Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes:...
-
date post
22-Dec-2015 -
Category
Documents
-
view
214 -
download
0
Transcript of Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes:...
![Page 1: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/1.jpg)
Chemistry 125: Lecture 57March 2, 2011
Spectroscopy Electronic & IR Spectroscopy
Normal Modes:Mixing and Independence
This
For copyright notice see final page of this file
![Page 2: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/2.jpg)
Spectroscopy forStructure 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. 12.7-12.8 pp. 533
Vibrational (Infrared) e.g. F&J sec. 15.4, pp. 707-713
NMR (Radio) e.g. F&J sec. 15.5-15.9, pp. 713-749
![Page 3: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/3.jpg)
“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.
![Page 4: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/4.jpg)
++
+
1s 2p
(1s + 2p)2
superposition e-density
time-dependent
Oscillation frequency given by the energy difference between
1s and 2p
![Page 5: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/5.jpg)
Time-Dependence Footnote A time-dependent wavefunction looks just like the spatial s we have been talking about, except that it is multiplied by eit = cos(wt) + i sin(wt), 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 eit e-it = 2. BUT when a problem involves actually mixing two states of different energy, one considers a wavefunction of the form eit + eit . 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+2pz) will become (1s-2pz).
* 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
![Page 6: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/6.jpg)
++
+
1s 2p
Oscillating dipole has“oscillator strength”
interacts with /generates / absorbs
light
(1s + 2p)2
superposition e-density
time-dependent
1s - 2p transitionis “allowed”
Oscillation frequency given by the energy difference between
1s and 2p
![Page 7: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/7.jpg)
+
+
+
1s 2s
(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 transitionis “forbidden”
Pulsing frequency given by the energy difference between
1s and 2s
![Page 8: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/8.jpg)
:
n-*
n-* Transitions ofOrganic “Chromophores”
:C X+
+ -
- Oscillating electric field wags electrons
up and down by mixing n with *.
:
n+*
The large energy gap between n and * makes this transition occur at high
frequency (in the ultraviolet).
![Page 9: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/9.jpg)
:
n-*
R
n-* Transitions ofOrganic “Chromophores”
:C X+
+ -
- 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
![Page 10: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/10.jpg)
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 OPPOPP
PPO
-Carotenyne
-CaroteneCCH
RR
HH2 Pd/Pb
hn D
CCH R
R H
![Page 11: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/11.jpg)
Autumn Scarlet(?) Tanager
©Birdwatchers Digest
Early Fall
isozeaxanthin-caroteneretinal
O
canthaxanthin
O: isolated
O: conjugated
Summer Scarlet(!) Tanager
with
kin
d p
erm
issi
on
of
Llo
yd S
pita
lnik
![Page 12: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/12.jpg)
Graph of a Spectrum (IR of Paxil)
(1) Color (wavelength)
(2) Molecular Energy Gap
(3) Molecular Vibration Frequency
(1) LightIntensity
(2) Light-InducedOverlap
(3) Light’s“Handle”
(changing dipole)
(1) Experiment
(2) Quantum Mechanics
(3) Classical Mechanics
Meaning of Axes :
![Page 13: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/13.jpg)
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”
![Page 14: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/14.jpg)
€
x = h sin(ωt)
€
dx
dt= hω cos(ωt)
€
d2x
dt 2= a = −hω2 sin(ωt)
€
a
x= −ω2
€
ω 2 =f
m
What Makes Vibration Sinusoidal?
€
a
x=
− f
m
€
a = F mNewton
Hooke F = - fx
€
ω =f
m
FrequencyConstant!independent of amplitude 2h
€
=−ω 2
displacement frequency
velocity
acceleration
(Text Fig12.6)
-fx
(half) amplitude
![Page 15: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/15.jpg)
FrequencyConstant!independent of amplitude 2h
Hooke, of Spring (1678)
© National Maritime Museum, Greenwich, LondonHarrison’s Marine Chronometer (1761)
![Page 16: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/16.jpg)
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 12
1 + 12= 0.9
12 12
12 + 12C-C = = 6.0
C-Cl = 12 35
12 + 35= 8.9
H-X stands apart
C-O = 12 16
12 + 16= 6.9 m1 m2
m1 + m2 =
√ fm
C-H sqrt (1/0.9)
C-O sqrt (1/6.9)
C=O sqrt (2/6.9)
~3000/cm ; 1014Hz
~1100 ~3 x 1013
~1500
~1900
(Cf. Eyring)
C=N sqrt (3/6.5)
Quartz Crystal Microbalance can weigh a monolayer of adhering molecules
(e.g. H2 + H2C=CH2 / Pt)
![Page 17: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/17.jpg)
Possibility of effective independence
Coupled Oscillatorsillustrate:
Complexity
“Normal” mode analysis
Phase of mixing
![Page 18: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/18.jpg)
Coupled Oscillators
Simple2 = f/m
![Page 19: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/19.jpg)
Coupled Oscillators
Coupled to Frozen Partner2 = (f +s)/m
Simple2 = f/m
![Page 20: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/20.jpg)
Coupled Oscillators
In-Phase Coupling
2 = 2f/2m = f/m
Simple
Coupled to Frozen Partner2 = (f +s)/m
2 = f/m
![Page 21: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/21.jpg)
Coupled Oscillators
2 = 2(f +2s)/2m = (f +2s)/m
Out-of-Phase Coupling
Simple
Coupled to Frozen Partner
In-Phase Coupling
2 = (f +s)/m
2 = f/m
2 = 2f/2m = f/m
•ip
oopcoupled
isolated
In such “Normal” Modes all atoms
oscillate at the same frequency
![Page 22: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/22.jpg)
oopip oop + ip
Coupled Oscillators
Superposition of Two Normal Modes of
different frequencyVibration switches between
oscillators as the two modes beat in- and out-of-
phase
Out-of-Phase Coupling
In-Phase CouplingIn such
“Normal” Modes all atoms
oscillate at the same frequency
2 = 2(f +2s)/2m = (f +2s)/m
2 = 2f/2m = f/m
![Page 23: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/23.jpg)
ipoop
Very Different Oscillators are ~Independent
Vibration remains localized when coupling is weak
compared to -mismatch
ip
oopcoupled
low
high
oop + ip
![Page 24: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/24.jpg)
A General Molecule of N Atoms has 3N Independent Geometric Parameters.
(e.g. as Cartesian Coordinates)
or3 to Fix Center of Mass
3 to Fix Orientation
3N-6 for Internal Vibrations(Normal Modes)
![Page 25: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/25.jpg)
3N-6 Mixed-up Normal Modes sounds hopelessly complex.
(though good for “fingerprint”)
(Cf. Energy-match / Overlap)
butmixing requires:
Frequency Match&
Coupling Mechanism ip
oopcoupled
isolated
![Page 26: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/26.jpg)
Butane C4H10
3 x (4 + 10) = 42 degrees of freedom
- 3 (translation) - 3 (rotation) = 36 vibrations
C4 : 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.
![Page 27: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/27.jpg)
C8 Straight Chain Hydrocarbons
OctaneC8H18
C-H stretch
C-CH3 umbrella+ C-C stretch
CH2
rockCH2 wag
CH2 scissors
26 atoms 72 normal modes (not all IR active)
C-H stretch
“Breathing” gives no net dipole change - no IR peak
Half ofC4H10’s tenC-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.
![Page 28: Chemistry 125: Lecture 57 March 2, 2011 Spectroscopy Electronic & IR Spectroscopy Normal Modes: Mixing and Independence This For copyright notice see final.](https://reader034.fdocuments.in/reader034/viewer/2022050714/56649d7e5503460f94a61a0d/html5/thumbnails/28.jpg)
End of Lecture 57March 2, 2011
Copyright © J. M. McBride 2011. 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).
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