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/