Chemistry 2

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Chemistry 2

• Lecture 11
• Electronic spec of polyatomic molecules
  chromophores and fluorescence

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Learning outcomes
Assumed knowledge
Excitations in the visible and ultraviolet
correspond to excitations of electrons between
orbitals. There are an infinite number of
different electronic states of atoms and
molecules.

• Be able to draw the potential energy curves for
  excited electronic states in diatomics that are
  bound and unbound
• Be able to explain the vibrational fine structure
  on the bands in electronic spectroscopy for bound
  excited states in terms of the classical
  Franck-Condon model
• Be able to explain the appearance of the band in
  electronic spectroscopy for unbound excited states

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Some random images of last lecture
Franck-Condon Principle
4
Franck-Condon Principle (reprise)
6 5 4 3 2 1 0
5
Electronic spectra of larger molecules
A diatomic (or other small) molecule
An atom
A large molecule
A molecule has 3N-6 different vibrational modes.
When you have no selection rules any more on
vibrational transitions then the spectrum quickly
becomes so complicated that the vibrational
states cannot be readily resolved.
6
Electronic spectra of larger molecules
A diatomic (or other small) molecule
An atom
A large molecule
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Jablonski Diagrams
Etot Eelec Evib
Again, this is the Born-Oppenheimer approximation.
8
Correlation between diatomic PES and Jablonski
diagram
Jablonski
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Nomenclature and spin states
In polyatomic molecules, the total electron spin,
S, is one of the few good quantum numbers. If
the total electron spin is zero S 0, then
there is only one way to arrange the spins, and
we have a singlet state, denoted, S (c.f. L0 for
atoms) If there is one unpaired electron the
total spin is S ½ and there are 2 ways the spin
can be aligned (up and down), and we have a
doublet state, denoted, D
Total Spin Name symbol
0 singlet S
½ doublet D
1 triplet T
If there are two unpaired spins then there are 3
ways the spins can be aligned (c.f. 3 x
p-orbitals for L1). This is a triplet state
that we denote, T
Total spin is also called multiplicity.
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Jablonski Diagrams
First excited singlet state
First excited triplet state
0 ground state (which is a singlet in this
case)
Only the ground state gets the symbol 0 Other
states are labelled in order, 1, 2, according
to their multiplicity
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Correlation between diatomic PES and Jablonski
(again)
The x-axis doesnt mean anything in a Jablonski
diagram. Position the states to best illustrate
the case at hand.
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Chromophores
Any electron in the molecule can be excited to an
unoccupied level. We can separate electrons in
to various types, that have characteristic
spectral properties. A chromophore is simply
that part of the molecule that is responsible for
the absorption.
Core electrons These electrons lie so low in
energy that it requires, typically, an X-ray
photon to excite them. These energies are
characteristic of the atom from which they
come. Valence electrons These electrons are
shared in one or more bonds, and are the highest
lying occupied states (HOMO, etc). Transitions
to low lying unoccupied levels (LUMO, etc) occur
in the UV and visible and are characteristic of
the bonds from which they come.
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Types of valence electrons
s-electrons are localised between two atoms and
tightly bound. Transitions from s-orbitals are
therefore quite high in energy (typically
vacuum-UV, 100-200 nm). p-electrons are more
delocalised (even in ethylene) than their s
counterparts. They are bound less tightly and
transitions from p orbitals occur at lower energy
(typically far UV, 150-250nm, for a single,
unconjugated p-orbital). n-electrons are not
involved in chemical bonding. The energy of a
non-bonding orbital lies typically between that
for bonding and antibonding orbitals. Transitions
are therefore lower energy. n-orbitals are
commonly O, N lone pairs, or Hückel p-orbitals
with E a
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Transitions involving valence electrons
Vacuum (or far) uv
Near uv
Visible
Near IR
p?p
s?s
n?p
n?s
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Chromophores in the near UV and visible

• There are two main ways that electronic spectra
  are shifted into the near-UV and visible regions
  of the spectrum
• Having enough electrons that higher-lying levels
  are filled. Remember that the electronic energy
  level spacing decreases with increasing quantum
  numbers (e.g. H-atom). Atoms/molecules with d
  and f-electrons often have spectra in the visible
  and even near-IR. Large atoms (e.g. Br, I) have
  electrons with large principle quantum number.

