 J=11, K=4&5 J=10, K=5&6 J=10, K=6&7 J=10, K=7&8 J=9, K=8&9 J=9, K=9&10 J=10, K=10&11 J=11, K=11&12 J=12,….   K=-5,7 do not cross below J=20  K=1,5 with 4, A, l =-1 (no direct crossings in data)   K=1 at lowest K first, high J~20 Interactions 2 2 S with 2 2 A  K=3 2 2 S with 2 2 A  K=7&4 J=19, K=8&5 J=19, K=9&6 J=18, K=10&7 J=17, K=11&8 J=16, K=12&9 J=15, K=13&10 J=15, more at higher J

9. 9 Molecular Spectroscopy Symposium 2010 21-25 June 2010 What is in the available data 2/3? Interactions 2 2, A with 4  K=-5,1,7 with 4 S, l=1   K=1 None until J>20   K=-5 K=6 & 1 at J=16, K=7 & 2 at J=18, and K=8 & 3 at J=14   K=7 None below J=20  K=-7,1,7 with 4 S, l=-1   K=-7 K=7 & 0 at J=13, K=8 & 1 at J=9   K=1 K>14 at ~J=20   K=7 None below J=20  K=-8,-2,4,10 with 4 A, l=1   K=-2 K=10-14 with 8-12 at J=16-20 more higher   K=-8, 4, 10 none below J=20  K=-10,-4,2,8 with 4 A, l=-1   K=-4 K=5-10 with 1-6 at J=12-20   K=-10,2,8 none below J=20 Interactions 4 A-S l =1 and l =-1  K=-3,3 for l =1 & l =1 and l =-1 & l =-1  No crossings below J=20

10. 10 Molecular Spectroscopy Symposium 2010 21-25 June 2010 What is in the available data 3/3? Interactions within 4 S, l =1 with S, l =-1;  K=-8,-2,4,10  No crossings observed for any interacting levels S, l =1 with A l =-1;  K=-5,1,7   K=1 K=1 & 2 at J=9, K=2 & 3 at J=12, K=3 & 4 at J=16, K=4 & 5 at J=19   K=-5,7 No crossings below J=20 S, l =-1 with A, l =1;  K=-7,-1,5   K=1 K=2 & 1 J=10, K=3 & 2 J=14, K=4 & 3 J=17 more above J=20   K=-7, 5 No crossings below J=20 A, l =1 with A, l =-1;  K=-8,-2,4,10   K=4 lowest K’s first starting ~J=20   K=-8,-2,10 No crossings below J=20

11. 11 Molecular Spectroscopy Symposium 2010 21-25 June 2010 Determination of Elements 2 2 S Rot  K=6,12 2 2 A Rot  K=6,12 4 S l =1 Rot  K=6,12 4 S l =-1 Rot  K=6,12 4 A l =1 Rot  K=6,12 4 A l =-1 Rot  K=6,12  K=3,9  l =0  K=3 (K- l )=0,6  K=1 (K- l )=0,6  K=-1 (K- l )=0,6  K=1  K=-5* (K- l )=0,6  K=-1  K=-7* (K- l )=3,9  K=-2  K=4 (K- l )=3,9  K=-4  K=2 (K- l )=3,9  K=-2  K=4 (K- l )=3,9  K=-4  K=2  K=3,9  l =0  K=3  K=3,9  l =0  K=3 (K- l )=3,9  K=1 (K- l )=3,9  K=-1 (K- l )=0,6  K=-2  K=4 (K- l )=0,6  K=-2  K=4 Red No Crossings to J=20 Yellow J>15 Crossings Green J<15 Crossings *Not in previous Hamiltonians

12. 12 Molecular Spectroscopy Symposium 2010 21-25 June 2010 Are level crossings required? GS and 2 states require  K=3 terms between A and S –Well determined including distortion GS and 2 states require  K=6 terms within A and S –Well determined including distortion Higher order terms were not needed in the GS and 2 states These terms slow down convergence All terms in 2 2 / 4 Hamiltonian are well determined –Often higher order distortion better determined than lower order Fit quality improves with more terms Still systematic problems at lowest K’s –More terms are probably needed More high quality data clearly helps the overall fit and reduces correlations –Need to include all  (K- l )=0,3 & 6 interaction –The  (K- l )=9 and 12 may also ultimately be required at J>20

13. 13 Molecular Spectroscopy Symposium 2010 21-25 June 2010 So Can 2 2 and 4 be Fit? (maybe) Best reduced RMS fitting all available data is 4.0 –Converges reasonable well –Errors show systematic problems –Highest J data does have some problems –Microwave RMS is just over 500 kHz or a reduced RMS of ~100 Reduced RMS is 1.4 letting it reject 250 of 8000 lines –Systematic problems –Not all constants in the fit –Convergence is not ideal –About half of the microwave lines are ejected All constants are well determined Convergence is slow Almost certainly requires additional terms Additional microwave data to constrain more constants would be valuable –Especially at the lowest K values

14. 14 Molecular Spectroscopy Symposium 2010 21-25 June 2010 Future Work Transitions to J>20 are in discharge spectrum –These will have to be assigned one J at a time due to the interactions Numerous new microwave transitions are available –Rotation inversion in 2 2 –Rotation inversion in 4 –Inversion in 4 –Rotation inversion between 2 2 and 4 –Inversion between 2 2 and 4 Additional long path spectra are also planned –Needed is more hot band information on 2 2

15. 15 Molecular Spectroscopy Symposium 2010 21-25 June 2010 Acknowledgement This work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration