CAOP Theoretical contributions Naga Rajesh Tummala Zilong Zheng

CAOP: Theoretical contributions Naga Rajesh Tummala Zilong Zheng Jean-Luc Bredas Veaceslav Coropceanu Joint ONR-AFOSR Organic Photovoltaics Program Review Washington, DC, May 17 -18, 2016

Targeted questions -How do the static disorder and dynamic disorder in organic films and D/A organic heterojunctions depend on the system morphology? -What is the impact of disorder on charge-transfer states, charge transport, charge separation and charge recombination processes in organic solar cells? -How large is the energy splitting between singlet and triplet CT states and how fast are the related intersystem crossing rates? -What are the upper and lower limits of the intrinsic lifetime of the lowest CT state?

Outline § Static and Dynamic Disorder § Energetic Disorder: Transport States § Energetic Disorder: Charge-Transfer States § “One-Atom Minimal Change” Project § New 3 D Acceptors § Conclusions

Static energetic disorder Amorphous structure e

Dynamic energetic disorder crystalline structure ± rel Q Local electron-phonon coupling

Total disorder Amorphous structure

Static and dynamic disorder components are not always additive charge transport Marcus electron transfer model static disorder - dynamic disorder - Miller-Abrahams electron transfer model static disorder - dynamic disorder -

Ensemble average versus time average mean value of the site-energy distribution variance (standard deviation) time average geometric configurations of a target molecule and its environment derived from MD simulations at different times ensemble average geometric configurations of a set of target molecules derived from MD simulations at a given time

Disorder: QM/MD results in e. V N. R. Tummala, et al. , J. Phys. Chem. Lett. , 6, 3657, 2015. In the case of amorphous structures the static disorder is usually larger than the dynamic disorder.

Disorder: Comparison with Experiment Fullerene σ (e. V) PCBM 0. 10 (triclinic) PCBM 0. 13 (amorphous) ICBA 0. 16 (pure isomer) (amorphous) Y. Shao, Y. Yuan, J. Huang, Nature Energy 1, 15001, 2016. SA = Solvent annealed with DCB TA = Thermal annealed N. R. Tummala, et al. , J. Phys. Chem. Lett. , 6, 3657, 2015. Gaussian fits of the DOS distributions extracted from impedance spectroscopy measurements

Charge-transfer states: non-radiative recombination CT Ea S 0 E

Charge-transfer states: optical properties Generalized Mulliken–Hush model CT molar extinction coefficient Ea S 0 E transition dipole moment no static disorderwith static disorder-

CT states: P 3 HT/PCBM Amorphous bulk Amorphous bilayer P 3 HT PCBM P 3 HT/PCBM coordinates were extracted from MD simulations

CT states: P 3 HT/PCBM 2 thousand - configurations B 3 LYP/6 -31 G(d) level

Crystalline Polymer Phase Face-on Edge-on Disorder in presence of perfectly crystalline P 3 HT is similar to the dynamic disorder in the anionic PCBM (avg. ~0. 07 e. V)

CT states: P 3 HT/PCBM Relaxed P 3 HT Face-on Edge-on

CT singlet states Energy gaps between CT states are around 0. 1~0. 2 e. V

CT triplet states Splitting energy 1 CT – 3 CT (e. V) ECT 1 ECT 2 ECT 3 singlet 0. 974 1. 116 1. 325 triplet 0. 968 1. 108 1. 320 ΔE(s-t) 0. 006 0. 008 0. 005 Small singlet-triplet splitting energies are estimated

Dynamic disorder: P 3 HT/PCBM Relaxation energy PCBM anion 0. 106 e. V P 3 HT cation 0. 233 e. V Reorganization energy λ= 0. 34 e. V σD =0. 14 e. V -> λ= 0. 38 e. V Total disorder Dynamic disorder for P 3 HT-PCBM (in e. V) Emax σ pair 1 0. 67 0. 17 pair 2 0. 98 0. 12 pair 3 1. 16 0. 12 pair 4 1. 01 0. 16 pair 5 1. 21 0. 17 pair 6 1. 18 0. 14 pair 7 0. 68 0. 15 pair 8 0. 75 0. 10 pair 9 0. 99 0. 18 pair 10 1. 28 0. 13 AVG. 0. 97 0. 14 ST. DEV. 0. 23 500 snapshots for each pair, each snapshot separated by 30 fs σT =0. 25 e. V ; σD =0. 14 e. V; σS =0. 20 e. V

“One-Atom Minimal Change” Project Use of quantum-chemical calculations and molecular mechanics /molecular dynamics simulations to examine: Excited-state electronic structure, interface electronic properties, transfer integrals, electron-vibrational couplings. Molecular packing, interface morphologies, disorder effects. LUMO HOMO X=C X = C, Si and Ge B 3 LYP/6 -31 G(d)

“One-Atom Minimal Change” Project X=C E(S 1) = 1. 67 e. V E(T 1) = 1. 08 e. V E(S 1) = 1. 61 e. V E(T 1) = 1. 15 e. V X=Si E(S 1) = 1. 75 e. V E(T 1) = 1. 21 e. V E(S 1) = 1. 64 e. V E(T 1) = 1. 12 e. V X=Ge E(S 1) = 1. 75 e. V E(T 1) = 1. 21 e. V E(S 1) = 1. 64 e. V E(T 1) = 1. 13 e. V x atom has only a minor effect on the lowest singlet and triplet states

New 3 D acceptors NDI SCPDT SDTG DCPT X= acceptor = NDI intra-molecular couplings for electrons (in me. V) SCPDT SDTG DCPT 6 3 12 7 4 8 73 64 80 large intra-molecular electronic couplings are estimated

Conclusions and future work A comparison of the results obtained from an ensemble average approach with those derived from a time average approach allows us to differentiate between the static and dynamic disorder components. In the case of amorphous structures the static disorder is usually larger than the dynamic disorder. The interface geometry has a strong effect on the energies and ordering of the singlet and triplet charge-transfer states. In all the investigated systems the singlet-triplet splitting energies were estimated to be in the range of 0 -10 me. V. Current work is focused on understanding: How large are the intersystem crossing rates between singlet and triplet CT states? What is the upper and lower limits of the intrinsic lifetime of the lowest CT state?