Towards a Global Fit of the Combined Millimeterwave

Towards a Global Fit of the Combined Millimeter-wave and High Resolution FTIR Data for the Lowest Eight Vibrational States of Hydrazoic Acid (HN 3) International Symposium of Molecular Spectroscopy, Urbana-Champaign, Illinois June 26, 2015 Brent K. Amberger, R. Claude Woods, Brian J. Esselman, Robert J. Mc. Mahon, Department of Chemistry, University of Wisconsin, Madison

Our Equilibrium Structure Determination of HN 3 Observations between 235 -450 GHz at room temperature -14 Isotopologues Studied -High level corrections for vibrationrotation interactions, xrefit in CFOUR used for structure determination (John Stanton)

Available HN 3 Transitions in our Range 260 -360 GHz a-type R branches b-type R and P branches

HN 3 Ground R-Branch Spectrum predicted K=1 from single state fit of K=0 through K=5 J= 13 12 K=1 K=0 K=2 K=3 K=10 K=9 K=8 K=7 K=6 K=5 K=4 K=1 Actual Assignments K=2 K=3 K=8 K=1 K=0 K=10 K=7 K=4 K=5 K=9 K=6 Perturbed lines are often very perturbed The highly perturbed lines are also the lowest intensity lines

Ground and Excited Vibrational State Transitions

Vibrational States and Perturbations Gc (Coriolis) 1266. 6 cm-1 ~1213 cm-1 1147. 40 cm-1 ~1143. 5 cm-1 ~1074 cm-1 Fermi Resonance Ga, Fa, Gb (Coriolis) 606. 4 cm-1 537. 3 cm-1 Fermi Resonance ν 3 2ν 6 ν 4 Ga, Fa, Gb (Coriolis) ν 5+ ν 6 G , F , G (Coriolis) 2ν 5 a a b Centrifugal Distortion (W 05) ν 6 Ga, Fa Gb (Coriolis) ν 5 Centrifugal Distortion (W 05) 0 cm-1 Ground

Extremely Useful Prior Infrared Studies Pure rotational ground state far IR Bendtsen, J. ; Nicolaisen F. M. , Journal of Molecular Spectroscopy 1986, 119, 456 -466. FTIR spectra and analysis of ν 5, ν 6 and ground state (i) Bendtsen, J. ; Hegelund, F. ; Nicolaisen, F. M. , Journal of Molecular Spectroscopy 1986, 118, 121 -131. (ii)Hegelund, F. ; Bendtsen, J. , Journal of Molecular Spectroscopy 1987, 124, 306 -316. IR spectrum of ν 4 Bendtsen, J. ; Nicolaisen, F. M. Journal of Molecular Spectroscopy 1989, 133, 193 -200. FTIR spectra and analysis of ν 3 and ν 4 Bendtsen, J. ; Nicolaisen, F. M. , Journal of Molecular Spectroscopy 1992, 152, 101 -108 Tunable diode laser spectrum of ν 3 Yamada, K. and Takami, M. , Journal of Molecular Spectroscopy 1980 84, 431 -446. BUT….

Energy (cm-1) K Energies for the Vibrational States K 2

Energy (cm-1) K Energies for the Vibrational States K 2

Using IR data to Find Pure Rotational Transitions 13 3 10 12 3 9 ν 5 Finding HN 3 v 5 13 3 10 – 12 3 9 13 3 10 12 3 9 P- branch IR transitions R- branch IR transitions 14 3 11 13 3 10 12 3 9 11 3 8 309933 MHz Ground state 309937 MHz

Frequency/JUp (MHz) 0 100 Steep negative slope 200 300 Jup 2 positive slope! 0 100 200 Jup 2 300 400 Steep negative slope 0 400 K=2 plus of ν 5 23 860 23 858 23 856 23 854 23 852 23 850 23 848 23 846 23 844 23 842 23 840 K=2 minus of ν 5 23850 23848 23846 23844 23842 23840 23838 23836 23834 23832 23830 Frequency/JUp (MHz) K=0 of ν 5 23840 23838 23836 23834 23832 23830 23828 23826 23824 23822 23820 Frequency/JUp (MHz) Linear Plots of Freq/Jup vs. Jup 2 100 K=5 of ν 5 23833 23831 23829 23827 23825 23823 23821 23819 23817 23815 0 100 200 Jup 2 300 400 modest negative slope (most common) 200 Jup 2 300 400

