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400
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05001000150020002500
Abso
rbance
(a.u
.)
Energy (wavenumber)
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Animate the Normal Modes of PF5
5.03 Inorganic Chemistry
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Selection Rule for Raman Spectroscopy
The Raman selection rule is based upon changes in molecularpolarizability during a vibration
The molecular polarizability may undergo a change during amolecular vibration
If the vibration or “normal mode” has the same symmetry asxz , yz , xy , x2, y2, or z2 then it involves a change in themolecular quadrupole moment during the vibration, bysymmetry, and otherwise not
There is a mutual exclusion rule for point groups having aninversion center: no vibration may be both IR and Ramanactive
5.03 Inorganic Chemistry
![Page 6: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/6.jpg)
Selection Rule for Raman Spectroscopy
The Raman selection rule is based upon changes in molecularpolarizability during a vibration
The molecular polarizability may undergo a change during amolecular vibration
If the vibration or “normal mode” has the same symmetry asxz , yz , xy , x2, y2, or z2 then it involves a change in themolecular quadrupole moment during the vibration, bysymmetry, and otherwise not
There is a mutual exclusion rule for point groups having aninversion center: no vibration may be both IR and Ramanactive
5.03 Inorganic Chemistry
![Page 7: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/7.jpg)
Selection Rule for Raman Spectroscopy
The Raman selection rule is based upon changes in molecularpolarizability during a vibration
The molecular polarizability may undergo a change during amolecular vibration
If the vibration or “normal mode” has the same symmetry asxz , yz , xy , x2, y2, or z2 then it involves a change in themolecular quadrupole moment during the vibration, bysymmetry, and otherwise not
There is a mutual exclusion rule for point groups having aninversion center: no vibration may be both IR and Ramanactive
5.03 Inorganic Chemistry
![Page 8: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/8.jpg)
Selection Rule for Raman Spectroscopy
The Raman selection rule is based upon changes in molecularpolarizability during a vibration
The molecular polarizability may undergo a change during amolecular vibration
If the vibration or “normal mode” has the same symmetry asxz , yz , xy , x2, y2, or z2 then it involves a change in themolecular quadrupole moment during the vibration, bysymmetry, and otherwise not
There is a mutual exclusion rule for point groups having aninversion center: no vibration may be both IR and Ramanactive
5.03 Inorganic Chemistry
![Page 9: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/9.jpg)
D6h Illustrates the Rule of Mutual Exclusion
5.03 Inorganic Chemistry
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Raman is a Light Scattering Phenomenon
5.03 Inorganic Chemistry
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AsP3 Characterization by Raman Spectroscopy
5.03 Inorganic Chemistry
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Using REDUCE for Vibrational AnalysisThe program only needs to know the # unshifted atoms for each class of operation
5.03 Inorganic Chemistry
![Page 14: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/14.jpg)
Using REDUCE for Vibrational AnalysisThe program only needs to know the # unshifted atoms for each class of operation
5.03 Inorganic Chemistry
![Page 15: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/15.jpg)
Using REDUCE for Vibrational AnalysisThe program only needs to know the # unshifted atoms for each class of operation
5.03 Inorganic Chemistry
![Page 16: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/16.jpg)
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Significance of the 19F NMR Spectrum of PF5Excerpt from 1960 paper by R. Stephen Berry
5.03 Inorganic Chemistry
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Significance of the 19F NMR Spectrum of PF5Excerpt from 1960 paper by R. Stephen Berry
Definition of the term fluxional process: a low-energy,reversible rearrangement
5.03 Inorganic Chemistry
![Page 19: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/19.jpg)
Significance of the 19F NMR Spectrum of PF5Excerpt from 1960 paper by R. Stephen Berry
Definition of the term fluxional process: a low-energy,reversible rearrangement
5.03 Inorganic Chemistry
![Page 20: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/20.jpg)
Significance of the 19F NMR Spectrum of PF5Excerpt from 1960 paper by R. Stephen Berry
5.03 Inorganic Chemistry
