Chemistry 2
Lecture 11
• Electronic spec of polyatomic molecules:
chromophores and fluorescence
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.
Learning outcomes
• 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
Some random images of
last lecture…
De’
we’
De”
Franck-Condon
Principle
we”
re” re’
Lecture 7
Franck-Condon Principle
(reprise)
Energy
Energy
Energy
6
5
4
3
2
1
0
0
1
2
0
1
2
R
R
3
4
5
3
4
5
Lecture 7
Electronic spectra of
larger molecules…
An atom
A diatomic (or other
small) molecule
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.
Lecture 7
Electronic spectra of
larger molecules…
A diatomic (or other
small) molecule
An atom
A large molecule
3s
2p
2s
1s
Lecture 7
Jablonski Diagrams…
Vibrational levels
Electronic states
(thin lines)
(thick lines)
Etot = Eelec + Evib
Again, this is the Born-Oppenheimer approximation.
Lecture 7
Correlation between diatomic
PES and Jablonski diagram
Jablonski
Lecture 7
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. L=0 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
If there are two unpaired spins:
then there are 3 ways the spins
can be aligned (c.f. 3 x porbitals for L=1). This is a
triplet state that we denote, T
Total spin is also called “multiplicity”.
Total
Spin
Name
symbol
0
singlet
S
½
1
doublet
triplet
D
T
Lecture 7
Jablonski Diagrams…
S1
First excited
singlet state
T1
S0
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
Lecture 7
Correlation between diatomic
PES and Jablonski (again)
S1
T1
S0
The x-axis doesn’t mean anything in a Jablonski diagram.
Position the states to best illustrate the case at hand.
Lecture 7
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.
Lecture 7
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 nonbonding 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
Lecture 7
Transitions involving
valence electrons
Vacuum
(or far) uv
Near
uv
Visible
Near IR
pp*
ss*
np*
ns*
100
200
300
400
500
600
700
800
Wavelength (nm)
Lecture 7
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:
1.
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 felectrons often have spectra in the visible and even near-IR. Large
atoms (e.g. Br, I) have electrons with large principle quantum number.
Ni(H2O)62+
Ni(H2NCH2CH2CH3)32+
Mn(H2O)62+
Lecture 7
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)
Lecture 7
Effect of chromophore
size
400
450
500
550
600
650
700
750
800
Wavelength (nm)
Chromophore
Lecture 7
Chromophores in the near UV
and visible
Aromatic chromophores:
Benzene
What is this structure?
Tetracene
Lecture 7
Chromophores at work
CH3
CH3
CH3
O
trans-retinal
(light absorber in eye)
CH3
CH3
N
N
C
O
C
O
Dibenzooxazolyl-ethylenes
(whiteners for clothes)
Lecture 7
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)
Let’s use a Jablonski diagram (ie large molecule
picture) to explore these processes…
Lecture 7
Slide taken from “Invitrogen” tutorial
(http://probes.invitrogen.com/resources/education/, or Level 2&3 computer labs)
Lecture 7
Slide taken from “Invitrogen” tutorial
(http://probes.invitrogen.com/resources/education/, or Level 2&3 computer lab)
Lecture 7
Slide taken from “Invitrogen” tutorial
(http://probes.invitrogen.com/resources/education/, or Level 3 computer lab)
Lecture 7
Slide taken from “Invitrogen” tutorial
(http://probes.invitrogen.com/resources/education/, or Level 3 computer lab)
Lecture 7
Slide taken from “Invitrogen” tutorial
(http://probes.invitrogen.com/resources/education/, or Level 3 computer lab)
Lecture 7
Slide taken from “Invitrogen” tutorial
(http://probes.invitrogen.com/resources/education/, or Level 3 computer lab)
Lecture 7
Summary
~10-12 s
S1
~10-8 s
S0
Fluorescence is ALWAYS
red-shifted (lower energy)
compared to absorption
1 = Absorption
2 = Non-radiative decay
3 = FluorescenceLecture 7
Energy
Energy
Energy
Franck-Condon Principle
(in reverse)
0
1
2
0
1
2
R
R
3
4
5
3
4
5
Lecture 7
Energy
Energy
Energy
Franck-Condon Principle
(in reverse)
0
1
2
0
1
2
R
R
3
4
5
3
4
5
Note: If vibrational
structure in the ground
and exited state are
similar, then the spectra
look the same, but
reversed -> the so-called
“mirror symmetry” Lecture 7
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
Lecture 7
The Origin of the Stokes
Shift and mirror symmetry
Stokes shift
v’=4
v’=0
sum =
Stokes
shift
v”=4
v”=0
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)
Lecture 7
Which dye
dissipates most heat
when excited?
