Radiative Transitions between Electronic States

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Radiative Transitions between Electronic States

• November 14, 2002.
• Michelle

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4.1 Paradigm Shifts

• Maxwell ? light as electromagnetic waves

Planck Quantization of energy E h?
Einstein Photons - quantized light consisting of
particles possessing bundles of energy

• DeBroglie ? light as a particle with wave
  properties
• E h? h(c/?) pc

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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 CO CC CC-CC CC-CO aromatics Mo
lar absorptivity ? measures absorption strength
units cm-1M-1 NOT cm2mol-1
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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.)
Exciton migration electron-hole pair hopping
from molecule to molecule in a crystal
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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
• Fluctuating dipoles are in resonance

E ?A?BR-3AB
True for all dipole-dipole interactions, magnetic
or electric
Energy of the dipole-dipole interaction falls off
as A and B move apart, given by R-6AB
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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
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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
A light wave generates a time-dependent force
field F
absorption photons being removed from the
electromagnetic field emission photons being
added (?) to the electromagnetic field
ABSORPTION (reverse for emission)
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4.4 Light as an Oscillating Electric Field

• Radiative transitions between states are induced
  by perturbations which make the two stateslook
  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
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4.4 Light as an Oscillating Electric Field
Force on an electron in a molecue by a light wave
Electrical force
Magnetic force
c gtgt 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

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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
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4.4 Light as an Oscillating Electric Field
Light and the hydrogen atom
Electric field interaction reshapes the electron
distribution of the 1s orbital
No node, no vibration ? 1 node, vibratory
motion Increase in of nodes essential for
absorption and vice versa for emission (related
to nodal nature of light wave)
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4.4 Light as an Oscillating Electric Field
Light and the hydrogen molecule

• Interaction involves ? and ? orbitals instead of
  s and p
• Absorption is ? ? ? or ? and is analogous to the
  s ? p transition in the hydrogen atom

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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
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4.4 Oscillator Strength
Probability of light absorption is related to the
oscillator strength f
Theoretical oscillator strength
Experimental absorption
f 4.3x10-9 ?? d?
Area under ? vs. wavenumber plot
Strong absorption gt f1
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?eri2 3he2
f 8?me? ltHgt2 3he2
Relationship between experimental and quantum
quantities
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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 ?

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4.5 Franck-Condon Absorption
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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

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4.6 State Mixing
State mixing is the first- or higher-order
correction to an original zero-order
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
Mixing coefficient
first order n, ?
?(S1) ?(n, ?) ??(?, ?)
zero order n, ?
zero order ?, ?

• Spatial overlap of mixing states
• Symmetry properties
• Nature and symmetry of H

• Features important to state mixing
• Energy gap between zero order configurations
• Magnitude of the matrix element that mixes the
  states

? lt?aH?bgt Ea - Eb
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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 ltT1HsoSngt ? 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
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4.6 Mechanisms for Mixing Singlet and Triplet
Measurement of forbidden absorptions and
emissions provide evidence of the identity of the
mixing state
n, ?
?, ?
Vibrational structure provides clues as to which
motions are most effective in mixing states
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4.7 Molecular Electronic Spectroscopy
Kashas Rule photochemical reactions occur from
the lowest excited singlet or triplet states

• absorption
• emission
• excitation

Ie 2.3 I0 ?Al?AeA for a weakly absorbing
solution of A
? log(I0/It)/lc
Optical density
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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
spin-forbidden 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 but cancel because of
symmetry
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4.7 Quantum Yields of Allowed Fluorescence
Quantum yield of emission is given by ?e
?k0e(k0e ?ki)-1 ?k0e?
Experimental lifetime
Formation efficiency of the emitting state
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 ?
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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 CO for H generally results in a
  substantial decrease in ?F
• Molecular rigidity enhances ?F
• ?F is an efficiency that compares relative
  transition probabilities, doesnt relate directly
  to rates

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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
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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

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4.8 Multiplicity Change in Radiative Transitions
Greater oscillator strength than n2 ? ?, ?

• In general fvfe(?, ?) gt fvfe(n, ?) because
  ?(?, ?) gt ?(n, ?) for S-S transitions where
  spin is not a factor
• Implies that fs (n, ?) gtgt 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 orbital mixing and minor S-O coupling
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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 oxygen
• Organic halides, organometallics
• Heavy atom rare gases

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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
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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 Ts are not rapidly equilibrated different
  phosphorescence parameters will be observed
  (above 10K this is usually not an issue)

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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 kdgtgtk0P
• Phosphorescence may be measured at room
  temperature if
• Triplet quenching impurities are rigorously
  excluded
• Unimolecular triplet deactivation must be lt104
  k0P at RT

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4.11 Excited State Structures
S1 and T1 states are electronic isomers of S0
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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
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4.12 Complexes and Exciplexes
Mixtures of molecules with low IP or high EA
often exhibit charge-transfer 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 A-
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4.12 Complexes and Exciplexes
Collision between M and polarizable ground state
N will usually result in a complex stablized by
some charge-transfer interactions if MN
properties are distinct this is an exciplex or
excimer Exciplex/mer emission will occur to a
very weakly bound or dissociative ground state
Energetic considerations
Favourable formation is a balance with entropic
considerations
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4.12 Complexes and Exciplexes

• Exciplex/excimer emission is featureless
• Excimer emission is not as solvent dependent as
  exciplex (less charge-transfer 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

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4.13 Delayed Fluorescence
The observed ?F may be longer than expected based
on prompt emission...
Thermal repopulation of S1 When the S-T gap is
small and the ISC is fast the S1 state can be
repopulated from Tn Effect disappears at low
temperatures
Triplet-triplet anihilation Combination of 2
triplets to form a sinlget state from which
emission is observed Es ? ET ET
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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