Singlet fission for solar energy conversion A theoretical insight. David Casanova

Transcription

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 Energy Singlet Fission: definition S 0 + S 1 T 1 + T 1 S 1 e - 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 σ* σ 1s α spin β spin occupied orbitals

13 Electronic states with RAS-SF Restricted Active Space Spin-Flip H 2 molecule Chemist s view virtual orbitals 1s σ* σ 1s HF singlet α spin β 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 σ* σ 1s HF singlet α spin β 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 σ* 1s σ 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 σ* 1s σ 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 a or b. Parameters n H and eigenvector n P indicat equat allowed holes in RAS1 response and particles resulting operators on the to the total electrons in RAS2 wh a or b. Parameters n RAS-SF H and n P indicate the maximum number of algorithms allowed holes in RAS1 and particles in RAS3. n elec correspond to the total electrons in RAS2 when the RAS1 orbitals are Restricted Active Space Spin-Flip Casanova, Head-Gordon PCCP Casanova, JCP ; JCC Journa configuration class occupation dimensions active m n m n hole h O m n+1 m n part p V m n-1 m n

20 a or b. Parameters n H and n P indicat aand or b. orbitals Parameters will be n RAS-SF H indicated and n P indicate by N algorithms elec theand maximum M, while number O, m, of and eigenvector equat allowed V will correspond holes in RAS1 to orthogonal the andorbitals particles in in each to RAS3. subspace orthogonal each n elec correspond RAS1, other. RAS2, to The response The each total typical resulting othe size nu allowed holes in RAS1 and particles to andthe RAS3. total The electrons r subindex denote spin and can take the values dure, as the Lan and RAS2 a or b. Parameters n H orbitals when the and n P will and RAS1 be orbitals indicated are will operators by beon Nindi the indicate the maximum number of eigenvector elec eq allowed holes in RAS1 V will and particles correspond in RAS3. n Casanova, V will JCP elec to response resulti 137 correspond the ; orbitals JCC to 720 in Journa the eac to the total electrons in RAS2 when the RAS1 orbitals are operators on th configuration class occupation dimensions to the total electrons in RAS2 wh Restricted Active Space Spin-Flip Casanova, Head-Gordon PCCP and RAS3. Theand r subindex RAS3. The denote r subind spin a or b. Parameters Jou active a or 1010 n b H Parameters and n P m indicate m n H ant n n allowed holes allowed in RAS1 holes and particles in RAS1ina m h O m hole to the total electrons to the total in RAS2 electrons n+1 n when part p V m n-1 m n H

21 a or b. Parameters n H and n P indicat aand or b. orbitals Parameters will be n RAS-SF H indicated and n P indicate by N algorithms elec theand maximum M, while number O, m, of and eigenvector equat allowed V will correspond holes in RAS1 to the andorbitals particles in each subspace RAS1, RAS2, The typical size allowed in RAS3. holes n elec correspond in RAS1 response and particles resulting to andthe RAS3. total The electrons r subindex RAS2 denote when spinthe andras1 can take orbitals the values are operators dure, asonthethe Lan a or b. Parameters n H and n P indicate the maximum number of eigenvector eq allowed holes in RAS1 and particles in RAS3. n Casanova, JCP elec correspond response resulti ; JCC Journa to the total electrons in RAS2 when the RAS1 orbitals are operators on th configuration class occupation dimensions to the total electrons in RAS2 wh Restricted Active Space Spin-Flip Casanova, Head-Gordon PCCP active m n m n Jou hole h O m n+1 m n part p V m n-1 m n Algorithm H Configuration driven TDDFT, CIS

