M.Sc Student | Abu-Hilu Musa |
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Subject | Quantum Mechanical Models for Dissipative Electorn-Transfer through Flexible Molecules |

Department | Department of Chemistry |

Supervisor | Professor Uri Peskin |

Full Thesis text |

Long-range coherent electron transfer between a donor and an acceptor is
often assisted by intermediate molecular bridge, via the superexchange
tunneling mechanism. The effect of electronic-nuclear coupling on the tunneling
oscillation rate and mechanism is analyzed using a generalized spin-boson
model, in which the two level system, representing the donor and the acceptor
is coupled to a dissipative nuclear bath only indirectly, via additional *N*
bridge sites. Phenomenological model studies representing the vibrating nuclei
as a time dependent force field showed that the tunneling matrix elements
depends on the vibration frequency of the bridge modes indicating a dependence
of the electronic tunneling on the bridge flexibility.

A Langevin-Schroedinger equation, based on a mean field approximation, was applied in order to study the corresponding many-body dynamics, including the feedback of the driven nuclei on the electronic dynamics. At zero temperature and when the electron tunneling is slower than the nuclear motion, the main effect of electronic-nuclear coupling is the dissipation of electronic energy at the bridge into nuclear vibrations. At a small coupling strength, the electronic tunneling matrix element increases due to this dissipative mechanism, but as the coupling strength increases the tunneling into the acceptor is suppressed and efficient dissipation leads to electronic trapping (solvation) at the bridge. This analysis agrees with numerous experimental and theoretical studies, emphasizing the importance of the nuclear bridge conformation and the bridge flexibility in controlling the electron transfer rate in donor-bridge-acceptor systems.

Electronic tunneling through molecular barriers is studied beyond the weak electronic nuclear coupling limit using an analytically solvable model, valid in the deep tunneling regime. An expression is obtained for the effective “through bridge” tunneling matrix element in the presence of electronic coupling to nuclear vibrations at the molecular bridge. A specific case of tunneling oscillations in a symmetric donor-bridgeacceptor complex (superexchange) is analyzed in detail showing that the frequency of tunneling oscillations increases with the strength of electronic nuclear coupling, with the number of electronic-nuclear coupling sites, and with the nuclear vibration frequency (molecular rigidity). Acceleration of the electronic tunneling by several orders of magnitude is demonstrated within the range of realistic model parameters.