Department of Chemistry, University of Wisconsin, Madison Millimeter-wave spectroscopy and global analysis of the lowest eight vibrational states of deuterated hydrazoic acid (DN3) 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

Considerations for DN3 vs. HN3 DN3 compared to HN3: More b-type lines in our range Slower intensity drop off in R line intensity with K Generally smaller perturbation effects Published IR data for 2ν6 as well as ground, ν5, ν6, ν4, and ν3 Re-ordering of vibrational energy levels HN3 A ~611 GHz DN3 A ~345 GHz Goal to obtain a simultaneous MMW/ FTIR fit for the 8 lowest vibrational states of DN3 To be successful we need correct assignments and decent starting values for as many spectroscopic constants as possible

Excited Vibrational States HN3 DN3 1266.6 cm-1 ν3 ~1213 cm-1 2ν6 1197.39 cm-1 ν3 1147.4 cm-1 ν4 1162.42 cm-1 2ν6 ~1143.5 cm-1 ν5+ ν6 ~1074 cm-1 ~1082 cm-1 ν5+ ν6 2ν5 ~991 cm-1 2ν5 ν4 954.77 cm-1 606.36 cm-1 ν6 586.49 cm-1 ν6 537.25 cm-1 ν5 495.74 cm-1 ν5 0 cm-1 Ground 0 cm-1 Ground

Predicted Spectra for HN3 and DN3 Our Range DN3

DN3 Ground State R-Branch K=1 K=0 K=1 J= 14  13 Spectrum predicted from a fit including K=0 through K=7 K=2 K=3 K=4 K=5 K=8 K=11 K=10 K=9 K=6 K=7 K=1 K=0 K=1 J= 14  13 K=2 Assignments K=3 K=4 K=5 K=8 K=11 K=10 K=9 K=6 K=7

The Spectrum and the Excited states ground ν6 ν5 ν4 ν3 2ν5 2ν6 ν5+ ν6

Extremely Useful Prior IR Works The pure rotational absorption spectrum DN3 in the far-infrared region Bendtsen, J. and F. M. Nicolaisen, Journal of Molecular Spectroscopy 1987, 125, 14-23. FTIR Spectra and simultaneous analysis of ν5 ν6 and ground Bendtsen, J.; Hegelund, F.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1988, 128, 309-320. FTIR spectra of ν4 and 2ν6 Bendtsen, J.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1991, 145, 123-129. FTIR spectra of ν2 and ν3 Hansen, C. S.; Bendtsen, J.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1996, 175, 239-245.

Loomis-Wood Plots Developed a list of ~100 series likely to be a-type R-branches. Attributed K- states and vibrational states to the series using all available means. Ran low on unassigned series and states at the same time! Rigorous checking of assignments.

Picking Series out of Loomis-Wood Plots This series of K=8 cannot cleanly be included in a single state for the ground state because of perturbation with ν5 K=7 This single state fit for the ground state is still very useful in finding lines for K=8 however.

Linear Plots and Assignment Confirmation Make these plots for all series believed to belong to R-Branches. Slope and intercept of these linear plots proved useful in assigning each series to a state and a K value. Slopes and intercepts were also useful in obtaining initial values for spectroscopic constants. (Nominal Frequency Range) (Using Spurious Harmonic in AMC)

Intercepts of K-series plots B+C of our fit = 22336.32 B+C of our fit = 22356.66 Slope = -2ΔJK

Fermi Resonances between 2ν6 & ν3 and between 2ν5 & ν4 k663 = -76.85 k554 = 13.38 Cubic Force Constants CCSD(T)/ANO2

Using (Frequency / Jupper) vs Jupper2 plots for all K states Intercept = -0.0152 MHz Intercept = -0.0150 MHz -4ΔJ= -0.0168 from SPFIT -4ΔJ= -0.0161 from SPFIT Intercept = -0.0157 MHz -4ΔJ= -0.0156 from SPFIT

A 3-State Fit MMW and FTIR data: Ground, ν5, and ν6 A (MHz) 342150.(38) B (MHz) 11385.12(24) C (MHz) 10971.54(24) ΔJ (kHz) 3.890(30) ΔJK (kHz) -10.0(46) ΔK (kHz) -65522.(254) δJ (kHz) 0.1767(15) δK (kHz) 85.(38) ΦJ (Hz) -0.171(17) ΦJK (Hz) -11.2(21) ΦKJ (Hz) -3706.(198) ΦK (Hz) 963610.(14269) LKKJ 179374.(3357) LK -20609300.(159482) E (MHz) 14862352.(47) N lines MM 210 N lines IR 349 σ (MHz) 2.5 σ IR (cm-1) .037 ν6 A (MHz) 339895.(38) B (MHz) 11349.91(24) C (MHz) 10986.41(24) ΔJ (kHz) 4.189(50) ΔJK (kHz) 876.3(35) ΔK (kHz) 239007.(738) δJ (kHz) 0.279(13) δK (kHz) -78.(47) ΦJ (Hz) 0.167(25) ΦJK (Hz) -7.1(24) ΦKJ (Hz) 473.(181) ΦK (Hz) -446610.(24901) LKKJ -151257.(3273) LK 10473100.(218238) E (MHz) 17583158.(56) N lines MM 141 N lines IR 507 σ (MHz) 2.3 σ IR (cm-1) .024 Perturbation Constants Ga (MHz) 599174.(87) Fa (MHz) 6.93(37) Gb (MHz) -946.(48) W05 616.(10) Ground State A (MHz) 344747.34(30) B (MHz) 11350.8535(97) C (MHz) 10964.916(10) ΔJ (kHz) 4.305(11) ΔJK (kHz) 397.0(18) ΔK (kHz) 92837.(63) δJ (kHz) 0.17260(32) δK (kHz) 301.8(13) ΦJ (Hz) 0.0034(34) ΦJK (Hz) 1.45(24) ΦKJ (Hz) -104.(13) ΦK (Hz) 112169.(1566) LKKJ -2860.(179) LK -151700.(9792) E (MHz) N lines MM 304 N lines IR 620 σ (MHz) 0.47MHz σ IR (cm-1) 0.0036 14 parameters per state X 3 4 Perturbation terms vibrational energies allowed to vary 655 MMW transitions 1476 IR transitions σMMW = 1.83 MHz σIR = 0.0229 cm-1

