Donor-acceptor electron transport mediated by solitons

We study the long-range electron and energy transfer mediated by solitons in a quasi-one-dimensional molecular chain (conjugated polymer, alpha-helical macromolecule, etc.) weakly bound to a donor and an acceptor. We show that for certain sets of parameter values in such systems an electron, initially located at the donor molecule, can tunnel to the molecular chain, where it becomes self-trapped in a soliton state, and propagates to the opposite end of the chain practically without energy dissipation. Upon reaching the end, the electron can either bounce back and move in the opposite direction or, for suitable parameter values of the system, tunnel to the acceptor. We estimate the energy efficiency of the donor-acceptor electron transport depending on the parameter values. Our calculations show that the soliton mechanism works for the parameter values of polypeptide macromolecules and conjugated polymers. We also investigate the donor-acceptor electron transport in thermalized molecular chains.

Figure 1

Properties of the stationary soliton as a function of its maximum density ${\text{max}}_n{\left|{\Psi }_n\right|}^2$. (a) Norm $N={\sum }_n{\left|{\Psi }_n\right|}^2$; (b) soliton width; (c) soliton energy.

Figure 2

Maximum of ${\left|\Psi \right|}^2$ as a function of $D_d$ and $J_d$ for $x_d=v_d=0.1$.

Figure 3

Electron probability ${\left|\Psi \right|}^2$ on the acceptor as a function of time (in adimensional units) for the parameter values listed in Table 1 for $x_d=x_a=0.1$ and $x_d=x_a=0.3$. $N=50$.

Figure 4

Absorption of soliton by the acceptor: ${\left|\Psi \right|}^2$ at $\tau =50$. $M_d=M_a=3$, $C=0.88$, $v_d=v_a=0.1$, $G=0.8$, $x_d=x_a=0.3$, $D_a=0.6$, and $J_d=0.7$; (a) as a function of $J_a$ for different $D_a$ and $A_a=4$; (b) as a function of $J_a$ for different $A_a$ and $D_a=0.3$; (c) as a function of $A_a$ for different $D_a$ and $J_a=0.12$; (d) as a function of $D_a$ for different $A_a$ and $J_a=0.12$.

Figure 5

Profile ${\left|\Psi \right|}^2$ of the soliton on a chain with 50 nodes. At $\tau =0$, not shown, the soliton is exclusively on the donor ($|{\Psi }_d{|}^2=1$). $M_d=M_a=3$, $C=0.88$, $v_d=v_a=0.1$, $G=0.8$, $x_d=x_a=0.3$, $D_d=0.6$, $J_d=0.7$, $D_a=0.3$, $J_a=0.12$, and $A_a=4$. (a) $\tau =2$, (b) $\tau =4$, (c) $\tau =10$, (d) $\tau =20$, (e) $\tau =28$, and (f) $\tau =40$.

Figure 6

Displacement $u$ of unit cells on a chain with 50 nodes. $M_d=M_a=3$, $C=0.88$, $v_d=v_a=0.1$, $G=0.8$, $x_d=x_a=0.3$, $D_d=0.6$, $J_d=0.7$, $D_a=0.3$, $J_a=0.12$, and $A_a=4$. (a) $\tau =4$, (b) $\tau =10$, (c) $\tau =20$, and (d) $\tau =28$.

Figure 7

${\left|\Psi \right|}^2$ on the acceptor for $x_d=x_a=0.3$, $D_d=0.6$, $J_d=0.7$, $D_a=0.3$, $J_a=0.12$, and $A_a=4$: (a) as a function of the temperature for chain of different length; (b) as a function of $\Gamma$ for various temperatures.