Electronic Structure and Geometry Relaxation at Excited State

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1 Electronic Structure and Geometry Relaxation at Excited State Speaker: Chun I Wang ( 王俊壹 )

2 Structure-Performance Relationship Processing schemes Solvent quality Thermal annealing Blend composition (ratio) Molecular features Regioregularity Defects Molecular architecture BHJ solar cells Polymer LED Thin-film transistors Continuum Performance of conjugated polymer-based devices Mesoscale Phase & film morphology Molecular scale Intra-molecular properties Interfacial arrangement Quantum length scale Electronic properties Absorption/emission Quantum efficiency Power conversion efficiency Open-circuit voltages (V oc ) Short-circuit current (I sc ) Phase separation Crystal/amorphous phases Aggregates Structures in solutions Chain conformation Pair alignment Inter-chain interaction Electronic excited state Exciton/charge transfer

3 Electronic Structure Configuration interaction approach Kasha's rule Geometry Relaxation at Excited State Change in bond length Torsion of backbone Exciton dynamics

4 Molecular Orbital (MO) & Electronic Configuration Frontier MOs of planar 10-mer PPV E LUMO+3 LUMO+2 LUMO+1 LUMO S 0 HOMO HOMO-1 HOMO-2 HOMO-3 I. Frank et al., J. Phys. Chem. B, 2007, 111,

5 Molecular Orbital (MO) & Electronic Configuration Octatetraene (8 π electrons) E LUMO+3 LUMO+2 LUMO+1 LUMO HOMO HOMO-1 HOMO-2 HOMO-3 Electronic configuration S 0 S 1 E 1 S 2 or E 2 E 2 = E 3 E 3

6 Effect of Electron Correlation E LUMO+3 S 1 S 2 HOMO LUMO HOMO-1 LUMO HOMO LUMO+1 Configuration interaction (CI) A linear combination of electronic configurations LUMO+2 LUMO+1 First excited state (S 1 ): LUMO HOMO HOMO-1 HOMO-2 E 1 + or E 2 E 3 E S1 = E 1 = E LUMO E HOMO Second excited state (S 2 ): E S2 = a E 2 + b E 3 = a E LUMO E HOMO 1 + b(e LUMO+1 E HOMO ) HOMO-3 where a and b are weighting coefficients J-L. Bredas et al., Acc. Chem. Res., 1999, 32, 267.

7 Configuration Interaction Approach E S 1 S 2 Configuration interaction (CI) LUMO+3 HOMO LUMO HOMO-1 LUMO HOMO LUMO+1 Case 1: E S1 < E S2 LUMO+2 LUMO+1 i.g., PPV, MEH-PPV, emitting conjugated polymers LUMO E 1 + E 3 First excited state (S 1 ): E S1 = E 1 = E LUMO E HOMO HOMO HOMO-1 E 2 Second excited state (S 2 ): HOMO-2 E S2 = a E 2 + b E 3 HOMO-3 = a E LUMO E HOMO 1 + b(e LUMO+1 E HOMO ) J-L. Bredas et al., Acc. Chem. Res., 1999, 32, 267.

8 Configuration Interaction Approach E S 1 S 2 S 2 S 1 Configuration interaction (CI) LUMO+3 HOMO LUMO HOMO-1 LUMO HOMO LUMO+1 Case 2: E S1 > E S2 LUMO+2 LUMO+1 i.g., octatetraene LUMO E 1 + E 3 First excited state (S 1 ): S 2 state E S1 = E 1 = E LUMO E HOMO HOMO HOMO-1 E 2 Second excited state (S 2 ): S 1 state HOMO-2 E S2 = a E 2 + b E 3 HOMO-3 = a E LUMO E HOMO 1 + b(e LUMO+1 E HOMO ) J-L. Bredas et al., Acc. Chem. Res., 1999, 32, 267.

9 Kasha's Rule Photon emission (fluorescence or phosphorescence) occurs in appreciable yield only from the lowest excited state, S 1. E LUMO+3 LUMO+2 PPV at S 1 Octatetraene at S 1 HOMO LUMO HOMO-1 LUMO HOMO LUMO+1 LUMO+1 LUMO hν hν + hν HOMO HOMO-1 HOMO-2 HOMO-3 J-L. Bredas et al., Acc. Chem. Res., 1999, 32, 267.

10 Geometry Relaxation at Excited State E S 1 Excited state Electrostatic force theory Coulombic force exerted on the nuclei induces movements of the nuclei to accompany the change in the electron distribution until the force diminish at excited state geometry. Electron density difference between S 0 and S 1 state Ground state E S 0 Reaction coordinate S. Tretiak et al., Phys. Rev. Lett., 2002, 89, H. Nakatsuji et al., J. Phys. Chem. A, 2007, 111, force acting on C nuclei increasing region decreasing region

11 Geometry Relaxation: Change in Bond Length Bond length alternation (BLA) The difference between carbon-carbon single and double bond lengths in the vinyl linkage along the backbone of the polymer Length of double bond Length of single bond BLA = d 1 + d 3 2 d 2 Electron Hole S. Tretiak et al., Phys. Rev. Lett., 2002, 89, H. Nakatsuji et al., J. Phys. Chem. A, 2007, 111, 5473 S. Tretiak et al., J. Phys. Chem. Lett., 2011, 2, 566. Orbital plot of 10-mer MEH-PPV at S 1 state

12 Exciton Self-Trapping Bond length alternation (BLA) Photoluminescence spectra PPV oligomers dispersed in PMMA matrix at 77 K Electron Hole Orbital plot of 10-mer MEH-PPV at S 1 state J. Cornil et al., Chem. Phys. Lett., 1997, 278, 139. S. Tretiak et al., Phys. Rev. Lett., 2002, 89,

13 Geometry Relaxation: Torsion of Backbone Excited state Torsional potential of 8-mer MEH-PPV Ground state Excited state E S 1 Ground state E S 0 Reaction coordinate S. Tretiak et al., Phys. Rev. Lett., 2002, 89, H. Lischka et al., J. Phys. Chem. A, 2013, 117, 2181.

14 Exciton Dynamics in Linear Oligomers Timescale of geometry relaxation Change in bond length Time-resolved fluorescence anisotropy decay profiles change in bond length: 10~100 fs Time-resolved fluorescence spectra for the linear oligothiophenes planarization of backbone : ~10 ps Torsion of backbone D. Kim et al., J. Phys. Chem. Lett., 2016, 7, 452.

15 Remaining Challenges to Be Solved What s a reliable QC calculation for π conjugated system? What s the effect of triplet sates? Would geometry relaxation at excited state occur in many body system? Recent experiments revealed that multi-chromophores (excitons) segment along a polymer chain, but there is not yet QC calculation demonstrating this phenomenon. An example of exciton dynamics for linear oligomer has been shown, but the exciton dynamics for more complicated systems are still unclear.

16 Conclusion Considering the effect of electron correlation, configuration interaction approach is a generally scheme to describe electronic structure at excited state. The change of charge distribution after excitation induces a set of driving force on the nuclei, and leads to the geometry relaxation of conjugated polymers. The exciton dynamics is attributed to the different time scale of bond-length change and backbone planarization, which result in exciton self-trapping and exciton delocalization, respectively.