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The microwave spectrum of partially deuterated species of dimethyl ether D. Lauvergnat, a L. Margulès, b R. A. Motyenko, b J.-C. Guillemin, c and L. H. Coudert d a LCP, CNRS/Université Paris-Sud, Orsay, France b PhLAM, CNRS/Université des Sciences et Technologies de Lille 1 Villeneuve d'Ascq, France c Sciences Chimiques de Rennes, Rennes, France d LISA, CNRS/Universités Paris Est et Denis Diderot, Créteil, France

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Why are we interested in deuterated species? A large number of unidentified lines in the ISM may be due to partially deuterated species. Measuring partially deuterated species provides astronomers with a tool to measure the [D]/[H] ratio. In this talk the microwave spectrum of the partially deuterated species of dimethyl ether CH 2 DOCH 3 will be investigated theoretically.

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Outline Torsional energy levels of the normal species Torsional energy levels of the deuterated species Torsional Hamiltonian Potential energy surface Torsional functions Nature of the torsional energy levels Microwave spectrum of the deuterated species

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Torsional coordinates The torsional angles 1 and 2 are used

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PES of the normal species with: 1. Durig, Li, and Groner, JMS 62 (1976) 159. 2. MP2 with cc-PVTZ basis set.

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Torsional energy levels: normal species 4 tunneling sublevels G 36

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Torsional function: normal species ( 1, 2 ) A 1 sublevel

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What happens when the molecule is deuterated? The kinetic energy part of the torsional Hamiltonian is modified because of the mass change. The effective potential energy function for the torsion is changed due to zero-point energy effects.

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Kinetic energy change 11

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Potential energy function change V 10 = 13.3 cm 10 cm Lauvergnat et al., JMS 256 (2009) 204 and Margulès et al., JMS 254 (2009) 55. D-out of plane D-in plane

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Torsional energy level calculation

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Torsional energy levels: deuterated species 9 tunneling sublevels 3 nondegenerate 3 doubly degenerate

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Torsional function of the 1 st A-type sublevel D-in plane

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Torsional function of the 2 nd A-type sublevel D-out of plane

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Torsional function of the 3 rd A-type sublevel D-out of plane

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Torsional energy levels D-in plane Torsional function centered around Internal rotation of the other methyl group D-out of plane Tunneling between and Internal rotation of the other methyl group

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The microwave spectrum Two sets of transitions. Set I Set II

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The next steps Overall rotation will be taken into account. Rotational dependence of the various tunneling splittings will be determined using the water dimer formalism. 1 The energy difference between the two sublevel sets should be calculated accurately. We can begin analyzing the microwave spectrum. 1. Hougen, JMS 114 (1985) 395 and Coudert and Hougen, JMS 139 (1990) 259.

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