photochemistry lecture 4 intramolecular energy transfer
TRANSCRIPT
Photochemistry
Lecture 4
Intramolecular energy transfer
Jablonski diagramS0 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., T1S0 or S1T1
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 zero-order Hamiltonian, H0
Full Hamiltonian
Wavefunction changes with time
dt
diH
SS dt
diH 0
'0 HHH
0)0(,1)0(1
)()()(22
TSTS
TTsS
aaaa
tatat
(1)
(2)
(3)
(4)
(5)
As shown e.g., in Gilbert and Baggott, p 67-68, substitute (4) and (3) into (1) and use of (2) leads to
dHi
adt
dSTT '*
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…..
For the radiationless transition between initial state i described by wavefunction I and final state f the transition rate constant is given by:
)(2
)( 2* EdHh
Ek fifif
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
Fermi’s Golden Rule
Born-Oppenheimer Separation
);()( QrQ fff
2**)(2
eififf dHdQEk
Density of states
Franck-Condon factor
Electronic matrix element
Q represents vibn co-ordinate
Effect of electronic matrix element
For intersystem crossing, use spin orbit coupling operator
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.
2
'* eif dHk
ii
iiso sHH .'
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
);()( QrQ fff
2**)(2
eififf dHdQEk
Franck-Condon factor
Absorption spectrum determined by (a) vibronic selection rules and (b) Franck-Condon overlap
Emission (fluorescence) or other processes follow relaxation to lowest vibrational level of S1
Energy transfer etc
Energy transfer starts from lowest level of S1 state
Franck Condon Overlap
Overlap between lowest vib level of S1 and high (degenerate) vib level of S0)
Effect of Franck Condon Factor
Energy Gap Law
Poor overlap Better overlap
Energy Gap Law Rate of intramolecular
energy transfer decreases with increasing energy gap
UsuallyS1-T1 < T1-S0 < S1-S0
Thus this factor tends to make ISC faster than IC
kisc for T1S0 for several species
Energy gap
Effect of deuterium substitution
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.
Rates of T1 – S0 intersystem crossing
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 spin-
correlation. 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.ohio-state.edu/~kohler/