Different Stokes
A.
B.
C.
D.
E.
F.
Note mirror symmetry in most, but not all dyes.
Lecture 7
Fluorescence spectrum
 f(lexc)
NRD
… animation …
Lecture 7
Real data…
Absorption
500
550
Fluorescence
600
650
700
Wavelength (nm)
- Fluorescence is always to longer wavelength
- Stokes shift = (abs. max.) – (fluor. max.) [= 50 nm here]
- Mirror symmetry
Lecture 7
Revision:
The Electromagnetic Spectrum
Revision: Light as a EM field
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?
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
|Y|2
The animation shows the time-dependence of an admixture of 20% v=1 into the v=0
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.
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
+ 0.2×
=
Is to 2p transition is allowed. Electrical
dipole is brought about by mixing 1s and
2p.
+ 0.2×
=
Is to 22 transition is forbidden. No
electrical dipole is brought about by
mixing 1s and 2s.
Which electronic transitions are allowed?





The allowed transitions are associated with electronic vibration
giving rise to an oscillating dipole
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
Depicting other electronic states
Excited Electronic States
1. Unbound
2. Bound
Ground Electronic State
There is an infinite number of excited
states, so we only draw the ones
relevant to the problem at hand.
Notice the different shape
potential energy curves including
different bond lengths…
Ladders upon ladders…
Each electronic state has its own
set of vibrational states.
De’
we’
Note that each electronic state
has its own set of vibrational
parameters, including:
- bond length, re
- dissociation energy, De
- vibrational frequency, we
De”
we”
Notice: single prime (’) = upper state
double prime (”) = lower state
re” re’
The Born-Oppenheimer Approximation
The total wavefunction for a molecule is a function of both
nuclear and electronic coordinates:
Y(r1…rn, R1…Rn)
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:
Y(r1…rn, R1…Rn) = elec (r1…rn; Ri) x vib(R1…Rn)
Total wavefunction = Electronic wavefunction at ×
each geometry
Nuclear wavefunction
The Born-Oppenheimer Approximation
Y(r1…rn, R1…Rn) = elec (r1…rn; Ri) x vib(R1…Rn)
Total wavefunction = Electronic wavefunction at × Nuclear wavefunction
each geometry
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!
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
Eelec
Etot
Spectroscopic implications of the B-O approx.
• In the IR spectroscopy lectures we introduced the concept of
a transition dipole moment:
μ 21   Y (ri , Ri )μˆ Y1 (rj , R j )drdR  0
*
2
|2
transition
dipole
moment
upper state
wavefunction
lower state integrate
dipole
moment wavefunction over all
operator
coords.
|1
using the B-O approximation:
μ 21   2*vib ( Ri ) 2*elec (ri )μˆ  1elec (rj )1vib ( R j )drdR
  2*vib ( Ri )μ( R) 1vib ( R j )dR
2. The transition moment is a smooth function of the nuclear coordinates.
Spectroscopic implications of the B-O approx.
μ 21   
*vib
2
( Ri )
 
*vib
2
( Ri )μ( R)  ( R j )dR
|2
( Ri )  ( R j )dR
|1
 μ0  
*vib
2
*elec
2
elec
vib
ˆ
(ri )μ  1 (rj )1 ( R j )drdR
vib
1
vib
1
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).
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?
Franck-Condon Principle (classical idea)
“Most probable bond length for a
molecule in the ground electronic
state is at the equilibrium bond
length, re.”
Energy
Classical interpretation:
0
1
2
3
R
4
5
The Franck-Condon Principle
states that as electrons move
very much faster than nuclei, the
nuclei as effectively stationary
during an electronic transition.
