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.

~1350 cm -1 ~300 cm -1 Wilson Mode 1 15 Varsányi Mode 2 15 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. Previous Assignment Schemes

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. The agreement with experimentally determined frequencies is excellent. However, the assignment of the calculated normal vibrational modes is more complicated... Comparison to the calculated normal modes to those determined by Varsányi in some cases is easy... But in many cases this is very difficult cm -1 Varsányi normal modes Calculated normal mode 6a 1 12 ~500 cm -1 ~800 cm -1 ~1000 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, , (2008) Fluorobenzene

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 where i is the number of the mode. A New Assignment Scheme

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

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

Why Fluorobenzene ?

Other Monosubstituted Benzene Molecules Toluene 15 amu Aniline 16 amu Phenylacetylene 25 amu Benzonitrile 26 amu

Other Monosubstituted Benzene Molecules

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- and tri- substituted benzene molecules. Conclusions

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