Promotion of Tunneling via Dissipative Molecular Bridges

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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

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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.

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The Electronic Model
Bridge
Donor
Acceptor
The deep tunneling frequency
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Structural (promoting) bridge modes
Introducing Vibronic Coupling
Electronically active (accepting) bridge modes
Not Considered
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Harmonic modes with an Ohmic (
) spectral density
Nuclear frequencies 5-500 1/cm - larger than the
tunneling frequency!
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Coupled Electronic-Nuclear Dynamics
A mean field approach
The Langevin-Schroedinger equation
T0
A non-linear dissipation term
Electronic Population at the bridge
M. Steinberg and U. Peskin, J. Chem. Phys. 109,
704-710 (1998)
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Simulations Effect of vibronic coupling
Weak coupling the tunneling frequency increases!
Strong couplingthe tunneling is suppressed !
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Interpretation time-dependent Hamiltonian
The Instantaneous electronic energy
Resonant Tunneling
Weak coupling Dissipation lowers the barrier
Strong coupling Irreversible electronic
energy dissipation

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Beyond weak electronic-nuclear coupling
On-site Hamiltonians
Vibronic Tunneling Pathways
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The effective tunneling matrix element
Recursive Perturbation Calculation
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Promotion of Tunneling
M. A.-Hilu and U. Peskin, J. Chem. Phys. 122
(2005).
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• Lower barrier for tunneling

• Multiple Dissipative pathways

• Frank Condon integrals

The slow electron adiabatic limit
Condition for tunneling promotion
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Site-directed Electronic Tunneling
Bridges are perturbations
A reduced N-level system
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A Linear D-A1-A2 Complex
Contact
The reduced matrix Hamiltonian in the deep
tunneling regime
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Site Directing in a D-A1-A2 Complex
D?A2
D?A1
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Site Directing by e-n Coupling
A single mode
D?A2
D?A1
D?D
An Ohmic bath
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Site directing in a multi-acceptor network
Tunneling to a selected electronic site
,
,
,
,
,
,
.
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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
  electronicnuclear 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.