![Page 21: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/21.jpg)
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The NMR Time ScaleExcerpt from 1983 paper by Robert G. Bryant, DOI: 10.1021/ed060p933
5.03 Inorganic Chemistry
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The NMR Time ScaleExcerpt from 1983 paper by Robert G. Bryant, DOI: 10.1021/ed060p933
5.03 Inorganic Chemistry
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Berry PseudorotationCass et al. J. Chem. Educ., 2006, 83, 336
An INTERMEDIATE is at a local minimum on the free energysurface
A TRANSITION STATE is at a local maximum
5.03 Inorganic Chemistry
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Berry PseudorotationCass et al. J. Chem. Educ., 2006, 83, 336
An INTERMEDIATE is at a local minimum on the free energysurface
A TRANSITION STATE is at a local maximum
5.03 Inorganic Chemistry
![Page 26: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/26.jpg)
Berry PseudorotationCass et al. J. Chem. Educ., 2006, 83, 336
An INTERMEDIATE is at a local minimum on the free energysurface
A TRANSITION STATE is at a local maximum
5.03 Inorganic Chemistry
![Page 27: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/27.jpg)
Features of the Pseudorotation
The point group of PF5 is D3h before and after thepseudorotation
BPR involves pairwise exchange of axial and equatorialfluorines
The transition state (TS) has C4v symmetry
A true TS has one negative root representing an imaginaryfrequency
Animation of this normal mode provides a movie of thereaction coordinate
5.03 Inorganic Chemistry
![Page 28: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/28.jpg)
Features of the Pseudorotation
The point group of PF5 is D3h before and after thepseudorotation
BPR involves pairwise exchange of axial and equatorialfluorines
The transition state (TS) has C4v symmetry
A true TS has one negative root representing an imaginaryfrequency
Animation of this normal mode provides a movie of thereaction coordinate
5.03 Inorganic Chemistry
![Page 29: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/29.jpg)
Features of the Pseudorotation
The point group of PF5 is D3h before and after thepseudorotation
BPR involves pairwise exchange of axial and equatorialfluorines
The transition state (TS) has C4v symmetry
A true TS has one negative root representing an imaginaryfrequency
Animation of this normal mode provides a movie of thereaction coordinate
5.03 Inorganic Chemistry
![Page 30: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/30.jpg)
Features of the Pseudorotation
The point group of PF5 is D3h before and after thepseudorotation
BPR involves pairwise exchange of axial and equatorialfluorines
The transition state (TS) has C4v symmetry
A true TS has one negative root representing an imaginaryfrequency
Animation of this normal mode provides a movie of thereaction coordinate
5.03 Inorganic Chemistry
![Page 31: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/31.jpg)
Features of the Pseudorotation
The point group of PF5 is D3h before and after thepseudorotation
BPR involves pairwise exchange of axial and equatorialfluorines
The transition state (TS) has C4v symmetry
A true TS has one negative root representing an imaginaryfrequency
Animation of this normal mode provides a movie of thereaction coordinate
5.03 Inorganic Chemistry
![Page 32: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/32.jpg)
Molecular Structure of SF4, Another Fluxional Molecule
5.03 Inorganic Chemistry
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NMR Investigation of Pseudorotation in SF4Excerpt from 1983 paper by Nancy S. True, DOI: 10.1021/ja00363a003
5.03 Inorganic Chemistry
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NMR Investigation of Pseudorotation in SF4Excerpt from 1983 paper by Nancy S. True, DOI: 10.1021/ja00363a003
5.03 Inorganic Chemistry
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Screenshot of our SF4 TS Vibrations Applet
5.03 Inorganic Chemistry
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Summary of Some Key Points
The reaction coordinate as a 2D slice of the potential energysurface (PES)
Intermediates versus Transition States
Intermediates are local minima, zero negative vibrationalmodes
Transition state structures are characterized by a singlenegative vibrational mode
Visualizing the imaginary mode of a TS is essentially a movieof the path from reactants to products
BPR as an example of a fluxional process
5.03 Inorganic Chemistry
![Page 37: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/37.jpg)
Summary of Some Key Points
The reaction coordinate as a 2D slice of the potential energysurface (PES)
