1

J-aggregates and H-aggregates

2

N+

Cl

N

B) dichloromethane 1.3 x 10-6 M

A) 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

3

4

Cyclohexane (dashed)

CH2BrCl (points)

Water (solid)

5

Interactions between 2 molecules. One of them is in an electronically excited state i : Electronic wave function for the initial excited state (D excited but not A) f : Electronic wave function for the final excited state (A excited but not D)

'i fH

* *1

(1) (2) (2) (1)2

i D A D A

* *1

(1) (2) (2) (1)2

f D A D A

Interaction H’ between the initial and the final state:

* * * *

1 1(1) (2) (2) (1) ' (1) (2) (2) (1)

2 2D A D A D A D A

H

* *( ) ( ) ' (1 1)2 (2)D A D AH

* *( ) ( ) ' (2 2)1 (1)D A D AH ex

C ex

C

6

The Coulomb term can be expanded into a sum of terms (multipole-multipole exp.)

1 2* 1122 cosin sin 2cos cos sD A

Therefore the perturbation H’C can be expressed as:

2

3 *0

*2

1'

4C D A D A

DAR

eH l l

n

First dominant term: dipole-dipole interaction between the transition dipole moments D and A for the transitions D*D and AA*

7

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.

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.

Medium and exciton theory strong interaction: molecular orbital theory

* 'D A C i C fH

8

*AAμ

*i D A

*f D A

2

20

3*'

4 DAC D A

D AeH l l

n R

lD and lA = coordinates of the electrons belonging to D and A

* * *

0

32

*1

4 DA

D A D D A AD AD A

n Re e

l l

*D Dμ

** 2

0

3 * *1

4 DA

AA

DD D D AA

Rn

μ μ

* 'D A i C fH

electronic transitionmoments

2* ( * , *)

2EnT D A D ADAk

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.

9

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 AAnd forms a basis for describing the rate of electronic EnT.

** 2

0

3 * *1

4 DA

AA

DD D D AA

Rn

μ μ

10

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.

i k i kA A A A

* *ki k iAA A A

* *ii k kAA A A

Energy E1

Energy E1

Excited state:

H’C caused by the electronic transition dipole moments.

* *1 2 1 2( , )i k i kA A A A

c c c c

1 2 1 2 1 2 1 2( , ) ( , ) ( , ) ( , )c c H c c c c c c

* * and i k i kA A A A

* * 0i k i kA A A A

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 excitedstates A*i…Ak and Ai…A*k is so weak that the splitting of these states is negligible.

Energy E0

Excited state:

Ground state:

The excited state is described by a linear combination of

11

11 12

21 22

0h h

h h

* *

1

2 i k i kA A A A

* *

1

2 i k i kA A A A

The node corresponding to the minus signin - is an excitation node (not an electron orbital node).

symmetric

antisymmetric

In both stationary states + and - the excitation is on both molecules i and k.

The excitation is collective or delocalized.

Phase relation of the wave functions which describe the interaction betweenA*i…Ak and Ai…A*k caused by AA*

(=±2).

1

1

C

C

E

E

2

0

3

* 2*

1

4

A

DA

AC AA

Rn

μ

* *1 2 1 2( , )i k i kA A A A

c c c c

At an excitation node, the phase relation between the transition moments of the respective molecular centres change phase.

12

C depends on the relative orientationof the transition dipole moments described by A*A.

11 12

21 22

0h h

h h

* *

1

2 i k i kA A A A

* *

1

2 i k i kA A A A

In both stationary states + and - the excitation is on both molecules.

1

1

C

C

E

E

1 2* 1122 cosin sin 2cos cos sA A

Exciton splitting caused by the interactionof the configurations due to the electronic transition dipole moments.

J-aggregate

H-aggregate

13

ˆ ˆi k i kM

ˆ ˆi k i kM

* *

1( )

2 i k i kA A A AM

* *

1( )

2 i k i kA A A AM

Selection rules for the transition moment: (Ai…Ak) [(A*i…Ak)( Ai…A*k)]:

Magnitude of the splitting (12 = 0 and 1 = 2)

2

*

2 3

0

21

41 3cos ( )AA

C

DAn R

μ

2*2

8

3e

AAcm

fhe

μ1 2 3 4 5

0

100

200

300

400

500

Ene

rgy

/ cm

-1

Distance / nm

M- is in both cases equal to 0

* *

1

2 i k i kA A A A

* *

1

2 i k i kA A A A