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Chromophores in the near UV and visible
2. Delocalised p-electrons. From your knowledge
of Hückel theory and particle-in-a-box, you
should understand that larger Hückel chromophores
have a larger number of more extended,
delocalised p orbitals, with lower energy.
Transitions involving larger chromophores occur
at lower energy.
b-carotene (all trans)
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Effect of chromophore size
Chromophore
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Chromophores in the near UV and visible
Aromatic chromophores
Tetracene
Benzene
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Chromophores at work
N
N
C
C
O
O
Dibenzooxazolyl-ethylenes (whiteners for clothes)
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After absorption, then what?

• After molecules absorb light they must eventually
  lose the energy in some process. We can separate
  these energy loss processes into two classes
• radiative transitions (fluorescence and
  phosphorescence)
• non-radiative transitions (internal conversion,
  intersystem crossing, non-radiative decay)
• Lets use a Jablonski diagram (ie large molecule
  picture) to explore these processes

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Slide taken from Invitrogen tutorial
(http//probes.invitrogen.com/resources/education
/, or Level 23 computer labs)
22
Slide taken from Invitrogen tutorial
(http//probes.invitrogen.com/resources/education
/, or Level 23 computer lab)
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Slide taken from Invitrogen tutorial
(http//probes.invitrogen.com/resources/education
/, or Level 3 computer lab)
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Slide taken from Invitrogen tutorial
(http//probes.invitrogen.com/resources/education
/, or Level 3 computer lab)
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Slide taken from Invitrogen tutorial
(http//probes.invitrogen.com/resources/education
/, or Level 3 computer lab)
26
Slide taken from Invitrogen tutorial
(http//probes.invitrogen.com/resources/education
/, or Level 3 computer lab)
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Summary
S1
S0
1 Absorption 2 Non-radiative decay 3
Fluorescence
Fluorescence is ALWAYS red-shifted (lower energy)
compared to absorption
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Franck-Condon Principle (in reverse)
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Franck-Condon Principle (in reverse)
Note If vibrational structure in the ground and
exited state are similar, then the spectra look
the same, but reversed -gt the so-called mirror
symmetry
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Stokes shift
Absorption
The shift between lmax(abs.) and lmax(fluor) is
called the STOKES SHIFT A bigger Stokes shift
will produce more dissipation of heat
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The Origin of the Stokes Shift and mirror symmetry
If the vibrational level structure in the ground
and excited electronic states is similar, then
the absorption and fluorescence spectra look
similar, but reversed. Notice that if 0?4 is
the most intense in absorption, 0?4 is also most
intense in emission. The Stokes shift here is
G(4) G(4)
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Different Stokes
Which dye dissipates most heat when excited?
B.
A.
C.
D.
F.
E.
Note mirror symmetry in most, but not all dyes.
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Fluorescence spectrum ? f(lexc)
NRD
animation
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- Fluorescence is always to longer wavelength-
Stokes shift (abs. max.) (fluor. max.) 50
nm here- Mirror symmetry
Real data
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Revision The Electromagnetic Spectrum
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Revision Light as a EM field
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wavefunctions and classical vibration
A molecule in a particular solution to the
vibrational Schrödinger equation has a stationary
probability distribution
So why do we call this vibration?
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wavefunctions and classical vibration
A molecule which is in a superposition of v 0
and v 1 will be in a non-stationary state
Y0
Y1
Y2
The animation shows the time-dependence of an
admixture of 20 v1 into the v0 wavefunction.
Mixing Y1 into the Y0 wavefunction shifts the
probability distribution to the right as drawn
(red). If the molecular dipole changes along the
coordinate then the vibration brings about an
oscillating dipole.
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wavefunctions and electronic vibration

0.2
If mixing some excited state character into the
ground state wavefunction changes the dipole,
then electric fields can do this. The transition
is said to be allowed.
Hydrogen
Is to 2p transition is allowed. Electrical dipole
is brought about by mixing 1s and 2p.
Is to 22 transition is forbidden. No electrical
dipole is brought about by mixing 1s and 2s.
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Which electronic transitions are allowed?
?
?
?
?
?
The allowed transitions are associated with
electronic vibration giving rise to an
oscillating dipole
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Electronic spectroscopy of diatomics