22 Any active, hole, or particle r-string is univocally described r;1 by In eq. (15), if c ¼ 0 and substring orbitals will R r,c corresponding be indicatedtobythe N jr RAS2 subspace, and with RAS-SF algorithms elec and r;1 i ¼M, while O, ^a s sm, and ^a i a or b. Parameters n {r, r 0 H and n P a orthe b. maximum Parameters i jrefi numbers2ras2 nof eigenvector } is necessary, equat s2ras2 H and ni2ras1 i2ras1 P indicat and allowed V will extra correspond holes orbital in index RAS1 to the for andorbitals the particles hole in(i in each [ RAS1) RAS3. subspace and n elec particle correspond RAS1, (a RAS2, [ sponding response The! typical resulting to asize! allowed holes in hol RAS3) to andthe RAS3. cases total The [eqs. electrons r (9 11)]. subindex The RAS2 denote R r,c when RAS2 spinthe and strings RAS1 can can take orbitals be Yn r the 1RAS1! Yn r 1and represented a or b. by Parameters a binary word n f R r,c values are b-space operators Y O particles! Y O jr dure, (rason ¼the b), the Lan are of length m with n r þ c 1 0 H and n P indicate jr r; 1 theimaximum ¼ ^a r; 1 i ¼ ^a a a number ^a ^a s s, that s ofminant eigenvector ^a ^a i jrefi i s2ras2 belonging i2ras1 eqt is, allowed occupied holes spin RAS1 orbitals, and and particles m in(n Casanova, r RAS3. þ c) n JCP 0 0 elec s, correspond 137 that 2012 is, 84105; following response JCC theresulti 720 ampli Journa unoccupied to the total spin electrons orbitals. in TheRAS2 list ofwhen all R r,c the strings RAS1 with orbitals n r þ care by operators introducingonanth Any active, Any hole, active, or hole, electrons in m orbitals will be denotedclass by L m particle particle n r occupation þc. r-string r-string is univocally is univoca desc configuration dimensions orbital with a hole i a substring a substring R r,c corresponding R r,c corresponding to the RAS2 to the subspace, RAS2 sub a Jou R r;0 and! extra and ~R r;0 ; m; orbital extra n r index orbital 1010 for index 1001 the hole for the m m (9) (i [ hole RAS1) (i [ and RAS1) part a active n n RAS3) cases RAS3) [eqs. cases (9 11)]. [eqs. The (9 11)]. The R r,c RAS2 R r,c strings RAS2 can stringb sented bysented a binary by aword binary f word 722 Journal of Computational Chemistry 2013, 34, h R r,c of length f R r,c ofmlength with m 2O m n with r þ c is, occupied is, hole occupied spin orbitals, spin orbitals, and m and n+1 (nm r þ n c) (n r 0þ 0 s, unoccupied unoccupied spin orbitals. spin orbitals. The list of Theall list of R r,c strings all R r,c with strin m p V m electrons electrons in part m orbitals in m will orbitals be denoted will be denoted by L m by n-1 n r þc n. L m n r þ R r;0! R~R r;0 r;0 ;! m; n ~R r;0 r ; m; n r to the total electrons in RAS2 wh Restricted Active Space Spin-Flip Casanova, Head-Gordon s2ras2 PCCP 10 i2ras Algorithm Integral driven 722 Journal 722 ofjournal Computational of Computational Chemistry Chemistry 2013, 34, 2013, , CAS, FCI

23 Singlet Fission: mechanism S 0 + S 1 1 (TT) T 1 + T 1 S* hν excitation S 0

24 Singlet Fission: mechanism S 0 + S 1 1 (TT) T 1 + T 1 S* hν excitation relaxation TT S 0

25 Singlet Fission: mechanism S 0 + S 1 1 (TT) T 1 + T 1 S* hν 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* hν 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 Fermi golden rule S 0 S 1 TT

38 Singlet Fission: chromophore coupling SF transition rate small -2.2 mev S 0 S 1 TT Fermi golden rule Tetracene dimer

39 Singlet Fission: chromophore coupling SF transition rate 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

40 Singlet Fission: chromophore coupling SF transition rate S 0 S 1 TT 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 S 0 S 1 TT 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 Energy gap ΔE F = E[ 5 ME] E[ 1 ME] 0 Fluorescence intensity (counts) quinoidal bithiophene 580nm 470nm Time (ns)!

45 Singlet Fission: in one molecule 1 molecule 2 chromophores Fission 1 ME T 1 + T 1 Energy gap % 1 TT ΔE 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) quinoidal bithiophene 580nm 470nm Time (ns)!

46 Singlet Fission: in one molecule 1 molecule 2 chromophores Fission 1 ME T 1 + T 1 Energy gap % 1 TT Radical character ΔE 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) quinoidal bithiophene 580nm 470nm Time (ns)!

47 Singlet Fission: in one molecule 1 molecule 2 chromophores Fission 1 ME T 1 + T 1 Energy gap ΔE F = E[ 5 ME] E[ 1 ME] 0 quinoidal bithiophene! % 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

49 Appendix

50 Singlet Fission: chromophore coupling Electronic coupling Probability of TT formation Singlet Fission rate Diabatic approach well characterized states physically sound and intuitive CT/CR role direct vs. mediated definition diabatic states is arbitrary Adiabatic approach eigenstates electronic Hamiltonian quantitative values CT/CR role non adiabatic transitions coherent population

51 Singlet Fission: electronic states Dimer model S 0

52 Singlet Fission: electronic states Dimer model S 0 T S* 5 TT 1 TT CT