Electron Transfer Through Dendrimers in Solution

1. Electron Transfer Through Dendrimers in Solution Deborah Evans University of New Mexico Department of Chemistry and the Albuquerque High Performance Computing Center

2. Dendrimers are synthetic realizations of Caley trees: Electron Transfer: Energy Transfer:

3. Electron Transfer Through Dendrimers: • Extensively branched macromolecules Crooks et al, JACS, 120 (1998) • form self-assembled monolayers Abruna and coworkers Langmuir, 15 (1999)

4. Electro-active dendrimers and encapsulation Cores: Fe-S, porphyrin, ferrocene: Gorman et al, JACS, 121 (1999)

5. STM and cyclic voltammetry Gorman et al JACS, 121 (1999)

6. Electron Transfer and Molecular Electronics: It's All About Contacts K.W. Hipps, Science The goal of building sophisticated electronic devices from individual molecules has spurred studies of single-molecules. The primary problems facing the molecular electronics designer are: measuring and predicting electron transport. • Molecular “wires”: Molecular break-junction experiments Reed et al JACS, 121 (1999)

7. Electron transport through linear chains: Nitzan et al, JPC, 104, 2001 bridge electron transfer: interferences and solvent dephasing Pollard and Friesner, JPC, 99, 1995

8. ET through solvated branched molecules • Photo-induced intra-molecular transfer Wasielewski et al JACS, 121 (1999)

9. Simulation of ET in solvated dendrimers: Experiments have many competing processes: • Intra-dendrimer transfer • solvent-induced relaxation / diffusion • surface effects • Surface-induced distortions Crooks et al, Anal. Chem. , 71 (1999)

10. Donors or Acceptors in solution: • D/A superexchange

11. Previous Modeling Extended systems: • infinite Caley trees • localized states • dimensionality (simply connected; branching) Electron Transfer Pathways: Electron transfer rate: |T|2 ~ 1 / K K Disorder: creates 1-D pathways to enhance rate Beratan, Onuchic, 1994

12. Solvent effects on ET • Solvent-dependent ET rates • flexible hydrophobic/hydrophilic • rigid dendrimers: Classical MC and MD studies of 1-4 generations: Newhouse, Evans, 2000. kJ/mol

13. Simulation of condensed phase ET • Split-operator methods : • Time-dependent simulation of photo- induced electron transfer • Solvent influence included as time- dependent fluctuations in the Hamiltonian A modified Checkerboard algorithm exploits the Caley tree connectivity

14. Phenomenological Density MatrixApproach : • Liouville density matrix equation of motion: • Solvent influence included as phenomenological decay rates • Steady-state rate constants determined for effective electron transfer rates through the molecular wire [Ratner, Nitzan et al, linear D-B-A]

15. Redfield Approach : • Approach used formulti-level electron transfer • Solvent included in the Redfield tensor elements Rijkl • Bath correlation functions taken from the high- temperature limit • Reduced density matrix of the system propagated using a symplectic integrator scheme:

16. Numerical Techniques : Photo-induced experiments (population dynamics): Steady-State (rates): : constant

17. Solvated Dendrimer models: • Tight-binding model for dendrimer: • D E ~ 1000 ; b ~ 100 • Solvent – system coupling • coupling strength ~ 5-10 • Assume Markovian limit

18. Results from numerical simulations: Effects of: • Dendrimer topology/geometry • Solvent-induced relaxation • Donor/acceptor energies • Side-branch chemistry • Thermal relaxation of the bridge On: • electron transfer rates • rectification • switching • conductance

19. Photo-induced Electron Transfer (3N) (4N) (5N) condensed dendrimers (14) (33) (52) extended dendrimers

20. Elicker, Evans, JPC 1999

21. Solvent relaxation effects:

22. Steady-state rates: Dendrimer bridges vs linear chains Evans et al , JPC, 2001 dendrimer linear

23. Generalized Chains

24. Forward Backward

25. Electronic Effects in Molecular Wires: molecule between two metal contacts: Conductance ( |G(V)|2) vs voltage (units of Eb)

26. Bridge Topology and Conductance linear chains side-branch structure side-branch position

27. number of side-branches longer bridges DENDRIMERS: second-generation third-generation

28. Steady-state rate: kSS Kalyanaraman and Evans, 2001

29. Landauer formula:

30. Photoinduced Electron Transfer through a dendrimer to acceptors diffusing in solution Aida et al, JACS 118 (1996) GOAL: to measure kET for electron transfer through the dendrimer framework

31. Simulations of solvent phase Photo-induced Electron Transfer to diffusing acceptors: Mallick and Evans, 2002 • Classical MD simulation of diffusing viologens • ET transfer rate to acceptors • Electron dynamics through the dendrimer following photoexcitation • (taking into account solvent dynamics)

32. Electron transfer rate from the dendrimer periphery to the diffusing viologens: Depends on time: Use Marcus expression with water as the solvent: ET to viologens is irreversible: treat the sites as absorbing boundary conditions

33. Classical Molecular Dynamics Simulations: NVE dynamics : dendrimer with viologen acceptors in water

34. Rate of transfer to viologen is • a dynamic variable that evolves along a simulation trajectory: L(t)

35. The second generation dendrimer: For the Aida experiments: rate is dominated by the intermolecular ET

36. The fourth generation dendrimer: Experimental studies: Observed kET = 2.6 × 109 s-1

37. Conclusions: • Electron transfer in dendrimers: • photo-induced • steady-state • Electron transfer rate depends on: • branching structure • enhanced over linear “wires” • solvent dynamics time-scale and coupling • strength • intermolecular ET rate to diffusing acceptors

40. Dendrimer RDF Malone, Evans 2000. r