Rovibrational Phase-Space Surfaces for

Analysis of the υ3/2υ4 Polyad Band of CF4

Justin Mitchell, William Harter, University of ArkansasVincent Boudon, CNRS - Université de Bourgogne

CF4

•Dramatic rotation-vibration coupling

•Similar in structure to other spherical top molecules

•SF6, Mo(CO)6, CH4, CD4,

CF4, GeF4

•High resolution is needed for astronomy and atmospheric science

•A field in need of qualitative analysis

How to get more information from phase-

space1.Write Hamiltonian in Tensor Expansion

2.Phase-Space Plots of Tensors

3.Contour with experimental/computational spectra making Rotational Energy Eigenvalue Surface (REES)

4.Topography of Level Clustering (fine structure)

1.Write Hamiltonian in Tensor Expansion

2.Phase-Space Plots of Tensors

3.Contour with experimental/computational spectra making Rotational Energy Eigenvalue Surface (REES)

4.Topography of Level Clustering (fine structure)

How to get more information from phase-

space

Tensor expansion

Rotation VibrationFitting Term

•Use vibrational basis•Treat rotation operators as classical

Champion, Loëte, Pierre, in “Spectroscopy of the Earth’s Atmosphere and Interstellar Medium,” (Rao, Weber, Eds), Academic Press, San Diego, 1992, p 339-422

How to get more information

1.Write Hamiltonian in Tensor Expansion

2.Phase-Space Plots of Tensors

3.Contour with experimental/computational spectra making Rotational Energy Eigenvalue Surface (REES)

4.Topography of Level Clustering (fine structure)

Rotational Energy Eigenvalue Surface

(REES)•Constant Total Angular

Momentum, J.

•x,y,z are Jx, Jy, and Jz

•Contours are Eigenvalues

•REES will have the same symmetry as the molecule

•Simple angular momentum relationships give approximate energy values

J=30

How to get more information

1.Write Hamiltonian in Tensor Expansion

2.Phase-Space Plots of Tensors

3.Contour with experimental/computational spectra making Rotational Energy Eigenvalue Surface (REES)

4.Topography of Level Clustering (fine structure)

Local symmetry structures

•Local symmetry determines clustering patterns

C4 C3

C2

C1

Harter, Paterson, Galbraith, J. Chem. Phys. 69, 4896, (1978)

REES for υ3

•Parameters used are from CF4, but with Bζ set to zero

•Cut exists to show lower surfaces

•Three surfaces because of triplet vibrational state

•Conical intersections exist between levels

Energies calculated using XTDS software

Wenger et. al, J. Mol. Spect. 251, 102 (2008)

Energy diagram with classical outline for υ3

Treatment similar to Dhont, Sadovskii, Zhilinskii, Boudon, J. Mol. Spectrosc.201, 95 (2000)

Scalar 2nd, 4th... terms removed to keep plot centered

υ3 with C1 structure

•C4, C3, and C2 axes are high

•Levels exist in C1 region

•Now only 1 level is below the surface

J=55

REES υ3/2υ4 CF4

•Interaction of 9 rovibronic phase surfaces

•Outer surface contours are dappled from scaling

• Cluster patterns match local symmetry conditions

•Cone locations predict engies

J=60

Energy diagram for υ3/2υ4

More on this from Boudon at

RI 09

Cone locations predict energies

J=60

Surface 6 Surface 3

Surface 4

Surface 5

Cone locations predict energies

J=50

Surface 6 Surface 3Surface 4

Surface 5

Conclusions

•REES can predict level clustering

•REES can predict some parts of spectra though not always to high precision

•REES adds to the qualitative toolbox for rovibronic spectroscopy

•Combinations of level diagrams and classical outlines show when behavior is semi-classical or fully quantum