Department of Chemistry, University of Wisconsin, Madison Towards a Global Fit of the Combined Millimeter-wave and High Resolution FTIR Data for the Lowest Eight Vibrational States of Hydrazoic Acid (HN3) International Symposium of Molecular Spectroscopy, Urbana-Champaign, Illinois June 26, 2015 Brent K. Amberger, R. Claude Woods, Brian J. Esselman, Robert J. McMahon, Department of Chemistry, University of Wisconsin, Madison

Our Equilibrium Structure Determination of HN3 Observations between 235-450 GHz at room temperature -14 Isotopologues Studied -High level corrections for vibration-rotation interactions, xrefit in CFOUR used for structure determination (John Stanton)

Available HN3 Transitions in our Range 260-360 GHz a-type R branches b-type R and P branches

HN3 Ground R-Branch K=1 J= 13  12 K=1 Spectrum predicted from single state fit of K=0 through K=5 K=0 K=2 K=3 K=10 K=4 K=9 K=8 K=7 K=5 K=6 K=1 K=1 K=0 Actual Assignments K=2 Perturbed lines are often very perturbed K=3 The highly perturbed lines are also the lowest intensity lines K=10 K=4 K=8 K=7 K=5 K=9 K=6

Ground and Excited Vibrational State Transitions

Vibrational States and Perturbations 1266.6 cm-1 ν3 Fermi Resonance Gc (Coriolis) ~1213 cm-1 2ν6 1147.40 cm-1 ν4 Ga, Fa, Gb (Coriolis) ~1143.5 cm-1 ν5+ ν6 Ga, Fa, Gb (Coriolis) ~1074 cm-1 2ν5 Fermi Resonance Centrifugal Distortion (W05) Ga, Fa, Gb (Coriolis) 606.4 cm-1 ν6 Ga, Fa Gb (Coriolis) 537.3 cm-1 ν5 Centrifugal Distortion (W05) 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 ν5, ν6 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 ν4 Bendtsen, J.; Nicolaisen, F. M. Journal of Molecular Spectroscopy 1989, 133, 193-200. FTIR spectra and analysis of ν3 and ν4 Bendtsen, J.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1992, 152, 101-108 Tunable diode laser spectrum of ν3 Yamada, K. and Takami, M., Journal of Molecular Spectroscopy 1980 84, 431-446. BUT….

K Energies for the Vibrational States ν3 ν4 ground ν6 ν5

K Energies for the Vibrational States Estimated values for 2ν5, 2ν6 and ν5+ ν6 ν3 ν4 2ν6 ν5+ ν6 ground ν6 2ν5 ν5

Using IR data to Find Pure Rotational Transitions ν5 Finding HN3 v5 13 3 10 – 12 3 9 13 3 10 13 3 10 12 3 9 12 3 9 P- branch IR transitions R- branch IR transitions 14 3 11 13 3 10 12 3 9 11 3 8 Ground state 309933 MHz 309937 MHz

Linear Plots of Freq/Jup vs. Jup2 Steep negative slope Steep negative slope modest negative slope (most common) positive slope!

Examples of Perturbed K-States Steep negative slope (highly perturbed) These two mutually perturbing states are easily recognized as perturbed due to abnormal slopes for their K values. Positive slope (highly perturbed)

Intercepts of Linear Plots vs. K2

Previous slide average shifted by one in K The average is much smoother than either separately.

A 3-State Fit of Millimeter-wave Data: Ground, ν5, and ν6 Ground State A (MHz) 610740.770(86) B (MHz) 12034.570(35) C (MHz) 11781.109(35) ΔJ (kHz) 4.8886(25) ΔJK (kHz) 669.451(73) ΔK (kHz) -25131.(66) δJ (kHz) 0.09413(78) δK (kHz) 201.(17) ΦJ (Hz) -0.0017(19) ΦJK (Hz) -1.17(10) ΦKJ (Hz) 579.0(27) E (MHz) [0] N lines 132 σ (MHz) 0.36 ν5 (537.3 cm-1) A (MHz) 589939.(25) B (MHz) 12067.591(85) C (MHz) 11784.766(85) ΔJ (kHz) 4.7422(33) ΔJK (kHz) -958.92(43) ΔK (kHz) -84990.(690) δJ (kHz) -0.06842(86) δK (kHz) 416.(18) ΦJ (Hz) -0.1222(29) ΦJK (Hz) 35.04(27) ΦKJ (Hz) -27927.(11) E (MHz) [16106800] N lines 136 σ (MHz) 0.77 ν6 (606.4 cm-1) A (MHz) 622737.(25) B (MHz) 12034.340(90) C (MHz) 11802.444(90) ΔJ (kHz) 5.2144(52) ΔJK (kHz) 2686.51(43) ΔK (kHz) -872710.(1170) δJ (kHz) -0.1968(27) δK (kHz) 371.(20) ΦJ (Hz) -0.1446(59) ΦJK (Hz) -22.03(36) ΦKJ (Hz) 25958.(13) E (MHz) [18178100] N lines 82 σ (MHz) 1.05 Perturbation Terms Ga /MHz 1140200.(400) Fa /MHz 7.28(71) Gb /MHz 1912.1(13) W05 1034.4(43) 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 HN3 1266.6 cm-1 ν3 Fermi Resonance Gc (Coriolis) ~1213 cm-1 2ν6 1147.40 cm-1 ν4 Ga, Fa, Gb (Coriolis) ~1143.5 cm-1 ν5+ ν6 Ga, Fa, Gb (Coriolis) ~1074 cm-1 2ν5 Fermi Resonance Centrifugal Distortion (W05) Ga, Fa, Gb (Coriolis) Ga, Fa, Gb (Coriolis) 606.4 cm-1 ν6 537.3 cm-1 ν5 Centrifugal Distortion (W05) 0 cm-1 Ground

Infrared and Microwave Patterns are the Same for ν3 and ν4 Bendtsen, J.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1992, 152, 101-108 ΔB4 = (B+C)K of ν4 – (B+C)K of ground state ΔB3 = (B+C)K of ν3 – (B+C)K of ground state

Infrared – Microwave (B+C)K for ν3 and ν4

Adding ν3 and ν4 (with K shifted by 1) Bendtsen, J.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1992, 152, 101-108 Consistent with the ΔK = 1 selection rules for c-type Coriolis resonance (Gc)

b-type transitions for ν3 and ν4 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 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 Perturbations bring a Q-branch series for ν3 into our range. b-type lines with J values ranging from 1 to 12.

Confident Assignment of the 2ν5 R-series Trendline on linear (less perturbed) region gives access to: Intercept = B+C Slope = -ΔJK

Next Steps Obtain solid assignments of a-type R-branches for ν5+ν6 and 2ν6. Find and assign b-type transitions for 2ν5, ν5+ν6, and 2ν6. Use linear least-squares plots to obtain as many initial values for as many parameters as possible. Obtain 5-state non-linear least-squares fit (SPFIT) for higher energy excited vibrational states. Determine the critical perturbation parameters for these higher states Ultimately obtain an 8-state global fit (“The Holy Grail”).

Thanks for Listening! The Research Group Professor Bob McMahon Professor Claude Woods Dr. Brian Esselman Brent Amberger Ben Haenni Zachary Heim Steph Knezz Matisha Kirkconnell Vanessa Orr Cara Schwarz Nick Walters Maria Zdanovskaia Advertisements Stay tuned for DN3 talk FE02 Brent Amberger also from our group: FE06 Nick Walters Millimeter- wave spectroscopy of formyl azide. Special thanks: John Stanton Mark Wendt