Kinetics of Charge Transfer Processes in Molecular Junctions
A kinetic master equation for state populations of a quantum system comprised of separate quantum subsystems, is derived. The equation allows one to describe the charge transfer processes in molecular junctions, where the molecule operates as a transmitter of electrons between the electrodes. Special attention is given to the derivation of contact and distant rate constants responsible for the formation of sequential (hopping) and direct (distant) components of the current, as well as for the time evolution of molecular state probabilities.
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A more exact form for the transfer rate (14) characterizing the quasiisoenergetic transitions in an open QS, has been derived in . The rate contains a specific Lorentzian. Note, however, that the area covered by this Lorentzian is mainly concentrated near E(a) ≈ E(b). Therefore, it becomes possible to simplify the form of the transfer rate K(a; b) using the delta-function instead of the Lorentzian (see also ). The advantage of such a substitution is in that the transfer rate can be calculated without specification of the stochastic field alternating the level positions.
After finishing the averaged procedure, the characteristics of a
stochastic field are concentrated in the specific Lorentzian .
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Quantity (38) is the proper energy with the modified molecular Hamiltonian H(eff). Its form follows from the diagonalization of the entire Hamiltonian (18) under the condition that the molecule-electrode couplings do not modify the band levels of the macroscopic electrodes (see [3, 8, 9, 23, 24]).
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