Singlet fission for solar energy conversion A theoretical insight
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1 Singlet fission for solar energy conversion A theoretical insight David Casanova Quantum Days in Bilbao July 16, 2014
2 Harvesting Solar Energy Solar energy 1h = 1 year human consumption We use ~ 0.07% Earth radiation ~0.1% world s energy demand radiation sea level Si c-si cell
3 Harvesting Solar Energy Solar energy 1h = 1 year human consumption We use ~ 0.07% Earth radiation ~0.1% world s energy demand Up conversion lanthanides ion pairs radiation sea level Si c-si cell up conversion
4 Harvesting Solar Energy Solar energy 1h = 1 year human consumption We use ~ 0.07% Earth radiation ~0.1% world s energy demand Up conversion lanthanides ion pairs Down conversion radiation sea level Quantum cutting 2!Si Si c-si cell rare earth glasses up conversion down conversion Multi Exciton Generation inorganic semiconductors Singlet Fission organic materials
5 Singlet Fission: definition S 0 + S 1 T 1 + T 1 S 1 e - Energy T 1 S 0 h +
6 Singlet Fission: definition S 0 + S 1 T 1 + T 1 S 1 e - Energy T 1 e - e - S 0 h + h +
7 Singlet Fission: definition S 1 S 0 + S 1 T 1 + T 1 e - Properties organic compounds bimolecular process spin allowed very fast! ps Energy e - e - T 1 S 0 h + h +
8 Singlet Fission: definition Energy S 1 T 1 S 0 + S 1 T 1 + T 1 e - e - e - Properties Requirements organic compounds bimolecular process spin allowed very fast! ps E(S 1 ) " 2E(T 1 ) E(T 2 ) > 2E(T 1 ) proper coupling S 0 h + h +
9 Singlet Fission: definition Energy S 1 T 1 S 0 + S 1 T 1 + T 1 e - e - e - Properties Requirements organic compounds bimolecular process spin allowed very fast! ps E(S 1 ) " 2E(T 1 ) E(T 2 ) > 2E(T 1 ) proper coupling S 0 h + h + Detecting SF triplet generation > 100% delayed fluorescence magnetic field effects
10 Singlet Fission: chronology 1965 photophysics of anthracene crystals 1968 low fluorescence in tetracene crystals 1980 carotenoids 1989 conjugated polymer 2004 proposed for photovoltaic applications 2006 theoretical guidelines!! new SF materials & development! 2013 SF in solar cells molecular crystals more materials theory & experiment energy conversion
11 Purpose: theory of SF Computational characterization electronic structure methods States involved in SF Relative energies Mechanisms Rates of SF Key factors for SF Development of computational tools Propose/design new SF materials
12 Electronic states with RAS-SF Restricted Active Space Spin-Flip H 2 molecule Chemist s view virtual orbitals 1s!*! 1s " spin # spin occupied orbitals
13 Electronic states with RAS-SF Restricted Active Space Spin-Flip H 2 molecule Chemist s view virtual orbitals 1s!*! 1s HF singlet " spin # spin Energy, mh occupied orbitals FCI bond length, Å
14 Electronic states with RAS-SF Restricted Active Space Spin-Flip H 2 molecule Chemist s view virtual orbitals 1s!*! 1s HF singlet " spin # spin Energy, mh HF triplet occupied orbitals FCI bond length, Å
15 Electronic states with RAS-SF Restricted Active Space Spin-Flip H 2 molecule Active Space RAS3 1s!* 1s! HF singlet RAS2 Energy, mh HF triplet FCI RAS1 bond length, Å
16 Electronic states with RAS-SF Restricted Active Space Spin-Flip H 2 molecule Active Space + High Spin RAS3 1s!* 1s! HF singlet RAS2 Energy, mh HF triplet FCI RAS1 bond length, Å
