Charge Transport through Biomolecular Wires in a Solvent: Bridging Molecular Dynamics and Model Hamiltonian Approaches

We present a hybrid method based on a combination of classical molecular dynamics simulations, quantum-chemical calculations, and a model Hamiltonian approach to describe charge transport through biomolecular wires with variable lengths in presence of a solvent. The core of our approach consists in a mapping of the biomolecular electronic structure, as obtained from density-functional based tight-binding calculations of molecular structures along molecular dynamics trajectories, onto a low-dimensional model Hamiltonian including the coupling to a dissipative bosonic environment. The latter encodes fluctuation effects arising from the solvent and from the molecular conformational dynamics. We apply this approach to the case of pG-pC and pA-pT DNA oligomers as paradigmatic cases and show that the DNA conformational fluctuations are essential in determining and supporting charge transport.

Figure 1

Typical time-averaged transmission function $⟨T(E){⟩}_t$ for pG-pC and pA-pT wires with seven base pairs each. The simulation time is 100 ps, and the average was performed every 5 ps. Inset: A snapshot of a pG-pC oligomer in a solvent drawn from the MD simulation. To avoid spurious boundary effects, only the innermost seven base pairs are used. The electronic structure at each snapshot is mapped onto an effective low-dimensional model Hamiltonian.

Figure 2

Coherence parameter $C_N(E)$ providing a qualitative measure for the importance of dynamical disorder; $C_N(E)\ll 1$ hints at the dominant role of fluctuations in determining the transport properties. The inset shows the energy-averaged $⟨C_N(E){⟩}_E$ as a function of the number of base pairs in the DNA chain.

Figure 3

Time-averaged current $⟨I(V){⟩}_t$ for a ${\mathrm{pG}}_7\mathrm{\text{−}}{\mathrm{pC}}_7$ oligomer. Results are shown for three different choices of the time frame ${\tau }_W=5$, 20, and 50 ps (for a definition see the main text). Inset: Autocorrelation function of the energy fluctuations $⟨{ϵ}_i(t){ϵ}_i(0)⟩$, nearest-neighbor correlation $⟨{ϵ}_i(t){ϵ}_{i+1}(0)⟩$, and hopping correlations $⟨V_{i,i+1}(t)V_{i,i+1}(0)⟩$.

Figure 4

$I\mathrm{\text{−}}V$ characteristics of pG-pC (upper panel) and pA-pT (lower panel) oligomers with three different numbers of base pairs $N=7$, 11, 15 calculated with the effective charge-bath model Hamiltonian [see Eq. (1)]. In all cases the effective electrode-molecule coupling parameter was chosen as $\Gamma =5\mathrm{meV}$ within a wide-band limit. Though for the shortest oligomer, pA-pT has a larger current than pG-pC, this behavior is weakened with increasing length.