Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final page of this file

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) e.g. F&J sec pp. 533 Vibrational (Infrared) e.g. F&J sec. 15.4, pp NMR (Radio) e.g. F&J sec , pp

“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.

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

Time-Dependence 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 = cos(  t) + i sin(  t), where i =  (-1),  is the energy (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 0.5/(  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. time cos

s2p 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

s2s (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

: 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).

: 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

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 C C H R R H H2H2 Pd/Pb h C C H R R H

Autumn Scarlet(?) Tanager ©Birdwatchers Digest Early Fall isozeaxanthin  -carotene retinal O canthaxanthin O: isolated O: conjugated Summer Scarlet(!) Tanager with kind permission of Lloyd Spitalnik

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 :

Infrared Spectroscopy Using Light to Fingerprint molecules, to identify Functional Groups, Infrared Spectroscopy. Using Light to Fingerprint molecules,,,,,,, and to use molecular dynamics to study Bonding and whether Atoms are linked by “Springs”

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

Frequency Constant! independent of amplitude 2h Hooke, of Spring (1678) © National Maritime Museum, Greenwich, London Harrison’s Marine Chronometer (1761)

Frequency  For atoms f should 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  =   C-C = = 6.0  C-Cl = 12  = 8.9  H-X stands apart  C-O = 12  = 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 ; Hz ~1100 ~3 x ~1500 ~1900 (Cf. Eyring) C=N  sqrt (3/6.5) Quartz Crystal Microbalance can weigh a monolayer of adhering molecules (e.g. H 2 + H 2 C=CH 2 / Pt)

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

Coupled Oscillators Simple   2 = f/m

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

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

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 oscillate at the same frequency

oop ip oop + ip Coupled Oscillators Superposition of Two Normal Modes of different frequency Vibration switches between oscillators as the two modes beat in- and out-of-phase Out-of-Phase Coupling In-Phase Coupling In such “Normal” Modes all atoms oscillate at the same frequency   2 = 2(f +2s)/2m = (f +2s)/m   2 = 2f/2m = f/m

ip oop Very Different Oscillators are ~Independent Vibration remains localized when coupling is weak compared to  -mismatch ip oop coupled low  high  oop + ip

A General Molecule of N Atoms has 3N Independent Geometric Parameters. (e.g. as Cartesian Coordinates) or 3 to Fix Center of Mass 3 to Fix Orientation 3N-6 for Internal Vibrations (Normal Modes)

3N-6 Mixed-up Normal Modes sounds hopelessly complex. (though good for “fingerprint”) (Cf. Energy-match / Overlap) but mixing requires: Frequency Match & Coupling Mechanism ip oop coupled isolated

Butane C 4 H 10 3 x (4 + 10) = 42 degrees of freedom - 3 (translation) - 3 (rotation) = 36 vibrations C 4 : 3 stretch, 2 bend, 1 twist 10 C-H : 10 stretch, 20 bend or twist Mixed (according to frequency-match / coupling) into 36 normal modes.

C 8 Straight Chain Hydrocarbons Octane C 8 H 18 C-H stretch C-CH 3 umbrella + C-C stretch CH 2 rock CH 2 wag CH 2 scissors 26 atoms  72 normal modes (not all IR active) C-H stretch “Breathing” gives no net dipole change - no IR peak Half of C 4 H 10 ’s ten C-H stretch normal modes have no “handle” E(t) helps push 8 H in and out E(t) helps push 4 Hs up and down Timing has been disabled on this slide so you can step back and forth with the arrow keys to study vibrational modes.

End of Lecture 57 March 2, 2011 Copyright © J. M. McBride 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