17 Electronic states with RAS-SF Restricted Active Space Spin-Flip Reference Reduced Full CI spin-flip excitations!!!
18 Electronic states with RAS-SF Restricted Active Space Spin-Flip Reference Reduced Full CI Casanova, Head-Gordon PCCP Casanova, JCP ; JCC Particle Hole spin-flip excitations +
19 X RAS-SF algorithms Restricted Active Space Spin-Flip Casanova, Head-Gordon PCCP Casanova, JCP ; JCC jrasi ¼ X R C R jri configuration ^jric class active hole occupation h dimensions 2O m n m n+1 m n m n part p V m n-1 m n
20 X X RAS-SF algorithms Restricted Active Space Spin-Flip Casanova, Head-Gordon PCCP Casanova, JCP ; JCC jrasi ¼ X C R jri R X hlj ^HjRiC R ¼ EC L R configuration ^jric class X active hole occupation h dimensions 2O m n m n+1 m n m n part p V m n-1 m n hlj H ^jric
21 X X RAS-SF algorithms Restricted Active Space Spin-Flip Casanova, Head-Gordon PCCP Casanova, JCP ; JCC jrasi ¼ X C R jri R X hlj ^HjRiC R ¼ EC L R configuration ^jric class active hole occupation h dimensions 2O m n m n+1 m n m n part p V m n-1 m n Algorithm H Configuration driven TDDFT, CIS
22 X X RAS-SF algorithms Restricted Active Space Spin-Flip Casanova, Head-Gordon PCCP Casanova, JCP ; JCC jrasi ¼ X C R jri R X hlj ^HjRiC R ¼ EC L R configuration ^jric class active hole occupation h dimensions 2O m n m n+1 m n m n hlj ^HjRi ¼ X lm A LR lm ðljmþþx B LR lmkq ðlmjkqþ lmkq part p V m n-1 m n R m ðljmþ ðlmjkqþ Algorithm Integral driven CAS, FCI
23 Singlet Fission: mechanism S 0 + S 1 1 (TT) T 1 + T 1 S* h$ excitation S 0
24 Singlet Fission: mechanism S 0 + S 1 1 (TT) T 1 + T 1 S* h$ excitation relaxation TT S 0
25 Singlet Fission: mechanism S 0 + S 1 1 (TT) T 1 + T 1 S* h$ excitation relaxation T TT fission T S 0 diffusion
26 Singlet Fission: mechanism S 0 + S 1 1 (TT) T 1 + T 1 charge resonance S* h$ excitation relaxation T TT fission T S 0 diffusion
27 Singlet Fission: electronic states SF precursor 1 TT Ŝ 2 1 TT = s(s +1) 1 TT 1 TT = T 1 T -1 T -1 T 1 T 0 T 0
28 Singlet Fission: electronic states SF precursor 1 TT Ŝ 2 1 TT = s(s +1) 1 TT 1 TT = T 1 T -1 T -1 T 1 T 0 T 0 Reference 5 TT
29 Singlet Fission: electronic states SF precursor 1 TT Ŝ 2 1 TT = s(s +1) 1 TT 1 TT = T 1 T -1 T -1 T 1 T 0 T 0 Reference 5 TT TT CT double spin-flip particle hole RAS-2SF wavefunction single exciton multiple exciton charge transfer
30 Singlet Fission: molecular vibration Intermolecular distortion Phonon like Chromophore coupling tetracene, pentacene JACS,
31 Singlet Fission: molecular vibration Intermolecular distortion Phonon like Chromophore coupling tetracene, pentacene JACS, Intramolecular distortion S 1 optimization Energy levels tetracene, DPT, rubrene JCTC a g breathing mode
32 Singlet Fission: molecular vibration Intramolecular distortion Tetracene SF thermally activated Jundt et al., CPL (1995) DPT large thermodynamic driving force for SF Roberts et al., JACS (2012)
33 Singlet Fission: molecular vibration Intramolecular distortion HOMO LUMO Tetracene DPT
34 Singlet Fission: molecular vibration Intramolecular distortion Crystal structure Tetracene herringbone lattice Holmes et al., Chem. Eur. J. (1999) DPT slip-stack structure Roberts et al., JACS (2012)
