Unravelling the assignments of the vibrations of the monosubstituted benzenes

Adrian M. Gardner and Timothy G. Wright 67 th International Symposium on Molecular Spectroscopy Ohio State University 19 th June 2012

Previous Assignment Schemes

• • 1 .

Mulliken Notation Vibrations are listed in order of symmetry.

Numbered in each symmetry group in decreasing frequency.

• 2 .

Wilson Notation Vibrations of substituted benzene molecules are labelled in terms of benzene vibrations.

• 3 .

Varsányi Notation Normal modes of vibration suggested explicitly for each type of substitution.

Previous Assignment Schemes

Wilson Mode 1 15 Varsányi Mode 2 15 ~1350 cm -1 ~300 cm -1 Calculated lowest frequency

b

2 mode of fluorobenzene.

1 1 Calculated at the B3LYP/aVDZ level. 2 G. Varsányi ,

Assignments of the Vibrational Spectra of Seven Hundred Benzene Derivatives,

(Wiley, New York, 1974) Vol. 2.

Fluorobenzene

• Vibrational frequencies have been calculated at the B3LYP/aVDZ level for the

S

0 electronic state of fluorobenzene. • The agreement with experimentally determined frequencies is excellent.

• However, the assignment of the calculated normal vibrational modes more complicated...

• Comparison to the calculated normal modes to those determined by Varsányi in some cases is easy.

Varsányi mode 6b Calculated 6b mode

Fluorobenzene

• Vibrational frequencies have been calculated at the B3LYP/aVDZ level for the

S

0 electronic state of fluorobenzene. • 6a 1 12 The agreement with experimentally determined frequencies is excellent.

• However, the assignment of the calculated normal vibrational modes is more complicated...

Varsányi normal modes • some cases is easy...

~800 cm -1 ~1000 cm -1 • But in many cases this is very difficult...

Calculated normal mode 814 cm -1

Fluorobenzene

• Through comparisons of the vibrational wavefunctions of benzene and fluorobenzene it is clear that the Wilson notation approach also fails in many cases.

• Pugliesi

et al.

3 recently investigated this using a Duschinsky mixing approach.

3. I. Pugliesi, N. M. Tonge, and M. C. R. Cockett,

J. Chem. Phys.,

129

, 104303, (2008)

A New Assignment Scheme

• Use the calculated normal modes of fluorobenzene as a basis for a labelling scheme for monosubstituted benzene vibrations.

• We propose each normal mode is denoted

M

i mode.

where i is the number of the

Chlorobenzene

Matrix representing the Duschinsky matrix a elements for benzene/chlorobenzene.

a Calculated using FC-LabII. I. Pugliesi and K. Müller-Dethlefs, J. Phys. Chem. A 110, 4657 (2006), a free download of the software can be found at http://www.fclab2.net/.

Chlorobenzene

Matrix representing the Duschinsky matrix a elements for fluorobenzene/chlorobenzene.

a Calculated using FC-LabII 7I. Pugliesi and K. Müller-Dethlefs, J. Phys. Chem. A 110, 4657 (2006), a free download of the software can be found at http://www.fclab2.net/.

Why Fluorobenzene

?

Other Monosubstituted Benzene Molecules

Toluene 15 amu Aniline 16 amu Phenylacetylene 25 amu Benzonitrile 26 amu

Other Monosubstituted Benzene Molecules

Conclusions

• A new assignment scheme has been proposed for monosubstitued benzene molecules based on the normal vibrational modes of fluorobenzene.

• This allows a significantly more consistent picture of the vibrational assignments of monosubtitued benzene molecules to made.

• This system is currently being extended to

di-

benzene molecules.

and

tri-

substituted

Acknowledgements

Prof. Tim Wright Dr. Alistair Green A. M. Gardner and T. G. Wright, J. Chem. Phys., 135, 114305 (2011)