analysis of the microwave spectrum of the three-top molecule trimethoxylmethane l. coudert, a g....
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Analysis of the microwave spectrum of the three-top molecule trimethoxylmethane
L. Coudert,a G. Feng,b and W. Caminatib
aLaboratoire Interuniversitaire des Systèmes Atmosphériques, Créteil, FrancebDipartimento de Chimica “G. Ciamician,” Universita de Bologna, Bologna, Italy
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The three conformers
TMM1
C1 symmetry
TMM2
C3 symmetry
375 cm
TMM3
Cs 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 HCO3 + the 3 methyl groups.
• The 3 axes of internal rotation are fixed.
• Each methyl group has C3v symmetry.
• Each axis of internal rotation is parallel to the C3 axis of symmetry.
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The exact Hamiltonian
Describing the internal rotation of each methyl group
with the angles α1, α2, and α3, 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 C3 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(α1,α2,α3)
H(α1=αp,α2,α3)
H(α1=αp,α2=αq,α3)
HR(α1=αp,α2=αq,α3=αn)
α1 active coordinate
α2 active coordinate
α3 active coordinate
1. Lauvergnat, Nauts, Justum, and Chapuisat, J. Chem. Phsy. 114 (2001) 65922. 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 29
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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 rotation1,2 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 functions189 246 34195
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Cs symmetry
17111727 16210854
N
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C3 symmetry
These DVR functions will be used
in the present investigation.