1. Chemistry 125: Lecture 56 March 1, 2010 Opening Dewar Benzene Spectroscopy Introduction Electronic and Infrared This For copyright notice see final page of this file

2. Opening Dewar Benzene (1866)

3. Calculated Isomers of Benzene (2004) 84 calculated to be < 100 kcal above benzene. 6 > 100 kcal above benzene have been prepared. (single bond breaking gives even less stable species) Dewar Benzene (1963) is 74 kcal above benzene but lasts 2 days at room temperature!

4. CCC angles require disrotatory motion  HOMO  * LUMO t 1/2 = 2 days (room temp) -11 kcal -75 kcal 25 33 conrotatory more strain aromatic  HOMO 66 kcal/mole more exothermic, but only 8 kcal/mole “faster”? good for 4n electrons  * LUMO

5. But shouldn’t “aromatic” 6-  -e transition state be good for disrotation? It is more fundamental that   LUMO doesn’t overlap  HOMOs (& vice versa).   

6. Spectroscopy for Structure and Dynamics “Sunbeams..passing through a Glass Prism to the opposite Wall, exhibited there a Spectrum of divers colours” Newton (1674) “Specters or straunge Sights, Visions and Apparitions” (1605) O.E.D. Electronic (Visible/UV, sec. 12.7-12.8 pp. 533 ) Vibrational (Infrared, sec. 15.4, pp. 707-713 ) NMR (Radio, sec. 15.5-15.9, pp. 713-749 )

7. “Atom in a Box” can be used to show: (1) Spectral transitions for H atom (levels, energy, wavelength) (2) Static shift of e-density from mixing 2s with 2p (same energy) (3) Oscillation of e-density from mixing orbitals with different energy because of change in relative phase* with time (add, then subtract). (b)“Breathing” from mixing 1s with 2s. (no interaction with light) (a) Oscillating “dipole” from mixing 1s with 2p. (makes or interacts with light) * This is a feature of time-dependent quantum mechanics, where the (complex) phase of a wavefunction changes at a rate proportional to its energy. When energies of the components differ, their relative phases vary in time.

8. + + + 1s2p (1s + 2p) 2 superposition e-density time-dependent Oscillation frequency given by the energy difference between 1s and 2p

9. Time-Dependance Footnote A time-dependent wavefunction looks just like the spatial  s we have been talking about, except that it is multiplied by e i  t, where i =  (-1),  is the energy (expressed in frequency units), of the spatial wavefunction  and t is time. In many cases this makes no difference, because when you “square” the wave function you get  e i  t   e -i  t =  2. BUT when a problem involves actually mixing two states of different energy, one considers a wavefunction of the form   e i   t +   e i   t. If  1 and  2 are different, this means that the two spatial functions cycle in- and out-of-phase with one another. If at a certain time they add, at a time 1/(  1 -  2 ) later they will subtract. e.g. (1s+2p z ) will become (1s-2p z ). * This is different from the mixing involved in forming hybrids or LCAO-MOs, where we just try to guess the best shape for an orbital of one particular energy for a molecule by analogy with known solutions for a simpler situation (atoms). * This is the source of the oscillation we observe when superimposing functions of different n using Atom-in-a-Box.

10. + + + 1s2p Oscillating dipole has “oscillator strength” interacts with / generates / absorbs light (1s + 2p) 2 superposition e-density time-dependent 1s - 2p transition is “allowed” Oscillation frequency given by the energy difference between 1s and 2p

11. + + + 1s2s (1s + 2s) 2 superposition e-density time-dependent Symmetrical “breathing” e-density deformation has no “oscillator strength” does not interact with light’s E-field. 1s - 2s transition is “forbidden” Pulsing frequency given by the energy difference between 1s and 2s

12. : n-*n-* n-  * Transitions of Organic “Chromophores” : CX + +- - Oscillating electric field wags electrons up and down by mixing n with  *. : n+*n+* The large energy gap between n and  * makes this transition occur at high frequency (in the ultraviolet).

13. : n-*n-* R n-  * Transitions of Organic “Chromophores” : CX + +- - Oscillating electric field wags electrons up and down by mixing n with  *. With sufficient “conjugation” the  * LUMO energy shifts close enough to n that the transition is at visible wavelength. e.g. the retinaldehyde imine of rhodopsin, which is the visual pigment in our eyes. + +- - + +- -  * mix approaches energy of 2p orbital

14. During work on the synthesis of Vitamin-A a Palladium-Lead catalyst was developed, with which one can hydrogenate a triple bond without attacking double bonds already present in the starting material or those created by the hydrogenation. Helvetica Chimica Acta, 35, 447 (1952) OPP PPO  -Carotenyne  -Carotene

15. isozeaxanthin  -carotene retinal O ©Birdwatchers Digest Autumn Scarlet(?) TanagerSpringSummer Scarlet(!) Tanager canthaxanthin O: isolated O: conjugated

16. Graph of a Spectrum (IR of Paxil) (1) Color (wavelength) (2) Molecular Energy Gap (3) Molecular Vibration Frequency (1)Light Intensity (2) Light- Induced Overlap (3) Light’s “Handle” (changing dipole) (1) Experiment (2) Quantum Mechanics (3) Classical Mechanics Meaning of Axes :

17. Infrared Spectroscopy Using Light to Fingerprint molecules and identify Functional Groups and to understand Bonding and whether Atoms are linked by “Springs”

18. What Makes Vibration Sinusoidal? Newton Hooke F = - fx Frequency Constant! independent of amplitude 2h displacementfrequency velocity acceleration (Text Fig12.6) -fx (half) amplitude

19. p. 16 Hooke, of Spring (1678) Harrison’s Marine Chronometer (1761)

20. Frequency  f would be Bond Stiffness (1, 2, 3?) m is mass or, for free diatomic, “reduced” mass  is dominated by the smaller mass! When Hooke’s Law Applies:  H-C = 1  12 1 + 12 = 0.9  C-C = 12  12 12 + 12 = 6.0  C-Cl = 12  35 12 + 35 = 8.9  H-X stands apart  C-O = 12  16 12 + 16 = 6.9  = m1  m2m1  m2 m 1 + m 2 √ f m C-H  sqrt (1/0.9) C-O  sqrt (1/6.9) C=O  sqrt (2/6.9) ~3000/cm ; 10 14 Hz ~1100 ~3 x 10 13 ~1500 ~1900 C=N  sqrt (3/6.5) (Cf. Eyring)

21. Possibility of effective independence Coupled Oscillators illustrate: Complexity “Normal” mode analysis Phase of mixing

22. Coupled Oscillators Simple   2 = f/m

23. Coupled Oscillators Coupled to Frozen Partner   2 = (f+s)/m Simple   2 = f/m

24. Coupled Oscillators In-Phase Coupling   2 = 2f/2m = f/m SimpleCoupled to Frozen Partner   2 = (f+s)/m   2 = f/m

25. Coupled Oscillators   2 = 2(f+2s)/2m = (f+2s)/m Out-of-Phase Coupling SimpleCoupled to Frozen Partner In-Phase Coupling   2 = (f+s)/m   2 = f/m   2 = 2f/2m = f/m ip oop coupled isolated In such “Normal” Modes all atoms have same frequency

26. End of Lecture 56 March 1, 2010 Copyright © J. M. McBride 2010. Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0) Use of this content constitutes your acceptance of the noted license and the terms and conditions of use. Materials from Wikimedia Commons are denoted by the symbol. Third party materials may be subject to additional intellectual property notices, information, or restrictions. The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0