DNA Electron Transfer Processes: Some Theoretical Notions

  • Yuri A. Berlin
  • Igor V. Kurnikov
  • David Beratan
  • Mark A. Ratner
  • Alexander L. BurinEmail author
Part of the Topics in Current Chemistry book series (TOPCURRCHEM, volume 237)


Charge motion within DNA stacks, probed by measurements of electric conductivity and by time-resolved and steady-state damage yield measurements, is determined by a complex mixture of electronic effects, coupling to quantum and classical degrees of freedom of the atomic motions in the bath, and the effects of static and dynamic disorder. The resulting phenomena are complex, and probably cannot be understood using a single integrated modeling viewpoint. We discuss aspects of the electronic structure and overlap among base pairs, the viability of simple electronic structure models including tight-binding band pictures, and the Condon approximation for electronic mixing. We also discuss the general effects of disorder and environmental coupling, resulting in motion that can span from the coherent regime through superexchange-type hopping to diffusion and gated transport. Comparison with experiment can be used to develop an effective phenomenological multiple-site hopping/superexchange model, but the microscopic understanding of the actual behaviors is not yet complete.


Electron transfer Hole transport Hopping Superexchange Coupling to the molecular surroundings 

Abbreviations and Symbols


Spacing between repeating units of the bridge




Polarization matrix


Elements of the polarization matrix


Transfer integral


Bridge connecting a donor and an acceptor


Falloff parameter for the distance dependence of the electron transfer rate


Annihilation operator for a hole at the i-th site of the chain describing the stack of Watson–Crick base pairs


Creation operator for a hole at the i-th site of the chain describing the stack of Watson–Crick base pairs




Width of the rectangular barrier


Donor–acceptor tunneling


Density of states weighted Franck–Condon factor


Deoxyribonucleic acid


Barrier height for the adiabatic hole motion


Difference in ionization potentials of adenine–thymine and guanine–cytosine base pairs


Energy barrier between the injection energy and the barrier height


Driving force for electron transfer


Electron transfer


Energy of the particle undergoing a tunneling transition through the rectangular barrier

\( E_{{B_{i} }} \)

Electronic energy of the bridge state ∣B i


Electronic energy associated with the “transfer electron” in the activated complex


Energy of the v-th vibrational state


Dielectric constant of the solvent






Planck constant


Effective donor–acceptor interaction


Highest occupied molecular orbital


Rate constant of electron transfer


Boltzmann constant


Pre-exponential factor in Eq. 6 for the rate of the elementary hopping step


Length of the bridge containing adenine–cytosine base pairs only


Lowest unoccupied molecular orbital


Marcus reorganization energy


Mass of the tunneling particle


Population of i-th site of the chain describing the stack of Watson–Crick base pairs


Number of sites through which the electron or hole tunnels


Neglect of differential overlap self-consistent field method


Products formed in the reactions of water with guanine radical cation G j +


Product formed in the reaction of water with the hole trapped by the guanine triple GGG


Probability of the system to be found in the vibrational state v


Effective vibronic frequency of the medium


Number of base pairs in the adenine–thymine bridge between two guanine sites


Spatial donor–acceptor separation


Spatial donor–acceptor separation in the certain reference state


Generalized Franck–Condon factor


Franck–Condon overlap factor


Conductivity prefactor






Landauer–Buttiker tunneling time for the rectangular barrier


Landauer–Buttiker tunneling time in a molecular orbital representation


Tunneling time


Height of the rectangular barrier through which the particle is tunneling


Average squared electronic mixing between donor and acceptor


Hamiltonian term describing the interaction between the bridge state ∣B i 〉 and the acceptor state ∣A〉


Hamiltonian term describing the interaction between the donor state ∣D〉 and the bridge state ∣B i


Half of the effective energy splitting for the electron transfer reaction


Set of vibronic states that modulates the electron coupling matrix element


Set of vibronic states that does not modulate the electron coupling matrix element


Average position of a hole on the chain describing the stack of Watson–Crick base pairs


Multidimensional coordinate characterizing the polarization of water molecules


Optimal value of the multidimensional coordinate characterizing the polarization of water molecules


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We are grateful to the Chemistry Division of the ONR, MOLETRONICS program at DARPA, and to the DoD/MURI program for support of the research at Northwestern. The work at Duke is supported by NIH and NSF. We are grateful to many colleagues, particularly A. Troisi, J. Jortner, N. Rösch, D. Porath, and C. Dekker for sharing their insights with us.


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Authors and Affiliations

  • Yuri A. Berlin
    • 1
  • Igor V. Kurnikov
    • 1
    • 2
  • David Beratan
    • 2
  • Mark A. Ratner
    • 1
  • Alexander L. Burin
    • 1
    • 3
    Email author
  1. 1.Department of Chemistry, Center for Nanofabrication and Molecular Self-Assembly and Materials Research Center Northwestern UniversityEvanstonUSA
  2. 2.Department of ChemistryDuke UniversityDurhamUSA
  3. 3.Department of ChemistryTulane UniversityNew OrleansUSA

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