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**Lecture 4 Intramolecular energy transfer**

Photochemistry Lecture 4 Intramolecular energy transfer

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Jablonski diagram S0 S1 T1

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**Fluorescence quantum yields**

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**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

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**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

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**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 (1) (2) (3) (4) (5)

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As shown e.g., in Gilbert and Baggott, p 67-68, substitute (4) and (3) into (1) and use of (2) leads to 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…..

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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: 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

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**Born-Oppenheimer Separation**

Q represents vibn co-ordinate Electronic matrix element Density of states Franck-Condon factor

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**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.

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El Sayed’s Rule Intersystem crossing is likely to be very slow unless it involves a change of orbital configuration.

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**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.

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**Effect of heavy-atom substitution**

Increase in strength of spin-orbit interaction

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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.

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**Effect of Franck Condon Factor**

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**Energy transfer starts from lowest level of S1 state**

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

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Franck Condon Overlap Overlap between lowest vib level of S1 and high (degenerate) vib level of S0)

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**Effect of Franck Condon Factor**

Poor overlap Better overlap Energy Gap Law

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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

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**kisc for T1S0 for several species**

Energy gap

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**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.

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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

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**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.

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**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

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**Observed decay rates for various DNA and RNA nucleosides**

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