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Analysis of the microwave spectrum of the three-top molecule trimethoxylmethane L. Coudert, a G. Feng, b and W. Caminati b a Laboratoire Interuniversitaire des Systèmes Atmosphériques, Créteil, France b Dipartimento de Chimica “G. Ciamician,” Universita de Bologna, Bologna, Italy
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The three conformers TMM1 C 1 symmetry TMM2 C 3 symmetry 375 cm TMM3 C s symmetry 316 cm 14 transitions
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Overview The internal rotation problem in trimethoxylmethane The Schrodinger equation Torsion-rotation energy levels Calculated tunneling patterns Observed tunneling patterns Analysis
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Internal rotation in trimethoxylmethane Trimethoxylmethane displays internal rotation of its three inequivalent methyl groups. Torsion-rotation energy levels should be obtained solving a 3-D Schrödinger equation.
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The model Assumptions: 4 rigid parts: frame HCO 3 + the 3 methyl groups. The 3 axes of internal rotation are fixed. Each methyl group has C 3v symmetry. Each axis of internal rotation is parallel to the C 3 axis of symmetry.
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The exact Hamiltonian Describing the internal rotation of each methyl group with the angles α 1, α 2, and α 3, the Hamiltonian is: 1 1. Ohashi, Hougen, Suenram, Lovas, Kawashima, Fujikate, and Pyka, JMS 227 (2003) 28
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Energy level calculation Calculation is carried with a DVR approach. 1,2 With a usual FIR basis set: [21 x 21 x 21] 2 = 9261 x 9261 With a DVR basis set: [21 x (2J+1) x 3] 2 1. Ligth and Carrington, Adv. Chem. Phys. (2003) 2. Lee and Tuckerman, J. Phys. Chem. A 110 (2006) 5549
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FIR and DVR functions for C 3 symmetry
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Potential energy function 1 2 3 1. Ab initio calculation at the MP2/6-311++G** level
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Solving the 3-D Schrödinger equation H(α 1,α 2,α 3 ) H(α 1 =α p,α 2,α 3 ) H(α 1 =α p,α 2 =α q,α 3 ) H R (α 1 =α p,α 2 =α q,α 3 =α n ) α 1 active coordinate α 2 active coordinate α 3 active coordinate 1. Lauvergnat, Nauts, Justum, and Chapuisat, J. Chem. Phsy. 114 (2001) 6592 2. Light and Bacic, J. Chem. Phys. 87 (1987) 4008
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Tunneling energy level diagram Ohashi, Hougen, Suenram, Lovas, Kawashima, Fujikate, and Pyka, JMS 227 (2003) 28 Total number of level is 27
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Statistical weights Total statistical weight is 2 9
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Calculated tunneling pattern
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Observed tunneling patterns
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Analysis The analysis should yield: height or the three barriers hindering the internal rotation direction cosine of the axes of internal rotation in the molecule-fixed-axis system assignment of the tunneling component is an issue
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FBR and DVR functions The FBR and DVR functions depend on the problem you want to solve and on the associated Gaussian quadrature. 1,2 Non-rigid molecule displaying internal rotation 1,2 parameterized by the angle α 1. Ligth and Carringyon, Adv. Chem. Phys. (2003) 2. Lee and Tuckerman, J. Phys. Chem. A 110 (2006) 5549
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No symmetry N DVR functions 189246 341 95
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C s symmetry 171 117 27 162 10854 N
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C 3 symmetry These DVR functions will be used in the present investigation.
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