Frequency/ JUp (MHz) Examples of Perturbed K-States K=7 of ν 5 23 926 23 924 23 922 23 920 23 918 23 916 23 914 23 912 23 910 23 908 23 906 Steep negative slope (highly perturbed) 0 Frequency/ JUp (MHz) 23 590 50 100 150 JUp 2 200 250 300 350 Positive slope (highly perturbed) K=8 of ground state 23 585 23 580 23 575 23 570 0 50 100 150 JUp 2 200 250 These two mutually perturbing states are easily recognized as perturbed due to abnormal slopes for their K values.

Intercepts of Linear Plots vs. K 2 Ground State 23950 Frequency (MHz) 23900 23850 23800 23750 23700 23650 23600 23550 Frequency (MHz) 0 20 40 K 2 60 80 100 ν 5 24050 23950 23850 23750 23650 23550 23450 23350 0 20 40 K 2 60 80 100

Previous slide average shifted by one in K Average of ground state (K+1) & ν 5 (K) intercepts 23850 23800 MHz 23750 23700 23650 23600 23550 0 20 40 60 80 100 K 2 The average is much smoother than either separately. 120

A 3 -State Fit of Millimeter-wave Data: Ground, ν 5, and ν 6 Ground State ν 5 (537. 3 cm-1) Perturbation Terms ν 6 (606. 4 cm-1) A (MHz) 610740. 770(86) A (MHz) 589939. (25) A (MHz) 622737. (25) Ga /MHz 1140200. (400) B (MHz) 12034. 570(35) B (MHz) 12067. 591(85) B (MHz) 12034. 340(90) Fa /MHz 7. 28(71) C (MHz) 11781. 109(35) C (MHz) 11784. 766(85) C (MHz) 11802. 444(90) Gb /MHz 1912. 1(13) ΔJ (k. Hz) 4. 8886(25) ΔJ (k. Hz) 4. 7422(33) ΔJ (k. Hz) 5. 2144(52) W 05 1034. 4(43) ΔJK (k. Hz) 669. 451(73) ΔJK (k. Hz) -958. 92(43) ΔJK (k. Hz) 2686. 51(43) ΔK (k. Hz) -25131. (66) ΔK (k. Hz) -84990. (690) ΔK (k. Hz) -872710. (1170) δJ (k. Hz) 0. 09413(78) δJ (k. Hz) -0. 06842(86) δJ (k. Hz) -0. 1968(27) δK (k. Hz) 201. (17) δK (k. Hz) 416. (18) δK (k. Hz) 371. (20) ΦJ (Hz) -0. 0017(19) ΦJ (Hz) -0. 1222(29) ΦJ (Hz) -0. 1446(59) ΦJK (Hz) -1. 17(10) ΦJK (Hz) 35. 04(27) ΦJK (Hz) -22. 03(36) ΦKJ (Hz) 579. 0(27) ΦKJ (Hz) -27927. (11) ΦKJ (Hz) 25958. (13) E (MHz) [0] E (MHz) [16106800] E (MHz) [18178100] N lines 132 N lines 136 N lines 82 σ (MHz) 0. 36 σ (MHz) 0. 77 σ (MHz) 1. 05 Energies of states were fixed 11 parameters per state X 3 4 Perturbation terms 350 total transitions including a and b type…. σ = 0. 73 MHz

The Higher Excited Vibrational States Gc (Coriolis) 1266. 6 cm-1 ~1213 cm-1 1147. 40 cm-1 ~1143. 5 cm-1 ~1074 cm-1 Fermi Resonance Ga, Fa, Gb (Coriolis) 606. 4 cm-1 537. 3 cm-1 HN 3 Fermi Resonance ν 3 2ν 6 Ga, Fa, Gb (Coriolis) ν 4 ν 5 + ν 6 Ga, Fa, Gb (Coriolis) 2ν 5 Centrifugal Distortion (W 05) Ga, Fa, Gb (Coriolis) ν 6 ν 5 Centrifugal Distortion (W 05) 0 cm-1 Ground

