Transcript trim.ppt
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, France bDipartimento de Chimica “G. Ciamician,” Universita de Bologna, Bologna, Italy The three conformers TMM1 TMM2 TMM3 C1 symmetry C3 symmetry Cs symmetry 375 cm-1 316 cm-1 14 transitions Overview • • • • • • The internal rotation problem in trimethoxylmethane The Schrodinger equation Torsion-rotation energy levels Calculated tunneling patterns Observed tunneling patterns Analysis 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. 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. 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 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 FIR and DVR functions for C3 symmetry Potential energy function 1 3 2 1. Ab initio calculation at the MP2/6-311++G** level Solving the 3-D Schrödinger equation H(α1,α2,α3) α1 active coordinate H(α1=αp,α2,α3) α2 active coordinate H(α1=αp,α2=αq,α3) α3 active coordinate HR(α1=αp,α2=αq,α3=αn) 1. Lauvergnat, Nauts, Justum, and Chapuisat, J. Chem. Phsy. 114 (2001) 6592 2. Light and Bacic, J. Chem. Phys. 87 (1987) 4008 Tunneling energy level diagram Total number of level is 27 Ohashi, Hougen, Suenram, Lovas, Kawashima, Fujikate, and Pyka, JMS 227 (2003) 28 Statistical weights Total statistical weight is 29 Calculated tunneling pattern Observed tunneling patterns 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 FBR and DVR functions Non-rigid molecule displaying internal rotation1,2 parameterized by the angle α The FBR and DVR functions depend on the problem you want to solve and on the associated Gaussian quadrature.1,2 1. Ligth and Carringyon, Adv. Chem. Phys. (2003) 2. Lee and Tuckerman, J. Phys. Chem. A 110 (2006) 5549 No symmetry N=9 95 189 246 341 19 DVR functions Cs symmetry 27 117 171 54 108 N=9 162 C3 symmetry These DVR functions will be used in the present investigation.