Electron Transfer Electron Transfer Through Dendrimers in Solution Through Dendrimers in Solution

Deborah EvansDeborah Evans

University of New MexicoUniversity of New Mexico

Department of Chemistry and theDepartment of Chemistry and theAlbuquerque High Performance Albuquerque High Performance Computing CenterComputing 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 encapsulationCores: Fe-S, porphyrin, ferrocene:

Gorman et al, JACS, 121 (1999)

STM and cyclic voltammetry

Gorman et alJACS, 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, 2000.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 theCaley tree connectivity tiHtiHtiHtiH eeee 321

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:

DLHi

],[

Redfield Approach :

Approach used for multi-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:

m kmkmknnnnnn RHi ''' ],[

Numerical Techniques :

Photo-induced experiments (population dynamics):

Steady-State (rates):

1)0( DD

AAAAA

)(tDD : constant

Solvated Dendrimer models:

Tight-binding model for dendrimer:

Solvent – system coupling

coupling strength ~ 5-10 Assume Markovian limit

E ~ 1000 ; ~ 100

|||| AAEDDEH ADdend

1cm

1cm 1cm

i NNj

bb

jibbE ||||

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 Eb)

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: SS

2

κ22

F

e

E

m

h

eg

Photoinduced Electron Transfer through a dendrimer to acceptors diffusing in solution

Aida et al, JACS118 (1996)

GOAL: to measure kET 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

KT

oG

etVt

4

2)(2|)(|)(

)(2|)(| tLetV )(tL

Electron transfer rate from the dendrimer periphery to the diffusing viologensdiffusing viologens:

Depends on time:Use Marcus expressionwith 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 acceptors in 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 kET = 2.6 × 109 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

Acknowledgements

$$:• NSF CAREER • PRF• University of New Mexico/AHPCC

Undergraduates:

• Sebastien Binette

• Ladonna Malone

• Eric Heatwole

• Bea Yu

• Camille-Dreyfus Teacher-Scholar• Research Corporation Cottrell Scholar• Wiley Young Investigator

Graduates:

• Govind Mallick

• Sean Elicker

Post-Docs:

• “CK” Kalaynaraman

• Vijaya Subramaniam

• Irene Newhouse

Collaborators:

• Shashi Karna

• Ranjit Pati

• Andy Pineda

Dendrimer RDF

Malone, Evans 2000.r