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

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

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

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

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

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)

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

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

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

 D/A superexchange  Donors or Acceptors in solution:

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

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

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

 Phenomenological Density Matrix Approach :  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]  Liouville density matrix equation of motion:

 Redfield Approach :  Approach used for multi-level electron transfer  Solvent included in the Redfield tensor elements R ijkl  Bath correlation functions taken from the high- temperature limit  Reduced density matrix of the system propagated using a symplectic integrator scheme:

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

Solvated Dendrimer models:  Tight-binding model for dendrimer:  Solvent – system coupling  coupling strength ~ 5-10  Assume Markovian limit   E ~ 1000 ;  ~ 100

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

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

Elicker, Evans, JPC 1999

Solvent relaxation effects:

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

Generalized Chains

Forward Backward

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

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

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

Steady-state rate:  SS Kalyanaraman and Evans, 2001

Landauer formula:

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

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

Electron transfer rate from the dendrimer periphery to the diffusing viologens 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

Classical Molecular Dynamics Simulations: NVE dynamics : dendrimer with viologen acceptorsin water

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

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

The fourth generation dendrimer: Experimental studies: Observed k ET = 2.6 × 10 9 s -1

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

Dendrimer RDF Malone, Evans r