Understanding Electronic Excitations in Complex Systems

Transcription

1 Understanding Electronic Excitations in Complex Systems Felix Plasser González Research Group Institute for Theoretical Chemistry, University of Vienna, Austria Innsbruck, September 23 rd, 2015

2 Introduction What happens to molecules after light irradiation? Photochemistry Photobiology Photovoltaics...

3 Introduction What happens to molecules after light irradiation? Two tasks for computational chemistry: Computation of excited states Interpretation of the results

4 Introduction 1. Solve the electronic Schrödinger equation Ground state Excited state 2. Analyze the results ĤΨ 0 (r 1,...,r n ) = E 0 Ψ 0 (r 1,...,r n ) ĤΨ I (r 1,...,r n ) = E I Ψ I (r 1,...,r n ) Excitation energy: E I E 0 Orbital transitions - which orbitals?

5 Introduction Which orbitals? Atomic orbitals HF/DFT molecular orbitals Natural orbitals Natural transition orbitals Localized molecular orbitals...

6 Introduction Not all phenomena of interest can be represented in the orbital transition picture Excitonic correlation Orbital relaxation Multiple-electron excitations

7 Examples Iridium Complex Singlet Fission in Tetracene

8 Test system Ir(ppy) 3 Ir(C 3 H 4 N) 3 N NH Ir Ir N N HN N H Model iridium complex 1 Small enough for high level calculations Big enough to get the main physics Big enough to see the computational challenges Excited states from a correlated ab-initio method ADC(2) Comparison of orbital representations 1 FP, A. Dreuw JPCA 2015, 119, 1023.

9 Hartree-Fock orbitals Frontier orbitals: mixed character Orbital transitions 21 A 51 A H L H L H-6 L H-5 L H-6 L H-5 L HOMO LUMO HOMO-1 LUMO+3 HOMO-5 Excited state character - mixture of everything? HOMO-6

10 Natural transition orbitals Orbital transformation to represent the excitation in a more compact form 1 Technically: Singular value decomposition of the transition density matrix D Natural transition orbitals (NTO) D = U diag D Transition density matrix U Hole orbital coefficients λ i Transition amplitudes V Particle orbital coefficients 1 R. Martin JCP 2003, 118, ( λ1,..., λ n ) V T

11 Natural transition orbitals 2 1 A 5 1 A 98% 99% Metal-to-ligand CT Rydberg state

12 Orbitals Canonical HF/DFT orbitals often not ideal for describing the excitation Solution: Transformation into the natural transition orbital representation Black-box and widely applicable procedure

13 Examples Iridium Complex Singlet Fission in Tetracene

14 Singlet Fission Photovoltaics One photon two charge carrier pairs Microscopic mechanism S 0 + S 0 hν S 0 + S 1 1 (TT) T 1 + T 1 Reaction proceeds through two-electron excited state Also charge transfer states important 1 Quantitative analysis of the results challenging! 1 J. Michl Chem. Rev. 2010, 110, 6891.

15 Wavefunction analysis Analysis of the 1-electron transition density matrix (1TDM) 1 1TDM γ 0I (r h,r e ) =... Ψ 0 (r h,r 2,...,r n )Ψ I (r e,r 2,...,r n )dr 2...dr n One-electron excitation character Charge transfer Ω = γ 0I (r h,r e ) 2 dr e dr h = γ 0I 2 A B Ω AB = A B γ 0I(r h,r e ) 2 dr e dr h total CT = Ω 12 + Ω 21 1 FP, S.A. Bäppler, M. Wormit, A. Dreuw JCP 2014, 141,

16 Tetracene Tetracene: Efficient singlet fission 1 Goal: understanding on a molecular level Start with crystal structure Three different dimer interactions 2 Study the dimers with CASSCF 1 W.-L. Chan, Manuel Ligges, X.-Y. Zhu Nature Chem. 2012, 4, X. Feng, A.V. Luzanov, A.I. Krylov J. Phys. Chem. Lett. 2013, 4, 3845.

17 Results for dimer interactions Tetracene dimer Compact quantitative information Find bright, two-electron excited, and charge transfer states E f Ω CT E f Ω CT E f Ω CT S S S S S

18 Conclusions / Outlook When is a detailed wavefunction analysis beneficial? State character not visible through canonical orbitals Multiple-electron excitations Charge transfer Orbital relaxation 1 Excitonic correlation effects 2 Tasks Quantitative description of state character Automatization Method comparison 1 FP, S.A. Bäppler, M. Wormit, A. Dreuw JCP 2014, 141, S.A. Bäppler, FP, M. Wormit, A. Dreuw PRA 2014, 90,

19 Application Examples Transition metal complexes 1 Delocalized excited states of stacked DNA bases 2 Excitons in conjugated organic polymers 3 Unpaired electrons in graphene nanoflakes 4 1 FP, A. Dreuw JPCA 2015, 119, FP, A. Aquino et al. JPCA 2012, 116, A. Panda, FP et al. JPCA 2013, 117, S.A. Bäppler et al. in preparation. 4 FP, H. Pasalic et al. ANIE 2013, 52, 2581.

20 Implementations Integrated wavefunction analysis library libwfa Q-Chem ADC, TDDFT Planned: Molcas, Columbus Post-processing TheoDORE 1 Molcas, Columbus Multi-reference methods Turbomole CC2, ADC(2), TDDFT Gaussian, ORCA, GAMESS,... TDDFT Tools ranging from simple automatized orbital plotting to sophisticated analysis methods. 1

21 Acknowledgements Heidelberg S. A. Bäppler B. Thomitzni M. Wormit A. Dreuw Vienna K. Kumpf C. Rauer S. Mai L. González Vienna/Lubbock/Tianjin H. Lischka