Energy
Franck-Condon Principle (classical idea)
In the ground state, the
molecule is most likely in v=0.
0
1
2
3
R
4
5
•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).
Energy
Franck-Condon Principle (classical idea)
0
1
2
3
R
4
5
•The Franck-Condon Principle
states that as electrons move
very much faster than nuclei, the
nuclei as effectively stationary
during an electronic transition.
Energy
Franck-Condon Principle (classical idea)
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.
0
1
2
3
R
4
5
Quantum (mathematical) description of FC
principle
*vib
vib
μ 21  μ 0  2 ( Ri ) 1 ( R j )dR
approximately constant
with geometry
Franck-Condon (FC)
factor
μ21 = constant × FC factor
FC factors are not as restrictive as IR selection rules (Dv=1). As a result there are
many more vibrational transitions in electronic spectroscopy.
FC factors, however, do determine the intensity.
Franck-Condon Principle (quantum idea)
In the ground state, what is the most likely position to find the nuclei?
3
v
Prob   2
2
1
Max. probability at Re
(0)
0
v=0
0
1
2
R
3
4
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
0
1
2
Wave number
3
4
v” = 0
Look at this more closely…
Negative overlap in middle
Positive overlap at edges
overall very small overlap
Negative overlap to left, postive overlap
to right
overall zero overlap
• Excellent overlap
everywhere
Franck-Condon
Factors
1
2
0
3
Wave number
4
Franck-Condon
Factors
v=10
Note: analogy with classical
picture of FC principle!
v. poor v=0 overlap
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
Absorption spectrum of binaphthyl
•Example of real spectra showing FC profile
16
17
15
18
19
20
21
22
14
23
13
24
12
25
11
26
27
28
10
9
(3) (4) (5)
30100
6
7
30200
8
30300
30400
30500
30600
-1
Wave number (cm )
30700
30800
30900
Absorption spectrum of CFCl
= CCl2 peaks
(0,n,0)
(0,n,1)
(0,n,2)
(1,n,0)
3
3
2
(0,n,0)
(0,n,1)
(0,n,2)
5
5
4
17000
18000
}
10
(0,0,1) hot bands
19000
20000
-1
Wave number (cm )
21000
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.
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.
Some real examples…
HI
A purely dissociative state
leads to a diffuse spectrum.
Some real examples…
I2
The dissociation limit observed in
the spectrum!
0.25
I2
Absorbance
0.20
0.15
0.10
0.05
0.00
16000
18000
20000
-1
Wave number (cm )
22000
Analyzing the spectrum…
All transitions are (in principle) possible. There is
no Dv selection rule
Vibrational structure
0.25
I2
Absorbance
0.20
0.15
0.10
0.05
0.00
16000
18000
20000
-1
Wave number (cm )
22000
Analysing the spectrum…
v”
0
v’
25
cm-1
18327.8
0
26
18405.4
0
27
18480.9
0
28
18555.6
0
29
18626.8
0
30
18706.3
0
31
18780.0
0
32
18846.6
0
33
18911.5
0
34
18973.9
0
35
19037.5
G( v)  (v  2 we  (v 
1

1 2w x
e e
2
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).
Analyzing the spectrum…
Etot  Eelec  Evib
2
Etot  Eelec  G( v)  Eelec  (v  1 2 we  (v  1 2  we xe
v”
0
v’
25
cm-1
18327.8
0
26
18405.4
0
27
18480.9
0
28
18555.6
0
29
18626.8
0
30
18706.3
0
31
18780.0
0
32
18846.6
0
33
18911.5
0
34
18973.9
10
0
35
19037.5
Dissociation energy = 19950 cm-1
20000
-1
Wave number (cm )
19500
19000
18500
Eelec = 15,667 cm-1
18000
we = 129.30 cm-1
wexe = 0.976 cm-1
17500
17000
20
30
40
50
v'
60
70
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
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/index.php
Practice Questions
1. Which of the following molecular parameters are likely to change when a molecule is
electronically excited?
(a) ωe (b) ωexe (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 v”=0 → v’=3 transition is
strongest?