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

The three conformers TMM1 C 1 symmetry TMM2 C 3 symmetry 375 cm  TMM3 C s symmetry 316 cm  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 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.

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

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 C 3 symmetry

Potential energy function Ab initio calculation at the MP2/ G** level

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) Light and Bacic, J. Chem. Phys. 87 (1987) 4008

Tunneling energy level diagram Ohashi, Hougen, Suenram, Lovas, Kawashima, Fujikate, and Pyka, JMS 227 (2003) 28 Total number of level is 27

Statistical weights Total statistical weight is 2 9

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 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

No symmetry N   DVR functions

C s symmetry N 

C 3 symmetry These DVR functions will be used in the present investigation.