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Unravelling the assignments of the vibrations of the monosubstituted benzenes Adrian M. Gardner and Timothy G. Wright 67th International Symposium on Molecular Spectroscopy Ohio State University 19th 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 Mode1 15 ~1350 cm-1 Varsányi Mode2 15 ~300 cm-1 Calculated lowest frequency b2 mode of fluorobenzene.1 1Calculated at the B3LYP/aVDZ level. 2G. 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 S0 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 S0 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 •Comparison to the calculated normal modes to-1those determined -1 ~500 cm ~800 cm ~1000 cm-1 by Varsányi in some cases is easy... •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 Mi where i is the number of the mode. Chlorobenzene Matrix representing the Duschinsky matrixa elements for benzene/chlorobenzene. aCalculated 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 matrixa elements for fluorobenzene/chlorobenzene. aCalculated 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- and tri-substituted benzene molecules. Acknowledgements Prof. Tim Wright Dr. Alistair Green A. M. Gardner and T. G. Wright, J. Chem. Phys., 135, 114305 (2011)