^{1}, Tomáš Kubař

^{1}, Rafael Gutiérrez

^{2}, Rodrigo A. Caetano

^{2,3}, Gianaurelio Cuniberti

^{2}and Marcus Elstner

^{1,a)}

### Abstract

We investigate in detail the chargetransportcharacteristics of DNA wires with various sequences and lengths in the presence of solvent. Our approach combines large-scale quantum/classical molecular dynamics (MD) simulations with transport calculations based on Landauer theory. The quantum mechanical transmission function of the wire is calculated along MD trajectories and thus encodes the influence of dynamical disorder arising from the environment (water, backbone, counterions) and from the internal base dynamics. We show that the correlated fluctuations of the base pair dynamics are crucial in determining the transport properties of the wire and that the effect of fluctuations can be quite different for sequences with low and high static disorders (differences in base ionization potentials). As a result, in structures with high static disorder as is the case of the studied Dickerson dodecamer, the weight of high-transmissive structures increases due to dynamical fluctuations and so does the calculated average transmission. Our analysis further supports the basic intuition of charge-transfer active conformations as proposed by Barton *et al.* [J. Am. Chem. Soc.126, 11471 (2004)]. However, not DNAconformations with good stacking contacts leading to large interbase hopping values are necessarily the most important, but rather those where the average fluctuation of ionization potentials along the base stack is small. The reason behind this is that the ensemble of conformations leads to average electronic couplings, which are large enough for sufficient transmission. On the other hand, the alignment of onsite energies is the critical parameter which gates the chargetransport.

This work was supported by the Deutsche Forschungsgemeinschaft (Project No. DFG-EL 206/5-1), the Deutsche Forschungsgemeinschaft under Contract Nos. CU 44/5-2 and CU 44/3-2, and by the South Korea Ministry of Education, Science and Technology Program “World Class University” under Contract No. R31-2008-000-10100-0.

I. INTRODUCTION

II. METHODOLOGY

A. Electronic structure

B. Chargetransport through a linear chain

C. Molecular dynamics approach

III. RESULTS

A. The influence of internal dynamics and environmental fluctuations on the transmission function

1. Transport through idealized static B-DNA

2. Transport through fluctuating bridges: No solvent effects

3. Transport through fluctuating bridges: Influence of the DNA backbone, water, and counterions

4. Length dependence

B. The role of DNAdynamics and coherent motion on charge transfer efficiency

C. Conformationalanalysis

D. Time scales and averaging for CT in DNA

IV. DISCUSSION AND CONCLUSIONS

### Key Topics

- DNA
- 96.0
- Charge transfer
- 36.0
- Conformational dynamics
- 28.0
- Solvents
- 21.0
- Molecular dynamics
- 20.0

## Figures

MD snapshot of the Dickerson dodecamer DNA: Backbone (pink), base pairs (green), solvent molecules (red and white lines), and sodium counterions (blue spheres). Also shown are the corresponding HOMOs on each of the base pairs being almost completely localized on the purine bases. DNA backbone, solvent, and sodium counterions comprise the electrostatic environment which is described via QM/MM coupling.

MD snapshot of the Dickerson dodecamer DNA: Backbone (pink), base pairs (green), solvent molecules (red and white lines), and sodium counterions (blue spheres). Also shown are the corresponding HOMOs on each of the base pairs being almost completely localized on the purine bases. DNA backbone, solvent, and sodium counterions comprise the electrostatic environment which is described via QM/MM coupling.

(a) Transmission of the ideal chain including (b) dynamical effects and the (c) effect of environment for various DNA sequences. Note the broader energy range in (c).

(a) Transmission of the ideal chain including (b) dynamical effects and the (c) effect of environment for various DNA sequences. Note the broader energy range in (c).

Time-dependent average over onsite energies obtained from a 100 ps MD simulation of a poly(G) heptamer . Snapshots were recorded every femtosecond.

Time-dependent average over onsite energies obtained from a 100 ps MD simulation of a poly(G) heptamer . Snapshots were recorded every femtosecond.

Length dependence of for poly(G) and poly(A). Shown are logarithmic transmission values for various DNA length, i.e., number of sites at two constant arbitrary energies which are the average onsite energies and for poly(A) and poly(G), respectively. The data points were fitted by functions of the form where ( is the stacking distance of ) and describes the decay rate of transmission. For poly(G) is and for poly(A) at . However, if an energy gap of 1.5 eV to is present both -values increase to 0.77 and for poly(A) and poly(G), respectively. In both cases the exponential decay of transmission in poly(G) is stronger than in poly(A). The complete curves for the different lengths can also be found in the supplementary material (Ref. 101).

