1. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Microwave spectroscopy o ｆ trans-ethyl methyl ether in the torsionally excited state 2 Norimichi Mori 1, Takanori Matsui 1, Kaori Kobayashi 1, Shozo Tsunekawa 1, and Nobukimi Ohashi 2 1. Department of Physics, University of Toyama, 3190 Gofuku,Toyama, 930-8555 Japan 2. Kanazawa University, Japan

2. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Introduction Saturated organic molecules are good candidates of interstellar species Analysis of two internal rotors is interesting In University of Toyama, molecules in the torsionally excited state have been studied

3. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Trans-ethyl methyl ether Dipole moment b-axis  a = 0.146 D  b = 1.165 D Two internal rotors V 3 = 891cm -1 -OCH 3 group torsion V 3 = 1150cm -1 -CCH 3 group torsion C1C2 C3 O  total =1.174(22) D

4. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Splitting caused by internal rotations v t =0, 44 1 43 ←44 0 44 OCH 3 2.26 MHz CCH 3 0.47 MHz 0.43 MHz AAEAEEAE

5. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Vibrational modes and previous microwave studies cm -1 Ground State （ v t =0 ） v t =1 278cm -1 CCH 3 torsion v t =2 Skeletal torsion 115cm -1 v t =1 v t =2 v t =3 v t =4 OCH 3 torsion vt=1 248cm -1 v t =3 v t =2 v t =1 Hayashi et al, J.Mol.Struct.28,147- 161(1975) 8.5 – 34 GHz molecular constants, dipole moment, potential barrier Fuchs et al,ApJS.144,277-286(2003) 60 - 350 GHz Two internal rotors were considered. vt=0 ， J ≦ 58,Ka ≦ 6 1362 lines assigned prediction up to 400GHz S.Tsunekawa et al, Molecules 8,103-119(2003) 18 – 200 GHz about 21,000 lines observed- >Atlas vt=0 ， J ≦ 72,Ka ≦ 5 722 lines assigned K.Kobayashi et al, J. Mol. Spectrosc., in press. J ≦ 91,Ka ≦ 6 1178 lines assigned K.Kobayashi et al, Columbus 2007 About 3,000 lines below 200 GHz are assigned so far. Torsionally excited state is a good candidate for these unassigned lines.

6. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Experiment Conventional microwave spectrometers 23 – 140 GHz The cell was cooled down to the dry ice temperature

7. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Observed spectra [MHz] v t = 1, 14 2 13 ← 14 1 14 AA AE EA EE1 EE2

8. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Assignments 1.Frequency prediction based on RAM Hamiltonian 2.Pattern prediction 3.Confirmation of Stark Component 4. Intensity ratio

9. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Pattern prediction of the torsionally excited state v t =0 v t =1 OCH 3 CCH 3 OCH 3 CCH 3

10. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Intensity ratio A-species N 1 / N 0 = 0.208 (194 K) E-species N 1 / N 0 = 0.181 (194 K) calculated(0.127) v t = 0 11 2 10 ← 11 1 11 v t = 1 AAAE EA EE1 EE2 EA AE

11. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Analysis considering two internal rotors ◆ Phenomenological Hamiltonian operator (S-reduced) ◆ A tunneling matrix method developed by J. T. Hougen was used in an analysis. ◆ Vibrational framework functions |n> = O n |1> (n = 1,2, …….., 9) O n : O1O2O3O1O2O3 E (123) (132) O4O5O6O4O5O6 (456) (465) (123)(456) O7O8O9O7O8O9 (123)(465) (132)(456) (132)(465) where coefficients A, B, …., q, … are functions or operators of large-amplitude vibration variables.

12. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy ◆ Parameters [ = tunneling matrix elements] to be determined in the fit:,,, and their centrifugal analogs : rotational and centrifugal distortion constants at an equilibrium configuration.,, ;,, ;…………. and their centrifugal analogs : effect of CH 3 internal rotation tunneling to rotational and centrifugal distortion constants.,,,,….. : Coriolis coupling constants. ********************************************************************** =, = etc. = -, = - etc.

13. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Pure rotationOCH 3 -torsionCCH 3 -torsion A1 27968.6686(31) B1 4152.56064(47) C1 3887.77132(48) DJ1 0.00097472(91) DJK1 -0.002236(14) DK1 0.09838(22) d11 -8.3613(70)×10 -5 d1J1 -1.542(40)×10 -9 d21 1.559(18)×10 -6 d2J1 -7.39(16)×10 -10 d31 -6.21(39)×10 -11 HJ1 8.97(53)×10 -9 HJK1 5.3(19)×10 -8 HKJ1 1.79(36)×10 -6 LJJK1 -1.870(72)×10 -10 A2 -2.7998(17) B2 -0.008298(84) C2 -0.000417(86) DJK2 -0.0002419(32) DK2 -0.025260(91) d12 6.68(79)×10 -8 d22 1.808(35)×10 -7 d32 -3.4(16)×10 -12 HKJ2 -2.50(15)×10 -6 A4 -1.2165(16) B4 -0.007572(32) DJK4 -0.0001884(31) DK4 -0.009931(87) d13 1.022(75)×10 -7 d24 1.587(24)×10 -7 HKJ4 -1.72(14)×10 -6 Coriolis-like q2 16.109(16) qJ2 -0.001073(16) qK2 -0.2763(10) q4 7.395(20) qJ4 -0.000866(16) qK4 -0.1150(12) (1  ) RMS = 67 kHz Molecular Constants (MHz)

14. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Symmetry assignment Expected pattern v t =0 v t =1 OCH 3 CCH 3 OCH 3 CCH 3 EEEAAEAA EAEEAAAE

15. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Established by 1. the necessity of Coriolis term in a separate fit, 2. splitting of EE components, 3. estimate of Coriolis parameters etc. from the PAM perturbation theory including torsion-torsion coupling. Reversed sequence v t = 1, 11 2 10 ← 11 1 11 AA AE EA EE1EE2

16. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Vibrational modes cm -1 Ground State （ v t =0 ） v t =1 278cm -1 CCH 3 torsion v t =2 Skeletal torsion 115cm -1 v t =1 v t =2 v t =3 v t =4 OCH 3 torsion vt=1 248cm -1 v t =3 v t =2

17. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Torsional-rotational Hamiltonian including torsion-torsion couplings

18. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Future study Assignments of transitions of higher J, K Consideration of the interaction between the OCH 3 -, CCH 3 - and skeletal-torsional states Assignments and analysis of the other excited states (second and third skeletal torsionally excited states are in progress)

19. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Toyama microwave atlas http://www.sci.u-toyama.ac.jp/phys/4ken/atlas/

20. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Database for trasition frequencies icluding unassigned lines

21. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Summary ・ The first assignments of the t-ethyl methyl ether in the first CCH 3 -group torsionally excited state ・ v t =1, J≤45 ， K≤4 870 lines ・ Analysis based on the tunneling matrix formulation : rms = 68 kHz with 37 parameters

22. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Acknoledgment National Astronomical Observatory of Japan (NAOJ) ALMA-J Grant-in- Aid from the Ministry of Education, Science, Sports and Culture of Japan.

23. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Block diagram of the Stark spectrometer Synthesized Sweeper PC Lock-in Amplifier Stark Generator Pre- amplifier Detector Stark Cell Ref.100kHz 100kHz Signal Microwave 2 - 40GHz

24. Jun 18th 2008 63rd International Symposium on Molecular Spectroscopy Low vibrational modes OCH 3 torsion CCH 3 torsion Skeletal torsion cm -1 CCO bending COC bending 115 cm -1 248 cm -1 278 cm -1 288 cm -1 475 cm -1 v t = 1 v t = 2 v t = 3 v t = 1