The rotationaltorsional microwave spectrum of mono deuterated acetamide

The rotational-torsional microwave spectrum of mono deuterated acetamide L. H. Coudert, H. Møllendal, and J. -C. Guillemin

Mono deuterated acetamide CH 2 DC(O)NH 2 • It is a convenient molecule to study internal rotation of a CH 2 D methyl group. • The generalized inertia tensor. • The Hamiltonian and its torsional matrix elements. • Energy levels.

The normal species of acetamide • Non-rigid molecule displaying internal rotation. • Its microwave spectrum is well understood. 1 -4 V 3 = 25 cm-1 • Hindering potential changes are small. • Distortion effects are small. • Largest effects come from the kinetic energy part. 1. Kojima et al. , J. Mol. Spec. 122, 408 (1987). 2. Suenram et al. , J. Mol. Spec. 208, 188 (2001). 3. Yamaguchi et al. , J. Mol. Spec. 215, 144 (2002). 4. Ilyushin et al. , J. Mol. Spec. 227, 115 (2004).

The model for the normal species The z-axis is parallel to the axis of internal rotation. The NH 2 group, the C and O atoms are in the xz-plane. Hecht and Dennison, J. Chem Phys. 26, 31 (1957)

Generalized inertia tensor, normal species

The model for the deuterated species The z-axis is parallel to the axis of internal rotation. The plane containing the NH 2 group, the C and O atoms is parallel the xz-plane. Quade and Lin, J. Chem Phys. 38, 540 (1963)

Generalized inertia tensor, deuterated species Quade and Lin, J. Chem Phys. 38, 540 (1963)

The exact quantum mechanical Hamiltonian The components of the inverse inertia tensor m(a) are a-dependent and do not have a closed form expression.

Torsional-rotational energy levels How do we calculate torsional matrix elements? De Lucia, Herbst, Anderson and Helminger, J. Mol. Spect. 134, 395 (1989)

DVR functions for periodic coordinates

The DVR function for nt=1 and q=1 ac = 0. 75 p

The DVR function for nt=17 and q=9 ac = 0. 53 p

The DVR function for nt=25 and q=4 ac = 0. 86 p

Using the DVR functions

Using the DVR functions

Energy calculation D Ka = ± 1, ± 2 matrix elements

Results: the J = 0 levels Normal species Deuterated species

Results: the J = 1 levels

A portion of the microwave spectrum