Radiative Transitions between
Electronic States
November 14, 2002.
Michelle
4.1 “Paradigm” Shifts
• Maxwell  light as electromagnetic waves
Blackbody Radiation
Photoelectric Effect
Wavelength dependence of energy
distribution of light emitted by a hot
object
Wavelength dependence of energy
of electrons emitted when light
strikes a metal
Planck
Einstein
Quantization of energy E = h
Photons - quantized light
consisting of particles
possessing “bundles” of energy
• DeBroglie  light as a particle with wave properties
E = h = h(c/) = pc
From the perspective of absorption and emission it is
more convenient to think of light in terms of an
oscillating electromagnetic wave
2
4.2-4.3 Absorption and Emission
Transitions between electronic energy levels
accompanied by absorption or emission of light
Photochemical region of the spectrum: 200-700 nm 143 kcal mol-1-41 kcal
mol-1
valence orbital (, , n)  antibonding orbital (*, *)
Chromophore: atom or group acting as a light absorber
Lumophore: atom or group acting as a light emitter
C=O
C=C
C=C-C=C
C=C-C=O
aromatics
Molar absorptivity  measures “absorption strength”
units cm-1M-1 NOT cm2mol-1
3
4.4 The Nature of Light
The classical theory of light is a convenient starting point providing a
pictorial and understandable physical representation of the interaction of
light and molecules
classical theory can be improved by applying quantum interpretations of
basic concepts (orbital, quantized energy etc.)
Dipoles as a model for interactions between electrons and
light
oscillating electric dipole field of the electromagnetic wave
oscillating dipoles due to electrons moving in orbitals
 Dipole-dipole interactions are through space and don’t require orbital overlap
(Interactions requiring overlap are “exchange interactions”)
Exciton migration: electron-hole pair hopping from molecule to
Examples
ofadipolar
molecule in
crystalinteractions: London dispersion forces, EPR, 4
NMR, large splittings for crystals (exciton interactions)
4.4 Dispersion Forces
Correlation of fluctuations in electronic charge distributions in
molecules
•Dipole on A drives
formation of dipole on
B and vice versa
E ~ ABR-3AB
Energy of the dipole-dipole
interaction falls off as A and B
move apart, given by R-6AB
•Fluctuating dipoles are
in “resonance”
True for all dipole-dipole
interactions, magnetic or
electric
5
4.4 Light as an Oscillating Electric Field
Frequency () of oscillating field must “match” a possible
electronic oscillation frequency (conservation of energy)
There must be an interaction or coupling between the field
(oscillating dipoles) and the electron
Interaction strength depends on field dipole and induced dipole
strength as well as distance between the two.
Laws of conservation of angular momentum must be obeyed
(electrons, nuclei, spins)
Spin change is highly resisted in absorption due to time
constraints
*the most important interaction between the
electromagnetic field and the electrons of a molecule can be
modeled as the interaction of 2 oscillating dipole systems
that behave as reciprocal energy-donor, energy-acceptors 6
4.4 Light as an Oscillating Electric Field
If the field can couple
to the electrons it can
exchange energy by
driving the system into
resonance at a
frequency common to
both
 electric
field
Direction of propogation
H magnetic field
A light wave generates a
time-dependent force field F
absorption: photons being removed from the
electromagnetic field
ABSORPTION
(reverse for emission) emission: photons being added (?) to the
electromagnetic field
7
4.4 Light as an Oscillating Electric Field
•
Radiative transitions between states are induced by
perturbations which make the two states”look alike” by inducing
a resonance
•
Resonance requires that the two states have the same energy
and momentum characteristics and a common frequency for
resonance
E = h
Energy difference
between two states
Frequency of light wave
oscillation
The energy of the photon must exactly match the
the energy level difference in the molecule
8
4.4 Light as an Oscillating Electric Field
Force on an electron in a molecue by a light wave
F = e + e[H v]
c
Electrical force
Magnetic force
c >> velectron
Force on an electron
F ~ e
•Major
force on electrons is due to the oscillating electric field of
the light wave
•Net
effect of the interaction is generation of a transitory
dipole moment in the molecule
9
4.4 Light as an Oscillating Electric Field
Electric dipole induced by an electric field generated between
two plates
Direction of induced dipole is always parallel to the direction
of the external electric field
10
4.4 Light as an Oscillating Electric Field
Light and the hydrogen atom
s orbital has
0 units of
angular
momentum (
h)
Electric field interaction reshapes
the electron distribution of the 1s
orbital
p orbital has
1
 photon
must have 1
unit
No node, no vibration  1 node, vibratory motion
Increase in # of nodes essential for absorption and vice versa for emission
11
(related to nodal nature of light “wave”)
4.4 Light as an Oscillating Electric Field
Light and the hydrogen molecule
involves  and 
orbitals instead of s and p
• Interaction
