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Consistent assignment of the vibrations
of para-disubstituted benzene molecules
Anna Andrejeva, Alison J. Lee and Timothy G. Wright
69th International Symposium on Molecular Spectroscopy
University of Illinois at Urbana-Champaign
RC07/ P516
Introduction
• Wilson1 nomenclature assigns the vibrations of a substituted benzene
molecule in terms of benzene vibrations
• Varsanyi2 scheme proposes a series of normal vibrational modes for a
series of different categories of substituted benzenes – arbitrary division of
‘light’ and ‘heavy’ substituents
• Mulliken3 scheme numbers the vibrations of a molecule according to
their symmetry and decreasing wavenumber. Creates difficulty e.g. toluene
and fluorobenzene
• Gardner-Wright4 - 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)
3. R. S. Mulliken, J. Chem. Phys., 23,1997 (1955)
2. G .Varsanyi, Assignments of the vibrational Spectra of 4. A. M. Gardner and T. G. Wright, 135, 114305 (2011)
Seven Hundred Benzene Derivatives ,Wiley, New York,
1974, Vol. I and II
Monosubstituted benzenes
Gardner-Wright scheme
Para-disubstituted benzenes
A. M. Gardner and T. G. Wright, 135, 114305 (2011)
Benzene vs pDFB
• 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.
Figure 1. Calculated Duschinsky matrix elements
for benzene S0 vs p-difluorobenzene S0.
• B3LYP/ aug-cc-pVTZ
-S1 TD-DFT
- Scaling factor 0.97
Gardner-Wright scheme
• Fluorobenzene is viewed as
prototypical system
• Fluorobenzene vibrational
modes serve as a model upon
which benzene derivative
vibrations are labelled.
• Each mode corresponding to
a vibration is given the symbol
Mi
• Vibrations having the same
atomic motion are given the
same label
Figure
Calculated
Duschinsky
matrix
elements
Figure 2.3.Calculated
Duschinsky
matrix
elements
for
fluorobenzene
S0 vs chlorobenzene
S0.
for fluorobenzene
S0 vs p-difluorobenzene
S0.
Why p- Difluorobenzene?
A1
Wavenumber / cm-1
Wavenumber / cm-1
A2
B2
B1
Substituent mass / amu
New Labelling Scheme - pDi
• p-Difluorobenzene vibrational
modes serve as a model upon
which benzene derivative
vibrations are labelled.
• Ordered by symmetry then
decreasing wavenumber
• Each mode corresponding
to a vibration is given the
symbol pDi
•Substituents treated as a
point mass
• Nearly complete
diagonalisation occurs
Wavenumber / cm-1
Wavenumber / cm-1
Comparison to experimental data5
A1
A2
B1
Substituent mass / amu
5. A. Stojiljković and D.H. Whiffen, Spectrochimica Acta, 12, 47 (1958)
B2
What about excited states?
Calculated Duschinsky matrix elements for p-DFB S0
and p-DFB S1
Calculated Duschinsky matrix elements for pDFB S0 and p-FT S1
• Can assign corresponding vibrational modes with confidence
Spectra Comparison
Adapted LIF spectrum from A. E. W. Knight
and S. H. Kable, J. Chem. Phys., 88, 7139
(1988)
(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)
Wavenumber / cm-1
Take home message
• Have applied Gardner-Wright scheme successfully to paradisubstituted benzene molecules – yielding a new labelling scheme
for para-disubstituted benzene molecules pDi
•The same vibrational motions have the same pDi label for all paradisubstituted benzene molecules regardless of the energy ordering or
changes in molecular symmetry, allowing straightforward
comparison between species
• Over horizon:
— study more extensively S1 states of para-disubstituted benzene
systems
—the effect of the meta and ortho substituent positions may have
on the vibrational modes.
Acknowledgements
• Prof. Tim Wright
• Alison Jasmin Lee
•
for the processor time on their HPC
• I. Pugliesi and C. Schriever for developing
•
for DTA Project Studentship
program
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