Analysis of the microwave spectrum of the three-top molecule trimethoxylmethane L. Coudert, a G....

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

The three conformers

TMM1

C1 symmetry

TMM2

C3 symmetry

375 cm

TMM3

Cs 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 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

2

3

1. Ab initio calculation at the MP2/6-311++G** level

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

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 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

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

No

symmetry

N

DVR functions189 246 34195

Cs symmetry

17111727 16210854

N

C3 symmetry

These DVR functions will be used

in the present investigation.