• For the same reason that we started our
  examination of IR spectroscopy with diatomic
  molecules (for simplicity), so too will we start
  electronic spectroscopy with diatomics.
• Some revision
• there are an infinite number of different
  electronic states of atoms and molecules
• changing the electron distribution will change
  the forces on the atoms, and therefore change the
  potential energy, including k, we, wexe, De, D0,
  etc

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Depicting other electronic states
Notice the different shape potential energy
curves including different bond lengths
There is an infinite number of excited states, so
we only draw the ones relevant to the problem at
hand.
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Ladders upon ladders
Each electronic state has its own set of
vibrational states.
Note that each electronic state has its own set
of vibrational parameters, including - bond
length, re - dissociation energy, De -
vibrational frequency, we
Notice single prime () upper state double
prime () lower state
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The Born-Oppenheimer Approximation

• The total wavefunction for a molecule is a
  function of both nuclear and electronic
  coordinates
• ?(r1rn, R1Rn)
• where the electron coordinates are denoted, ri ,
  and the nuclear coordinates, Ri.

The Born-Oppenheimer approximation uses the fact
the nuclei, being much heavier than the
electrons, move 1000x more slowly than the
electrons. This suggests that we can separate
the wavefunction into two components ?(r1rn,
R1Rn) ?elec (r1rn Ri) x ?vib(R1Rn)
Total wavefunction
Electronic wavefunction at each geometry
Nuclear wavefunction
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The Born-Oppenheimer Approximation
?(r1rn, R1Rn) ?elec (r1rn Ri) x ?vib(R1Rn)
Electronic wavefunction at each geometry
Total wavefunction
Nuclear wavefunction
The B-O Approximation allows us to think about
(and calculate) the motion of the electrons and
nuclei separately. The total wavefunction is
constructed by holding the nuclei at a fixed
distance, then calculating the electronic
wavefunction at that distance. Then we choose a
new distance, recalculate the electronic part,
and so on, until the whole potential energy
surface is calculated.
While the B-O approximation does break down,
particularly for some excited electronic states,
the implications for the way that we interpret
electronic spectroscopy are enormous!
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Spectroscopic implications of the B-O approx.

• 1. The total energy of the molecule is the sum
  of electronic and vibrational energies
• Etot Eelec Evib

Evib
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Spectroscopic implications of the B-O approx.

• In the IR spectroscopy lectures we introduced the
  concept of a transition dipole moment

upper state wavefunction
lower state wavefunction
transition dipole moment
dipole moment operator
integrate over all coords.
using the B-O approximation
2. The transition moment is a smooth function of
the nuclear coordinates.
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Spectroscopic implications of the B-O approx.
2. The transition moment is a smooth function of
the nuclear coordinates. If it is constant then
we may take it outside the integral and we are
left with a vibrational overlap integral. This is
known as the Franck-Condon approximation.
3. The transition moment is derived only from
the electronic term. A consequence of this is
that the vibrational quantum numbers, v, do not
constrain the transition (no Dv selection rule).
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Electronic Absorption
There are no vibrational selection rules, so any
Dv is possible.
But, there is a distinct favouritism for certain
Dv. Why is this?
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Franck-Condon Principle (classical idea)

• Classical interpretation
• Most probable bond length for a molecule in the
  ground electronic state is at the equilibrium
  bond length, re.

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Franck-Condon Principle (classical idea)

• The Franck-Condon Principle states that as
  electrons move very much faster than nuclei, the
  nuclei as effectively stationary during an
  electronic transition.

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Franck-Condon Principle (classical idea)

• The Franck-Condon Principle states that as
  electrons move very much faster than nuclei, the
  nuclei as effectively stationary during an
  electronic transition.

The electron excitation is effectively
instantaneous the nuclei do not have a chance
to move. The transition is represented by a
VERTICAL ARROW on the diagram (R does not change).
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Franck-Condon Principle (classical idea)

• The Franck-Condon Principle states that as
  electrons move very much faster than nuclei, the
  nuclei as effectively stationary during an
  electronic transition.