Intermediates versus Transition States
Intermediates are local minima, zero negative vibrationalmodes
Transition state structures are characterized by a singlenegative vibrational mode
Visualizing the imaginary mode of a TS is essentially a movieof the path from reactants to products
BPR as an example of a fluxional process
5.03 Inorganic Chemistry
![Page 38: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/38.jpg)
Summary of Some Key Points
The reaction coordinate as a 2D slice of the potential energysurface (PES)
Intermediates versus Transition States
Intermediates are local minima, zero negative vibrationalmodes
Transition state structures are characterized by a singlenegative vibrational mode
Visualizing the imaginary mode of a TS is essentially a movieof the path from reactants to products
BPR as an example of a fluxional process
5.03 Inorganic Chemistry
![Page 39: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/39.jpg)
Summary of Some Key Points
The reaction coordinate as a 2D slice of the potential energysurface (PES)
Intermediates versus Transition States
Intermediates are local minima, zero negative vibrationalmodes
Transition state structures are characterized by a singlenegative vibrational mode
Visualizing the imaginary mode of a TS is essentially a movieof the path from reactants to products
BPR as an example of a fluxional process
5.03 Inorganic Chemistry
![Page 40: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/40.jpg)
Summary of Some Key Points
The reaction coordinate as a 2D slice of the potential energysurface (PES)
Intermediates versus Transition States
Intermediates are local minima, zero negative vibrationalmodes
Transition state structures are characterized by a singlenegative vibrational mode
Visualizing the imaginary mode of a TS is essentially a movieof the path from reactants to products
BPR as an example of a fluxional process
5.03 Inorganic Chemistry
![Page 41: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/41.jpg)
Summary of Some Key Points
The reaction coordinate as a 2D slice of the potential energysurface (PES)
Intermediates versus Transition States
Intermediates are local minima, zero negative vibrationalmodes
Transition state structures are characterized by a singlenegative vibrational mode
Visualizing the imaginary mode of a TS is essentially a movieof the path from reactants to products
BPR as an example of a fluxional process
5.03 Inorganic Chemistry
![Page 42: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/42.jpg)
Summary of Some Key Points
Symmetry properties informs discussion of structure andvibrational spectra
Selection rules for IR and Raman spectroscopy
Vibrational analysis, use REDUCE to check your work
Time scales vary for different kinds of measurement (NMRversus IR)
The power of multinuclear NMR for studying inorganicsystems
5.03 Inorganic Chemistry
![Page 43: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/43.jpg)
Summary of Some Key Points
Symmetry properties informs discussion of structure andvibrational spectra
Selection rules for IR and Raman spectroscopy
Vibrational analysis, use REDUCE to check your work
Time scales vary for different kinds of measurement (NMRversus IR)
The power of multinuclear NMR for studying inorganicsystems
5.03 Inorganic Chemistry
![Page 44: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/44.jpg)
Summary of Some Key Points
Symmetry properties informs discussion of structure andvibrational spectra
Selection rules for IR and Raman spectroscopy
Vibrational analysis, use REDUCE to check your work
Time scales vary for different kinds of measurement (NMRversus IR)
The power of multinuclear NMR for studying inorganicsystems
5.03 Inorganic Chemistry
![Page 45: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/45.jpg)
Summary of Some Key Points
Symmetry properties informs discussion of structure andvibrational spectra
Selection rules for IR and Raman spectroscopy
Vibrational analysis, use REDUCE to check your work
Time scales vary for different kinds of measurement (NMRversus IR)
The power of multinuclear NMR for studying inorganicsystems
5.03 Inorganic Chemistry
![Page 46: Character Tables - Massachusetts Institute of Technology](https://reader034.vdocuments.us/reader034/viewer/2022050302/626ee6ca20e9a450d536f8ae/html5/thumbnails/46.jpg)
Summary of Some Key Points
Symmetry properties informs discussion of structure andvibrational spectra
Selection rules for IR and Raman spectroscopy
Vibrational analysis, use REDUCE to check your work
Time scales vary for different kinds of measurement (NMRversus IR)
The power of multinuclear NMR for studying inorganicsystems
5.03 Inorganic Chemistry