From Molecules to Aggregates
•Born-Oppenheimer approximation •Frank-Condon Shift •Aggregates
Anouncement: Handout:
the course website has moved to hackman.mit.edu/6977 Bulović et al., Chemical Physics 210, 1 (1996).
Acknowledgment: figures in slides 3,6 are from Electronic Processes in Organic Crystals and Polymers by M. Pope and C.E. Swenberg @ MIT
February 19, 2002 – Organic Optoelectronics - Lecture 5
Electronic Transitions in Molecules
S1
E
a2*
dashed lines are vibrational energy levels with vibrational probability functions drawn on top
c1* c0*
a0* EA
S0
The energy shift between absorption and emission peaks is known as the Franck-Condon Shift
c2*
a1*
hνB
EB
EA = absorption energy EB = emission energy rO = equilibrium distance ∆r = nuclear displacement
MOLECULAR CONFIGURATION ENERGY DIAGRAM OF ELECTRONIC STATES S0 and S1 FOR A DIATOMIC MOLECULE
a2
c2
a1
c1
a0
c0
∆r r0
r´
r
1
The ground state, S0, and the excited state, S1, potential energy curves with vibrational probability functions showing how a mirrorimage relationship can arise between electronic absorption and emission bands
Born-Oppenheimer Approximation Electronic transition probability, F, is given by the Fermi’s Golden Rule:
r F = Ψi µ Ψf
Dipole moment operator is given as:
µ = q∑ rj
r
(with electronic charge q, and rj equal to the distance to the jth electron)
r
Born-Oppenheimer approximation expresses Ψm as a product of electronic wavefunctions for space and spin orbitals (Φmand Sm, respectively), and wavefunction Θm describing nuclear vibrations.
Ψm = Θm Sm Φm then
F = Θi Θ f
Si S f
r Φi µ Φ f
2
Born-Oppenheimer Approximation (cont.)
F = Θi Θ f
Si S f
r Φi µ Φ f
If any of the terms in F is zero then the electronic transition from state i to state f is “forbidden” Spin selection Rules require that ∆S = 0 during an electronic transition, thus S Æ T and T Æ S radiative transitions are forbidden. Shortcomings: • Since Born-Oppenheimer approximation decouples electronic and nuclear (vibrational) wavefunctions, it breaks down near degeneracies. • If does not explain “forbidden” transitions in absorption and luminescence which arise from spin-orbit coupling.
Calculated vibronic transitions in absorption, assuming harmonic approximation and that only one vibrational symmetry mode is operative. The peak of the vibronic spectrum shifts to higher energy as the configuration coordinate shift, ∆Q, between the ground and the excited electronic state increases
The molecule makes a transition from the ground vibrational state to the state with a vibrational wavefunction that most strongly resembles the initial vibrational wavefunction
3
Combination of two Fermions
S = |↑↑> S = |↓↓> 1 S = 2 (|↑↓> + |↓↑>) 1 2
S=
symmetric states ‘TRIPLETS’
antisymmetric state ‘SINGLETS’
(|↑↓> − |↓↑>)
SINGLETS COMPRISE 25% OF EXCITONS
Wavefunction
S describes the spin state of the excited electron
Examples of Molecular Absorption and Luminescence S1
PTCDA Solution in DMSO
3 2 1
Luminescence
0
R0
RELATIVE POSITION
Luminescence and absorption spectra of PTCDA single molecules in solution show a series of vibronic peaks.
1.5
2.0
2.5 Energy [eV]
Absorption
S1 [0-3]
E
S1 [0-1]
PTCDA
S0
S1 [0-2]
0
S1 [0-1]
S1 [0-0] S1 [0-0]
3 2 1
3.0
4
Transparent OLEDs – use of the Frank-Condon Shift EL Light 500 Å ITO
-
5050-100 Å Mg-Ag
V
ETL HTL ITO Glass
+
EL Light
Alphanumeric TOLED Display
> 70% transparent Bulovic´ et al., Nature 380, 29 (1996). Parthasarathy et al., Appl. Phys. Lett. 72, 2138 (1998).
Electronic Processes in Molecules JABLONSKI DIAGRAM
ENERGY TRANSFER
S1
S: spin=0 (singlet) states T: spin=1 (triplet) states
INTERSYSTEM CROSSING
1-10 ns PHOSPHORESCENCE
FÖRSTER, DEXTER or RADIATIVE
FLUORESCENCE
INTERNAL CONVERSION
10 ps
ABSORPTION
Energy
density of available S and T states on surrounding molecules
T1
>100 ns
S0
5
Fluorescence E
Phosphorescence
singlet
S1 excited T triplet excited state 1 state
E
S1
T1
FLUORESCENCE state S0 ground (singlet)
singlet exciton • symmetry conserved fast process ~10-9s
S0
PHOSPHORESCENCE
triplet exciton • triplet to ground state transition is not permitted slow process ~ 1s
Generation of Excitons Photo generation
Electrical generation
if molecule absorbs a photon, symmetry of molecule is unchanged
if electrons and holes recombine to form an exciton, their spins are uncorrelated
⇒ only singlets
⇒ singlets and triplets
Why do we care about singlets and triplets? • only singlets contribute to fluorescence • triplets contribute to phosphorescence (low efficiency process)
6
S1 [0-3]
S1 [0-2]
S1 [0-1]
S1 [0-1]
Fluorescence
CT [0-F]
CT [0-ST]
S1 [0-0] S1 [0-0]
PTCDA Solution (~ 2µM in DMSO)
1.5
2.0
2.5
3.0
Absorption
3.5
Energy [eV]
Solution Absorption PTCDA in DMSO
Absorption [a.u.]
6
2 µM
AGGREGATE State
1.6 µM . . .
4
0.25 µM
AGGREGATE STATE ABSORPTION increases with PTCDA solution concentration
2
0
1.8
2.0
2.2
2.4
2.6
2.8
3.0
Energy [eV]
7
Crystalline Organic Films PTCDA PTCDA
CHARGED CARRIER MOBILITY INCREASES WITH INCREASED π−π ORBITAL OVERLAP
11.96 Å
GOOD CARRIER MOBILITY IN THE STACKING DIRECTION 17.34 Å
µ = 0.1 cm2/Vs – stacking direction µ = 10-5 cm2/Vs – in-plane direction
z
3.21Å
Highest mobilities obtained on single crystal pentacene µ = 10 5 cm2/Vs at 10K tetracene µ = 10 4 cm2/Vs at 10K (Schön, et al., Science 2000).
y x
substrate
8