is    or * and is
analogous to the s  p
transition in the hydrogen atom
• Absorption
12
4.4 Light as a Stream of Particles:
Photons
•
The photon as a reagent that may collide and react with
molecules
•
Long  photons have little energy and momentum, short 
photons have a lot of both
•
Largest cross-section of an individual chromophore is ~10 Å
•
Nuclei are effectively frozen in space as a photon passes
Spectroscopic Properties and Theoretical Properties
In order to use the laws of quantum mechanics to describe
fundamental properties we have to consider these terms:
f oscillator strength
i transition dipole moment
P transition probabilities
13
4.4 Oscillator Strength
Probability of light absorption is related to the oscillator strength f
Theoretical
oscillator strength
Strong absorption => f~1
f~
4.3x10-9 ∫
d
Experimental
absorption
Area under  vs. wavenumber plot
Rate constant for emission k0e is related to  by:
k0e ~ 4.3x10-9 -20 ∫ d ~ -20
f
Oscillator strength can be related to transition dipole moment by:
Transition dipole
moment
f = 8me 2i ~ 10-5|eri|2
3he2
f = 8me <H>2
3he2
Relationship between experimental
14 and
quantum quantities
4.5 The Shape of Absorption and Emission Specta
• Electronic
transitions in molecules are not as “pure” as they are in
atoms, in molecules relative nuclei motions must be considered
• An
ensemble of nuclear configurations are observed
• “most
prominent vibrational progression is associated with the
vibration whose eqm position is most changed by the transition” ? 15
4.5 Franck-Condon & Absorption
16
4.5 Franck-Condon & Emission
•
The most probable transitions
produce an elongated ground state,
while absorption initiallly produces a
compressed excited state
•
In both cases of absorption and
emission, transition occurs from the
=0 level of the initial state to some
vibrational level of the final state 
which level is dependent on the
displacement between  and *
•
Band spacing in the resulting
spectrum is determined by the
vibrational structure in the final state
17
4.6 State Mixing
State mixing is the first- or higher-order correction to an original zeroorder approximation of single orbital configurations or single spin
multiplicities
Example: an n, * S1 state actually contains a finite amount of , *
character mixed in so the first order wavefunction is given by:
first order
n, *
(S1) = (n, *) + (, *)
Features important to state
mixing:
•
•
Mixing coefficient
Energy gap between zero
order configurations
Magnitude of the matrix
element that mixes the
states
zero order zero order
n, *
, *
•
Spatial overlap of
mixing states
 = <a|H|b>
Ea - Eb
•
Symmetry properties
•
Nature and symmetry
of H
< n|H| >
= 0 when n and 
are orthogonal
18
4.6 Mechanisms for Mixing Singlet and Triplet
Singlet-triplet transitions are
strictly forbidden in first order
but spin-orbit coupling mixes
singlet and triplet states so
that
transitions
become
allowed
1. Direct coupling of T1 and Sn
<T1|Hso|Sn> ≠ 0
2. Indirect electronic coupling
via and intermediate
triplet state (mixing of T1 with
upper vibrational triplets)
3. Turning on 1. and 2. via
vibrational motions of the
molecule
19
4.6 Mechanisms for Mixing Singlet and Triplet
n, *
, *
Measurement of “forbidden”
absorptions and emissions
provide evidence of the
identity of the mixing state
Vibrational structure provides
clues as to which motions
are most effective in mixing
states
20
4.7 Molecular Electronic Spectroscopy
Kasha’s Rule: photochemical reactions occur from the lowest excited singlet
or triplet states
absorption
•
 ~ [log(I0/It)]/lc
Optical density
•
emission
•
excitation
Ie = 2.3 I0 AlAe[A]
for a weakly absorbing solution of A
21
4.7 Spin-Allowed Transitions
“allowedness” is measured by the oscillator strength f which
can be dissected into:
f = (fe x fv x fs) fmax
fe - electronic factors, fv - Franck-Condon factors, fs - spin-orbit factors
A perfectly allowed transition has f = 1
A spin allowed transition has fs = 1 and for a spinforbidden transition fs depends on spin-orbit coupling
fe
Overlap forbiddeness: poor spatial overlap of orbitals
involved in electronic transition
Orbital forbiddeness: wavefunctions which overlap in space
22
but cancel because of symmetry
4.7 Quantum Yields of Allowed Fluorescence
Quantum yield of emission is given by:
e =
Formation efficiency
of the emitting state
*k0e(k0e
+
ki)-1
=
*k0e
Experimental
lifetime
All rate constants that
deactivate the excited state
ki is very sensitive to experimental conditions:
•Diffusional quenching and thermal chemical reactions may
compete with radiative decay
•Certain molecular motions may also provide competitive
decay pathways
•Measurements at low temperature (77K) cause ki terms to
become small relative to k0e
F = kF(kF + kST)-1 = kF 
23
4.7 Quantum Yields of Allowed Fluorescence
Generalizations from experimental observations:
•
Rigid aromatic hydrocarbons are measurably fluorescent
•
Low value of F for these molecules is usually the result of
competing ISC
•
Substitution of H for X generally results in a decrease in F
•
Substitution of C=O for H generally results in a substantial
decrease in F
•
Molecular rigidity enhances F