35 Singlet Fission: molecular vibration Intramolecular distortion Tetracene energy, ev S 1 TT S 2 DPT energy, ev
36 Singlet Fission: molecular vibration Intramolecular distortion Tetracene energy, ev kt S 1 TT S 2 DPT energy, ev conical intersection
37 Singlet Fission: chromophore coupling SF transition rate S 0 S 1 TT ω(sf) = 2π h TT Ĥ S 0S 1 2 ρ[e] Fermi golden rule S 0 S 1 TT
38 Singlet Fission: chromophore coupling SF transition rate ω(sf) = 2π h TT Ĥ S 0S 1 2 ρ[e] small -2.2 mev S 0 S 1 TT Fermi golden rule Tetracene dimer
39 Singlet Fission: chromophore coupling SF transition rate ω(sf) = 2π h TT Ĥ S 0S 1 2 ρ[e] S 0 S 1 TT Fermi golden rule Tetracene dimer small -2.2 mev excitonic CT Findings Direct coupling very weak Largest couplings to CT states JCTC
![Singlet Fission: chromophore coupling SF transition rate ω(sf) = 2π h TT Ĥ S 0S 1 X S 0 S 1 TT Ĥ XX Ĥ S 0S 1 E X 2 TT ρ[e] Tetracene dimer 1 st](/docs-images/89/98778206/images/40-5.jpg "order 2 nd order direct coupling mediated coupling excitonic CT Findings Direct coupling very weak Largest couplings to CT states JCTC 10 2014")
40 Singlet Fission: chromophore coupling SF transition rate ω(sf) = 2π h TT Ĥ S 0S 1 X S 0 S 1 TT Ĥ XX Ĥ S 0S 1 E X 2 TT ρ[e] Tetracene dimer 1 st order 2 nd order direct coupling mediated coupling excitonic CT Findings Direct coupling very weak Largest couplings to CT states JCTC
41 Singlet Fission: chromophore coupling SF transition rate ω(sf) = 2π h TT Ĥ S 0S 1 X S 0 S 1 TT Ĥ XX Ĥ S 0S 1 E X 2 TT ρ[e] Tetracene dimer 1 st order 2 nd order direct coupling mediated coupling excitonic CT -2.2 mev mev Findings Direct coupling very weak Largest couplings to CT states SF mediated by CT states JCTC
42 1 molecule 2 chromophores Singlet Fission: in one molecule
43 Singlet Fission: in one molecule 1 molecule 2 chromophores quinoidal bithiophene Fluorescence intensity (counts) nm 470nm Time (ns)
44 Singlet Fission: in one molecule 1 molecule 2 chromophores Fission 1 ME T 1 + T 1 quinoidal bithiophene Energy gap!e F = E[ 5 ME] " E[ 1 ME] # 0 Fluorescence intensity (counts) nm 470nm Time (ns)
45 Singlet Fission: in one molecule 1 molecule 2 chromophores Fission 1 ME T 1 + T 1 quinoidal bithiophene Energy gap % 1 TT!E F = E[ 5 ME] " E[ 1 ME] # 0 [ 1 TT] [ 1 ME]! 100% Contribution of 1 TT in the overall 1 ME wavefunction Fluorescence intensity (counts) nm 470nm Time (ns)
46 Singlet Fission: in one molecule 1 molecule 2 chromophores Fission 1 ME T 1 + T 1 quinoidal bithiophene Energy gap % 1 TT Radical character!e F = E[ 5 ME] " E[ 1 ME] # 0 [ 1 TT] [ 1 ME]! 100% Contribution of 1 TT in the overall 1 ME wavefunction N U = " 1! 1! n i N U! 4 Number of unpaired electrons of 1 ME i Fluorescence intensity (counts) nm 470nm Time (ns)
47 Singlet Fission: in one molecule 1 molecule 2 chromophores Fission 1 ME T 1 + T 1 quinoidal bithiophene Energy gap!e F = E[ 5 ME] " E[ 1 ME] # 0 % 1 TT Contribution of 1 TT in the overall 1 ME wavefunction Radical character [ 1 TT] [ 1 ME]! 100% N U = " 1! 1! n i N U! 4 Number of unpaired electrons of 1 ME i
48 Eskerrik asko coming Collaborations Theodore Goodson (U. Michigan) Juan Casado (U. Malaga) QOT2 Funding Research Fellowship IT SAIOTEK S-PC13UN002
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