1. Promotion of Tunneling via Dissipative Molecular Bridges
Uri Peskin
Department of Chemistry,
Technion - Israel Institute of Technology
and
The Lise Meitner Center for Computational
Quantum Chemistry

2. Introduction
Dissipation, de-coherence and heat production due to electronic-nuclear coupling are inevitable during electron transfer through molecular bridges and wires.
We study the effects of electronic-nuclear coupling on electronic deep-tunneling in donor-bridge-acceptor molecular complexes.
The involved many body dynamics associated with generalized spin-boson models, requires high dimensional quantum mechanical tools and is computationally challenging.
We formulate the entangled electronic-nuclear dynamics beyond the weak electronic-nuclear (system-bath) coupling limit, in terms of summations over vibronic tunneling pathways. For limiting cases of physical (and chemical) interest, exact analytic expressions are obtained for dynamical observables.

3. The deep tunneling frequency:
The Electronic Model
Bridge
Donor
Acceptor
The deep tunneling frequency:

4. Structural (promoting) bridge modes:
Introducing Vibronic Coupling
Bridge
Donor
Acceptor
Electronically active (accepting) bridge modes:
Structural (promoting) bridge modes:
Not Considered

5. Nuclear frequencies 5-500 1/cm - larger than the tunneling frequency!
Donor/Acceptor
Bridge
Harmonic modes with an Ohmic ( ) spectral density
Nuclear frequencies /cm - larger than the tunneling frequency!

6. Coupled Electronic-Nuclear Dynamics
A mean field approach
The Langevin-Schroedinger equation
T=0
A non-linear dissipation term
Electronic
Population
at the bridge
M. Steinberg and U. Peskin, J. Chem. Phys. 109, (1998)

7. Simulations: Effect of vibronic coupling
Weak coupling: the tunneling
frequency increases!
Strong coupling:the tunneling is suppressed !

8. Interpretation: time-dependent Hamiltonian
The Instantaneous electronic energy:
Resonant
Tunneling
Weak coupling:
Dissipation lowers the barrier
Strong coupling:
“Irreversible” electronic
energy dissipation

9. Beyond weak electronic-nuclear coupling Vibronic Tunneling Pathways
On-site Hamiltonians
Vibronic Tunneling Pathways

10. The effective tunneling matrix element
Recursive Perturbation Calculation

11. Promotion of Tunneling:
M. A.-Hilu and U. Peskin, J. Chem. Phys. 122 (2005).

12. The “slow electron” “adiabatic” limit:
Lower barrier for tunneling
Multiple “Dissipative” pathways
Frank Condon integrals
The “slow electron” “adiabatic” limit:
Condition for tunneling promotion:

13. “Site-directed” Electronic Tunneling
Bridges are perturbations
A reduced N-level system

14. A Linear D-A1-A2 Complex Contact The reduced matrix Hamiltonian
in the deep tunneling regime:

15. Site Directing in a D-A1-A2 Complex

16. Site Directing by e-n Coupling
A single mode:
DA2
DD
DA1
An Ohmic bath:

17. Site directing in a multi-acceptor network
Tunneling to a selected electronic site , , , , , , .

18. Summary and Conclusions
Off-resonant (deep) tunneling (super-exchange) in long-range electron transfer through molecular barriers was studied.
A generalized McConnell model was introduced for studying the role of electronic-nuclear coupling at bridges in molecular Donor-Bridge-Acceptor complexes.
Simulations of the coupled electronic-nuclear dynamics suggest that a pollaronic effect at weak electronic–nuclear coupling promotes off-resonant tunneling through molecules.
A rigorous approach was introduced for calculations of electronic tunneling frequencies beyond the weak electronic-nuclear coupling, predicting acceleration by orders of magnitudes in the realistic regime of molecular parameters
Site directed tunneling was demonstrated in models of molecular networks. The rigorous formulation would enable to predict the effect of electronic nuclear coupling on site-directed tunneling in such complex networks.