Rotational Spectroscopy and Search for Methoxymethanol in the ISM Roman A. Motiyenko, Laurent Margulès Laboratoire PhLAM, UMR 8523 CNRS - Université Lille 1, Villeneuve d’Ascq, France Jean-Claude Guillemin Institut des Sciences Chimiques de Rennes, UMR 6226 CNRS - ENSCR, Rennes, France Didier Despois Laboratoire d’Astrophysique de Bordeaux, Université de Bordeaux, Floirac, France. Arnaud Belloche Max-Planck-Institut für Radioastronomie, Bonn, Germany 06/27/2016 – 60 years of Molecules, Motion and Matrix Elements (NIST)

The Lille THz spectrometer 10 – 18 GHz Millitech AMC (x4) : 50 – 75 GHz VDI AMC-10 (x6) : 75 – 110 GHz VDI AMC-35x (x12) : 118 – 170 GHz x2 x3 x5 x2x3 x3x3 x3x3 f, GHz

The fast-scan box Inspired by Medvedev et al. Optics Letters 35 (2010) 1533 – 1535 Agilent E8257D Frequency switching time min: 25 ms/point Frequency switching time typical: 35 ms/point Time to cover 150 – 1500 GHz: ~ 180h Agilent E8257D + Fast-scan box Frequency switching time: 50 µs/point Frequency switching time typical: 4 ms/point Time to cover 150 – 1500 GHz: ~ 23h ~ 3 decrease in S/N ratio Synthesized fast-scan – at each point the frequency is determined with the accuracy of the reference clock (frequency standard); line measurement accuracy – the same as for « slow » scan The principle – up-conversion of direct digital synthesizer into RF RF synthesizer provides frequency switching with large step once per scan DDS synthesizer provides fast frequency switching with small frequency step Typically, a scan consists to acquire 1000 - 2000 points

The fast-scan box No signal-to-noise difference between old and new setup when the acqusition time is the same

Garrod, Widicus Weaver & Herbst, ApJ, 682 : 283-302, 2008 Methoxymthanol - Astrophysical interest Both CH3O and CH2OH may be formed from methanol photolysis in ices Methoxymethanol (CH3OCH2OH) is predicted to form from reactions of CH3O and CH2OH in ices CH3O detected in the ISM (Cernicharo et al., ApJL 759 : L43, 2012) CH2OH is not yet detected Garrod, Widicus Weaver & Herbst, ApJ, 682 : 283-302, 2008

Stable conformations MP2/aug-cc-pVQZ Gg+ Gg- Tg E (kJ/mol) 8.5 10.9 8.5 10.9 A (MHz) 17255.37 17193.46 32695.06 B (MHz) 5639.84 5685.01 4383.01 C (MHz) 4867.86 4813.62 4102.33 µa (D) 0.22 0.77 1.48 µb (D) 0.08 1.22 0.97 µc (D) 0.13 2.0 1.26

Stable conformations Gauche-gauche Gauche-gauche’ Trans-gauche 0.51 E (kJ/mol) 8.5 10.9 Boltz.@300 K 1 0.033 0.012 µa (D) 0.22 0.77 1.48 Normalized intensities without taking the partition function into account: Ia 0.51 0.20 0.29 I ~ µ2×exp(-ħω/kT)

Experiment Sample synthesized by J.-C. Guillemin Methoxymethanol unstable under room temperature Spectra measured in flow mode Pyrex absorption cell CH3OH and H2CO as major impurities THz source Absorbtion cell Detector to diffusion + rotary pump Sample at ~ 250 K At room temperature In this study: ∆t = 1 ms/point due to weak intensities Each spectrum averaged 8 times – effective acquisition time 8 ms/point Frequency range: 150 – 470 MHz

CH3OH and H2CO as major impurities Analysis 235 – 265 GHz, ~660000 points, recorded in 92 minutes CH3OH and H2CO as major impurities

Analysis Gg: B+C = 10.506 GHz Tg: B+C = 8.485 GHz

Internal rotation Gg Gg’ V3 = 517 cm-1 V3 = 607 cm-1 B3LYP/6-311++(3df, 2pd) 250,25 – 240,24 A 251,25 – 241,24 E Gg Gg’ V3 = 517 cm-1 V3 = 607 cm-1 249,15 – 239,14 A 249,16 – 239,15 A 249,15 – 239,14 E 249,16 – 239,15 E No symmetry: XIAM code used for fitting and predicting the spectra XIAM allows fitting of structural parameters (angles ε and δ)