The most likely place to find an oscillating
object is at its turning point (where it slows
down and reverses). So the most likely transition
is to a turning point on the excited state.
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Quantum (mathematical) description of FC principle
approximately constant with geometry
Franck-Condon (FC) factor
µ21 constant FC factor
FC factors are not as restrictive as IR selection
rules (?v1). As a result there are many more
vibrational transitions in electronic
spectroscopy. FC factors, however, do determine
the intensity.
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Franck-Condon Principle (quantum idea)
In the ground state, what is the most likely
position to find the nuclei?
Max. probability at Re
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Franck-Condon Factors
If electronic excitation is much faster than
nuclei move, then wavefunction cannot change.
The most likely transition is the one that has
most overlap with the excited state wavefunction.
2
1
v 0
v 0
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Look at this more closely

• Excellent overlap everywhere

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Franck-Condon Factors
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Franck-Condon Factors
v10
Note analogy with classical picture of FC
principle!
v. poor v0 overlap
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Electronic Absorption
There are no vibrational selection rules, so any
Dv is possible.
Relative vibrational intensities come from the FC
factor
µ21 constant FC factor
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Absorption spectrum of binaphthyl

• Example of real spectra showing FC profile

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Absorption spectrum of CFCl
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Unbound states (1)
If the excited state is dissociative, e.g. a p
state, then there are no vibrational states and
the absorption spectrum is broad and diffuse.
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Unbound states (2)
Even if the excited state is bound, it is
possible to access a range of vibrations, right
into the dissociative continuum. Then the
spectrum is structured for low energy and diffuse
at higher energy.
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Some real examples
A purely dissociative state leads to a diffuse
spectrum.
HI
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Some real examples
The dissociation limit observed in the spectrum!
I2
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Analyzing the spectrum
All transitions are (in principle) possible.
There is no Dv selection rule
Vibrational structure
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Analysing the spectrum
v 0
0
0
0
0
0
0
0
0
0
0
cm-1 18327.8
18405.4
18480.9
18555.6
18626.8
18706.3
18780.0
18846.6
18911.5
18973.9
19037.5
v 25
26
27
28
29
30
31
32
33
34
35
How would you solve this? (you have too much
data!)
1. Take various combinations of v and solve for
we and wexe simultaneously. Average the
answers. 2. Fit the equation to your data (using
XL or some other program).
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Analyzing the spectrum
cm-1 18327.8
18405.4
18480.9
18555.6
18626.8
18706.3
18780.0
18846.6
18911.5
18973.9
19037.5
v 25
26
27
28
29
30
31
32
33
34
35
v 0
0
0
0
0
0
0
0
0
0
0
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Summary

• The potential energy curve and the equilibrium
  geometry in an electronic excited state will be
  different to the ground state
• An excited state may have no equilibrium
  geometry unbound
• For bound excited states, transitions to the
  individual vibrational levels of the excited
  state are observed
• The energies of these transitions depend on the
  vibrational levels of the excited state
• The intensities of the lines depend on the
  Franck-Condon factors with vertical transition
  being the strongest
• For unbound excited states, the electronic
  spectrum is broad and diffuse

The take home message from this lecture is to
understand the (classical) Franck-Condon Principle
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Next lecture

• The vibrational spectroscopy of polyatomic
  molecules.

Week 12 homework

• Vibrational spectroscopy worksheet in tutorials
• Practice problems at the end of lecture notes
• Play with the IR Tutor in the 3rd floor
  computer lab and with the online simulations
• http//assign3.chem.usyd.edu.au/spectroscopy/ind
  ex.php

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Practice Questions

• 1. Which of the following molecular parameters
  are likely to change when a molecule is
  electronically excited?
• (a) ?e (b) ?exe (c) µ (d) De (e) k

2. Consider the four sketches below, each
depicting an electronic transition in a diatomic
molecule. Note that more than one answer may be
possible (a) Which depicts a transition to a
dissociative state? (b) Which depicts a
transition in a molecule that has a larger bond
length in the excited state? (c) Which would
show the largest intensity in the 0-0
transition? (d) Which represents molecules that
can dissociate after electronic
excitation? (e) Which represents the states of a
molecule for which the v0 ? v3 transition is
strongest?