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DNA Electron Transfer Processes: Some Theoretical Notions

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

Abstract

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.

Keywords

Electron transfer Hole transport Hopping Superexchange Coupling to the molecular surroundings 

Abbreviations and Symbols

a

Spacing between repeating units of the bridge

A

Adenine

A

Polarization matrix

Aij

Elements of the polarization matrix

b

Transfer integral

B

Bridge connecting a donor and an acceptor

β

Falloff parameter for the distance dependence of the electron transfer rate

ci

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

ci+

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

C

Cytosine

D

Width of the rectangular barrier

D–A

Donor–acceptor tunneling

(DWFC)

Density of states weighted Franck–Condon factor

DNA

Deoxyribonucleic acid

Δb

Barrier height for the adiabatic hole motion

ΔE

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

ΔEb

Energy barrier between the injection energy and the barrier height

ΔG0

Driving force for electron transfer

ET

Electron transfer

E

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

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

Electronic energy of the bridge state ∣B i

Etun

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

Ev

Energy of the v-th vibrational state

ε

Dielectric constant of the solvent

g

Conductance

G

Guanine

ħ

Planck constant

HDA

Effective donor–acceptor interaction

HOMO

Highest occupied molecular orbital

k

Rate constant of electron transfer

kB

Boltzmann constant

k0

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

L

Length of the bridge containing adenine–cytosine base pairs only

LUMO

Lowest unoccupied molecular orbital

λ

Marcus reorganization energy

m

Mass of the tunneling particle

ni

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

N

Number of sites through which the electron or hole tunnels

NDO SCF

Neglect of differential overlap self-consistent field method

PG

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

PGGG

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

Pv

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

ωv

Effective vibronic frequency of the medium

q

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

r

Spatial donor–acceptor separation

r0

Spatial donor–acceptor separation in the certain reference state

ρFCv(E)

Generalized Franck–Condon factor

Svw

Franck–Condon overlap factor

σ0

Conductivity prefactor

T

Thymine

T

Temperature

τLB

Landauer–Buttiker tunneling time for the rectangular barrier

τLB-M

Landauer–Buttiker tunneling time in a molecular orbital representation

τt

Tunneling time

U

Height of the rectangular barrier through which the particle is tunneling

<V2>

Average squared electronic mixing between donor and acceptor

VBiA

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

VDBi

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

Vrp

Half of the effective energy splitting for the electron transfer reaction

v

Set of vibronic states that modulates the electron coupling matrix element

w

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

x

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

Xk

Multidimensional coordinate characterizing the polarization of water molecules

Xopt

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

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Notes

Acknowledgements

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
  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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