DN3 Energy Levels and Perturbations Fermi Resonance 1197.39 cm-1 ν3 1162.42 cm-1 2ν6 Gc (Coriolis) Ga, Fa, Gb (Coriolis) ~1082 cm-1 ν5+ ν6 Ga, Fa, Gb (Coriolis) ~991 cm-1 2ν5 ν4 Fermi Resonance 954.77 cm-1 Centrifugal Distortion (W05) Ga, Fa, Gb (Coriolis) 586.49 cm-1 ν6 Ga, Fa, Gb (Coriolis) 495.74 cm-1 ν5 W05 (centrifugal distortion) 0 cm-1 Ground

Perturbation Terms for Three-State Fit HN3 CCSD(T)/ANO2 Present Work Hegelund & Bendtsen 1987 Ga56 (cm-1) 36.77 38.033(12) [38.06] Gb56 (cm-1) -0.0389 0.06378(43) 0.06252(13) W05 (cm-1) 0.0345(14) 0.04261(7) DN3 CCSD(T)/ANO2 Present Work Bendtsen et al 1988 Ga56 (cm-1) 20.74 19.9863(29) [18.86] Gb56 (cm-1) -0.0368 -0.0316(16) 0.071(6) W05 (cm-1) 0.0206(3) 0.0312(6)

Analysis of Splittings in K=1 K=2 and K=3

What do K=1, K=2, and K=3 Splittings tell us? From the Wang Formula: 𝐸 1 + − 𝐸 1 − 𝐽 𝑈𝑝 = 𝐵−𝐶 +ℎ𝑖𝑔ℎ𝑒𝑟 𝑡𝑒𝑟𝑚𝑠 K=1 Splittings 𝐸 2 + − 𝐸 2 − ( 𝐽 𝑈𝑝 −1) 𝐽 𝑈𝑝 ( 𝐽 𝑈𝑝 +1) = 1 8 (𝐵−𝐶) 2 𝐴− 𝐵+𝐶 2 +ℎ𝑖𝑔ℎ𝑒𝑟 𝑡𝑒𝑟𝑚𝑠 K=2 Splittings Slopes of Splitting Curves K=1 K=2 K=3 ν5 Without Ga 414.62 0.0698 2.16*10-6 With Ga 385.30 0.0913 3.68*10-6 ν6 363.22 0.0462 1.09 *10-6 336.29 0.0312 5.65 *10-7

Complete K state energy plot Ground state Slope = 333548.85 A-(B+C)/2= 333589.46 Quadratic term = -90.29 MHz -ΔK = -92.84 MHz Cubic term = 0.0767 MHz ΦK = 0.1122

Analyzing the Difference between ν5 & ν6 K Energies therefore 1 2 𝑠𝑙𝑜𝑝𝑒 ≅ Ga Ga from slope = 19.88 cm-1 Ga from our 3-state fit = 19.98 cm-1 𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = 𝐸 0 𝑣6 - 𝐸 0 𝑣5 𝐸 0 𝑣6 - 𝐸 0 𝑣5 From intercept = 90.78 cm-1 𝐸 0 𝑣6 - 𝐸 0 𝑣5 From literature = 90.75 cm-1

Checking Assignments DN3 2ν6 We also found b-type lines for all but 2ν5 and ν5+ν6 2ν6 313986.3528 MHz 11 1 11 243508.2152 12 0 12 267676.3 (extrapolated from 4 K=0 transitions) 10 1 10 338153.8206 11 0 11 267675.7460 + 313986.3528 - 243508.2009 - 338153.8206 = 0.616MHz

Summary Accomplished so far: Assigned a-type R branches for 8 lowest energy vibrational states Assigned b-type lines for 6 of these states Achieved a reasonable 3-state fit of combined MMW/ FTIR data Found ways to extract some key spectroscopic constants from the data Elusive long-term goal: 8-state fit!

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 Advertisement also from our group: FE06 Nick Walters Millimeter- wave spectroscopy of formyl azide. Special thanks: John Stanton Mark Wendt