Non-Condon theory of nonadiabatic electron transfer reactions in V-shaped donor–bridge–acceptor complexes

Abstract

The rate of nonadiabatic long-distance electron transfer ͑ET͒ is derived for the direct and superexchange electronic coupling between the donor and acceptor. The model takes into account a non-Condon thermal modulation of the electronic coupling through the interaction of the system transition dipoles with the polarization fluctuations of the solvent. Going from a linear donorbridge-acceptor complexes to a bent, V-shaped geometry lowers the system symmetry resulting in several novel properties of the ET matrix element based on the fact that permanent and transition dipoles in the system are not polarized along the direction of ET. The effective ET matrix element H ET gains two zeros as a function of the donor-acceptor vertical energy gap. The positions of zeros of H ET depend on the sign relations between the donor-bridge and bridge-acceptor electronic couplings and corresponding transition dipoles. The ET matrix element becomes dependent on solvent through the solvent refractive index and the inhomogeneous width of the donor-acceptor optical transition. The former factor is mainly responsible for the temperature slope of ͉H ET ͉. The derivative d͉H ET ͉/dT switches its sign at the zero points of H ET. The distance decay parameter of the donor-acceptor coupling is shown to vary linearly with the inhomogeneous width of the optical transition between the donor and acceptor.

Molecular quantum-dot cellular automata: From molecular structure to circuit dynamics

“…I. Our strategy is to conduct the state-of-the-art ab initio calculation on the single QCA cells to determine the three energies corresponding to the 0, 1, and null states, and construct a 3 ϫ 3 model Hamiltonian with the three-state approximation, 24,26…”

“…The more detailed discussion of the model Hamiltonian of a donor-bridge-acceptor complex can be found in Ref. 26.…”

Protein dynamics and electron transfer: Electronic decoherence and non-Condon effects

“…Bridge motion can cause large and rapid donor-acceptor matrix element fluctuations, affecting the tunneling pathway structure and the interferences among pathways (25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37). The coupling matrix element fluctuations may have large contributions from solvent-polarization fluctuations (23), and these fluctuations facilitate electronically forbidden and gated ET (38)(39)(40)(41)(42)(43)(44)(45)(46)(47). Finally, bridge-nuclear relaxation creates inelastic tunneling pathway channels (11,20,24,(47)(48)(49) that can change the mechanism of ET from superexchange to resonant tunneling to sequential hopping (11,(41)(42)(43)(44)(50)(51)(52)(53)(54)(55)(56)(57)(58)(59)(60)(61)…”

On the role of non-diagonal system–environment interactions in bridge-mediated electron transfer

“…27 Milischuk and Matyushov explored non-Condon effects for nonadiabatic electron transfer reactions in donor-bridge-acceptor systems. 28 The importance of non-Condon effects was further highlighted for ET at oligothiophene-fullerene interfaces via multi-layer MCTDH simulations 29 and the role of off-diagonal couplings was emphasized for the formation of charge-transfer states in polymeric solar cells. 30 Condensed phase ET beyond the Condon approximation was recently explored by Mavros and Van Voorhis.…”