Internal rotation XIAM fit Theory Gg Theory Gg’ A (MHz) 17237.9491(12) 17255.37 17193.46 B (MHz) 5567.81516(29) 5639.84 5685.01 C (MHz) 4813.04187(33) 4867.86 4813.62 V3 (cm-1) 545.93(39) 517 607 δ (rad) 0.90252(40) 0.932 0.942 ε (rad) 0.3819(13) 0.397 0.359 +13 parameters rms (MHz) 0.04 N lines 1189 J max, Ka max 48, 14 δ – the angle between the internal rotation axis and the principal axis z ε – the angle between the principal axis x and the projection of the internal rotation axis onto xy-plane

Internal rotation Strong µa lines Theory Weak µb lines Weak µb lines µa (D) 0.22 µb (D) 0.08 µc (D) 0.13 µa (D) 0.77 µb (D) 1.22 µc (D) 2.0 Gg Gg’ Experiment

OH tunneling in Tg conformation Splittings ~40 MHz Theory Experiment

OH tunneling in Tg conformation J+12,J – J2,J-1 J’’ 19 20 21 22 23 24 25 26 27 28 29

OH tunneling in Tg conformation J+12,J-1 – J2,J-2 J’’ 19 20 21 22 23 24 25 26 27 28 29

Hindered internal rotation of the hydroxyl group Tunneling between the two equivalent Tg configurations split each rotational level into two components. The analysis of rotational spectrum is complicated by Coriolis-type coupling between the tunneling substates 00,0 DE = 90.6 GHz (3.02 cm-1) 0+ 0- selection rules: µa, µb: +  + & -  - µc: +  -

The Hamiltonian and the global fit Pickett’s Reduced Axis Method (RAM, Pickett H.M. J. Chem. Phys. 1972, 56, 1715. ) formalism was used The Hamiltonian in the matrix form: Where: Hrot – Watson A-reduction Hamiltonian in the Ir coordinate representation H∆ – the rotational dependence of the energy difference, it allows fitting a single set of rotational constants for both 0+ and 0- states HI – Coriolis interaction terms and their centrifugal distortion corrections

The Hamiltonian and the global fit The ∆E and F terms in the Hamiltonian are usually highly correlated In the absence of v = 0  1 transitions one of the terms should be fixed Usually it is better to fix ∆E and to let F to vary We performed a series of fits with ∆E fixed in the range 60 – 200 GHz to find a global rms minimum global rms minimum rms as a function of (11) parameter (410001) as a function of (11) parameter preliminary fit: Parameter Experiment Theory MP2/aug-cc-pVTZ A (MHz) 32327.73(38) 32695.1 B (MHz) 4350.33185(267) 4383.01 C (MHz) 4070.97384(267) 4102.33 +8 parameters ΔE (MHz) 90679.9( 32) Fbc -0.1905(264) Fac 36.8131(165) N lines 175 rms (MHz) 0.044 quest for µc transitions to decorrelate ∆E term

Assignment of Gg’ conformation Experim. Gg Theory Gg Theory Gg’ Scaled Gg’ A (MHz) 17237.949 17255.37 17193.46 17176.11 B (MHz) 5567.815 5639.84 5685.01 5612.44 C (MHz) 4813.041 4867.86 4813.62 4759.46 J+10,J+1 – J0,J

Assignment of Gg’ conformation B3LYP/6-311++(3df, 2pd)

Results The most stable Gg conformation of methoxymethanol assigned and analyzed Accurate predictions of transition frequencies for the v=0 state of Gg conformation in the frequency range up to 500 GHz and for J up to 50 Gg’ and Tg conformations have pure spectroscopic interest Tg conformation assigned, its spectrum exhibits splittings due to OH tunneling Gg’ conformation tentatively assigned A. Belloche: methoxymethanol is not detected in ALMA Sgr B2 (N2) survey due to high line blending. Its abundance upper limit is at least 4 times lower in comparison with methyl formate (to be corrected by vibrational partition function) Hays & Widicus Weaver, JPCA 117: 7142-7148, 2013 Acknowledgements Action sur Projets de l'INSU : "Physique et Chimie du Milieu Interstellaire" ANR-13-BS05-0008-02 IMOLABS