F is an efficiency that compares relative transition
probabilities, doesn’t relate directly to rates
24
4.7 Quantum Yields of Allowed Fluorescence
The highest energy vibrational
band in an emission spectrum
usually corresponds to the 0,0
transition
ET and ES can be obtained
If there is no fine structure the
onset of emission is used to
guess the upper limit of E
25
4.8 Spin-Orbit Coupling
•
The value of (S0T) and k0P(T  S0) are directly related to
the degree of spin-orbit coupling between S0 and T
•
S-O coupling depends on:
•Nuclear
•
charge
•Availability
of transitions between “orthogonal” orbitals
•Availability
of a one atom center transition
Degree of S-O coupling is related to , a S-O coupling
constant
•
depends on the orbital configurations involved
26
4.8 Multiplicity Change in Radiative Transitions
Greater oscillator strength than n2  , *
•
In general fvfe(, *) > fvfe(n, *)
because (, *) > (n, *) for
S-S transitions where spin is
not a factor
•
Implies that fs (n, *) >> fs (,
*) for spin-forbidden radiative
transitions
•
a radiative transition n2 *
where the electron jumps from
px to py on the same atom is
very favourable because of the
momentum change
(compensating for the spin
momentum change)
In planar molecules, out of plane vibrations can cause
27
orbital mixing and minor S-O coupling
4.9 Perturbation of S0T Absorption
Compound possessing lowest energy , * or heavy atoms are usually
insensitive to spin-orbit perturbations
•S0T(,
*) of aromatics is generally enhanced by S-O perturbation
•S0T(n,
*) of ketones is insensitive to S-O perturbation
•S0T
enhancers
•Molecular
•Organic
•Heavy
oxygen
halides, organometallics
atom rare gases
28
4.9 Perturbation of S0T Absorption
Internal versus external heavy atom effect
Note position
dependence
Useful for determining the
nature of the excited state
29
4.9 Triplet Sublevels
•
A triplet state at room temperature is actually a rapidly
equilibrating mixture of 3 states (sublevels Tx Ty Tz)
•
Absorption initially produces only one of the three levels
•
Normally absorption to the sublevels is not resolved
•
Molecules in different sublevels have their electrons in
different planes
•
If T’s are not rapidly equilibrated different phosphorescence
parameters will be observed (above 10K this is usually not
an issue)
30
4.9 Phosphorescence
•
•
•
P is not a reliable parameter for characterizing T
P ~ STk0P(k0P + kTS)-1 gives the quantum yield for
phosphorescence when measured at 77 K and only ISC is
competing
No reports of phosphorescence from nonaromatic hydrocarbons
•ISC
is inefficient for flexible molecules
•T1 S0 is spin forbidden AND Franck-Condon forbidden (twisted triplet)
•Large kd due to surface “touching” between T1 and S0
•
•
•
Theoretical relationship between P or T and molecular structure
is not direct
Small P may be due to low ST or to kd>>k0P
Phosphorescence may be measured at room temperature if:
•Triplet
quenching impurities are rigorously excluded
•Unimolecular triplet deactivation must be <104 k0P at RT
31
4.11 Excited State Structures
S1 and T1 states are
electronic isomers of
S0
32
4.12 Complexes and Exciplexes
•
2 or more molecules may participate in a cooperative
absorption or emission
•
Spectroscopic characteristics are:
•
Observation of a new absorption band not characteristic of
starting components
•
Observation of a new emission band not characteristic of starting
components
•
Concentration dependence of the new absorption/emission
intensity
Exciplex or excimer: an excited molecular complex that is dissociated
or only weakly associated in the ground state
33
4.12 Complexes and Exciplexes
Mixtures of molecules
with low IP or high EA
often exhibit chargetransfer absorption
bands (EDA bands)
This type of
absorption is very
sensitive to changes
in solvent polarity
Transition from *
can be thought of as
D,AD+ A34
4.12 Complexes and Exciplexes
Energetic considerations
Collision between M* and
polarizable ground state N
will usually result in a
complex stablized by some
charge-transfer
interactions
if M*N properties are
distinct this is an exciplex
or excimer
Exciplex/mer emission will
occur to a very weakly
bound or dissociative
ground state
Favourable formation is a
balance with entropic
considerations
35
4.12 Complexes and Exciplexes
• Exciplex/excimer
emission is
featureless
• Excimer
emission is not as
solvent dependent as
exciplex (less chargetransfer stabilization)
• Intramolecular
exciplexes/eximers are also
possible when the linkage is
of the appropriate length
• Formation
of excited state
complexes can also be
monitored by time-resolved
spectroscopy
36
4.13 Delayed Fluorescence
The observed F may be longer than expected based on
“prompt” emission...
Thermal repopulation
of S1
Triplet-triplet
anihilation
When the S-T gap is
small and the ISC is
fast the S1 state can
be repopulated from
Tn
Combination of 2
triplets to form a
sinlget state from
which emission is
observed
Effect disappears at
low temperatures
Es  ET + ET
37
4.14 The Azulene Anomaly
Emission from upper
excited states
Large S2-S1 gap slows
down the interconversion
which would normally
cause all emission to be
from S1
38