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Consistent assignment of the vibrations of para-disubstituted benzene molecules Anna Andrejeva, Alison J. Lee and Timothy G. Wright 69 th International Symposium on Molecular Spectroscopy University of Illinois at Urbana-Champaign RC07/ P516

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Introduction Wilson 1 nomenclature assigns the vibrations of a substituted benzene molecule in terms of benzene vibrations Varsanyi 2 scheme proposes a series of normal vibrational modes for a series of different categories of substituted benzenes arbitrary division of light and heavy substituents Mulliken 3 scheme numbers the vibrations of a molecule according to their symmetry and decreasing wavenumber. Creates difficulty e.g. toluene and fluorobenzene Gardner-Wright 4 - new nomenclature where ring- localised vibrations having the same atomic motion are given the same label, allowing these vibrations to be compared straightforwardly across different substituted benzenes 1.E. B. Wilson Jr., Phys. Rev., 45, 706 (1934) 2.G.Varsanyi, Assignments of the vibrational Spectra of Seven Hundred Benzene Derivatives,Wiley, New York, 1974, Vol. I and II 3.R. S. Mulliken, J. Chem. Phys., 23,1997 (1955) 4.A. M. Gardner and T. G. Wright, 135, 114305 (2011)

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Monosubstituted benzenes Gardner-Wright scheme A. M. Gardner and T. G. Wright, 135, 114305 (2011) Para-disubstituted benzenes

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Benzene vs pDFB Figure 1. Calculated Duschinsky matrix elements for benzene S 0 vs p-difluorobenzene S 0. Benzene vs p-difluorobenzene vibrational mode comparison via a generalised Duschinsky approach. This shows whether a vibration is a pure Wilson mode or not. Vibrational modes are highly mixed, indicating use of Wilson notation describing substituted benzene vibrations is questionable. B3LYP/ aug-cc-pVTZ -S 1 TD-DFT - Scaling factor 0.97

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Figure 2. Calculated Duschinsky matrix elements for fluorobenzene S 0 vs chlorobenzene S 0. Fluorobenzene is viewed as prototypical system Gardner-Wright scheme Fluorobenzene vibrational modes serve as a model upon which benzene derivative vibrations are labelled. Vibrations having the same atomic motion are given the same label Each mode corresponding to a vibration is given the symbol M i Figure 3. Calculated Duschinsky matrix elements for fluorobenzene S 0 vs p-difluorobenzene S 0.

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Wavenumber / cm -1 Why p- Difluorobenzene? A1A1 A2A2 B2B2 B1B1 Substituent mass / amu

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New Labelling Scheme - p D i p-Difluorobenzene vibrational modes serve as a model upon which benzene derivative vibrations are labelled. Nearly complete diagonalisation occurs Each mode corresponding to a vibration is given the symbol p D i Ordered by symmetry then decreasing wavenumber Substituents treated as a point mass

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Wavenumber / cm -1 Substituent mass / amu A1A1 A2A2 B1B1 B2B2 Comparison to experimental data 5 5. A. Stojiljkovi and D.H. Whiffen, Spectrochimica Acta, 12, 47 (1958)

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What about excited states? Can assign corresponding vibrational modes with confidence Calculated Duschinsky matrix elements for p-DFB S 0 and p-DFB S 1 Calculated Duschinsky matrix elements for p- DFB S 0 and p-FT S 1

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Spectra Comparison Wavenumber / cm -1 (1+1) REMPI spectrum from V. L. Ayles, C. J. Hammond, D. E. Bergeron, Q. J. Richards and T. G. Wright, J. Chem. Phys., 126, 244304 (2007) Adapted LIF spectrum from A. E. W. Knight and S. H. Kable, J. Chem. Phys., 88, 7139 (1988)

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Take home message Have applied Gardner-Wright scheme successfully to para- disubstituted benzene molecules yielding a new labelling scheme for para-disubstituted benzene molecules p D i The same vibrational motions have the same p D i label for all para- disubstituted benzene molecules regardless of the energy ordering or changes in molecular symmetry, allowing straightforward comparison between species Over horizon: study more extensively S 1 states of para-disubstituted benzene systems the effect of the meta and ortho substituent positions may have on the vibrational modes.

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Acknowledgements Prof. Tim Wright for the processor time on their HPC I. Pugliesi and C. Schriever for developing program for DTA Project Studentship Alison Jasmin Lee