Length dependence of for poly(G) and poly(A). Shown are logarithmic transmission values for various DNA length, i.e., number of sites at two constant arbitrary energies which are the average onsite energies and for poly(A) and poly(G), respectively. The data points were fitted by functions of the form where ( is the stacking distance of ) and describes the decay rate of transmission. For poly(G) is and for poly(A) at . However, if an energy gap of 1.5 eV to is present both -values increase to 0.77 and for poly(A) and poly(G), respectively. In both cases the exponential decay of transmission in poly(G) is stronger than in poly(A). The complete curves for the different lengths can also be found in the supplementary material (Ref. 101).

Comparison of for the MD simulation of a poly(A) heptamer with two statistical models. Top panel: The electronic couplings for the three models are set to 0.05 eV. The average transmission function is calculated for onsite energies from the MD simulation time series (blue); for onsite energies drawn from the respective probability distribution functions on each site (green); and the Anderson model (red) where all onsite energies are randomly drawn from a square-box distribution. Bottom panel: Now the original MD time series of onsite energies is used, the same for the three models, while is calculated for electronic couplings from the original MD time series (blue); for drawn from their respective probability distribution functions (green) and the Anderson model (red), respectively. The used probability distribution functions for and are shown in the supplementary material (Ref. 101).

Comparison of for the MD simulation of a poly(A) heptamer with two statistical models. Top panel: The electronic couplings for the three models are set to 0.05 eV. The average transmission function is calculated for onsite energies from the MD simulation time series (blue); for onsite energies drawn from the respective probability distribution functions on each site (green); and the Anderson model (red) where all onsite energies are randomly drawn from a square-box distribution. Bottom panel: Now the original MD time series of onsite energies is used, the same for the three models, while is calculated for electronic couplings from the original MD time series (blue); for drawn from their respective probability distribution functions (green) and the Anderson model (red), respectively. The used probability distribution functions for and are shown in the supplementary material (Ref. 101).

Statistical analysis of in a poly(G) heptamer for the 30 ns data with electronic parameters for every picosecond (30 000 DNA conformations). depending on and (top); number of conformations found in a given interval of and (bottom).

Statistical analysis of in a poly(G) heptamer for the 30 ns data with electronic parameters for every picosecond (30 000 DNA conformations). depending on and (top); number of conformations found in a given interval of and (bottom).

Plot of depending on for fixed values of based on the same data as used in Fig. 6.

Plot of depending on for fixed values of based on the same data as used in Fig. 6.

Conformational analysis: The amount of conformations that make up 90% of ; calculation of electronic parameters with QM/MM-environment for every picosecond snapshot along the 30 ns MD simulation; comparison between poly(G) and poly(A) heptamers; the values are sorted beginning with the largest.

Conformational analysis: The amount of conformations that make up 90% of ; calculation of electronic parameters with QM/MM-environment for every picosecond snapshot along the 30 ns MD simulation; comparison between poly(G) and poly(A) heptamers; the values are sorted beginning with the largest.

Conformational analysis: The amount of conformations that make up 90% of based on the calculation of electronic parameters with QM/MM environment and *in vacuo*. Comparison between the homogenous poly(G) heptamer (left) and the central heptamer of the heterogeneous Dickerson sequence (right). The values are sorted beginning with the largest.

Conformational analysis: The amount of conformations that make up 90% of based on the calculation of electronic parameters with QM/MM environment and *in vacuo*. Comparison between the homogenous poly(G) heptamer (left) and the central heptamer of the heterogeneous Dickerson sequence (right). The values are sorted beginning with the largest.

Average transmission for various sets of averaged electronic parameters for poly(A) (top) and poly(GT) (bottom). Both of them obtained from 100 ps MD data with a time step of 1 fs.

Average transmission for various sets of averaged electronic parameters for poly(A) (top) and poly(GT) (bottom). Both of them obtained from 100 ps MD data with a time step of 1 fs.

Snapshot of a 3 ps time series for the transmission at for poly(A) (top) and poly(GT) (bottom), respectively, based on the simulation data as used in Fig. 10.

Snapshot of a 3 ps time series for the transmission at for poly(A) (top) and poly(GT) (bottom), respectively, based on the simulation data as used in Fig. 10.

## Tables

Electronic couplings for a hole transfer in idealized static A- and B-DNA without QM/MM environment compared to MD averaged values with standard deviations including the QM/MM environment for helical parameters of the idealized A- and B-DNA. See Refs. 99 and 100. All values are in eV.

Electronic couplings for a hole transfer in idealized static A- and B-DNA without QM/MM environment compared to MD averaged values with standard deviations including the QM/MM environment for helical parameters of the idealized A- and B-DNA. See Refs. 99 and 100. All values are in eV.

Maximum current values (at voltage ) for seven DNA heptamers sequences for static B-DNA structures for the average current of the MD structures with and without QM/MM environment. All values are in nanoamperes.

Maximum current values (at voltage ) for seven DNA heptamers sequences for static B-DNA structures for the average current of the MD structures with and without QM/MM environment. All values are in nanoamperes.

Correlation coefficient of with and .

Correlation coefficient of with and .

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