J-aggregates and H-aggregates Seminar on J and H aggregates, G. Calzaferri

1-butanol magenta 7.4 x 10-6 M 1.3 x 10-5 M, 1.7 x 10-5 M 1.75 x 10-5 M, 1.8 x 10-5 M black 2.2 x 10-5 M B) dichloromethane 1.3 x 10-6 M

Cyclohexane (dashed) CH2BrCl (points) Water (solid)

Interactions between 2 molecules Interactions between 2 molecules. One of them is in an electronically excited state Yi : Electronic wave function for the initial excited state (D excited but not A) Yf : Electronic wave function for the final excited state (A excited but not D) Interaction H’ between the initial and the final state:

The Coulomb term can be expanded into a sum of terms (multipole-multipole exp.) First dominant term: dipole-dipole interaction between the transition dipole moments mD and mA for the transitions D*®D and A®A* Therefore the perturbation H’C can be expressed as:

Weak interaction between donor and acceptor molecules Strong interaction: the electronic spectra of a mixture of donors and acceptors are different from those of their diluted solutions. Weak interaction: the electronic spectrum of a mixture of donors and acceptors is a superposition of the spectra of the diluted solutions. Medium and exciton theory strong interaction: molecular orbital theory Only the Coulomb term plays a role for weak interactions. The exchange term requires orbital overlap between the D* and A, which causes larger interaction.

Only the Coulomb term plays a role for weak interactions, since the exchange term requires orbital overlap between the D* and A, which causes larger interaction. lD and lA = coordinates of the electrons belonging to D and A electronic transition moments

This equation not only forms a basis for describing the rate of electronic EnT. This equation gives information about the influence of this interaction on the electronic states of D* and A And forms a basis for describing the rate of electronic EnT.

J-aggregates and H-aggregates (Scheibe 1932) Pair of molecules Ai and Ak at a distance R. R is so large that the interaction in the electronic ground state is negligibly small. Electronically excited states: A*i…Ak resp. Ai…A*k Negligible overlap of the wave functions between (A*i and Ak ) and (Ai and A*k). This does not necessarily mean that the interaction between the electronically excited states A*i…Ak and Ai…A*k is so weak that the splitting of these states is negligible. Ground state: Energy E0 Excited state: Energy E1 Excited state: Energy E1 H’C caused by the electronic transition dipole moments. The excited state is described by a linear combination of

The excitation is collective or delocalized. symmetric antisymmetric In both stationary states F+ and F- the excitation is on both molecules i and k. Phase relation of the wave functions which describe the interaction between A*i…Ak and Ai…A*k caused by mAA* (k=±2). The node corresponding to the minus sign in F- is an excitation node (not an electron orbital node). At an excitation node, the phase relation between the transition moments of the respective molecular centres change phase.

Exciton splitting caused by the interaction of the configurations due to the electronic transition dipole moments. In both stationary states F+ and F- the excitation is on both molecules. bC depends on the relative orientation of the transition dipole moments described by kA*A. J-aggregate H-aggregate

Magnitude of the splitting (f12 = 0 and q1 = q2) Selection rules for the transition moment: (Ai…Ak) ® [(A*i…Ak)«( Ai…A*k)]: M- is in both cases equal to 0 Seminar on J and H aggregates, G. Calzaferri