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

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.

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

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

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

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, 704-710 (1998)

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

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

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

The effective tunneling matrix element Recursive Perturbation Calculation

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

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

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

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

Site Directing in a D-A1-A2 Complex

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

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

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.