Infrared and Microwave Patterns are the Same for ν 3 and ν 4 ΔB 4 and ΔB 3 vs K 2 40, 00 20, 00 0 10 20 -20, 00 30 40 ν 3 -40, 00 ν 4 -60, 00 -80, 00 -100, 00 Bendtsen, J. ; Nicolaisen, F. M. , Journal of Molecular Spectroscopy 1992, 152, 101 -108 K 2 ΔB 4 = (B+C)K of ν 4 – (B+C)K of ground state ΔB 3 = (B+C)K of ν 3 – (B+C)K of ground state

Infrared – Microwave (B+C)K for ν 3 and ν 4 IR – MMW (MHz) ν 3 IR (B+C) vs mic intercepts (MHz) vs K 2 70 60 50 40 30 20 10 0 0 5 10 15 20 K 2 25 30 35 40 IR – MMW (MHz) ν 4 IR (B+C) - mic intercepts (MHz) vs K 2 70 60 50 40 30 20 10 0 0 5 10 15 20 K 2 25 30 35 40

Adding ν 3 and ν 4 (with K shifted by 1) Average of ν 3, K-1 and ν 4, K (B+C)K's 23 800 Frequency (MHz) 23 780 23 760 23 740 23 720 23 700 23 680 23 660 23 640 0 Bendtsen, J. ; Nicolaisen, F. M. , Journal of Molecular Spectroscopy 1992, 152, 101 -108 1 2 3 K 4 5 6 7 Consistent with the ΔK = 1 selection rules for c-type Coriolis resonance (Gc)

b-type transitions for ν 3 and ν 4 b-type P-branch lines for K=0 to 1 obs prediction 300 0 -1 0 5 10 15 b-type P-branch ν 3 K=0 to 1 obs-IR prediction 20 250 -2 200 -3 -4 14 1 14 - 15 0 15 15 1 15 - 16 0 16 16 1 16 - 17 0 17 17 1 17 - 18 0 18 18 1 18 - 19 0 19 -5 -6 -7 -8 24 1 24 - 25 0 25 25 1 25 - 26 0 26 26 1 26 - 27 0 27 27 1 27 - 28 0 28 28 1 28 --29 0 29 150 100 R 2 = 0, 9974 -9 50 0 0 1 2 3 ν 3 Q-branch obs first differences 1600 Perturbations bring a Q-branch series for ν 3 into our range. 1400 1200 1000 b-type lines with J values ranging from 1 to 12. 800 600 400 200 0 -15 -20 -25 0 0 2 4 6 8 10 12 -30 5 6 b-type K=0 to 1 Q-branches of ν 3 obs -IR prediction -5 -10 4 5 10 15

Confident Assignment of the 2ν 5 R-series Intercepts for 2ν 5 vs K 2 Trendline on linear (less perturbed) region gives access to: 23890 R 2 = 0, 9999 Frequency (MHz) 23880 Intercept = B+C 23870 23860 Slope = -ΔJK 23850 23840 Fermi Resonance with ν 4 23830 23820 23810 0 10 20 30 K 2 40 50 60

Next Steps 1)Obtain solid assignments of a-type R-branches for ν 5+ν 6 and 2ν 6. 2)Find assign b-type transitions for 2ν 5, ν 5+ν 6, and 2ν 6. 3) Use linear least-squares plots to obtain as many initial values for as many parameters as possible. 4)Obtain 5 -state non-linear least-squares fit (SPFIT) for higher energy excited vibrational states. Determine the critical perturbation parameters for these higher states 5)Ultimately obtain an 8 -state global fit (“The Holy Grail”).

Thanks for Listening! The Research Group Professor Bob Mc. Mahon Professor Claude Woods Dr. Brian Esselman Brent Amberger Ben Haenni Zachary Heim Steph Knezz Matisha Kirkconnell Vanessa Orr Cara Schwarz Nick Walters Maria Zdanovskaia Special thanks: John Stanton Mark Wendt Advertisements Stay tuned for DN 3 talk FE 02 Brent Amberger also from our group: FE 06 Nick Walters Millimeter- wave spectroscopy of formyl azide.