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Photochemistry
Lecture 4
Intramolecular energy
transfer
Jablonski diagram
S0
S1
T1
Fluorescence quantum yields
Intramolecular energy transfer




Collision free radiationless process; molecule
evolves into different electronic state without loss
or gain of energy
Excess electronic energy transferred to
vibrations, followed by fast relaxation.
Represented by horizontal line on Jablonski
Diagram
Internal Conversion (IC)


No change of spin state e.g., S0  S1
Intersystem Crossing (ISC)

Change of spin state e.g., T1S0 or S1T1
What determines rate of intramolecular
processes and what is the mechanism?

Take viewpoint that the S1 state formed by
photoexcitation is not a true eigenstate of the full
Hamiltonian

Spin-orbit coupling mixes S1 state with T1 state
(ISC) or T1 with S0

Nuclear kinetic energy (vibration) mixes S1 state
with S0 state (IC) or S2 with S1

Non-stationary state evolves with time
Quantum mechanical picture


Time dependent
Schrodinger Equation
(MQM 3e p19)
Assume S1 and T1 states
are eigenfunctions of zeroorder Hamiltonian, H0
d
H  i  
dt
d
H 0 S  i  S
dt
H  H0  H '

Full Hamiltonian

Wavefunction changes with
time
 (t )  aS (t ) s  aT (t ) T
aS  aT  1 aS (0)  1, aT (0)  0
2
(1)
(2)
(3)
(4)
2
(5)

As shown e.g., in Gilbert and Baggott, p 6768, substitute (4) and (3) into (1) and use
of (2) leads to
d
i
aT    T * H ' S d
dt

i.e., the rate of change of the coefficient (representing
amplitude of wavefunction transferred to T1 state)
depends on the matrix element of the perturbation
operator.
Consideration of degeneracy of final states in triplet
manifold (density of vibrational states) leads to…..
Fermi’s Golden Rule
For the radiationless transition between initial state i
described by wavefunction I and final state f the
transition rate constant is given by:
2
kif ( E ) 
h

*
f
Hi d  f ( E )
2
H is that part of the Hamiltonian responsible
for driving the process.
- spin orbit coupling operator for ISC
- nuclear kinetic energy operator for IC
f(E) is the density of vibrational states for f
Born-Oppenheimer Separation
Q represents
vibn co-ordinate
f   f (Q) f (r; Q)
2
k
 f ( E )   *f  i dQ   *f Hi d e

Density of
states
2
Franck-Condon
factor
Electronic
matrix element
Effect of electronic matrix element

k   f * H ' i d e
2
For intersystem crossing, use spin orbit coupling
operator
H '  H so  i  i .si
i

Intersystem crossing is intrinsically slow as singlet
triplet interaction small for most organic
molecules.

H'= Hso transforms like a rotation – never as the
totally symmetric representation.
El Sayed’s Rule

Intersystem crossing is likely to be very slow
unless it involves a change of orbital
configuration.
El Sayed’s Rule – further comments
El Sayed – ISC allowed if change of orbital
configuration
In aromatic carbonyl fast ISC is S1  T2
followed by internal conversion T2  T1.
Effect of heavy-atom substitution
Increase in strength of spin-orbit interaction
Internal conversion

Internal conversion nearly always involves
change of orbital configuration.

Nuclear kinetic energy operator is totally
symmetric, suggesting IC is formally forbidden.

However separation of Franck Condon factor not
strictly valid because Hamiltonian depends on
nuclear co-ordinates.
Effect of Franck Condon Factor
f   f (Q) f (r; Q)
2
k
 f ( E )   *f  i dQ   *f Hi d e

2
Franck-Condon
factor
Energy transfer starts from lowest level
of S1 state
Absorption spectrum
determined by (a) vibronic
selection rules and (b)
Franck-Condon overlap
Energy
transfer etc
Emission (fluorescence) or
other processes follow
relaxation to lowest
vibrational level of S1
Franck Condon Overlap
Overlap between lowest vib
level of S1 and high
(degenerate) vib level of S0)
Effect of Franck Condon Factor
Poor overlap
Energy Gap Law
Better overlap
Energy Gap Law

Rate of intramolecular
energy transfer
decreases with
increasing energy gap

Usually
S1-T1 < T1-S0 < S1-S0
Thus this factor tends to
make ISC faster than
IC
kisc for T1S0 for several species
Energy gap
Effect of deuterium substitution
Rates of T1 – S0 intersystem crossing
The vibrational frequency of deuterium substituted
compounds is lower than unsubstituted
Thus higher quantum numbers (more nodes) involved in
final state for same energy gap – poorer overlap.
Kasha’s rule
Emitting electronic energy level of given
multiplicity is the lowest excited level of that
multiplicity.
 Consequence of energy gap law (FC factor)
 In general E(S2)-E(S1) << E(S1)-E(S0)

S3
S2
S1
S0
Thus fast internal
conversion
between higher
singlet states
Exception: azulene – S2-S1  S1-S0
Why are intramolecular processes
important?
The reactions of triplet states may be
fundamentally different from excited singlet
state: different potential energy surface
characterising the reaction.
 e.g, -cleavage of carbonyl compounds
typically 2 orders of magnitude faster via
triplet state.
 Triplet excited state may be metastable with
respect to decay to ground state, thus
reactive processes can compete effectively.

Why does all this matter? (cont)




Collisional energy transfer is bound by spincorrelation.
Use of fluorescence labelling potentially undermined
by intramolecular energy transfer (ditto stimulated
emission in a dye laser).
UV radiation damage to nucleic acid bases
minimized by very fast internal conversion ( ps) –
genetic material survives.
Internal conversion from S2 to S1 important in
photosynthesis
Observed decay rates for various DNA
and RNA nucleosides
www.chemistry.ohiostate.edu/~kohler/